TSTP Solution File: SEU705^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU705^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n028.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 : Tue May 21 03:29:18 EDT 2024

% Result   : Theorem 138.39s 18.00s
% Output   : CNFRefutation 138.39s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :  575
% Syntax   : Number of formulae    :  682 (  51 unt; 346 typ;   0 def)
%            Number of atoms       : 3015 ( 703 equ;   0 cnn)
%            Maximal formula atoms :  915 (   8 avg)
%            Number of connectives : 12228 ( 835   ~; 916   |; 595   &;8164   @)
%                                         ( 315 <=>;1403  =>;   0  <=;   0 <~>)
%            Maximal formula depth : 1029 (  13 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  605 ( 605   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  350 ( 346 usr; 231 con; 0-4 aty)
%            Number of variables   : 2608 ( 226   ^2234   !; 148   ?;2608   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_22,type,
    in: $i > $i > $o ).

thf(decl_23,type,
    exu: ( $i > $o ) > $o ).

thf(decl_24,type,
    setextAx: $o ).

thf(decl_25,type,
    emptyset: $i ).

thf(decl_26,type,
    emptysetAx: $o ).

thf(decl_27,type,
    setadjoin: $i > $i > $i ).

thf(decl_28,type,
    setadjoinAx: $o ).

thf(decl_29,type,
    powerset: $i > $i ).

thf(decl_30,type,
    powersetAx: $o ).

thf(decl_31,type,
    setunion: $i > $i ).

thf(decl_32,type,
    setunionAx: $o ).

thf(decl_33,type,
    omega: $i ).

thf(decl_34,type,
    omega0Ax: $o ).

thf(decl_35,type,
    omegaSAx: $o ).

thf(decl_36,type,
    omegaIndAx: $o ).

thf(decl_37,type,
    replAx: $o ).

thf(decl_38,type,
    foundationAx: $o ).

thf(decl_39,type,
    wellorderingAx: $o ).

thf(decl_40,type,
    descr: ( $i > $o ) > $i ).

thf(decl_41,type,
    descrp: $o ).

thf(decl_42,type,
    dsetconstr: $i > ( $i > $o ) > $i ).

thf(decl_43,type,
    dsetconstrI: $o ).

thf(decl_44,type,
    dsetconstrEL: $o ).

thf(decl_45,type,
    dsetconstrER: $o ).

thf(decl_46,type,
    exuE1: $o ).

thf(decl_47,type,
    prop2set: $o > $i ).

thf(decl_48,type,
    prop2setE: $o ).

thf(decl_49,type,
    emptysetE: $o ).

thf(decl_50,type,
    emptysetimpfalse: $o ).

thf(decl_51,type,
    notinemptyset: $o ).

thf(decl_52,type,
    exuE3e: $o ).

thf(decl_53,type,
    setext: $o ).

thf(decl_54,type,
    emptyI: $o ).

thf(decl_55,type,
    noeltsimpempty: $o ).

thf(decl_56,type,
    setbeta: $o ).

thf(decl_57,type,
    nonempty: $i > $o ).

thf(decl_58,type,
    nonemptyE1: $o ).

thf(decl_59,type,
    nonemptyI: $o ).

thf(decl_60,type,
    nonemptyI1: $o ).

thf(decl_61,type,
    setadjoinIL: $o ).

thf(decl_62,type,
    emptyinunitempty: $o ).

thf(decl_63,type,
    setadjoinIR: $o ).

thf(decl_64,type,
    setadjoinE: $o ).

thf(decl_65,type,
    setadjoinOr: $o ).

thf(decl_66,type,
    setoftrueEq: $o ).

thf(decl_67,type,
    powersetI: $o ).

thf(decl_68,type,
    emptyinPowerset: $o ).

thf(decl_69,type,
    emptyInPowerset: $o ).

thf(decl_70,type,
    powersetE: $o ).

thf(decl_71,type,
    setunionI: $o ).

thf(decl_72,type,
    setunionE: $o ).

thf(decl_73,type,
    subPowSU: $o ).

thf(decl_74,type,
    exuE2: $o ).

thf(decl_75,type,
    nonemptyImpWitness: $o ).

thf(decl_76,type,
    uniqinunit: $o ).

thf(decl_77,type,
    notinsingleton: $o ).

thf(decl_78,type,
    eqinunit: $o ).

thf(decl_79,type,
    singletonsswitch: $o ).

thf(decl_80,type,
    upairsetE: $o ).

thf(decl_81,type,
    upairsetIL: $o ).

thf(decl_82,type,
    upairsetIR: $o ).

thf(decl_83,type,
    emptyE1: $o ).

thf(decl_84,type,
    vacuousDall: $o ).

thf(decl_85,type,
    quantDeMorgan1: $o ).

thf(decl_86,type,
    quantDeMorgan2: $o ).

thf(decl_87,type,
    quantDeMorgan3: $o ).

thf(decl_88,type,
    quantDeMorgan4: $o ).

thf(decl_89,type,
    prop2setI: $o ).

thf(decl_90,type,
    set2prop: $i > $o ).

thf(decl_91,type,
    prop2set2propI: $o ).

thf(decl_92,type,
    notdexE: $o ).

thf(decl_93,type,
    notdallE: $o ).

thf(decl_94,type,
    exuI1: $o ).

thf(decl_95,type,
    exuI3: $o ).

thf(decl_96,type,
    exuI2: $o ).

thf(decl_97,type,
    inCongP: $o ).

thf(decl_98,type,
    in__Cong: $o ).

thf(decl_99,type,
    exuE3u: $o ).

thf(decl_100,type,
    exu__Cong: $o ).

thf(decl_101,type,
    emptyset__Cong: $o ).

thf(decl_102,type,
    setadjoin__Cong: $o ).

thf(decl_103,type,
    powerset__Cong: $o ).

thf(decl_104,type,
    setunion__Cong: $o ).

thf(decl_105,type,
    omega__Cong: $o ).

thf(decl_106,type,
    exuEu: $o ).

thf(decl_107,type,
    descr__Cong: $o ).

thf(decl_108,type,
    dsetconstr__Cong: $o ).

thf(decl_109,type,
    subset: $i > $i > $o ).

thf(decl_112,type,
    subsetI1: $o ).

thf(decl_113,type,
    eqimpsubset2: $o ).

thf(decl_114,type,
    eqimpsubset1: $o ).

thf(decl_115,type,
    subsetI2: $o ).

thf(decl_116,type,
    emptysetsubset: $o ).

thf(decl_117,type,
    subsetE: $o ).

thf(decl_118,type,
    subsetE2: $o ).

thf(decl_119,type,
    notsubsetI: $o ).

thf(decl_120,type,
    notequalI1: $o ).

thf(decl_121,type,
    notequalI2: $o ).

thf(decl_122,type,
    subsetRefl: $o ).

thf(decl_123,type,
    subsetTrans: $o ).

thf(decl_124,type,
    setadjoinSub: $o ).

thf(decl_125,type,
    setadjoinSub2: $o ).

thf(decl_126,type,
    subset2powerset: $o ).

thf(decl_127,type,
    setextsub: $o ).

thf(decl_128,type,
    subsetemptysetimpeq: $o ).

thf(decl_129,type,
    powersetI1: $o ).

thf(decl_130,type,
    powersetE1: $o ).

thf(decl_131,type,
    inPowerset: $o ).

thf(decl_132,type,
    powersetsubset: $o ).

thf(decl_133,type,
    sepInPowerset: $o ).

thf(decl_134,type,
    sepSubset: $o ).

thf(decl_135,type,
    binunion: $i > $i > $i ).

thf(decl_136,type,
    binunionIL: $o ).

thf(decl_137,type,
    upairset2IR: $o ).

thf(decl_138,type,
    binunionIR: $o ).

thf(decl_139,type,
    binunionEcases: $o ).

thf(decl_140,type,
    binunionE: $o ).

thf(decl_141,type,
    binunionLsub: $o ).

thf(decl_142,type,
    binunionRsub: $o ).

thf(decl_143,type,
    binintersect: $i > $i > $i ).

thf(decl_144,type,
    binintersectI: $o ).

thf(decl_145,type,
    binintersectSubset5: $o ).

thf(decl_146,type,
    binintersectEL: $o ).

thf(decl_147,type,
    binintersectLsub: $o ).

thf(decl_148,type,
    binintersectSubset2: $o ).

thf(decl_149,type,
    binintersectSubset3: $o ).

thf(decl_150,type,
    binintersectER: $o ).

thf(decl_151,type,
    disjointsetsI1: $o ).

thf(decl_152,type,
    binintersectRsub: $o ).

thf(decl_153,type,
    binintersectSubset4: $o ).

thf(decl_154,type,
    binintersectSubset1: $o ).

thf(decl_155,type,
    bs114d: $o ).

thf(decl_157,type,
    setminus: $i > $i > $i ).

thf(decl_158,type,
    setminusI: $o ).

thf(decl_159,type,
    setminusEL: $o ).

thf(decl_160,type,
    setminusER: $o ).

thf(decl_161,type,
    setminusSubset2: $o ).

thf(decl_162,type,
    setminusERneg: $o ).

thf(decl_163,type,
    setminusELneg: $o ).

thf(decl_164,type,
    setminusILneg: $o ).

thf(decl_165,type,
    setminusIRneg: $o ).

thf(decl_166,type,
    setminusLsub: $o ).

thf(decl_167,type,
    setminusSubset1: $o ).

thf(decl_168,type,
    symdiff: $i > $i > $i ).

thf(decl_169,type,
    symdiffE: $o ).

thf(decl_170,type,
    symdiffI1: $o ).

thf(decl_171,type,
    symdiffI2: $o ).

thf(decl_172,type,
    symdiffIneg1: $o ).

thf(decl_173,type,
    symdiffIneg2: $o ).

thf(decl_174,type,
    iskpair: $i > $o ).

thf(decl_175,type,
    secondinupair: $o ).

thf(decl_176,type,
    setukpairIL: $o ).

thf(decl_177,type,
    setukpairIR: $o ).

thf(decl_178,type,
    kpairiskpair: $o ).

thf(decl_179,type,
    kpair: $i > $i > $i ).

thf(decl_180,type,
    kpairp: $o ).

thf(decl_181,type,
    cartprod: $i > $i > $i ).

thf(decl_182,type,
    singletonsubset: $o ).

thf(decl_183,type,
    singletoninpowerset: $o ).

thf(decl_184,type,
    singletoninpowunion: $o ).

thf(decl_185,type,
    upairset2E: $o ).

thf(decl_186,type,
    upairsubunion: $o ).

thf(decl_187,type,
    upairinpowunion: $o ).

thf(decl_188,type,
    ubforcartprodlem1: $o ).

thf(decl_189,type,
    ubforcartprodlem2: $o ).

thf(decl_190,type,
    ubforcartprodlem3: $o ).

thf(decl_191,type,
    cartprodpairin: $o ).

thf(decl_192,type,
    cartprodmempair1: $o ).

thf(decl_193,type,
    cartprodmempair: $o ).

thf(decl_194,type,
    setunionE2: $o ).

thf(decl_195,type,
    setunionsingleton1: $o ).

thf(decl_196,type,
    setunionsingleton2: $o ).

thf(decl_197,type,
    setunionsingleton: $o ).

thf(decl_198,type,
    singleton: $i > $o ).

thf(decl_199,type,
    singletonprop: $o ).

thf(decl_200,type,
    ex1: $i > ( $i > $o ) > $o ).

thf(decl_201,type,
    ex1E1: $o ).

thf(decl_202,type,
    ex1I: $o ).

thf(decl_203,type,
    ex1I2: $o ).

thf(decl_204,type,
    singletonsuniq: $o ).

thf(decl_209,type,
    setukpairinjL1: $o ).

thf(decl_210,type,
    kfstsingleton: $o ).

thf(decl_211,type,
    theprop: $o ).

thf(decl_212,type,
    kfst: $i > $i ).

thf(decl_213,type,
    kfstpairEq: $o ).

thf(decl_214,type,
    cartprodfstin: $o ).

thf(decl_215,type,
    setukpairinjL2: $o ).

thf(decl_216,type,
    setukpairinjL: $o ).

thf(decl_217,type,
    setukpairinjR11: $o ).

thf(decl_218,type,
    setukpairinjR12: $o ).

thf(decl_219,type,
    setukpairinjR1: $o ).

thf(decl_220,type,
    upairequniteq: $o ).

thf(decl_221,type,
    setukpairinjR2: $o ).

thf(decl_222,type,
    setukpairinjR: $o ).

thf(decl_223,type,
    ksndsingleton: $o ).

thf(decl_224,type,
    ksnd: $i > $i ).

thf(decl_225,type,
    ksndpairEq: $o ).

thf(decl_226,type,
    kpairsurjEq: $o ).

thf(decl_227,type,
    cartprodsndin: $o ).

thf(decl_228,type,
    cartprodpairmemEL: $o ).

thf(decl_229,type,
    cartprodpairmemER: $o ).

thf(decl_230,type,
    cartprodmempaircEq: $o ).

thf(decl_231,type,
    cartprodfstpairEq: $o ).

thf(decl_232,type,
    cartprodsndpairEq: $o ).

thf(decl_233,type,
    cartprodpairsurjEq: $o ).

thf(decl_234,type,
    breln: $i > $i > $i > $o ).

thf(decl_235,type,
    dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).

thf(decl_236,type,
    dpsetconstrI: $o ).

thf(decl_237,type,
    dpsetconstrSub: $o ).

thf(decl_238,type,
    setOfPairsIsBReln: $o ).

thf(decl_239,type,
    dpsetconstrERa: $o ).

thf(decl_240,type,
    dpsetconstrEL1: $o ).

thf(decl_241,type,
    dpsetconstrEL2: $o ).

thf(decl_242,type,
    dpsetconstrER: $o ).

thf(decl_243,type,
    func: $i > $i > $i > $o ).

thf(decl_244,type,
    funcSet: $i > $i > $i ).

thf(decl_245,type,
    funcImageSingleton: $o ).

thf(decl_246,type,
    apProp: $o ).

thf(decl_247,type,
    ap: $i > $i > $i > $i > $i ).

thf(decl_248,type,
    app: $o ).

thf(decl_249,type,
    infuncsetfunc: $o ).

thf(decl_250,type,
    ap2p: $o ).

thf(decl_251,type,
    funcinfuncset: $o ).

thf(decl_252,type,
    lamProp: $o ).

thf(decl_253,type,
    lam: $i > $i > ( $i > $i ) > $i ).

thf(decl_254,type,
    lamp: $o ).

thf(decl_255,type,
    lam2p: $o ).

thf(decl_256,type,
    brelnall1: $o ).

thf(decl_257,type,
    brelnall2: $o ).

thf(decl_258,type,
    ex1E2: $o ).

thf(decl_259,type,
    funcGraphProp1: $o ).

thf(decl_260,type,
    funcGraphProp3: $o ).

thf(decl_261,type,
    funcGraphProp2: $o ).

thf(decl_262,type,
    funcextLem: $o ).

thf(decl_263,type,
    funcGraphProp4: $o ).

thf(decl_264,type,
    subbreln: $o ).

thf(decl_265,type,
    eqbreln: $o ).

thf(decl_266,type,
    funcext: $o ).

thf(decl_267,type,
    funcext2: $o ).

thf(decl_268,type,
    ap2apEq1: $o ).

thf(decl_269,type,
    ap2apEq2: $o ).

thf(decl_270,type,
    beta1: $o ).

thf(decl_271,type,
    eta1: $o ).

thf(decl_272,type,
    lam2lamEq: $o ).

thf(decl_273,type,
    beta2: $o ).

thf(decl_274,type,
    eta2: $o ).

thf(decl_275,type,
    iffalseProp1: $o ).

thf(decl_276,type,
    iffalseProp2: $o ).

thf(decl_277,type,
    iftrueProp1: $o ).

thf(decl_278,type,
    iftrueProp2: $o ).

thf(decl_279,type,
    ifSingleton: $o ).

thf(decl_280,type,
    if: $i > $o > $i > $i > $i ).

thf(decl_281,type,
    epred1_0: $o ).

thf(decl_282,type,
    esk1_2: $i > $i > $i ).

thf(decl_283,type,
    esk2_2: $i > $i > $i ).

thf(decl_284,type,
    esk3_2: $i > $i > $i ).

thf(decl_285,type,
    esk4_1: $i > $i ).

thf(decl_286,type,
    esk5_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_287,type,
    esk6_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_288,type,
    esk7_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_289,type,
    esk8_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_290,type,
    esk9_1: $i > $i ).

thf(decl_291,type,
    esk10_2: ( $i > $o ) > $i > $i ).

thf(decl_292,type,
    esk11_2: ( $i > $o ) > $i > $i ).

thf(decl_293,type,
    esk12_1: ( $i > $o ) > $i ).

thf(decl_294,type,
    esk13_2: ( $i > $o ) > $i > $i ).

thf(decl_295,type,
    esk14_1: ( $i > $o ) > $i ).

thf(decl_296,type,
    esk15_2: $i > $i > $i ).

thf(decl_297,type,
    esk16_2: $i > $i > $i ).

thf(decl_298,type,
    esk17_1: $i > $i ).

thf(decl_299,type,
    esk18_1: $i > $i ).

thf(decl_300,type,
    esk19_1: $i > $i ).

thf(decl_301,type,
    esk20_2: $i > $i > $i ).

thf(decl_302,type,
    esk21_3: $i > $i > $o > $i ).

thf(decl_303,type,
    esk22_2: ( $i > $o ) > $i > $i ).

thf(decl_304,type,
    esk23_1: ( $i > $o ) > $i ).

thf(decl_305,type,
    esk24_1: $i > $i ).

thf(decl_306,type,
    esk25_2: $i > ( $i > $o ) > $i ).

thf(decl_307,type,
    esk26_2: $i > ( $i > $o ) > $i ).

thf(decl_308,type,
    esk27_2: $i > ( $i > $o ) > $i ).

thf(decl_309,type,
    esk28_2: $i > ( $i > $o ) > $i ).

thf(decl_310,type,
    esk29_2: $i > ( $i > $o ) > $i ).

thf(decl_311,type,
    esk30_2: $i > ( $i > $o ) > $i ).

thf(decl_312,type,
    esk31_2: ( $i > $o ) > $i > $i ).

thf(decl_313,type,
    esk32_1: ( $i > $o ) > $i ).

thf(decl_314,type,
    esk33_1: ( $i > $o ) > $i ).

thf(decl_315,type,
    esk34_1: ( $i > $o ) > $i ).

thf(decl_316,type,
    esk35_1: ( $i > $o ) > $i ).

thf(decl_317,type,
    esk36_2: ( $i > $o ) > $i > $i ).

thf(decl_318,type,
    esk37_1: ( $i > $o ) > $i ).

thf(decl_319,type,
    esk38_2: ( $i > $o ) > $i > $i ).

thf(decl_320,type,
    esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_321,type,
    esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_322,type,
    esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_323,type,
    esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_324,type,
    esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_325,type,
    esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_326,type,
    esk45_2: ( $i > $o ) > $i > $i ).

thf(decl_327,type,
    esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_328,type,
    esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_329,type,
    esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_330,type,
    esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_331,type,
    esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_332,type,
    esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_333,type,
    esk52_2: $i > $i > $i ).

thf(decl_334,type,
    esk53_2: $i > $i > $i ).

thf(decl_335,type,
    esk54_2: $i > $i > $i ).

thf(decl_336,type,
    esk55_3: $i > $i > $i > $i ).

thf(decl_337,type,
    esk56_3: $i > $i > $i > $i ).

thf(decl_338,type,
    esk57_2: $i > $i > $i ).

thf(decl_339,type,
    esk58_2: $i > ( $i > $o ) > $i ).

thf(decl_340,type,
    esk59_2: $i > ( $i > $o ) > $i ).

thf(decl_341,type,
    esk60_2: $i > ( $i > $o ) > $i ).

thf(decl_342,type,
    esk61_2: $i > ( $i > $o ) > $i ).

thf(decl_343,type,
    esk62_3: $i > ( $i > $o ) > $i > $i ).

thf(decl_344,type,
    esk63_3: $i > ( $i > $o ) > $i > $i ).

thf(decl_345,type,
    esk64_2: $i > ( $i > $o ) > $i ).

thf(decl_346,type,
    esk65_2: $i > ( $i > $o ) > $i ).

thf(decl_347,type,
    esk66_2: $i > ( $i > $o ) > $i ).

thf(decl_348,type,
    esk67_1: $i > $i ).

thf(decl_349,type,
    esk68_1: $i > $i ).

thf(decl_350,type,
    esk69_4: $i > $i > $i > $i > $i ).

thf(decl_351,type,
    esk70_3: $i > $i > ( $i > $i ) > $i ).

thf(decl_352,type,
    esk71_3: $i > $i > ( $i > $i ) > $i ).

thf(decl_353,type,
    esk72_3: $i > $i > ( $i > $i ) > $i ).

thf(decl_354,type,
    esk73_4: $i > $i > $i > ( $i > $o ) > $i ).

thf(decl_355,type,
    esk74_4: $i > $i > $i > ( $i > $o ) > $i ).

thf(decl_356,type,
    esk75_4: $i > $i > $i > ( $i > $o ) > $i ).

thf(decl_357,type,
    esk76_4: $i > $i > $i > ( $i > $o ) > $i ).

thf(decl_358,type,
    esk77_4: $i > $i > $i > $i > $i ).

thf(decl_359,type,
    esk78_4: $i > $i > $i > $i > $i ).

thf(decl_360,type,
    esk79_4: $i > $i > $i > $i > $i ).

thf(decl_361,type,
    esk80_4: $i > $i > $i > $i > $i ).

thf(decl_362,type,
    esk81_4: $i > $i > $i > $i > $i ).

thf(decl_363,type,
    esk82_4: $i > $i > $i > $i > $i ).

thf(decl_364,type,
    esk83_4: $i > $i > $i > $i > $i ).

thf(decl_365,type,
    esk84_4: $i > $i > $i > $i > $i ).

thf(decl_366,type,
    esk85_4: $i > $i > $i > $i > $i ).

thf(decl_367,type,
    esk86_3: $i > $i > ( $i > $i ) > $i ).

thf(decl_368,type,
    esk87_3: $i > $i > ( $i > $i ) > $i ).

thf(decl_369,type,
    esk88_3: $i > $i > ( $i > $i ) > $i ).

thf(decl_370,type,
    esk89_4: $i > $o > $i > $i > $i ).

thf(decl_371,type,
    esk90_0: $i ).

thf(decl_372,type,
    epred2_0: $o ).

thf(decl_373,type,
    esk91_0: $i ).

thf(decl_374,type,
    esk92_0: $i ).

thf(ex1,axiom,
    ( ex1
    = ( ^ [X4: $i,X1: $i > $o] :
          ( singleton
          @ ( dsetconstr @ X4
            @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1) ).

thf(singleton,axiom,
    ( singleton
    = ( ^ [X4: $i] :
        ? [X2: $i] :
          ( ( in @ X2 @ X4 )
          & ( X4
            = ( setadjoin @ X2 @ emptyset ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).

thf(replAx,axiom,
    ( replAx
  <=> ! [X6: $i > $i > $o,X4: $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( exu
              @ ^ [X3: $i] : ( X6 @ X2 @ X3 ) ) )
       => ? [X5: $i] :
          ! [X2: $i] :
            ( ( in @ X2 @ X5 )
          <=> ? [X3: $i] :
                ( ( in @ X3 @ X4 )
                & ( X6 @ X3 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx) ).

thf(exu,axiom,
    ( exu
    = ( ^ [X1: $i > $o] :
        ? [X2: $i] :
          ( ( X1 @ X2 )
          & ! [X3: $i] :
              ( ( X1 @ X3 )
             => ( X2 = X3 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).

thf(descrp,axiom,
    ( descrp
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [X2: $i] : ( X1 @ X2 ) )
       => ( X1
          @ ( descr
            @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp) ).

thf(exuE1,axiom,
    ( exuE1
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [X2: $i] : ( X1 @ X2 ) )
       => ? [X2: $i] :
            ( ( X1 @ X2 )
            & ! [X3: $i] :
                ( ( X1 @ X3 )
               => ( X2 = X3 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).

thf(exuE3e,axiom,
    ( exuE3e
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [X2: $i] : ( X1 @ X2 ) )
       => ? [X2: $i] : ( X1 @ X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).

thf(nonempty,axiom,
    ( nonempty
    = ( ^ [X2: $i] : ( X2 != emptyset ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).

thf(nonemptyI,axiom,
    ( nonemptyI
  <=> ! [X4: $i,X1: $i > $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ( X1 @ X2 )
         => ( nonempty
            @ ( dsetconstr @ X4
              @ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI) ).

thf(exuE2,axiom,
    ( exuE2
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [X2: $i] : ( X1 @ X2 ) )
       => ? [X2: $i] :
          ! [X3: $i] :
            ( ( X1 @ X3 )
          <=> ( X3 = X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2) ).

thf(exuI1,axiom,
    ( exuI1
  <=> ! [X1: $i > $o] :
        ( ? [X2: $i] :
            ( ( X1 @ X2 )
            & ! [X3: $i] :
                ( ( X1 @ X3 )
               => ( X2 = X3 ) ) )
       => ( exu
          @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI1) ).

thf(exuI3,axiom,
    ( exuI3
  <=> ! [X1: $i > $o] :
        ( ? [X2: $i] : ( X1 @ X2 )
       => ( ! [X2: $i,X3: $i] :
              ( ( X1 @ X2 )
             => ( ( X1 @ X3 )
               => ( X2 = X3 ) ) )
         => ( exu
            @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI3) ).

thf(exuI2,axiom,
    ( exuI2
  <=> ! [X1: $i > $o] :
        ( ? [X2: $i] :
          ! [X3: $i] :
            ( ( X1 @ X3 )
          <=> ( X3 = X2 ) )
       => ( exu
          @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI2) ).

thf(exuE3u,axiom,
    ( exuE3u
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [X2: $i] : ( X1 @ X2 ) )
       => ! [X2: $i,X3: $i] :
            ( ( X1 @ X2 )
           => ( ( X1 @ X3 )
             => ( X2 = X3 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u) ).

thf(exu__Cong,axiom,
    ( exu__Cong
  <=> ! [X1: $i > $o,X17: $i > $o] :
        ( ! [X2: $i,X3: $i] :
            ( ( X2 = X3 )
           => ( ( X1 @ X2 )
            <=> ( X17 @ X3 ) ) )
       => ( ( exu
            @ ^ [X2: $i] : ( X1 @ X2 ) )
        <=> ( exu
            @ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong) ).

thf(exuEu,axiom,
    ( exuEu
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [X2: $i] : ( X1 @ X2 ) )
       => ! [X2: $i,X3: $i] :
            ( ( X1 @ X2 )
           => ( ( X1 @ X3 )
             => ( X2 = X3 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuEu) ).

thf(descr__Cong,axiom,
    ( descr__Cong
  <=> ! [X1: $i > $o,X17: $i > $o] :
        ( ! [X2: $i,X3: $i] :
            ( ( X2 = X3 )
           => ( ( X1 @ X2 )
            <=> ( X17 @ X3 ) ) )
       => ( ( exu
            @ ^ [X2: $i] : ( X1 @ X2 ) )
         => ( ( exu
              @ ^ [X2: $i] : ( X17 @ X2 ) )
           => ( ( descr
                @ ^ [X2: $i] : ( X1 @ X2 ) )
              = ( descr
                @ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',descr__Cong) ).

thf(singletonprop,axiom,
    ( singletonprop
  <=> ! [X4: $i,X1: $i > $o] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ! [X3: $i] :
                ( ( in @ X3 @ X4 )
               => ( ( X1 @ X2 )
                 => ( ( X1 @ X3 )
                   => ( X2 = X3 ) ) ) ) )
       => ( ? [X2: $i] :
              ( ( in @ X2 @ X4 )
              & ( X1 @ X2 ) )
         => ( singleton
            @ ( dsetconstr @ X4
              @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonprop) ).

thf(ex1E1,axiom,
    ( ex1E1
  <=> ! [X4: $i,X1: $i > $o] :
        ( ( ex1 @ X4
          @ ^ [X2: $i] : ( X1 @ X2 ) )
       => ? [X2: $i] :
            ( ( in @ X2 @ X4 )
            & ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E1) ).

thf(ex1I,axiom,
    ( ex1I
  <=> ! [X4: $i,X1: $i > $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ( X1 @ X2 )
         => ( ! [X3: $i] :
                ( ( in @ X3 @ X4 )
               => ( ( X1 @ X3 )
                 => ( X3 = X2 ) ) )
           => ( ex1 @ X4
              @ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I) ).

thf(ex1I2,axiom,
    ( ex1I2
  <=> ! [X4: $i,X1: $i > $o] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ! [X3: $i] :
                ( ( in @ X3 @ X4 )
               => ( ( X1 @ X2 )
                 => ( ( X1 @ X3 )
                   => ( X2 = X3 ) ) ) ) )
       => ( ? [X2: $i] :
              ( ( in @ X2 @ X4 )
              & ( X1 @ X2 ) )
         => ( ex1 @ X4
            @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I2) ).

thf(kfstsingleton,axiom,
    ( kfstsingleton
  <=> ! [X18: $i] :
        ( ( iskpair @ X18 )
       => ( singleton
          @ ( dsetconstr @ ( setunion @ X18 )
            @ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X18 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstsingleton) ).

thf(ksndsingleton,axiom,
    ( ksndsingleton
  <=> ! [X18: $i] :
        ( ( iskpair @ X18 )
       => ( singleton
          @ ( dsetconstr @ ( setunion @ X18 )
            @ ^ [X2: $i] :
                ( X18
                = ( kpair @ ( kfst @ X18 ) @ X2 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndsingleton) ).

thf(setOfPairsIsBReln,axiom,
    ( setOfPairsIsBReln
  <=> ! [X4: $i,X5: $i,X24: $i > $i > $o] :
        ( breln @ X4 @ X5
        @ ( dpsetconstr @ X4 @ X5
          @ ^ [X2: $i,X3: $i] : ( X24 @ X2 @ X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln) ).

thf(breln,axiom,
    ( breln
    = ( ^ [X4: $i,X5: $i,X7: $i] : ( subset @ X7 @ ( cartprod @ X4 @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).

thf(funcImageSingleton,axiom,
    ( funcImageSingleton
  <=> ! [X4: $i,X5: $i,X29: $i] :
        ( ( func @ X4 @ X5 @ X29 )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( singleton
              @ ( dsetconstr @ X5
                @ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcImageSingleton) ).

thf(ex1E2,axiom,
    ( ex1E2
  <=> ! [X4: $i,X1: $i > $o] :
        ( ( ex1 @ X4
          @ ^ [X2: $i] : ( X1 @ X2 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ! [X3: $i] :
                ( ( in @ X3 @ X4 )
               => ( ( X1 @ X2 )
                 => ( ( X1 @ X3 )
                   => ( X2 = X3 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E2) ).

thf(ifSingleton,axiom,
    ( ifSingleton
  <=> ! [X4: $i,X43: $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X4 )
           => ( singleton
              @ ( dsetconstr @ X4
                @ ^ [X14: $i] :
                    ( ( X43
                      & ( X14 = X2 ) )
                    | ( ~ X43
                      & ( X14 = X3 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifSingleton) ).

thf(dsetconstrI,axiom,
    ( dsetconstrI
  <=> ! [X4: $i,X1: $i > $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ( X1 @ X2 )
         => ( in @ X2
            @ ( dsetconstr @ X4
              @ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).

thf(dsetconstrEL,axiom,
    ( dsetconstrEL
  <=> ! [X4: $i,X1: $i > $o,X2: $i] :
        ( ( in @ X2
          @ ( dsetconstr @ X4
            @ ^ [X3: $i] : ( X1 @ X3 ) ) )
       => ( in @ X2 @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).

thf(dsetconstrER,axiom,
    ( dsetconstrER
  <=> ! [X4: $i,X1: $i > $o,X2: $i] :
        ( ( in @ X2
          @ ( dsetconstr @ X4
            @ ^ [X3: $i] : ( X1 @ X3 ) ) )
       => ( X1 @ X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).

thf(setbeta,axiom,
    ( setbeta
  <=> ! [X4: $i,X1: $i > $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ( in @ X2
            @ ( dsetconstr @ X4
              @ ^ [X3: $i] : ( X1 @ X3 ) ) )
        <=> ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setbeta) ).

thf(nonemptyE1,axiom,
    ( nonemptyE1
  <=> ! [X4: $i] :
        ( ( nonempty @ X4 )
       => ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).

thf(nonemptyI1,axiom,
    ( nonemptyI1
  <=> ! [X4: $i] :
        ( ? [X2: $i] : ( in @ X2 @ X4 )
       => ( nonempty @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).

thf(setoftrueEq,axiom,
    ( setoftrueEq
  <=> ! [X4: $i] :
        ( ( dsetconstr @ X4
          @ ^ [X2: $i] : $true )
        = X4 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq) ).

thf(nonemptyImpWitness,axiom,
    ( nonemptyImpWitness
  <=> ! [X4: $i] :
        ( ( nonempty @ X4 )
       => ? [X2: $i] :
            ( ( in @ X2 @ X4 )
            & $true ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness) ).

thf(emptyE1,axiom,
    ( emptyE1
  <=> ! [X4: $i,X1: $i > $o] :
        ( ? [X2: $i] :
            ( ( in @ X2 @ X4 )
            & ( X1 @ X2 ) )
       => ( ( ( dsetconstr @ X4
              @ ^ [X2: $i] : ( X1 @ X2 ) )
            = emptyset )
         => ~ $true ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyE1) ).

thf(dsetconstr__Cong,axiom,
    ( dsetconstr__Cong
  <=> ! [X4: $i,X5: $i] :
        ( ( X4 = X5 )
       => ! [X1: $i > $o,X17: $i > $o] :
            ( ! [X2: $i] :
                ( ( in @ X2 @ X4 )
               => ! [X3: $i] :
                    ( ( in @ X3 @ X5 )
                   => ( ( X2 = X3 )
                     => ( ( X1 @ X2 )
                      <=> ( X17 @ X3 ) ) ) ) )
           => ( ( dsetconstr @ X4
                @ ^ [X2: $i] : ( X1 @ X2 ) )
              = ( dsetconstr @ X5
                @ ^ [X2: $i] : ( X17 @ X2 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstr__Cong) ).

thf(sepInPowerset,axiom,
    ( sepInPowerset
  <=> ! [X4: $i,X1: $i > $o] :
        ( in
        @ ( dsetconstr @ X4
          @ ^ [X2: $i] : ( X1 @ X2 ) )
        @ ( powerset @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepInPowerset) ).

thf(sepSubset,axiom,
    ( sepSubset
  <=> ! [X4: $i,X1: $i > $o] :
        ( subset
        @ ( dsetconstr @ X4
          @ ^ [X2: $i] : ( X1 @ X2 ) )
        @ X4 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepSubset) ).

thf(theprop,axiom,
    ( theprop
  <=> ! [X21: $i] :
        ( ( singleton @ X21 )
       => ( in @ ( setunion @ X21 ) @ X21 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',theprop) ).

thf(dpsetconstrI,axiom,
    ( dpsetconstrI
  <=> ! [X4: $i,X5: $i,X22: $i > $i > $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X5 )
           => ( ( X22 @ X2 @ X3 )
             => ( in @ ( kpair @ X2 @ X3 )
                @ ( dpsetconstr @ X4 @ X5
                  @ ^ [X14: $i,X18: $i] : ( X22 @ X14 @ X18 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrI) ).

thf(dpsetconstrSub,axiom,
    ( dpsetconstrSub
  <=> ! [X4: $i,X5: $i,X23: $i > $i > $o] :
        ( subset
        @ ( dpsetconstr @ X4 @ X5
          @ ^ [X2: $i,X3: $i] : ( X23 @ X2 @ X3 ) )
        @ ( cartprod @ X4 @ X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrSub) ).

thf(dpsetconstrERa,axiom,
    ( dpsetconstrERa
  <=> ! [X4: $i,X5: $i,X25: $i > $i > $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X5 )
           => ( ( in @ ( kpair @ X2 @ X3 )
                @ ( dpsetconstr @ X4 @ X5
                  @ ^ [X14: $i,X18: $i] : ( X25 @ X14 @ X18 ) ) )
             => ( X25 @ X2 @ X3 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrERa) ).

thf(dpsetconstrEL1,axiom,
    ( dpsetconstrEL1
  <=> ! [X4: $i,X5: $i,X26: $i > $i > $o,X2: $i,X3: $i] :
        ( ( in @ ( kpair @ X2 @ X3 )
          @ ( dpsetconstr @ X4 @ X5
            @ ^ [X14: $i,X18: $i] : ( X26 @ X14 @ X18 ) ) )
       => ( in @ X2 @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL1) ).

thf(dpsetconstrEL2,axiom,
    ( dpsetconstrEL2
  <=> ! [X4: $i,X5: $i,X27: $i > $i > $o,X2: $i,X3: $i] :
        ( ( in @ ( kpair @ X2 @ X3 )
          @ ( dpsetconstr @ X4 @ X5
            @ ^ [X14: $i,X18: $i] : ( X27 @ X14 @ X18 ) ) )
       => ( in @ X3 @ X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL2) ).

thf(dpsetconstrER,axiom,
    ( dpsetconstrER
  <=> ! [X4: $i,X5: $i,X28: $i > $i > $o,X2: $i,X3: $i] :
        ( ( in @ ( kpair @ X2 @ X3 )
          @ ( dpsetconstr @ X4 @ X5
            @ ^ [X14: $i,X18: $i] : ( X28 @ X14 @ X18 ) ) )
       => ( X28 @ X2 @ X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrER) ).

thf(apProp,axiom,
    ( apProp
  <=> ! [X4: $i,X5: $i,X29: $i] :
        ( ( func @ X4 @ X5 @ X29 )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( in
              @ ( setunion
                @ ( dsetconstr @ X5
                  @ ^ [X3: $i] : ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) )
              @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',apProp) ).

thf(lamProp,axiom,
    ( lamProp
  <=> ! [X4: $i,X5: $i,X30: $i > $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( in @ ( X30 @ X2 ) @ X5 ) )
       => ( func @ X4 @ X5
          @ ( dpsetconstr @ X4 @ X5
            @ ^ [X2: $i,X3: $i] :
                ( ( X30 @ X2 )
                = X3 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamProp) ).

thf(lamp,axiom,
    ( lamp
  <=> ! [X4: $i,X5: $i,X31: $i > $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( in @ ( X31 @ X2 ) @ X5 ) )
       => ( func @ X4 @ X5
          @ ( lam @ X4 @ X5
            @ ^ [X2: $i] : ( X31 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamp) ).

thf(lam2p,axiom,
    ( lam2p
  <=> ! [X4: $i,X5: $i,X32: $i > $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( in @ ( X32 @ X2 ) @ X5 ) )
       => ( in
          @ ( lam @ X4 @ X5
            @ ^ [X2: $i] : ( X32 @ X2 ) )
          @ ( funcSet @ X4 @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2p) ).

thf(brelnall1,axiom,
    ( brelnall1
  <=> ! [X4: $i,X5: $i,X33: $i] :
        ( ( breln @ X4 @ X5 @ X33 )
       => ! [X1: $i > $o] :
            ( ! [X2: $i] :
                ( ( in @ X2 @ X4 )
               => ! [X3: $i] :
                    ( ( in @ X3 @ X5 )
                   => ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
                     => ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
           => ! [X2: $i] :
                ( ( in @ X2 @ X33 )
               => ( X1 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall1) ).

thf(brelnall2,axiom,
    ( brelnall2
  <=> ! [X4: $i,X5: $i,X33: $i] :
        ( ( breln @ X4 @ X5 @ X33 )
       => ! [X1: $i > $o] :
            ( ! [X2: $i] :
                ( ( in @ X2 @ X4 )
               => ! [X3: $i] :
                    ( ( in @ X3 @ X5 )
                   => ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
                     => ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
           => ! [X2: $i] :
                ( ( in @ X2 @ X33 )
               => ( X1 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall2) ).

thf(subbreln,axiom,
    ( subbreln
  <=> ! [X4: $i,X5: $i,X33: $i] :
        ( ( breln @ X4 @ X5 @ X33 )
       => ! [X35: $i] :
            ( ( breln @ X4 @ X5 @ X35 )
           => ( ! [X2: $i] :
                  ( ( in @ X2 @ X4 )
                 => ! [X3: $i] :
                      ( ( in @ X3 @ X5 )
                     => ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
                       => ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
             => ( subset @ X33 @ X35 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subbreln) ).

thf(eqbreln,axiom,
    ( eqbreln
  <=> ! [X4: $i,X5: $i,X33: $i] :
        ( ( breln @ X4 @ X5 @ X33 )
       => ! [X35: $i] :
            ( ( breln @ X4 @ X5 @ X35 )
           => ( ! [X2: $i] :
                  ( ( in @ X2 @ X4 )
                 => ! [X3: $i] :
                      ( ( in @ X3 @ X5 )
                     => ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
                       => ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
             => ( ! [X2: $i] :
                    ( ( in @ X2 @ X4 )
                   => ! [X3: $i] :
                        ( ( in @ X3 @ X5 )
                       => ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
                         => ( in @ ( kpair @ X2 @ X3 ) @ X33 ) ) ) )
               => ( X33 = X35 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqbreln) ).

thf(beta1,axiom,
    ( beta1
  <=> ! [X4: $i,X5: $i,X36: $i > $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( in @ ( X36 @ X2 ) @ X5 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( ( ap @ X4 @ X5
                @ ( lam @ X4 @ X5
                  @ ^ [X3: $i] : ( X36 @ X3 ) )
                @ X2 )
              = ( X36 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta1) ).

thf(eta1,axiom,
    ( eta1
  <=> ! [X4: $i,X5: $i,X29: $i] :
        ( ( func @ X4 @ X5 @ X29 )
       => ( ( lam @ X4 @ X5
            @ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
          = X29 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta1) ).

thf(lam2lamEq,axiom,
    ( lam2lamEq
  <=> ! [X4: $i,X5: $i,X37: $i > $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( in @ ( X37 @ X2 ) @ X5 ) )
       => ( ( lam @ X4 @ X5
            @ ^ [X2: $i] : ( X37 @ X2 ) )
          = ( lam @ X4 @ X5
            @ ^ [X2: $i] : ( X37 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2lamEq) ).

thf(beta2,axiom,
    ( beta2
  <=> ! [X4: $i,X5: $i,X38: $i > $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( in @ ( X38 @ X2 ) @ X5 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( ( ap @ X4 @ X5
                @ ( lam @ X4 @ X5
                  @ ^ [X3: $i] : ( X38 @ X3 ) )
                @ X2 )
              = ( X38 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta2) ).

thf(eta2,axiom,
    ( eta2
  <=> ! [X4: $i,X5: $i,X29: $i] :
        ( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
       => ( ( lam @ X4 @ X5
            @ ^ [X2: $i] : ( ap @ X4 @ X5 @ X29 @ X2 ) )
          = X29 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta2) ).

thf(iffalseProp1,axiom,
    ( iffalseProp1
  <=> ! [X4: $i,X39: $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X4 )
           => ( ~ X39
             => ( in @ X3
                @ ( dsetconstr @ X4
                  @ ^ [X14: $i] :
                      ( ( X39
                        & ( X14 = X2 ) )
                      | ( ~ X39
                        & ( X14 = X3 ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp1) ).

thf(iffalseProp2,axiom,
    ( iffalseProp2
  <=> ! [X4: $i,X40: $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X4 )
           => ( ~ X40
             => ( ( dsetconstr @ X4
                  @ ^ [X14: $i] :
                      ( ( X40
                        & ( X14 = X2 ) )
                      | ( ~ X40
                        & ( X14 = X3 ) ) ) )
                = ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp2) ).

thf(iftrueProp1,axiom,
    ( iftrueProp1
  <=> ! [X4: $i,X41: $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X4 )
           => ( X41
             => ( in @ X2
                @ ( dsetconstr @ X4
                  @ ^ [X14: $i] :
                      ( ( X41
                        & ( X14 = X2 ) )
                      | ( ~ X41
                        & ( X14 = X3 ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueProp1) ).

thf(iftrueProp2,axiom,
    ( iftrueProp2
  <=> ! [X4: $i,X42: $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X4 )
           => ( X42
             => ( ( dsetconstr @ X4
                  @ ^ [X14: $i] :
                      ( ( X42
                        & ( X14 = X2 ) )
                      | ( ~ X42
                        & ( X14 = X3 ) ) ) )
                = ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueProp2) ).

thf(ifp,conjecture,
    ( setextAx
   => ( emptysetAx
     => ( setadjoinAx
       => ( powersetAx
         => ( setunionAx
           => ( omega0Ax
             => ( omegaSAx
               => ( omegaIndAx
                 => ( replAx
                   => ( foundationAx
                     => ( wellorderingAx
                       => ( descrp
                         => ( dsetconstrI
                           => ( dsetconstrEL
                             => ( dsetconstrER
                               => ( exuE1
                                 => ( prop2setE
                                   => ( emptysetE
                                     => ( emptysetimpfalse
                                       => ( notinemptyset
                                         => ( exuE3e
                                           => ( setext
                                             => ( emptyI
                                               => ( noeltsimpempty
                                                 => ( setbeta
                                                   => ( nonemptyE1
                                                     => ( nonemptyI
                                                       => ( nonemptyI1
                                                         => ( setadjoinIL
                                                           => ( emptyinunitempty
                                                             => ( setadjoinIR
                                                               => ( setadjoinE
                                                                 => ( setadjoinOr
                                                                   => ( setoftrueEq
                                                                     => ( powersetI
                                                                       => ( emptyinPowerset
                                                                         => ( emptyInPowerset
                                                                           => ( powersetE
                                                                             => ( setunionI
                                                                               => ( setunionE
                                                                                 => ( subPowSU
                                                                                   => ( exuE2
                                                                                     => ( nonemptyImpWitness
                                                                                       => ( uniqinunit
                                                                                         => ( notinsingleton
                                                                                           => ( eqinunit
                                                                                             => ( singletonsswitch
                                                                                               => ( upairsetE
                                                                                                 => ( upairsetIL
                                                                                                   => ( upairsetIR
                                                                                                     => ( emptyE1
                                                                                                       => ( vacuousDall
                                                                                                         => ( quantDeMorgan1
                                                                                                           => ( quantDeMorgan2
                                                                                                             => ( quantDeMorgan3
                                                                                                               => ( quantDeMorgan4
                                                                                                                 => ( prop2setI
                                                                                                                   => ( prop2set2propI
                                                                                                                     => ( notdexE
                                                                                                                       => ( notdallE
                                                                                                                         => ( exuI1
                                                                                                                           => ( exuI3
                                                                                                                             => ( exuI2
                                                                                                                               => ( inCongP
                                                                                                                                 => ( in__Cong
                                                                                                                                   => ( exuE3u
                                                                                                                                     => ( exu__Cong
                                                                                                                                       => ( emptyset__Cong
                                                                                                                                         => ( setadjoin__Cong
                                                                                                                                           => ( powerset__Cong
                                                                                                                                             => ( setunion__Cong
                                                                                                                                               => ( omega__Cong
                                                                                                                                                 => ( exuEu
                                                                                                                                                   => ( descr__Cong
                                                                                                                                                     => ( dsetconstr__Cong
                                                                                                                                                       => ( subsetI1
                                                                                                                                                         => ( eqimpsubset2
                                                                                                                                                           => ( eqimpsubset1
                                                                                                                                                             => ( subsetI2
                                                                                                                                                               => ( emptysetsubset
                                                                                                                                                                 => ( subsetE
                                                                                                                                                                   => ( subsetE2
                                                                                                                                                                     => ( notsubsetI
                                                                                                                                                                       => ( notequalI1
                                                                                                                                                                         => ( notequalI2
                                                                                                                                                                           => ( subsetRefl
                                                                                                                                                                             => ( subsetTrans
                                                                                                                                                                               => ( setadjoinSub
                                                                                                                                                                                 => ( setadjoinSub2
                                                                                                                                                                                   => ( subset2powerset
                                                                                                                                                                                     => ( setextsub
                                                                                                                                                                                       => ( subsetemptysetimpeq
                                                                                                                                                                                         => ( powersetI1
                                                                                                                                                                                           => ( powersetE1
                                                                                                                                                                                             => ( inPowerset
                                                                                                                                                                                               => ( powersetsubset
                                                                                                                                                                                                 => ( sepInPowerset
                                                                                                                                                                                                   => ( sepSubset
                                                                                                                                                                                                     => ( binunionIL
                                                                                                                                                                                                       => ( upairset2IR
                                                                                                                                                                                                         => ( binunionIR
                                                                                                                                                                                                           => ( binunionEcases
                                                                                                                                                                                                             => ( binunionE
                                                                                                                                                                                                               => ( binunionLsub
                                                                                                                                                                                                                 => ( binunionRsub
                                                                                                                                                                                                                   => ( binintersectI
                                                                                                                                                                                                                     => ( binintersectSubset5
                                                                                                                                                                                                                       => ( binintersectEL
                                                                                                                                                                                                                         => ( binintersectLsub
                                                                                                                                                                                                                           => ( binintersectSubset2
                                                                                                                                                                                                                             => ( binintersectSubset3
                                                                                                                                                                                                                               => ( binintersectER
                                                                                                                                                                                                                                 => ( disjointsetsI1
                                                                                                                                                                                                                                   => ( binintersectRsub
                                                                                                                                                                                                                                     => ( binintersectSubset4
                                                                                                                                                                                                                                       => ( binintersectSubset1
                                                                                                                                                                                                                                         => ( bs114d
                                                                                                                                                                                                                                           => ( setminusI
                                                                                                                                                                                                                                             => ( setminusEL
                                                                                                                                                                                                                                               => ( setminusER
                                                                                                                                                                                                                                                 => ( setminusSubset2
                                                                                                                                                                                                                                                   => ( setminusERneg
                                                                                                                                                                                                                                                     => ( setminusELneg
                                                                                                                                                                                                                                                       => ( setminusILneg
                                                                                                                                                                                                                                                         => ( setminusIRneg
                                                                                                                                                                                                                                                           => ( setminusLsub
                                                                                                                                                                                                                                                             => ( setminusSubset1
                                                                                                                                                                                                                                                               => ( symdiffE
                                                                                                                                                                                                                                                                 => ( symdiffI1
                                                                                                                                                                                                                                                                   => ( symdiffI2
                                                                                                                                                                                                                                                                     => ( symdiffIneg1
                                                                                                                                                                                                                                                                       => ( symdiffIneg2
                                                                                                                                                                                                                                                                         => ( secondinupair
                                                                                                                                                                                                                                                                           => ( setukpairIL
                                                                                                                                                                                                                                                                             => ( setukpairIR
                                                                                                                                                                                                                                                                               => ( kpairiskpair
                                                                                                                                                                                                                                                                                 => ( kpairp
                                                                                                                                                                                                                                                                                   => ( singletonsubset
                                                                                                                                                                                                                                                                                     => ( singletoninpowerset
                                                                                                                                                                                                                                                                                       => ( singletoninpowunion
                                                                                                                                                                                                                                                                                         => ( upairset2E
                                                                                                                                                                                                                                                                                           => ( upairsubunion
                                                                                                                                                                                                                                                                                             => ( upairinpowunion
                                                                                                                                                                                                                                                                                               => ( ubforcartprodlem1
                                                                                                                                                                                                                                                                                                 => ( ubforcartprodlem2
                                                                                                                                                                                                                                                                                                   => ( ubforcartprodlem3
                                                                                                                                                                                                                                                                                                     => ( cartprodpairin
                                                                                                                                                                                                                                                                                                       => ( cartprodmempair1
                                                                                                                                                                                                                                                                                                         => ( cartprodmempair
                                                                                                                                                                                                                                                                                                           => ( setunionE2
                                                                                                                                                                                                                                                                                                             => ( setunionsingleton1
                                                                                                                                                                                                                                                                                                               => ( setunionsingleton2
                                                                                                                                                                                                                                                                                                                 => ( setunionsingleton
                                                                                                                                                                                                                                                                                                                   => ( singletonprop
                                                                                                                                                                                                                                                                                                                     => ( ex1E1
                                                                                                                                                                                                                                                                                                                       => ( ex1I
                                                                                                                                                                                                                                                                                                                         => ( ex1I2
                                                                                                                                                                                                                                                                                                                           => ( singletonsuniq
                                                                                                                                                                                                                                                                                                                             => ( setukpairinjL1
                                                                                                                                                                                                                                                                                                                               => ( kfstsingleton
                                                                                                                                                                                                                                                                                                                                 => ( theprop
                                                                                                                                                                                                                                                                                                                                   => ( kfstpairEq
                                                                                                                                                                                                                                                                                                                                     => ( cartprodfstin
                                                                                                                                                                                                                                                                                                                                       => ( setukpairinjL2
                                                                                                                                                                                                                                                                                                                                         => ( setukpairinjL
                                                                                                                                                                                                                                                                                                                                           => ( setukpairinjR11
                                                                                                                                                                                                                                                                                                                                             => ( setukpairinjR12
                                                                                                                                                                                                                                                                                                                                               => ( setukpairinjR1
                                                                                                                                                                                                                                                                                                                                                 => ( upairequniteq
                                                                                                                                                                                                                                                                                                                                                   => ( setukpairinjR2
                                                                                                                                                                                                                                                                                                                                                     => ( setukpairinjR
                                                                                                                                                                                                                                                                                                                                                       => ( ksndsingleton
                                                                                                                                                                                                                                                                                                                                                         => ( ksndpairEq
                                                                                                                                                                                                                                                                                                                                                           => ( kpairsurjEq
                                                                                                                                                                                                                                                                                                                                                             => ( cartprodsndin
                                                                                                                                                                                                                                                                                                                                                               => ( cartprodpairmemEL
                                                                                                                                                                                                                                                                                                                                                                 => ( cartprodpairmemER
                                                                                                                                                                                                                                                                                                                                                                   => ( cartprodmempaircEq
                                                                                                                                                                                                                                                                                                                                                                     => ( cartprodfstpairEq
                                                                                                                                                                                                                                                                                                                                                                       => ( cartprodsndpairEq
                                                                                                                                                                                                                                                                                                                                                                         => ( cartprodpairsurjEq
                                                                                                                                                                                                                                                                                                                                                                           => ( dpsetconstrI
                                                                                                                                                                                                                                                                                                                                                                             => ( dpsetconstrSub
                                                                                                                                                                                                                                                                                                                                                                               => ( setOfPairsIsBReln
                                                                                                                                                                                                                                                                                                                                                                                 => ( dpsetconstrERa
                                                                                                                                                                                                                                                                                                                                                                                   => ( dpsetconstrEL1
                                                                                                                                                                                                                                                                                                                                                                                     => ( dpsetconstrEL2
                                                                                                                                                                                                                                                                                                                                                                                       => ( dpsetconstrER
                                                                                                                                                                                                                                                                                                                                                                                         => ( funcImageSingleton
                                                                                                                                                                                                                                                                                                                                                                                           => ( apProp
                                                                                                                                                                                                                                                                                                                                                                                             => ( app
                                                                                                                                                                                                                                                                                                                                                                                               => ( infuncsetfunc
                                                                                                                                                                                                                                                                                                                                                                                                 => ( ap2p
                                                                                                                                                                                                                                                                                                                                                                                                   => ( funcinfuncset
                                                                                                                                                                                                                                                                                                                                                                                                     => ( lamProp
                                                                                                                                                                                                                                                                                                                                                                                                       => ( lamp
                                                                                                                                                                                                                                                                                                                                                                                                         => ( lam2p
                                                                                                                                                                                                                                                                                                                                                                                                           => ( brelnall1
                                                                                                                                                                                                                                                                                                                                                                                                             => ( brelnall2
                                                                                                                                                                                                                                                                                                                                                                                                               => ( ex1E2
                                                                                                                                                                                                                                                                                                                                                                                                                 => ( funcGraphProp1
                                                                                                                                                                                                                                                                                                                                                                                                                   => ( funcGraphProp3
                                                                                                                                                                                                                                                                                                                                                                                                                     => ( funcGraphProp2
                                                                                                                                                                                                                                                                                                                                                                                                                       => ( funcextLem
                                                                                                                                                                                                                                                                                                                                                                                                                         => ( funcGraphProp4
                                                                                                                                                                                                                                                                                                                                                                                                                           => ( subbreln
                                                                                                                                                                                                                                                                                                                                                                                                                             => ( eqbreln
                                                                                                                                                                                                                                                                                                                                                                                                                               => ( funcext
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( funcext2
                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ap2apEq1
                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ap2apEq2
                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( beta1
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( eta1
                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( lam2lamEq
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( beta2
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( eta2
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( iffalseProp1
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( iffalseProp2
                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( iftrueProp1
                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( iftrueProp2
                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ifSingleton
                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X4: $i,X45: $o,X2: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X2 @ X4 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X3: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X4 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ ( if @ X4 @ X45 @ X2 @ X3 ) @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifp) ).

thf(setextAx,axiom,
    ( setextAx
  <=> ! [X4: $i,X5: $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
          <=> ( in @ X2 @ X5 ) )
       => ( X4 = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx) ).

thf(emptysetAx,axiom,
    ( emptysetAx
  <=> ! [X2: $i] :
        ~ ( in @ X2 @ emptyset ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).

thf(setadjoinAx,axiom,
    ( setadjoinAx
  <=> ! [X2: $i,X4: $i,X3: $i] :
        ( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
      <=> ( ( X3 = X2 )
          | ( in @ X3 @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).

thf(powersetAx,axiom,
    ( powersetAx
  <=> ! [X4: $i,X5: $i] :
        ( ( in @ X5 @ ( powerset @ X4 ) )
      <=> ! [X2: $i] :
            ( ( in @ X2 @ X5 )
           => ( in @ X2 @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).

thf(setunionAx,axiom,
    ( setunionAx
  <=> ! [X4: $i,X2: $i] :
        ( ( in @ X2 @ ( setunion @ X4 ) )
      <=> ? [X5: $i] :
            ( ( in @ X2 @ X5 )
            & ( in @ X5 @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).

thf(omega0Ax,axiom,
    ( omega0Ax
  <=> ( in @ emptyset @ omega ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).

thf(omegaSAx,axiom,
    ( omegaSAx
  <=> ! [X2: $i] :
        ( ( in @ X2 @ omega )
       => ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).

thf(omegaIndAx,axiom,
    ( omegaIndAx
  <=> ! [X4: $i] :
        ( ( ( in @ emptyset @ X4 )
          & ! [X2: $i] :
              ( ( ( in @ X2 @ omega )
                & ( in @ X2 @ X4 ) )
             => ( in @ ( setadjoin @ X2 @ X2 ) @ X4 ) ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ omega )
           => ( in @ X2 @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).

thf(foundationAx,axiom,
    ( foundationAx
  <=> ! [X4: $i] :
        ( ? [X2: $i] : ( in @ X2 @ X4 )
       => ? [X5: $i] :
            ( ( in @ X5 @ X4 )
            & ~ ? [X2: $i] :
                  ( ( in @ X2 @ X5 )
                  & ( in @ X2 @ X4 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx) ).

thf(wellorderingAx,axiom,
    ( wellorderingAx
  <=> ! [X4: $i] :
      ? [X5: $i] :
        ( ! [X7: $i] :
            ( ( in @ X7 @ X5 )
           => ! [X2: $i] :
                ( ( in @ X2 @ X7 )
               => ( in @ X2 @ X4 ) ) )
        & ! [X2: $i,X3: $i] :
            ( ( ( in @ X2 @ X4 )
              & ( in @ X3 @ X4 ) )
           => ( ! [X7: $i] :
                  ( ( in @ X7 @ X5 )
                 => ( ( in @ X2 @ X7 )
                  <=> ( in @ X3 @ X7 ) ) )
             => ( X2 = X3 ) ) )
        & ! [X7: $i,X8: $i] :
            ( ( ( in @ X7 @ X5 )
              & ( in @ X8 @ X5 ) )
           => ( ! [X2: $i] :
                  ( ( in @ X2 @ X7 )
                 => ( in @ X2 @ X8 ) )
              | ! [X2: $i] :
                  ( ( in @ X2 @ X8 )
                 => ( in @ X2 @ X7 ) ) ) )
        & ! [X7: $i] :
            ( ( ! [X2: $i] :
                  ( ( in @ X2 @ X7 )
                 => ( in @ X2 @ X4 ) )
              & ? [X2: $i] : ( in @ X2 @ X7 ) )
           => ? [X8: $i,X2: $i] :
                ( ( in @ X8 @ X5 )
                & ( in @ X2 @ X7 )
                & ~ ? [X3: $i] :
                      ( ( in @ X3 @ X8 )
                      & ( in @ X3 @ X7 ) )
                & ! [X9: $i] :
                    ( ( in @ X9 @ X5 )
                   => ( ! [X3: $i] :
                          ( ( in @ X3 @ X9 )
                         => ( in @ X3 @ X8 ) )
                      | ( in @ X2 @ X9 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).

thf(prop2setE,axiom,
    ( prop2setE
  <=> ! [X10: $o,X2: $i] :
        ( ( in @ X2 @ ( prop2set @ X10 ) )
       => X10 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).

thf(emptysetE,axiom,
    ( emptysetE
  <=> ! [X2: $i] :
        ( ( in @ X2 @ emptyset )
       => ! [X11: $o] : X11 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).

thf(emptysetimpfalse,axiom,
    ( emptysetimpfalse
  <=> ! [X2: $i] :
        ( ( in @ X2 @ emptyset )
       => ~ $true ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).

thf(notinemptyset,axiom,
    ( notinemptyset
  <=> ! [X2: $i] :
        ~ ( in @ X2 @ emptyset ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).

thf(setext,axiom,
    ( setext
  <=> ! [X4: $i,X5: $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( in @ X2 @ X5 ) )
       => ( ! [X2: $i] :
              ( ( in @ X2 @ X5 )
             => ( in @ X2 @ X4 ) )
         => ( X4 = X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).

thf(emptyI,axiom,
    ( emptyI
  <=> ! [X4: $i] :
        ( ! [X2: $i] :
            ~ ( in @ X2 @ X4 )
       => ( X4 = emptyset ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).

thf(noeltsimpempty,axiom,
    ( noeltsimpempty
  <=> ! [X4: $i] :
        ( ! [X2: $i] :
            ~ ( in @ X2 @ X4 )
       => ( X4 = emptyset ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).

thf(setadjoinIL,axiom,
    ( setadjoinIL
  <=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).

thf(emptyinunitempty,axiom,
    ( emptyinunitempty
  <=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).

thf(setadjoinIR,axiom,
    ( setadjoinIR
  <=> ! [X2: $i,X4: $i,X3: $i] :
        ( ( in @ X3 @ X4 )
       => ( in @ X3 @ ( setadjoin @ X2 @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR) ).

thf(setadjoinE,axiom,
    ( setadjoinE
  <=> ! [X2: $i,X4: $i,X3: $i] :
        ( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
       => ! [X12: $o] :
            ( ( ( X3 = X2 )
             => X12 )
           => ( ( ( in @ X3 @ X4 )
               => X12 )
             => X12 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).

thf(setadjoinOr,axiom,
    ( setadjoinOr
  <=> ! [X2: $i,X4: $i,X3: $i] :
        ( ( in @ X3 @ ( setadjoin @ X2 @ X4 ) )
       => ( ( X3 = X2 )
          | ( in @ X3 @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinOr) ).

thf(powersetI,axiom,
    ( powersetI
  <=> ! [X4: $i,X5: $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X5 )
           => ( in @ X2 @ X4 ) )
       => ( in @ X5 @ ( powerset @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).

thf(emptyinPowerset,axiom,
    ( emptyinPowerset
  <=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).

thf(emptyInPowerset,axiom,
    ( emptyInPowerset
  <=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyInPowerset) ).

thf(powersetE,axiom,
    ( powersetE
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X5 @ ( powerset @ X4 ) )
       => ( ( in @ X2 @ X5 )
         => ( in @ X2 @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE) ).

thf(setunionI,axiom,
    ( setunionI
  <=> ! [X4: $i,X2: $i,X5: $i] :
        ( ( in @ X2 @ X5 )
       => ( ( in @ X5 @ X4 )
         => ( in @ X2 @ ( setunion @ X4 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI) ).

thf(setunionE,axiom,
    ( setunionE
  <=> ! [X4: $i,X2: $i] :
        ( ( in @ X2 @ ( setunion @ X4 ) )
       => ! [X13: $o] :
            ( ! [X5: $i] :
                ( ( in @ X2 @ X5 )
               => ( ( in @ X5 @ X4 )
                 => X13 ) )
           => X13 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).

thf(subPowSU,axiom,
    ( subPowSU
  <=> ! [X4: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU) ).

thf(uniqinunit,axiom,
    ( uniqinunit
  <=> ! [X2: $i,X3: $i] :
        ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
       => ( X2 = X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).

thf(notinsingleton,axiom,
    ( notinsingleton
  <=> ! [X2: $i,X3: $i] :
        ( ( X2 != X3 )
       => ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).

thf(eqinunit,axiom,
    ( eqinunit
  <=> ! [X2: $i,X3: $i] :
        ( ( X2 = X3 )
       => ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).

thf(singletonsswitch,axiom,
    ( singletonsswitch
  <=> ! [X2: $i,X3: $i] :
        ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
       => ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch) ).

thf(upairsetE,axiom,
    ( upairsetE
  <=> ! [X2: $i,X3: $i,X14: $i] :
        ( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
       => ( ( X14 = X2 )
          | ( X14 = X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetE) ).

thf(upairsetIL,axiom,
    ( upairsetIL
  <=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).

thf(upairsetIR,axiom,
    ( upairsetIR
  <=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).

thf(vacuousDall,axiom,
    ( vacuousDall
  <=> ! [X1: $i > $o,X2: $i] :
        ( ( in @ X2 @ emptyset )
       => ( X1 @ X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).

thf(quantDeMorgan1,axiom,
    ( quantDeMorgan1
  <=> ! [X4: $i,X1: $i > $o] :
        ( ~ ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ( X1 @ X2 ) )
       => ? [X2: $i] :
            ( ( in @ X2 @ X4 )
            & ~ ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).

thf(quantDeMorgan2,axiom,
    ( quantDeMorgan2
  <=> ! [X4: $i,X1: $i > $o] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ~ ( X1 @ X2 ) )
       => ~ ? [X2: $i] :
              ( ( in @ X2 @ X4 )
              & ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan2) ).

thf(quantDeMorgan3,axiom,
    ( quantDeMorgan3
  <=> ! [X4: $i,X1: $i > $o] :
        ( ~ ? [X2: $i] :
              ( ( in @ X2 @ X4 )
              & ( X1 @ X2 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ~ ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3) ).

thf(quantDeMorgan4,axiom,
    ( quantDeMorgan4
  <=> ! [X4: $i,X1: $i > $o] :
        ( ? [X2: $i] :
            ( ( in @ X2 @ X4 )
            & ~ ( X1 @ X2 ) )
       => ~ ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4) ).

thf(prop2setI,axiom,
    ( prop2setI
  <=> ! [X15: $o] :
        ( X15
       => ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).

thf(prop2set2propI,axiom,
    ( prop2set2propI
  <=> ! [X16: $o] :
        ( X16
       => ( set2prop @ ( prop2set @ X16 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2set2propI) ).

thf(notdexE,axiom,
    ( notdexE
  <=> ! [X4: $i,X1: $i > $o] :
        ( ~ ? [X2: $i] :
              ( ( in @ X2 @ X4 )
              & ( X1 @ X2 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ~ ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdexE) ).

thf(notdallE,axiom,
    ( notdallE
  <=> ! [X4: $i,X1: $i > $o] :
        ( ~ ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ( X1 @ X2 ) )
       => ? [X2: $i] :
            ( ( in @ X2 @ X4 )
            & ~ ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdallE) ).

thf(inCongP,axiom,
    ( inCongP
  <=> ! [X4: $i,X5: $i] :
        ( ( X4 = X5 )
       => ! [X2: $i,X3: $i] :
            ( ( X2 = X3 )
           => ( ( in @ X2 @ X4 )
             => ( in @ X3 @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inCongP) ).

thf(in__Cong,axiom,
    ( in__Cong
  <=> ! [X4: $i,X5: $i] :
        ( ( X4 = X5 )
       => ! [X2: $i,X3: $i] :
            ( ( X2 = X3 )
           => ( ( in @ X2 @ X4 )
            <=> ( in @ X3 @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).

thf(emptyset__Cong,axiom,
    ( emptyset__Cong
  <=> ( emptyset = emptyset ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset__Cong) ).

thf(setadjoin__Cong,axiom,
    ( setadjoin__Cong
  <=> ! [X2: $i,X3: $i] :
        ( ( X2 = X3 )
       => ! [X14: $i,X18: $i] :
            ( ( X14 = X18 )
           => ( ( setadjoin @ X2 @ X14 )
              = ( setadjoin @ X3 @ X18 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong) ).

thf(powerset__Cong,axiom,
    ( powerset__Cong
  <=> ! [X4: $i,X5: $i] :
        ( ( X4 = X5 )
       => ( ( powerset @ X4 )
          = ( powerset @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong) ).

thf(setunion__Cong,axiom,
    ( setunion__Cong
  <=> ! [X4: $i,X5: $i] :
        ( ( X4 = X5 )
       => ( ( setunion @ X4 )
          = ( setunion @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong) ).

thf(omega__Cong,axiom,
    ( omega__Cong
  <=> ( omega = omega ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong) ).

thf(subsetI1,axiom,
    ( subsetI1
  <=> ! [X4: $i,X5: $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( in @ X2 @ X5 ) )
       => ( subset @ X4 @ X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1) ).

thf(eqimpsubset2,axiom,
    ( eqimpsubset2
  <=> ! [X4: $i,X5: $i] :
        ( ( X4 = X5 )
       => ( subset @ X5 @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2) ).

thf(eqimpsubset1,axiom,
    ( eqimpsubset1
  <=> ! [X4: $i,X5: $i] :
        ( ( X4 = X5 )
       => ( subset @ X4 @ X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset1) ).

thf(subsetI2,axiom,
    ( subsetI2
  <=> ! [X4: $i,X5: $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( in @ X2 @ X5 ) )
       => ( subset @ X4 @ X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2) ).

thf(emptysetsubset,axiom,
    ( emptysetsubset
  <=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset) ).

thf(subsetE,axiom,
    ( subsetE
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( subset @ X4 @ X5 )
       => ( ( in @ X2 @ X4 )
         => ( in @ X2 @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE) ).

thf(subsetE2,axiom,
    ( subsetE2
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( subset @ X4 @ X5 )
       => ( ~ ( in @ X2 @ X5 )
         => ~ ( in @ X2 @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE2) ).

thf(notsubsetI,axiom,
    ( notsubsetI
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ~ ( in @ X2 @ X5 )
         => ~ ( subset @ X4 @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',notsubsetI) ).

thf(notequalI1,axiom,
    ( notequalI1
  <=> ! [X4: $i,X5: $i] :
        ( ~ ( subset @ X4 @ X5 )
       => ( X4 != X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1) ).

thf(notequalI2,axiom,
    ( notequalI2
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ~ ( in @ X2 @ X5 )
         => ( X4 != X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI2) ).

thf(subsetRefl,axiom,
    ( subsetRefl
  <=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl) ).

thf(subsetTrans,axiom,
    ( subsetTrans
  <=> ! [X4: $i,X5: $i,X7: $i] :
        ( ( subset @ X4 @ X5 )
       => ( ( subset @ X5 @ X7 )
         => ( subset @ X4 @ X7 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTrans) ).

thf(setadjoinSub,axiom,
    ( setadjoinSub
  <=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub) ).

thf(setadjoinSub2,axiom,
    ( setadjoinSub2
  <=> ! [X4: $i,X2: $i,X5: $i] :
        ( ( subset @ X4 @ X5 )
       => ( subset @ X4 @ ( setadjoin @ X2 @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub2) ).

thf(subset2powerset,axiom,
    ( subset2powerset
  <=> ! [X4: $i,X5: $i] :
        ( ( subset @ X4 @ X5 )
       => ( in @ X4 @ ( powerset @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset) ).

thf(setextsub,axiom,
    ( setextsub
  <=> ! [X4: $i,X5: $i] :
        ( ( subset @ X4 @ X5 )
       => ( ( subset @ X5 @ X4 )
         => ( X4 = X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub) ).

thf(subsetemptysetimpeq,axiom,
    ( subsetemptysetimpeq
  <=> ! [X4: $i] :
        ( ( subset @ X4 @ emptyset )
       => ( X4 = emptyset ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).

thf(powersetI1,axiom,
    ( powersetI1
  <=> ! [X4: $i,X5: $i] :
        ( ( subset @ X5 @ X4 )
       => ( in @ X5 @ ( powerset @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).

thf(powersetE1,axiom,
    ( powersetE1
  <=> ! [X4: $i,X5: $i] :
        ( ( in @ X5 @ ( powerset @ X4 ) )
       => ( subset @ X5 @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).

thf(inPowerset,axiom,
    ( inPowerset
  <=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inPowerset) ).

thf(powersetsubset,axiom,
    ( powersetsubset
  <=> ! [X4: $i,X5: $i] :
        ( ( subset @ X4 @ X5 )
       => ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset) ).

thf(binunionIL,axiom,
    ( binunionIL
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL) ).

thf(upairset2IR,axiom,
    ( upairset2IR
  <=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR) ).

thf(binunionIR,axiom,
    ( binunionIR
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X5 )
       => ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIR) ).

thf(binunionEcases,axiom,
    ( binunionEcases
  <=> ! [X4: $i,X5: $i,X2: $i,X19: $o] :
        ( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
       => ( ( ( in @ X2 @ X4 )
           => X19 )
         => ( ( ( in @ X2 @ X5 )
             => X19 )
           => X19 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases) ).

thf(binunionE,axiom,
    ( binunionE
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
       => ( ( in @ X2 @ X4 )
          | ( in @ X2 @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE) ).

thf(binunionLsub,axiom,
    ( binunionLsub
  <=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).

thf(binunionRsub,axiom,
    ( binunionRsub
  <=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub) ).

thf(binintersectI,axiom,
    ( binintersectI
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ( in @ X2 @ X5 )
         => ( in @ X2 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI) ).

thf(binintersectSubset5,axiom,
    ( binintersectSubset5
  <=> ! [X4: $i,X5: $i,X7: $i] :
        ( ( subset @ X7 @ X4 )
       => ( ( subset @ X7 @ X5 )
         => ( subset @ X7 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset5) ).

thf(binintersectEL,axiom,
    ( binintersectEL
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
       => ( in @ X2 @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL) ).

thf(binintersectLsub,axiom,
    ( binintersectLsub
  <=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub) ).

thf(binintersectSubset2,axiom,
    ( binintersectSubset2
  <=> ! [X4: $i,X5: $i] :
        ( ( subset @ X4 @ X5 )
       => ( ( binintersect @ X4 @ X5 )
          = X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2) ).

thf(binintersectSubset3,axiom,
    ( binintersectSubset3
  <=> ! [X4: $i,X5: $i] :
        ( ( ( binintersect @ X4 @ X5 )
          = X5 )
       => ( subset @ X5 @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3) ).

thf(binintersectER,axiom,
    ( binintersectER
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
       => ( in @ X2 @ X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER) ).

thf(disjointsetsI1,axiom,
    ( disjointsetsI1
  <=> ! [X4: $i,X5: $i] :
        ( ~ ? [X2: $i] :
              ( ( in @ X2 @ X4 )
              & ( in @ X2 @ X5 ) )
       => ( ( binintersect @ X4 @ X5 )
          = emptyset ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjointsetsI1) ).

thf(binintersectRsub,axiom,
    ( binintersectRsub
  <=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub) ).

thf(binintersectSubset4,axiom,
    ( binintersectSubset4
  <=> ! [X4: $i,X5: $i] :
        ( ( subset @ X5 @ X4 )
       => ( ( binintersect @ X4 @ X5 )
          = X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4) ).

thf(binintersectSubset1,axiom,
    ( binintersectSubset1
  <=> ! [X4: $i,X5: $i] :
        ( ( ( binintersect @ X4 @ X5 )
          = X4 )
       => ( subset @ X4 @ X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset1) ).

thf(bs114d,axiom,
    ( bs114d
  <=> ! [X4: $i,X5: $i,X7: $i] :
        ( ( binintersect @ X4 @ ( binunion @ X5 @ X7 ) )
        = ( binunion @ ( binintersect @ X4 @ X5 ) @ ( binintersect @ X4 @ X7 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',bs114d) ).

thf(setminusI,axiom,
    ( setminusI
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ~ ( in @ X2 @ X5 )
         => ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI) ).

thf(setminusEL,axiom,
    ( setminusEL
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
       => ( in @ X2 @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusEL) ).

thf(setminusER,axiom,
    ( setminusER
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ ( setminus @ X4 @ X5 ) )
       => ~ ( in @ X2 @ X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER) ).

thf(setminusSubset2,axiom,
    ( setminusSubset2
  <=> ! [X4: $i,X5: $i] :
        ( ( subset @ X4 @ X5 )
       => ( ( setminus @ X4 @ X5 )
          = emptyset ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset2) ).

thf(setminusERneg,axiom,
    ( setminusERneg
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
       => ( ( in @ X2 @ X4 )
         => ( in @ X2 @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusERneg) ).

thf(setminusELneg,axiom,
    ( setminusELneg
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) )
       => ( ~ ( in @ X2 @ X5 )
         => ~ ( in @ X2 @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusELneg) ).

thf(setminusILneg,axiom,
    ( setminusILneg
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ~ ( in @ X2 @ X4 )
       => ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusILneg) ).

thf(setminusIRneg,axiom,
    ( setminusIRneg
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X5 )
       => ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusIRneg) ).

thf(setminusLsub,axiom,
    ( setminusLsub
  <=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusLsub) ).

thf(setminusSubset1,axiom,
    ( setminusSubset1
  <=> ! [X4: $i,X5: $i] :
        ( ( ( setminus @ X4 @ X5 )
          = emptyset )
       => ( subset @ X4 @ X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1) ).

thf(symdiffE,axiom,
    ( symdiffE
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ ( symdiff @ X4 @ X5 ) )
       => ! [X20: $o] :
            ( ( ( in @ X2 @ X4 )
             => ( ~ ( in @ X2 @ X5 )
               => X20 ) )
           => ( ( ~ ( in @ X2 @ X4 )
               => ( ( in @ X2 @ X5 )
                 => X20 ) )
             => X20 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffE) ).

thf(symdiffI1,axiom,
    ( symdiffI1
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ~ ( in @ X2 @ X5 )
         => ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI1) ).

thf(symdiffI2,axiom,
    ( symdiffI2
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ~ ( in @ X2 @ X4 )
       => ( ( in @ X2 @ X5 )
         => ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI2) ).

thf(symdiffIneg1,axiom,
    ( symdiffIneg1
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ( in @ X2 @ X5 )
         => ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg1) ).

thf(symdiffIneg2,axiom,
    ( symdiffIneg2
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ~ ( in @ X2 @ X4 )
       => ( ~ ( in @ X2 @ X5 )
         => ~ ( in @ X2 @ ( symdiff @ X4 @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg2) ).

thf(secondinupair,axiom,
    ( secondinupair
  <=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).

thf(setukpairIL,axiom,
    ( setukpairIL
  <=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIL) ).

thf(setukpairIR,axiom,
    ( setukpairIR
  <=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIR) ).

thf(kpairiskpair,axiom,
    ( kpairiskpair
  <=> ! [X2: $i,X3: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair) ).

thf(kpairp,axiom,
    ( kpairp
  <=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).

thf(singletonsubset,axiom,
    ( singletonsubset
  <=> ! [X4: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsubset) ).

thf(singletoninpowerset,axiom,
    ( singletoninpowerset
  <=> ! [X4: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowerset) ).

thf(singletoninpowunion,axiom,
    ( singletoninpowunion
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowunion) ).

thf(upairset2E,axiom,
    ( upairset2E
  <=> ! [X2: $i,X3: $i,X14: $i] :
        ( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
       => ( ( X14 = X2 )
          | ( X14 = X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2E) ).

thf(upairsubunion,axiom,
    ( upairsubunion
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X5 )
           => ( subset @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( binunion @ X4 @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsubunion) ).

thf(upairinpowunion,axiom,
    ( upairinpowunion
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X5 )
           => ( in @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairinpowunion) ).

thf(ubforcartprodlem1,axiom,
    ( ubforcartprodlem1
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X5 )
           => ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem1) ).

thf(ubforcartprodlem2,axiom,
    ( ubforcartprodlem2
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X5 )
           => ( in @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem2) ).

thf(ubforcartprodlem3,axiom,
    ( ubforcartprodlem3
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X5 )
           => ( in @ ( kpair @ X2 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem3) ).

thf(cartprodpairin,axiom,
    ( cartprodpairin
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X5 )
           => ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairin) ).

thf(cartprodmempair1,axiom,
    ( cartprodmempair1
  <=> ! [X4: $i,X5: $i,X18: $i] :
        ( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
       => ? [X2: $i] :
            ( ( in @ X2 @ X4 )
            & ? [X3: $i] :
                ( ( in @ X3 @ X5 )
                & ( X18
                  = ( kpair @ X2 @ X3 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair1) ).

thf(cartprodmempair,axiom,
    ( cartprodmempair
  <=> ! [X4: $i,X5: $i,X18: $i] :
        ( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
       => ( iskpair @ X18 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair) ).

thf(setunionE2,axiom,
    ( setunionE2
  <=> ! [X4: $i,X2: $i] :
        ( ( in @ X2 @ ( setunion @ X4 ) )
       => ? [X21: $i] :
            ( ( in @ X21 @ X4 )
            & ( in @ X2 @ X21 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE2) ).

thf(setunionsingleton1,axiom,
    ( setunionsingleton1
  <=> ! [X4: $i] : ( subset @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) @ X4 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton1) ).

thf(setunionsingleton2,axiom,
    ( setunionsingleton2
  <=> ! [X4: $i] : ( subset @ X4 @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton2) ).

thf(setunionsingleton,axiom,
    ( setunionsingleton
  <=> ! [X2: $i] :
        ( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
        = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton) ).

thf(singletonsuniq,axiom,
    ( singletonsuniq
  <=> ! [X2: $i,X3: $i] :
        ( ( ( setadjoin @ X2 @ emptyset )
          = ( setadjoin @ X3 @ emptyset ) )
       => ( X2 = X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsuniq) ).

thf(setukpairinjL1,axiom,
    ( setukpairinjL1
  <=> ! [X2: $i,X3: $i,X14: $i] :
        ( ( in @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
       => ( X2 = X14 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL1) ).

thf(kfstpairEq,axiom,
    ( kfstpairEq
  <=> ! [X2: $i,X3: $i] :
        ( ( kfst @ ( kpair @ X2 @ X3 ) )
        = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstpairEq) ).

thf(cartprodfstin,axiom,
    ( cartprodfstin
  <=> ! [X4: $i,X5: $i,X18: $i] :
        ( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
       => ( in @ ( kfst @ X18 ) @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstin) ).

thf(setukpairinjL2,axiom,
    ( setukpairinjL2
  <=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
        ( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
       => ( X2 = X14 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL2) ).

thf(setukpairinjL,axiom,
    ( setukpairinjL
  <=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
        ( ( ( kpair @ X2 @ X3 )
          = ( kpair @ X14 @ X18 ) )
       => ( X2 = X14 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL) ).

thf(setukpairinjR11,axiom,
    ( setukpairinjR11
  <=> ! [X2: $i,X3: $i] :
        ( ( X2 = X3 )
       => ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
          = ( setadjoin @ X2 @ emptyset ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR11) ).

thf(setukpairinjR12,axiom,
    ( setukpairinjR12
  <=> ! [X2: $i,X3: $i] :
        ( ( X2 = X3 )
       => ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ emptyset ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR12) ).

thf(setukpairinjR1,axiom,
    ( setukpairinjR1
  <=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
        ( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
       => ( ( X14 = X18 )
         => ( X3 = X18 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR1) ).

thf(upairequniteq,axiom,
    ( upairequniteq
  <=> ! [X2: $i,X3: $i,X14: $i] :
        ( ( ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) )
          = ( setadjoin @ X14 @ emptyset ) )
       => ( X2 = X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairequniteq) ).

thf(setukpairinjR2,axiom,
    ( setukpairinjR2
  <=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
        ( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) )
       => ( X3 = X18 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR2) ).

thf(setukpairinjR,axiom,
    ( setukpairinjR
  <=> ! [X2: $i,X3: $i,X14: $i,X18: $i] :
        ( ( ( kpair @ X2 @ X3 )
          = ( kpair @ X14 @ X18 ) )
       => ( X3 = X18 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR) ).

thf(ksndpairEq,axiom,
    ( ksndpairEq
  <=> ! [X2: $i,X3: $i] :
        ( ( ksnd @ ( kpair @ X2 @ X3 ) )
        = X3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndpairEq) ).

thf(kpairsurjEq,axiom,
    ( kpairsurjEq
  <=> ! [X18: $i] :
        ( ( iskpair @ X18 )
       => ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
          = X18 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairsurjEq) ).

thf(cartprodsndin,axiom,
    ( cartprodsndin
  <=> ! [X4: $i,X5: $i,X18: $i] :
        ( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
       => ( in @ ( ksnd @ X18 ) @ X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndin) ).

thf(cartprodpairmemEL,axiom,
    ( cartprodpairmemEL
  <=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
        ( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
       => ( in @ X2 @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemEL) ).

thf(cartprodpairmemER,axiom,
    ( cartprodpairmemER
  <=> ! [X4: $i,X5: $i,X2: $i,X3: $i] :
        ( ( in @ ( kpair @ X2 @ X3 ) @ ( cartprod @ X4 @ X5 ) )
       => ( in @ X3 @ X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemER) ).

thf(cartprodmempaircEq,axiom,
    ( cartprodmempaircEq
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X5 )
           => ( ( kpair @ X2 @ X3 )
              = ( kpair @ X2 @ X3 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempaircEq) ).

thf(cartprodfstpairEq,axiom,
    ( cartprodfstpairEq
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X5 )
           => ( ( kfst @ ( kpair @ X2 @ X3 ) )
              = X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstpairEq) ).

thf(cartprodsndpairEq,axiom,
    ( cartprodsndpairEq
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X5 )
           => ( ( ksnd @ ( kpair @ X2 @ X3 ) )
              = X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndpairEq) ).

thf(cartprodpairsurjEq,axiom,
    ( cartprodpairsurjEq
  <=> ! [X4: $i,X5: $i,X18: $i] :
        ( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
       => ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
          = X18 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairsurjEq) ).

thf(app,axiom,
    ( app
  <=> ! [X4: $i,X5: $i,X29: $i] :
        ( ( func @ X4 @ X5 @ X29 )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',app) ).

thf(infuncsetfunc,axiom,
    ( infuncsetfunc
  <=> ! [X4: $i,X5: $i,X29: $i] :
        ( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
       => ( func @ X4 @ X5 @ X29 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc) ).

thf(ap2p,axiom,
    ( ap2p
  <=> ! [X4: $i,X5: $i,X29: $i] :
        ( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2p) ).

thf(funcinfuncset,axiom,
    ( funcinfuncset
  <=> ! [X4: $i,X5: $i,X29: $i] :
        ( ( func @ X4 @ X5 @ X29 )
       => ( in @ X29 @ ( funcSet @ X4 @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcinfuncset) ).

thf(funcGraphProp1,axiom,
    ( funcGraphProp1
  <=> ! [X4: $i,X5: $i,X29: $i] :
        ( ( func @ X4 @ X5 @ X29 )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp1) ).

thf(funcGraphProp3,axiom,
    ( funcGraphProp3
  <=> ! [X4: $i,X5: $i,X29: $i] :
        ( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp3) ).

thf(funcGraphProp2,axiom,
    ( funcGraphProp2
  <=> ! [X4: $i,X5: $i,X29: $i] :
        ( ( func @ X4 @ X5 @ X29 )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ! [X3: $i] :
                ( ( in @ X3 @ X5 )
               => ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
                 => ( ( ap @ X4 @ X5 @ X29 @ X2 )
                    = X3 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp2) ).

thf(funcextLem,axiom,
    ( funcextLem
  <=> ! [X4: $i,X5: $i,X29: $i] :
        ( ( func @ X4 @ X5 @ X29 )
       => ! [X34: $i] :
            ( ( func @ X4 @ X5 @ X34 )
           => ( ! [X2: $i] :
                  ( ( in @ X2 @ X4 )
                 => ( ( ap @ X4 @ X5 @ X29 @ X2 )
                    = ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
             => ! [X2: $i] :
                  ( ( in @ X2 @ X4 )
                 => ! [X3: $i] :
                      ( ( in @ X3 @ X5 )
                     => ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
                       => ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcextLem) ).

thf(funcGraphProp4,axiom,
    ( funcGraphProp4
  <=> ! [X4: $i,X5: $i,X29: $i] :
        ( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ! [X3: $i] :
                ( ( in @ X3 @ X5 )
               => ( ( in @ ( kpair @ X2 @ X3 ) @ X29 )
                 => ( ( ap @ X4 @ X5 @ X29 @ X2 )
                    = X3 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp4) ).

thf(funcext,axiom,
    ( funcext
  <=> ! [X4: $i,X5: $i,X29: $i] :
        ( ( func @ X4 @ X5 @ X29 )
       => ! [X34: $i] :
            ( ( func @ X4 @ X5 @ X34 )
           => ( ! [X2: $i] :
                  ( ( in @ X2 @ X4 )
                 => ( ( ap @ X4 @ X5 @ X29 @ X2 )
                    = ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
             => ( X29 = X34 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext) ).

thf(funcext2,axiom,
    ( funcext2
  <=> ! [X4: $i,X5: $i,X29: $i] :
        ( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
       => ! [X34: $i] :
            ( ( in @ X34 @ ( funcSet @ X4 @ X5 ) )
           => ( ! [X2: $i] :
                  ( ( in @ X2 @ X4 )
                 => ( ( ap @ X4 @ X5 @ X29 @ X2 )
                    = ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
             => ( X29 = X34 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext2) ).

thf(ap2apEq1,axiom,
    ( ap2apEq1
  <=> ! [X4: $i,X5: $i,X29: $i] :
        ( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( ( ap @ X4 @ X5 @ X29 @ X2 )
              = ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq1) ).

thf(ap2apEq2,axiom,
    ( ap2apEq2
  <=> ! [X4: $i,X5: $i,X29: $i] :
        ( ( func @ X4 @ X5 @ X29 )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( ( ap @ X4 @ X5 @ X29 @ X2 )
              = ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq2) ).

thf(if,axiom,
    ( if
    = ( ^ [X4: $i,X44: $o,X2: $i,X3: $i] :
          ( setunion
          @ ( dsetconstr @ X4
            @ ^ [X14: $i] :
                ( ( X44
                  & ( X14 = X2 ) )
                | ( ~ X44
                  & ( X14 = X3 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',if) ).

thf(c_0_228,plain,
    ( ex1
    = ( ^ [Z0: $i,Z1: $i > $o] :
        ? [X757: $i] :
          ( ( in @ X757
            @ ( dsetconstr @ Z0
              @ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
          & ( ( dsetconstr @ Z0
              @ ^ [Z2: $i] : ( Z1 @ Z2 ) )
            = ( setadjoin @ X757 @ emptyset ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[ex1]) ).

thf(c_0_229,plain,
    ( singleton
    = ( ^ [Z0: $i] :
        ? [X2: $i] :
          ( ( in @ X2 @ Z0 )
          & ( Z0
            = ( setadjoin @ X2 @ emptyset ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[singleton]) ).

thf(c_0_230,plain,
    ( replAx
  <=> ! [X6: $i > $i > $o,X4: $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( exu
              @ ^ [Z0: $i] : ( X6 @ X2 @ Z0 ) ) )
       => ? [X5: $i] :
          ! [X2: $i] :
            ( ( in @ X2 @ X5 )
          <=> ? [X3: $i] :
                ( ( in @ X3 @ X4 )
                & ( X6 @ X3 @ X2 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[replAx]) ).

thf(c_0_231,plain,
    ( exu
    = ( ^ [Z0: $i > $o] :
        ? [X2: $i] :
          ( ( Z0 @ X2 )
          & ! [X3: $i] :
              ( ( Z0 @ X3 )
             => ( X2 = X3 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[exu]) ).

thf(c_0_232,plain,
    ( descrp
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ( X1
          @ ( descr
            @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[descrp]) ).

thf(c_0_233,plain,
    ( exuE1
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ? [X2: $i] :
            ( ( X1 @ X2 )
            & ! [X3: $i] :
                ( ( X1 @ X3 )
               => ( X2 = X3 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[exuE1]) ).

thf(c_0_234,plain,
    ( exuE3e
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ? [X2: $i] : ( X1 @ X2 ) ) ),
    inference(fof_simplification,[status(thm)],[exuE3e]) ).

thf(c_0_235,plain,
    ( nonempty
    = ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
    inference(fof_simplification,[status(thm)],[nonempty]) ).

thf(c_0_236,plain,
    ( nonemptyI
  <=> ! [X4: $i,X1: $i > $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ( X1 @ X2 )
         => ( nonempty
            @ ( dsetconstr @ X4
              @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[nonemptyI]) ).

thf(c_0_237,plain,
    ( exuE2
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ? [X2: $i] :
          ! [X3: $i] :
            ( ( X1 @ X3 )
          <=> ( X3 = X2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[exuE2]) ).

thf(c_0_238,plain,
    ( exuI1
  <=> ! [X1: $i > $o] :
        ( ? [X2: $i] :
            ( ( X1 @ X2 )
            & ! [X3: $i] :
                ( ( X1 @ X3 )
               => ( X2 = X3 ) ) )
       => ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ),
    inference(fof_simplification,[status(thm)],[exuI1]) ).

thf(c_0_239,plain,
    ( exuI3
  <=> ! [X1: $i > $o] :
        ( ? [X2: $i] : ( X1 @ X2 )
       => ( ! [X2: $i,X3: $i] :
              ( ( X1 @ X2 )
             => ( ( X1 @ X3 )
               => ( X2 = X3 ) ) )
         => ( exu
            @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[exuI3]) ).

thf(c_0_240,plain,
    ( exuI2
  <=> ! [X1: $i > $o] :
        ( ? [X2: $i] :
          ! [X3: $i] :
            ( ( X1 @ X3 )
          <=> ( X3 = X2 ) )
       => ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ),
    inference(fof_simplification,[status(thm)],[exuI2]) ).

thf(c_0_241,plain,
    ( exuE3u
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ! [X2: $i,X3: $i] :
            ( ( X1 @ X2 )
           => ( ( X1 @ X3 )
             => ( X2 = X3 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[exuE3u]) ).

thf(c_0_242,plain,
    ( exu__Cong
  <=> ! [X1: $i > $o,X17: $i > $o] :
        ( ! [X2: $i,X3: $i] :
            ( ( X2 = X3 )
           => ( ( X1 @ X2 )
            <=> ( X17 @ X3 ) ) )
       => ( ( exu
            @ ^ [Z0: $i] : ( X1 @ Z0 ) )
        <=> ( exu
            @ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[exu__Cong]) ).

thf(c_0_243,plain,
    ( exuEu
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ! [X2: $i,X3: $i] :
            ( ( X1 @ X2 )
           => ( ( X1 @ X3 )
             => ( X2 = X3 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[exuEu]) ).

thf(c_0_244,plain,
    ( descr__Cong
  <=> ! [X1: $i > $o,X17: $i > $o] :
        ( ! [X2: $i,X3: $i] :
            ( ( X2 = X3 )
           => ( ( X1 @ X2 )
            <=> ( X17 @ X3 ) ) )
       => ( ( exu
            @ ^ [Z0: $i] : ( X1 @ Z0 ) )
         => ( ( exu
              @ ^ [Z0: $i] : ( X17 @ Z0 ) )
           => ( ( descr
                @ ^ [Z0: $i] : ( X1 @ Z0 ) )
              = ( descr
                @ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[descr__Cong]) ).

thf(c_0_245,plain,
    ( singletonprop
  <=> ! [X4: $i,X1: $i > $o] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ! [X3: $i] :
                ( ( in @ X3 @ X4 )
               => ( ( X1 @ X2 )
                 => ( ( X1 @ X3 )
                   => ( X2 = X3 ) ) ) ) )
       => ( ? [X2: $i] :
              ( ( in @ X2 @ X4 )
              & ( X1 @ X2 ) )
         => ( singleton
            @ ( dsetconstr @ X4
              @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[singletonprop]) ).

thf(c_0_246,plain,
    ( ex1E1
  <=> ! [X4: $i,X1: $i > $o] :
        ( ( ex1 @ X4
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ? [X2: $i] :
            ( ( in @ X2 @ X4 )
            & ( X1 @ X2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[ex1E1]) ).

thf(c_0_247,plain,
    ( ex1
    = ( ^ [Z0: $i,Z1: $i > $o] :
        ? [X757: $i] :
          ( ( in @ X757
            @ ( dsetconstr @ Z0
              @ ^ [Z2: $i] : ( Z1 @ Z2 ) ) )
          & ( ( dsetconstr @ Z0
              @ ^ [Z2: $i] : ( Z1 @ Z2 ) )
            = ( setadjoin @ X757 @ emptyset ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_228,c_0_229]) ).

thf(c_0_248,plain,
    ( ex1I
  <=> ! [X4: $i,X1: $i > $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ( X1 @ X2 )
         => ( ! [X3: $i] :
                ( ( in @ X3 @ X4 )
               => ( ( X1 @ X3 )
                 => ( X3 = X2 ) ) )
           => ( ex1 @ X4
              @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[ex1I]) ).

thf(c_0_249,plain,
    ( ex1I2
  <=> ! [X4: $i,X1: $i > $o] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ! [X3: $i] :
                ( ( in @ X3 @ X4 )
               => ( ( X1 @ X2 )
                 => ( ( X1 @ X3 )
                   => ( X2 = X3 ) ) ) ) )
       => ( ? [X2: $i] :
              ( ( in @ X2 @ X4 )
              & ( X1 @ X2 ) )
         => ( ex1 @ X4
            @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[ex1I2]) ).

thf(c_0_250,plain,
    ( kfstsingleton
  <=> ! [X18: $i] :
        ( ( iskpair @ X18 )
       => ( singleton
          @ ( dsetconstr @ ( setunion @ X18 )
            @ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[kfstsingleton]) ).

thf(c_0_251,plain,
    ( ksndsingleton
  <=> ! [X18: $i] :
        ( ( iskpair @ X18 )
       => ( singleton
          @ ( dsetconstr @ ( setunion @ X18 )
            @ ^ [Z0: $i] :
                ( X18
                = ( kpair @ ( kfst @ X18 ) @ Z0 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[ksndsingleton]) ).

thf(c_0_252,plain,
    ( setOfPairsIsBReln
  <=> ! [X4: $i,X5: $i,X24: $i > $i > $o] :
        ( breln @ X4 @ X5
        @ ( dpsetconstr @ X4 @ X5
          @ ^ [Z0: $i,Z1: $i] : ( X24 @ Z0 @ Z1 ) ) ) ),
    inference(fof_simplification,[status(thm)],[setOfPairsIsBReln]) ).

thf(c_0_253,plain,
    ( breln
    = ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
    inference(fof_simplification,[status(thm)],[breln]) ).

thf(c_0_254,plain,
    ( funcImageSingleton
  <=> ! [X4: $i,X5: $i,X29: $i] :
        ( ( func @ X4 @ X5 @ X29 )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( singleton
              @ ( dsetconstr @ X5
                @ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X29 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[funcImageSingleton]) ).

thf(c_0_255,plain,
    ( ex1E2
  <=> ! [X4: $i,X1: $i > $o] :
        ( ( ex1 @ X4
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ! [X3: $i] :
                ( ( in @ X3 @ X4 )
               => ( ( X1 @ X2 )
                 => ( ( X1 @ X3 )
                   => ( X2 = X3 ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[ex1E2]) ).

thf(c_0_256,plain,
    ( ifSingleton
  <=> ! [X4: $i,X43: $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X4 )
           => ( singleton
              @ ( dsetconstr @ X4
                @ ^ [Z0: $i] :
                    ( ( X43
                      & ( Z0 = X2 ) )
                    | ( ~ X43
                      & ( Z0 = X3 ) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[ifSingleton]) ).

thf(c_0_257,plain,
    ( replAx
    = ( ! [X6: $i > $i > $o,X4: $i] :
          ( ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ? [X728: $i] :
                  ( ( X6 @ X2 @ X728 )
                  & ! [X729: $i] :
                      ( ( X6 @ X2 @ X729 )
                     => ( X728 = X729 ) ) ) )
         => ? [X5: $i] :
            ! [X2: $i] :
              ( ( in @ X2 @ X5 )
            <=> ? [X3: $i] :
                  ( ( in @ X3 @ X4 )
                  & ( X6 @ X3 @ X2 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_230,c_0_231]) ).

thf(c_0_258,plain,
    ( descrp
    = ( ! [X1: $i > $o] :
          ( ? [X730: $i] :
              ( ( X1 @ X730 )
              & ! [X731: $i] :
                  ( ( X1 @ X731 )
                 => ( X730 = X731 ) ) )
         => ( X1
            @ ( descr
              @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_232,c_0_231]) ).

thf(c_0_259,plain,
    ( dsetconstrI
  <=> ! [X4: $i,X1: $i > $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ( X1 @ X2 )
         => ( in @ X2
            @ ( dsetconstr @ X4
              @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[dsetconstrI]) ).

thf(c_0_260,plain,
    ( dsetconstrEL
  <=> ! [X4: $i,X1: $i > $o,X2: $i] :
        ( ( in @ X2
          @ ( dsetconstr @ X4
            @ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
       => ( in @ X2 @ X4 ) ) ),
    inference(fof_simplification,[status(thm)],[dsetconstrEL]) ).

thf(c_0_261,plain,
    ( dsetconstrER
  <=> ! [X4: $i,X1: $i > $o,X2: $i] :
        ( ( in @ X2
          @ ( dsetconstr @ X4
            @ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
       => ( X1 @ X2 ) ) ),
    inference(fof_simplification,[status(thm)],[dsetconstrER]) ).

thf(c_0_262,plain,
    ( exuE1
    = ( ! [X1: $i > $o] :
          ( ? [X732: $i] :
              ( ( X1 @ X732 )
              & ! [X733: $i] :
                  ( ( X1 @ X733 )
                 => ( X732 = X733 ) ) )
         => ? [X2: $i] :
              ( ( X1 @ X2 )
              & ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_233,c_0_231]) ).

thf(c_0_263,plain,
    ( exuE3e
    = ( ! [X1: $i > $o] :
          ( ? [X734: $i] :
              ( ( X1 @ X734 )
              & ! [X735: $i] :
                  ( ( X1 @ X735 )
                 => ( X734 = X735 ) ) )
         => ? [X2: $i] : ( X1 @ X2 ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_234,c_0_231]) ).

thf(c_0_264,plain,
    ( setbeta
  <=> ! [X4: $i,X1: $i > $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ( in @ X2
            @ ( dsetconstr @ X4
              @ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
        <=> ( X1 @ X2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[setbeta]) ).

thf(c_0_265,axiom,
    ( nonemptyE1
    = ( ! [X4: $i] :
          ( ( X4 != emptyset )
         => ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyE1,c_0_235]) ).

thf(c_0_266,plain,
    ( nonemptyI
    = ( ! [X4: $i,X1: $i > $o,X2: $i] :
          ( ( in @ X2 @ X4 )
         => ( ( X1 @ X2 )
           => ( ( dsetconstr @ X4
                @ ^ [Z0: $i] : ( X1 @ Z0 ) )
             != emptyset ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_236,c_0_235]) ).

thf(c_0_267,axiom,
    ( nonemptyI1
    = ( ! [X4: $i] :
          ( ? [X2: $i] : ( in @ X2 @ X4 )
         => ( X4 != emptyset ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyI1,c_0_235]) ).

thf(c_0_268,plain,
    ( setoftrueEq
  <=> ! [X4: $i] :
        ( ( dsetconstr @ X4
          @ ^ [Z0: $i] : $true )
        = X4 ) ),
    inference(fof_simplification,[status(thm)],[setoftrueEq]) ).

thf(c_0_269,plain,
    ( exuE2
    = ( ! [X1: $i > $o] :
          ( ? [X736: $i] :
              ( ( X1 @ X736 )
              & ! [X737: $i] :
                  ( ( X1 @ X737 )
                 => ( X736 = X737 ) ) )
         => ? [X2: $i] :
            ! [X3: $i] :
              ( ( X1 @ X3 )
            <=> ( X3 = X2 ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_237,c_0_231]) ).

thf(c_0_270,axiom,
    ( nonemptyImpWitness
    = ( ! [X4: $i] :
          ( ( X4 != emptyset )
         => ? [X2: $i] :
              ( ( in @ X2 @ X4 )
              & $true ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_235]) ).

thf(c_0_271,plain,
    ( emptyE1
  <=> ! [X4: $i,X1: $i > $o] :
        ( ? [X2: $i] :
            ( ( in @ X2 @ X4 )
            & ( X1 @ X2 ) )
       => ( ( ( dsetconstr @ X4
              @ ^ [Z0: $i] : ( X1 @ Z0 ) )
            = emptyset )
         => ~ $true ) ) ),
    inference(fof_simplification,[status(thm)],[emptyE1]) ).

thf(c_0_272,plain,
    ( exuI1
    = ( ! [X1: $i > $o] :
          ( ? [X2: $i] :
              ( ( X1 @ X2 )
              & ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) )
         => ? [X738: $i] :
              ( ( X1 @ X738 )
              & ! [X739: $i] :
                  ( ( X1 @ X739 )
                 => ( X738 = X739 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_238,c_0_231]) ).

thf(c_0_273,plain,
    ( exuI3
    = ( ! [X1: $i > $o] :
          ( ? [X2: $i] : ( X1 @ X2 )
         => ( ! [X2: $i,X3: $i] :
                ( ( X1 @ X2 )
               => ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) )
           => ? [X740: $i] :
                ( ( X1 @ X740 )
                & ! [X741: $i] :
                    ( ( X1 @ X741 )
                   => ( X740 = X741 ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_239,c_0_231]) ).

thf(c_0_274,plain,
    ( exuI2
    = ( ! [X1: $i > $o] :
          ( ? [X2: $i] :
            ! [X3: $i] :
              ( ( X1 @ X3 )
            <=> ( X3 = X2 ) )
         => ? [X742: $i] :
              ( ( X1 @ X742 )
              & ! [X743: $i] :
                  ( ( X1 @ X743 )
                 => ( X742 = X743 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_240,c_0_231]) ).

thf(c_0_275,plain,
    ( exuE3u
    = ( ! [X1: $i > $o] :
          ( ? [X744: $i] :
              ( ( X1 @ X744 )
              & ! [X745: $i] :
                  ( ( X1 @ X745 )
                 => ( X744 = X745 ) ) )
         => ! [X2: $i,X3: $i] :
              ( ( X1 @ X2 )
             => ( ( X1 @ X3 )
               => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_241,c_0_231]) ).

thf(c_0_276,plain,
    ( exu__Cong
    = ( ! [X1: $i > $o,X17: $i > $o] :
          ( ! [X2: $i,X3: $i] :
              ( ( X2 = X3 )
             => ( ( X1 @ X2 )
              <=> ( X17 @ X3 ) ) )
         => ( ? [X746: $i] :
                ( ( X1 @ X746 )
                & ! [X747: $i] :
                    ( ( X1 @ X747 )
                   => ( X746 = X747 ) ) )
          <=> ? [X748: $i] :
                ( ( X17 @ X748 )
                & ! [X749: $i] :
                    ( ( X17 @ X749 )
                   => ( X748 = X749 ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_242,c_0_231]) ).

thf(c_0_277,plain,
    ( exuEu
    = ( ! [X1: $i > $o] :
          ( ? [X750: $i] :
              ( ( X1 @ X750 )
              & ! [X751: $i] :
                  ( ( X1 @ X751 )
                 => ( X750 = X751 ) ) )
         => ! [X2: $i,X3: $i] :
              ( ( X1 @ X2 )
             => ( ( X1 @ X3 )
               => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_243,c_0_231]) ).

thf(c_0_278,plain,
    ( descr__Cong
    = ( ! [X1: $i > $o,X17: $i > $o] :
          ( ! [X2: $i,X3: $i] :
              ( ( X2 = X3 )
             => ( ( X1 @ X2 )
              <=> ( X17 @ X3 ) ) )
         => ( ? [X752: $i] :
                ( ( X1 @ X752 )
                & ! [X753: $i] :
                    ( ( X1 @ X753 )
                   => ( X752 = X753 ) ) )
           => ( ? [X754: $i] :
                  ( ( X17 @ X754 )
                  & ! [X755: $i] :
                      ( ( X17 @ X755 )
                     => ( X754 = X755 ) ) )
             => ( ( descr
                  @ ^ [Z0: $i] : ( X1 @ Z0 ) )
                = ( descr
                  @ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_244,c_0_231]) ).

thf(c_0_279,plain,
    ( dsetconstr__Cong
  <=> ! [X4: $i,X5: $i] :
        ( ( X4 = X5 )
       => ! [X1: $i > $o,X17: $i > $o] :
            ( ! [X2: $i] :
                ( ( in @ X2 @ X4 )
               => ! [X3: $i] :
                    ( ( in @ X3 @ X5 )
                   => ( ( X2 = X3 )
                     => ( ( X1 @ X2 )
                      <=> ( X17 @ X3 ) ) ) ) )
           => ( ( dsetconstr @ X4
                @ ^ [Z0: $i] : ( X1 @ Z0 ) )
              = ( dsetconstr @ X5
                @ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[dsetconstr__Cong]) ).

thf(c_0_280,plain,
    ( sepInPowerset
  <=> ! [X4: $i,X1: $i > $o] :
        ( in
        @ ( dsetconstr @ X4
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
        @ ( powerset @ X4 ) ) ),
    inference(fof_simplification,[status(thm)],[sepInPowerset]) ).

thf(c_0_281,plain,
    ( sepSubset
  <=> ! [X4: $i,X1: $i > $o] :
        ( subset
        @ ( dsetconstr @ X4
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
        @ X4 ) ),
    inference(fof_simplification,[status(thm)],[sepSubset]) ).

thf(c_0_282,plain,
    ( singletonprop
    = ( ! [X4: $i,X1: $i > $o] :
          ( ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ! [X3: $i] :
                  ( ( in @ X3 @ X4 )
                 => ( ( X1 @ X2 )
                   => ( ( X1 @ X3 )
                     => ( X2 = X3 ) ) ) ) )
         => ( ? [X2: $i] :
                ( ( in @ X2 @ X4 )
                & ( X1 @ X2 ) )
           => ? [X756: $i] :
                ( ( in @ X756
                  @ ( dsetconstr @ X4
                    @ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
                & ( ( dsetconstr @ X4
                    @ ^ [Z0: $i] : ( X1 @ Z0 ) )
                  = ( setadjoin @ X756 @ emptyset ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_245,c_0_229]) ).

thf(c_0_283,plain,
    ( ex1E1
    = ( ! [X4: $i,X1: $i > $o] :
          ( ? [X758: $i] :
              ( ( in @ X758
                @ ( dsetconstr @ X4
                  @ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
              & ( ( dsetconstr @ X4
                  @ ^ [Z0: $i] : ( X1 @ Z0 ) )
                = ( setadjoin @ X758 @ emptyset ) ) )
         => ? [X2: $i] :
              ( ( in @ X2 @ X4 )
              & ( X1 @ X2 ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_246,c_0_247]) ).

thf(c_0_284,plain,
    ( ex1I
    = ( ! [X4: $i,X1: $i > $o,X2: $i] :
          ( ( in @ X2 @ X4 )
         => ( ( X1 @ X2 )
           => ( ! [X3: $i] :
                  ( ( in @ X3 @ X4 )
                 => ( ( X1 @ X3 )
                   => ( X3 = X2 ) ) )
             => ? [X759: $i] :
                  ( ( in @ X759
                    @ ( dsetconstr @ X4
                      @ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
                  & ( ( dsetconstr @ X4
                      @ ^ [Z0: $i] : ( X1 @ Z0 ) )
                    = ( setadjoin @ X759 @ emptyset ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_248,c_0_247]) ).

thf(c_0_285,plain,
    ( ex1I2
    = ( ! [X4: $i,X1: $i > $o] :
          ( ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ! [X3: $i] :
                  ( ( in @ X3 @ X4 )
                 => ( ( X1 @ X2 )
                   => ( ( X1 @ X3 )
                     => ( X2 = X3 ) ) ) ) )
         => ( ? [X2: $i] :
                ( ( in @ X2 @ X4 )
                & ( X1 @ X2 ) )
           => ? [X760: $i] :
                ( ( in @ X760
                  @ ( dsetconstr @ X4
                    @ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
                & ( ( dsetconstr @ X4
                    @ ^ [Z0: $i] : ( X1 @ Z0 ) )
                  = ( setadjoin @ X760 @ emptyset ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_249,c_0_247]) ).

thf(c_0_286,plain,
    ( kfstsingleton
    = ( ! [X18: $i] :
          ( ( iskpair @ X18 )
         => ? [X761: $i] :
              ( ( in @ X761
                @ ( dsetconstr @ ( setunion @ X18 )
                  @ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) ) )
              & ( ( dsetconstr @ ( setunion @ X18 )
                  @ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X18 ) )
                = ( setadjoin @ X761 @ emptyset ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_250,c_0_229]) ).

thf(c_0_287,axiom,
    ( theprop
    = ( ! [X21: $i] :
          ( ? [X762: $i] :
              ( ( in @ X762 @ X21 )
              & ( X21
                = ( setadjoin @ X762 @ emptyset ) ) )
         => ( in @ ( setunion @ X21 ) @ X21 ) ) ) ),
    inference(apply_def,[status(thm)],[theprop,c_0_229]) ).

thf(c_0_288,plain,
    ( ksndsingleton
    = ( ! [X18: $i] :
          ( ( iskpair @ X18 )
         => ? [X763: $i] :
              ( ( in @ X763
                @ ( dsetconstr @ ( setunion @ X18 )
                  @ ^ [Z0: $i] :
                      ( X18
                      = ( kpair @ ( kfst @ X18 ) @ Z0 ) ) ) )
              & ( ( dsetconstr @ ( setunion @ X18 )
                  @ ^ [Z0: $i] :
                      ( X18
                      = ( kpair @ ( kfst @ X18 ) @ Z0 ) ) )
                = ( setadjoin @ X763 @ emptyset ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_251,c_0_229]) ).

thf(c_0_289,plain,
    ( dpsetconstrI
  <=> ! [X4: $i,X5: $i,X22: $i > $i > $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X5 )
           => ( ( X22 @ X2 @ X3 )
             => ( in @ ( kpair @ X2 @ X3 )
                @ ( dpsetconstr @ X4 @ X5
                  @ ^ [Z0: $i,Z1: $i] : ( X22 @ Z0 @ Z1 ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[dpsetconstrI]) ).

thf(c_0_290,plain,
    ( dpsetconstrSub
  <=> ! [X4: $i,X5: $i,X23: $i > $i > $o] :
        ( subset
        @ ( dpsetconstr @ X4 @ X5
          @ ^ [Z0: $i,Z1: $i] : ( X23 @ Z0 @ Z1 ) )
        @ ( cartprod @ X4 @ X5 ) ) ),
    inference(fof_simplification,[status(thm)],[dpsetconstrSub]) ).

thf(c_0_291,plain,
    ( setOfPairsIsBReln
    = ( ! [X4: $i,X5: $i,X24: $i > $i > $o] :
          ( subset
          @ ( dpsetconstr @ X4 @ X5
            @ ^ [Z0: $i,Z1: $i] : ( X24 @ Z0 @ Z1 ) )
          @ ( cartprod @ X4 @ X5 ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_252,c_0_253]) ).

thf(c_0_292,plain,
    ( dpsetconstrERa
  <=> ! [X4: $i,X5: $i,X25: $i > $i > $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X5 )
           => ( ( in @ ( kpair @ X2 @ X3 )
                @ ( dpsetconstr @ X4 @ X5
                  @ ^ [Z0: $i,Z1: $i] : ( X25 @ Z0 @ Z1 ) ) )
             => ( X25 @ X2 @ X3 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[dpsetconstrERa]) ).

thf(c_0_293,plain,
    ( dpsetconstrEL1
  <=> ! [X4: $i,X5: $i,X26: $i > $i > $o,X2: $i,X3: $i] :
        ( ( in @ ( kpair @ X2 @ X3 )
          @ ( dpsetconstr @ X4 @ X5
            @ ^ [Z0: $i,Z1: $i] : ( X26 @ Z0 @ Z1 ) ) )
       => ( in @ X2 @ X4 ) ) ),
    inference(fof_simplification,[status(thm)],[dpsetconstrEL1]) ).

thf(c_0_294,plain,
    ( dpsetconstrEL2
  <=> ! [X4: $i,X5: $i,X27: $i > $i > $o,X2: $i,X3: $i] :
        ( ( in @ ( kpair @ X2 @ X3 )
          @ ( dpsetconstr @ X4 @ X5
            @ ^ [Z0: $i,Z1: $i] : ( X27 @ Z0 @ Z1 ) ) )
       => ( in @ X3 @ X5 ) ) ),
    inference(fof_simplification,[status(thm)],[dpsetconstrEL2]) ).

thf(c_0_295,plain,
    ( dpsetconstrER
  <=> ! [X4: $i,X5: $i,X28: $i > $i > $o,X2: $i,X3: $i] :
        ( ( in @ ( kpair @ X2 @ X3 )
          @ ( dpsetconstr @ X4 @ X5
            @ ^ [Z0: $i,Z1: $i] : ( X28 @ Z0 @ Z1 ) ) )
       => ( X28 @ X2 @ X3 ) ) ),
    inference(fof_simplification,[status(thm)],[dpsetconstrER]) ).

thf(c_0_296,plain,
    ( funcImageSingleton
    = ( ! [X4: $i,X5: $i,X29: $i] :
          ( ( func @ X4 @ X5 @ X29 )
         => ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ? [X764: $i] :
                  ( ( in @ X764
                    @ ( dsetconstr @ X5
                      @ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X29 ) ) )
                  & ( ( dsetconstr @ X5
                      @ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X29 ) )
                    = ( setadjoin @ X764 @ emptyset ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_254,c_0_229]) ).

thf(c_0_297,plain,
    ( apProp
  <=> ! [X4: $i,X5: $i,X29: $i] :
        ( ( func @ X4 @ X5 @ X29 )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( in
              @ ( setunion
                @ ( dsetconstr @ X5
                  @ ^ [Z0: $i] : ( in @ ( kpair @ X2 @ Z0 ) @ X29 ) ) )
              @ X5 ) ) ) ),
    inference(fof_simplification,[status(thm)],[apProp]) ).

thf(c_0_298,plain,
    ( lamProp
  <=> ! [X4: $i,X5: $i,X30: $i > $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( in @ ( X30 @ X2 ) @ X5 ) )
       => ( func @ X4 @ X5
          @ ( dpsetconstr @ X4 @ X5
            @ ^ [Z0: $i,Z1: $i] :
                ( ( X30 @ Z0 )
                = Z1 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[lamProp]) ).

thf(c_0_299,plain,
    ( lamp
  <=> ! [X4: $i,X5: $i,X31: $i > $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( in @ ( X31 @ X2 ) @ X5 ) )
       => ( func @ X4 @ X5
          @ ( lam @ X4 @ X5
            @ ^ [Z0: $i] : ( X31 @ Z0 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[lamp]) ).

thf(c_0_300,plain,
    ( lam2p
  <=> ! [X4: $i,X5: $i,X32: $i > $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( in @ ( X32 @ X2 ) @ X5 ) )
       => ( in
          @ ( lam @ X4 @ X5
            @ ^ [Z0: $i] : ( X32 @ Z0 ) )
          @ ( funcSet @ X4 @ X5 ) ) ) ),
    inference(fof_simplification,[status(thm)],[lam2p]) ).

thf(c_0_301,axiom,
    ( brelnall1
    = ( ! [X4: $i,X5: $i,X33: $i] :
          ( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
         => ! [X1: $i > $o] :
              ( ! [X2: $i] :
                  ( ( in @ X2 @ X4 )
                 => ! [X3: $i] :
                      ( ( in @ X3 @ X5 )
                     => ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
                       => ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
             => ! [X2: $i] :
                  ( ( in @ X2 @ X33 )
                 => ( X1 @ X2 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[brelnall1,c_0_253]) ).

thf(c_0_302,axiom,
    ( brelnall2
    = ( ! [X4: $i,X5: $i,X33: $i] :
          ( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
         => ! [X1: $i > $o] :
              ( ! [X2: $i] :
                  ( ( in @ X2 @ X4 )
                 => ! [X3: $i] :
                      ( ( in @ X3 @ X5 )
                     => ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
                       => ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
             => ! [X2: $i] :
                  ( ( in @ X2 @ X33 )
                 => ( X1 @ X2 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[brelnall2,c_0_253]) ).

thf(c_0_303,plain,
    ( ex1E2
    = ( ! [X4: $i,X1: $i > $o] :
          ( ? [X765: $i] :
              ( ( in @ X765
                @ ( dsetconstr @ X4
                  @ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
              & ( ( dsetconstr @ X4
                  @ ^ [Z0: $i] : ( X1 @ Z0 ) )
                = ( setadjoin @ X765 @ emptyset ) ) )
         => ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ! [X3: $i] :
                  ( ( in @ X3 @ X4 )
                 => ( ( X1 @ X2 )
                   => ( ( X1 @ X3 )
                     => ( X2 = X3 ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_255,c_0_247]) ).

thf(c_0_304,axiom,
    ( subbreln
    = ( ! [X4: $i,X5: $i,X33: $i] :
          ( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
         => ! [X35: $i] :
              ( ( subset @ X35 @ ( cartprod @ X4 @ X5 ) )
             => ( ! [X2: $i] :
                    ( ( in @ X2 @ X4 )
                   => ! [X3: $i] :
                        ( ( in @ X3 @ X5 )
                       => ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
                         => ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
               => ( subset @ X33 @ X35 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[subbreln,c_0_253]) ).

thf(c_0_305,axiom,
    ( eqbreln
    = ( ! [X4: $i,X5: $i,X33: $i] :
          ( ( subset @ X33 @ ( cartprod @ X4 @ X5 ) )
         => ! [X35: $i] :
              ( ( subset @ X35 @ ( cartprod @ X4 @ X5 ) )
             => ( ! [X2: $i] :
                    ( ( in @ X2 @ X4 )
                   => ! [X3: $i] :
                        ( ( in @ X3 @ X5 )
                       => ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
                         => ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
               => ( ! [X2: $i] :
                      ( ( in @ X2 @ X4 )
                     => ! [X3: $i] :
                          ( ( in @ X3 @ X5 )
                         => ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
                           => ( in @ ( kpair @ X2 @ X3 ) @ X33 ) ) ) )
                 => ( X33 = X35 ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[eqbreln,c_0_253]) ).

thf(c_0_306,plain,
    ( beta1
  <=> ! [X4: $i,X5: $i,X36: $i > $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( in @ ( X36 @ X2 ) @ X5 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( ( ap @ X4 @ X5
                @ ( lam @ X4 @ X5
                  @ ^ [Z0: $i] : ( X36 @ Z0 ) )
                @ X2 )
              = ( X36 @ X2 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[beta1]) ).

thf(c_0_307,plain,
    ( eta1
  <=> ! [X4: $i,X5: $i,X29: $i] :
        ( ( func @ X4 @ X5 @ X29 )
       => ( ( lam @ X4 @ X5
            @ ^ [Z0: $i] : ( ap @ X4 @ X5 @ X29 @ Z0 ) )
          = X29 ) ) ),
    inference(fof_simplification,[status(thm)],[eta1]) ).

thf(c_0_308,plain,
    ( lam2lamEq
  <=> ! [X4: $i,X5: $i,X37: $i > $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( in @ ( X37 @ X2 ) @ X5 ) )
       => ( ( lam @ X4 @ X5
            @ ^ [Z0: $i] : ( X37 @ Z0 ) )
          = ( lam @ X4 @ X5
            @ ^ [Z0: $i] : ( X37 @ Z0 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[lam2lamEq]) ).

thf(c_0_309,plain,
    ( beta2
  <=> ! [X4: $i,X5: $i,X38: $i > $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( in @ ( X38 @ X2 ) @ X5 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( ( ap @ X4 @ X5
                @ ( lam @ X4 @ X5
                  @ ^ [Z0: $i] : ( X38 @ Z0 ) )
                @ X2 )
              = ( X38 @ X2 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[beta2]) ).

thf(c_0_310,plain,
    ( eta2
  <=> ! [X4: $i,X5: $i,X29: $i] :
        ( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
       => ( ( lam @ X4 @ X5
            @ ^ [Z0: $i] : ( ap @ X4 @ X5 @ X29 @ Z0 ) )
          = X29 ) ) ),
    inference(fof_simplification,[status(thm)],[eta2]) ).

thf(c_0_311,plain,
    ( iffalseProp1
  <=> ! [X4: $i,X39: $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X4 )
           => ( ~ X39
             => ( in @ X3
                @ ( dsetconstr @ X4
                  @ ^ [Z0: $i] :
                      ( ( X39
                        & ( Z0 = X2 ) )
                      | ( ~ X39
                        & ( Z0 = X3 ) ) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[iffalseProp1]) ).

thf(c_0_312,plain,
    ( iffalseProp2
  <=> ! [X4: $i,X40: $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X4 )
           => ( ~ X40
             => ( ( dsetconstr @ X4
                  @ ^ [Z0: $i] :
                      ( ( X40
                        & ( Z0 = X2 ) )
                      | ( ~ X40
                        & ( Z0 = X3 ) ) ) )
                = ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[iffalseProp2]) ).

thf(c_0_313,plain,
    ( iftrueProp1
  <=> ! [X4: $i,X41: $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X4 )
           => ( X41
             => ( in @ X2
                @ ( dsetconstr @ X4
                  @ ^ [Z0: $i] :
                      ( ( X41
                        & ( Z0 = X2 ) )
                      | ( ~ X41
                        & ( Z0 = X3 ) ) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[iftrueProp1]) ).

thf(c_0_314,plain,
    ( iftrueProp2
  <=> ! [X4: $i,X42: $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X4 )
           => ( X42
             => ( ( dsetconstr @ X4
                  @ ^ [Z0: $i] :
                      ( ( X42
                        & ( Z0 = X2 ) )
                      | ( ~ X42
                        & ( Z0 = X3 ) ) ) )
                = ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[iftrueProp2]) ).

thf(c_0_315,plain,
    ( ifSingleton
    = ( ! [X4: $i,X43: $o,X2: $i] :
          ( ( in @ X2 @ X4 )
         => ! [X3: $i] :
              ( ( in @ X3 @ X4 )
             => ? [X766: $i] :
                  ( ( in @ X766
                    @ ( dsetconstr @ X4
                      @ ^ [Z0: $i] :
                          ( ( X43
                            & ( Z0 = X2 ) )
                          | ( ~ X43
                            & ( Z0 = X3 ) ) ) ) )
                  & ( ( dsetconstr @ X4
                      @ ^ [Z0: $i] :
                          ( ( X43
                            & ( Z0 = X2 ) )
                          | ( ~ X43
                            & ( Z0 = X3 ) ) ) )
                    = ( setadjoin @ X766 @ emptyset ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_256,c_0_229]) ).

thf(c_0_316,plain,
    ( epred1_0
  <=> ! [X796: $i] :
      ? [X797: $i] :
        ( ! [X798: $i] :
            ( ( in @ X798 @ X797 )
           => ! [X799: $i] :
                ( ( in @ X799 @ X798 )
               => ( in @ X799 @ X796 ) ) )
        & ! [X800: $i,X801: $i] :
            ( ( ( in @ X800 @ X796 )
              & ( in @ X801 @ X796 ) )
           => ( ! [X802: $i] :
                  ( ( in @ X802 @ X797 )
                 => ( ( in @ X800 @ X802 )
                  <=> ( in @ X801 @ X802 ) ) )
             => ( X800 = X801 ) ) )
        & ! [X803: $i,X804: $i] :
            ( ( ( in @ X803 @ X797 )
              & ( in @ X804 @ X797 ) )
           => ( ! [X805: $i] :
                  ( ( in @ X805 @ X803 )
                 => ( in @ X805 @ X804 ) )
              | ! [X806: $i] :
                  ( ( in @ X806 @ X804 )
                 => ( in @ X806 @ X803 ) ) ) )
        & ! [X807: $i] :
            ( ( ! [X808: $i] :
                  ( ( in @ X808 @ X807 )
                 => ( in @ X808 @ X796 ) )
              & ? [X809: $i] : ( in @ X809 @ X807 ) )
           => ? [X810: $i,X811: $i] :
                ( ( in @ X810 @ X797 )
                & ( in @ X811 @ X807 )
                & ~ ? [X812: $i] :
                      ( ( in @ X812 @ X810 )
                      & ( in @ X812 @ X807 ) )
                & ! [X813: $i] :
                    ( ( in @ X813 @ X797 )
                   => ( ! [X814: $i] :
                          ( ( in @ X814 @ X813 )
                         => ( in @ X814 @ X810 ) )
                      | ( in @ X811 @ X813 ) ) ) ) ) ) ),
    introduced(definition) ).

thf(c_0_317,negated_conjecture,
    ~ ( ! [X767: $i,X768: $i] :
          ( ! [X769: $i] :
              ( ( in @ X769 @ X767 )
            <=> ( in @ X769 @ X768 ) )
         => ( X767 = X768 ) )
     => ( ! [X770: $i] :
            ~ ( in @ X770 @ emptyset )
       => ( ! [X771: $i,X772: $i,X773: $i] :
              ( ( in @ X773 @ ( setadjoin @ X771 @ X772 ) )
            <=> ( ( X773 = X771 )
                | ( in @ X773 @ X772 ) ) )
         => ( ! [X774: $i,X775: $i] :
                ( ( in @ X775 @ ( powerset @ X774 ) )
              <=> ! [X776: $i] :
                    ( ( in @ X776 @ X775 )
                   => ( in @ X776 @ X774 ) ) )
           => ( ! [X777: $i,X778: $i] :
                  ( ( in @ X778 @ ( setunion @ X777 ) )
                <=> ? [X779: $i] :
                      ( ( in @ X778 @ X779 )
                      & ( in @ X779 @ X777 ) ) )
             => ( ( in @ emptyset @ omega )
               => ( ! [X780: $i] :
                      ( ( in @ X780 @ omega )
                     => ( in @ ( setadjoin @ X780 @ X780 ) @ omega ) )
                 => ( ! [X781: $i] :
                        ( ( ( in @ emptyset @ X781 )
                          & ! [X782: $i] :
                              ( ( ( in @ X782 @ omega )
                                & ( in @ X782 @ X781 ) )
                             => ( in @ ( setadjoin @ X782 @ X782 ) @ X781 ) ) )
                       => ! [X783: $i] :
                            ( ( in @ X783 @ omega )
                           => ( in @ X783 @ X781 ) ) )
                   => ( ! [X784: $i > $i > $o,X785: $i] :
                          ( ! [X786: $i] :
                              ( ( in @ X786 @ X785 )
                             => ? [X787: $i] :
                                  ( ( X784 @ X786 @ X787 )
                                  & ! [X788: $i] :
                                      ( ( X784 @ X786 @ X788 )
                                     => ( X787 = X788 ) ) ) )
                         => ? [X789: $i] :
                            ! [X790: $i] :
                              ( ( in @ X790 @ X789 )
                            <=> ? [X791: $i] :
                                  ( ( in @ X791 @ X785 )
                                  & ( X784 @ X791 @ X790 ) ) ) )
                     => ( ! [X792: $i] :
                            ( ? [X793: $i] : ( in @ X793 @ X792 )
                           => ? [X794: $i] :
                                ( ( in @ X794 @ X792 )
                                & ~ ? [X795: $i] :
                                      ( ( in @ X795 @ X794 )
                                      & ( in @ X795 @ X792 ) ) ) )
                       => ( epred1_0
                         => ( ! [X815: $i > $o] :
                                ( ? [X816: $i] :
                                    ( ( X815 @ X816 )
                                    & ! [X817: $i] :
                                        ( ( X815 @ X817 )
                                       => ( X816 = X817 ) ) )
                               => ( X815
                                  @ ( descr
                                    @ ^ [Z0: $i] : ( X815 @ Z0 ) ) ) )
                           => ( ! [X818: $i,X819: $i > $o,X820: $i] :
                                  ( ( in @ X820 @ X818 )
                                 => ( ( X819 @ X820 )
                                   => ( in @ X820 @ ( dsetconstr @ X818 @ X819 ) ) ) )
                             => ( ! [X821: $i,X822: $i > $o,X823: $i] :
                                    ( ( in @ X823 @ ( dsetconstr @ X821 @ X822 ) )
                                   => ( in @ X823 @ X821 ) )
                               => ( ! [X824: $i,X825: $i > $o,X826: $i] :
                                      ( ( in @ X826 @ ( dsetconstr @ X824 @ X825 ) )
                                     => ( X825 @ X826 ) )
                                 => ( ! [X827: $i > $o] :
                                        ( ? [X828: $i] :
                                            ( ( X827 @ X828 )
                                            & ! [X829: $i] :
                                                ( ( X827 @ X829 )
                                               => ( X828 = X829 ) ) )
                                       => ? [X830: $i] :
                                            ( ( X827 @ X830 )
                                            & ! [X831: $i] :
                                                ( ( X827 @ X831 )
                                               => ( X830 = X831 ) ) ) )
                                   => ( ! [X832: $o,X833: $i] :
                                          ( ( in @ X833 @ ( prop2set @ X832 ) )
                                         => X832 )
                                     => ( ! [X834: $i] :
                                            ( ( in @ X834 @ emptyset )
                                           => ! [X835: $o] : X835 )
                                       => ( ! [X836: $i] :
                                              ( ( in @ X836 @ emptyset )
                                             => ~ $true )
                                         => ( ! [X837: $i] :
                                                ~ ( in @ X837 @ emptyset )
                                           => ( ! [X838: $i > $o] :
                                                  ( ? [X839: $i] :
                                                      ( ( X838 @ X839 )
                                                      & ! [X840: $i] :
                                                          ( ( X838 @ X840 )
                                                         => ( X839 = X840 ) ) )
                                                 => ? [X841: $i] : ( X838 @ X841 ) )
                                             => ( ! [X842: $i,X843: $i] :
                                                    ( ! [X844: $i] :
                                                        ( ( in @ X844 @ X842 )
                                                       => ( in @ X844 @ X843 ) )
                                                   => ( ! [X845: $i] :
                                                          ( ( in @ X845 @ X843 )
                                                         => ( in @ X845 @ X842 ) )
                                                     => ( X842 = X843 ) ) )
                                               => ( ! [X846: $i] :
                                                      ( ! [X847: $i] :
                                                          ~ ( in @ X847 @ X846 )
                                                     => ( X846 = emptyset ) )
                                                 => ( ! [X848: $i] :
                                                        ( ! [X849: $i] :
                                                            ~ ( in @ X849 @ X848 )
                                                       => ( X848 = emptyset ) )
                                                   => ( ! [X850: $i,X851: $i > $o,X852: $i] :
                                                          ( ( in @ X852 @ X850 )
                                                         => ( ( in @ X852 @ ( dsetconstr @ X850 @ X851 ) )
                                                          <=> ( X851 @ X852 ) ) )
                                                     => ( ! [X853: $i] :
                                                            ( ( X853 != emptyset )
                                                           => ? [X854: $i] : ( in @ X854 @ X853 ) )
                                                       => ( ! [X855: $i,X856: $i > $o,X857: $i] :
                                                              ( ( in @ X857 @ X855 )
                                                             => ( ( X856 @ X857 )
                                                               => ( ( dsetconstr @ X855 @ X856 )
                                                                 != emptyset ) ) )
                                                         => ( ! [X858: $i] :
                                                                ( ? [X859: $i] : ( in @ X859 @ X858 )
                                                               => ( X858 != emptyset ) )
                                                           => ( ! [X860: $i,X861: $i] : ( in @ X860 @ ( setadjoin @ X860 @ X861 ) )
                                                             => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                               => ( ! [X862: $i,X863: $i,X864: $i] :
                                                                      ( ( in @ X864 @ X863 )
                                                                     => ( in @ X864 @ ( setadjoin @ X862 @ X863 ) ) )
                                                                 => ( ! [X865: $i,X866: $i,X867: $i] :
                                                                        ( ( in @ X867 @ ( setadjoin @ X865 @ X866 ) )
                                                                       => ! [X868: $o] :
                                                                            ( ( ( X867 = X865 )
                                                                             => X868 )
                                                                           => ( ( ( in @ X867 @ X866 )
                                                                               => X868 )
                                                                             => X868 ) ) )
                                                                   => ( ! [X869: $i,X870: $i,X871: $i] :
                                                                          ( ( in @ X871 @ ( setadjoin @ X869 @ X870 ) )
                                                                         => ( ( X871 = X869 )
                                                                            | ( in @ X871 @ X870 ) ) )
                                                                     => ( ! [X872: $i] :
                                                                            ( ( dsetconstr @ X872
                                                                              @ ^ [Z0: $i] : $true )
                                                                            = X872 )
                                                                       => ( ! [X873: $i,X874: $i] :
                                                                              ( ! [X875: $i] :
                                                                                  ( ( in @ X875 @ X874 )
                                                                                 => ( in @ X875 @ X873 ) )
                                                                             => ( in @ X874 @ ( powerset @ X873 ) ) )
                                                                         => ( ! [X876: $i] : ( in @ emptyset @ ( powerset @ X876 ) )
                                                                           => ( ! [X877: $i] : ( in @ emptyset @ ( powerset @ X877 ) )
                                                                             => ( ! [X878: $i,X879: $i,X880: $i] :
                                                                                    ( ( in @ X879 @ ( powerset @ X878 ) )
                                                                                   => ( ( in @ X880 @ X879 )
                                                                                     => ( in @ X880 @ X878 ) ) )
                                                                               => ( ! [X881: $i,X882: $i,X883: $i] :
                                                                                      ( ( in @ X882 @ X883 )
                                                                                     => ( ( in @ X883 @ X881 )
                                                                                       => ( in @ X882 @ ( setunion @ X881 ) ) ) )
                                                                                 => ( ! [X884: $i,X885: $i] :
                                                                                        ( ( in @ X885 @ ( setunion @ X884 ) )
                                                                                       => ! [X886: $o] :
                                                                                            ( ! [X887: $i] :
                                                                                                ( ( in @ X885 @ X887 )
                                                                                               => ( ( in @ X887 @ X884 )
                                                                                                 => X886 ) )
                                                                                           => X886 ) )
                                                                                   => ( ! [X888: $i,X889: $i] :
                                                                                          ( ( in @ X889 @ X888 )
                                                                                         => ( in @ X889 @ ( powerset @ ( setunion @ X888 ) ) ) )
                                                                                     => ( ! [X890: $i > $o] :
                                                                                            ( ? [X891: $i] :
                                                                                                ( ( X890 @ X891 )
                                                                                                & ! [X892: $i] :
                                                                                                    ( ( X890 @ X892 )
                                                                                                   => ( X891 = X892 ) ) )
                                                                                           => ? [X893: $i] :
                                                                                              ! [X894: $i] :
                                                                                                ( ( X890 @ X894 )
                                                                                              <=> ( X894 = X893 ) ) )
                                                                                       => ( ! [X895: $i] :
                                                                                              ( ( X895 != emptyset )
                                                                                             => ? [X896: $i] :
                                                                                                  ( ( in @ X896 @ X895 )
                                                                                                  & $true ) )
                                                                                         => ( ! [X897: $i,X898: $i] :
                                                                                                ( ( in @ X897 @ ( setadjoin @ X898 @ emptyset ) )
                                                                                               => ( X897 = X898 ) )
                                                                                           => ( ! [X899: $i,X900: $i] :
                                                                                                  ( ( X899 != X900 )
                                                                                                 => ~ ( in @ X900 @ ( setadjoin @ X899 @ emptyset ) ) )
                                                                                             => ( ! [X901: $i,X902: $i] :
                                                                                                    ( ( X901 = X902 )
                                                                                                   => ( in @ X901 @ ( setadjoin @ X902 @ emptyset ) ) )
                                                                                               => ( ! [X903: $i,X904: $i] :
                                                                                                      ( ( in @ X903 @ ( setadjoin @ X904 @ emptyset ) )
                                                                                                     => ( in @ X904 @ ( setadjoin @ X903 @ emptyset ) ) )
                                                                                                 => ( ! [X905: $i,X906: $i,X907: $i] :
                                                                                                        ( ( in @ X907 @ ( setadjoin @ X905 @ ( setadjoin @ X906 @ emptyset ) ) )
                                                                                                       => ( ( X907 = X905 )
                                                                                                          | ( X907 = X906 ) ) )
                                                                                                   => ( ! [X908: $i,X909: $i] : ( in @ X908 @ ( setadjoin @ X908 @ ( setadjoin @ X909 @ emptyset ) ) )
                                                                                                     => ( ! [X910: $i,X911: $i] : ( in @ X911 @ ( setadjoin @ X910 @ ( setadjoin @ X911 @ emptyset ) ) )
                                                                                                       => ( ! [X912: $i,X913: $i > $o] :
                                                                                                              ( ? [X914: $i] :
                                                                                                                  ( ( in @ X914 @ X912 )
                                                                                                                  & ( X913 @ X914 ) )
                                                                                                             => ( ( ( dsetconstr @ X912 @ X913 )
                                                                                                                  = emptyset )
                                                                                                               => ~ $true ) )
                                                                                                         => ( ! [X915: $i > $o,X916: $i] :
                                                                                                                ( ( in @ X916 @ emptyset )
                                                                                                               => ( X915 @ X916 ) )
                                                                                                           => ( ! [X917: $i,X918: $i > $o] :
                                                                                                                  ( ~ ! [X919: $i] :
                                                                                                                        ( ( in @ X919 @ X917 )
                                                                                                                       => ( X918 @ X919 ) )
                                                                                                                 => ? [X920: $i] :
                                                                                                                      ( ( in @ X920 @ X917 )
                                                                                                                      & ~ ( X918 @ X920 ) ) )
                                                                                                             => ( ! [X921: $i,X922: $i > $o] :
                                                                                                                    ( ! [X923: $i] :
                                                                                                                        ( ( in @ X923 @ X921 )
                                                                                                                       => ~ ( X922 @ X923 ) )
                                                                                                                   => ~ ? [X924: $i] :
                                                                                                                          ( ( in @ X924 @ X921 )
                                                                                                                          & ( X922 @ X924 ) ) )
                                                                                                               => ( ! [X925: $i,X926: $i > $o] :
                                                                                                                      ( ~ ? [X927: $i] :
                                                                                                                            ( ( in @ X927 @ X925 )
                                                                                                                            & ( X926 @ X927 ) )
                                                                                                                     => ! [X928: $i] :
                                                                                                                          ( ( in @ X928 @ X925 )
                                                                                                                         => ~ ( X926 @ X928 ) ) )
                                                                                                                 => ( ! [X929: $i,X930: $i > $o] :
                                                                                                                        ( ? [X931: $i] :
                                                                                                                            ( ( in @ X931 @ X929 )
                                                                                                                            & ~ ( X930 @ X931 ) )
                                                                                                                       => ~ ! [X932: $i] :
                                                                                                                              ( ( in @ X932 @ X929 )
                                                                                                                             => ( X930 @ X932 ) ) )
                                                                                                                   => ( ! [X933: $o] :
                                                                                                                          ( X933
                                                                                                                         => ( in @ emptyset @ ( prop2set @ X933 ) ) )
                                                                                                                     => ( ! [X934: $o] :
                                                                                                                            ( X934
                                                                                                                           => ( set2prop @ ( prop2set @ X934 ) ) )
                                                                                                                       => ( ! [X935: $i,X936: $i > $o] :
                                                                                                                              ( ~ ? [X937: $i] :
                                                                                                                                    ( ( in @ X937 @ X935 )
                                                                                                                                    & ( X936 @ X937 ) )
                                                                                                                             => ! [X938: $i] :
                                                                                                                                  ( ( in @ X938 @ X935 )
                                                                                                                                 => ~ ( X936 @ X938 ) ) )
                                                                                                                         => ( ! [X939: $i,X940: $i > $o] :
                                                                                                                                ( ~ ! [X941: $i] :
                                                                                                                                      ( ( in @ X941 @ X939 )
                                                                                                                                     => ( X940 @ X941 ) )
                                                                                                                               => ? [X942: $i] :
                                                                                                                                    ( ( in @ X942 @ X939 )
                                                                                                                                    & ~ ( X940 @ X942 ) ) )
                                                                                                                           => ( ! [X943: $i > $o] :
                                                                                                                                  ( ? [X944: $i] :
                                                                                                                                      ( ( X943 @ X944 )
                                                                                                                                      & ! [X945: $i] :
                                                                                                                                          ( ( X943 @ X945 )
                                                                                                                                         => ( X944 = X945 ) ) )
                                                                                                                                 => ? [X946: $i] :
                                                                                                                                      ( ( X943 @ X946 )
                                                                                                                                      & ! [X947: $i] :
                                                                                                                                          ( ( X943 @ X947 )
                                                                                                                                         => ( X946 = X947 ) ) ) )
                                                                                                                             => ( ! [X948: $i > $o] :
                                                                                                                                    ( ? [X949: $i] : ( X948 @ X949 )
                                                                                                                                   => ( ! [X950: $i,X951: $i] :
                                                                                                                                          ( ( X948 @ X950 )
                                                                                                                                         => ( ( X948 @ X951 )
                                                                                                                                           => ( X950 = X951 ) ) )
                                                                                                                                     => ? [X952: $i] :
                                                                                                                                          ( ( X948 @ X952 )
                                                                                                                                          & ! [X953: $i] :
                                                                                                                                              ( ( X948 @ X953 )
                                                                                                                                             => ( X952 = X953 ) ) ) ) )
                                                                                                                               => ( ! [X954: $i > $o] :
                                                                                                                                      ( ? [X955: $i] :
                                                                                                                                        ! [X956: $i] :
                                                                                                                                          ( ( X954 @ X956 )
                                                                                                                                        <=> ( X956 = X955 ) )
                                                                                                                                     => ? [X957: $i] :
                                                                                                                                          ( ( X954 @ X957 )
                                                                                                                                          & ! [X958: $i] :
                                                                                                                                              ( ( X954 @ X958 )
                                                                                                                                             => ( X957 = X958 ) ) ) )
                                                                                                                                 => ( ! [X959: $i,X960: $i] :
                                                                                                                                        ( ( X959 = X960 )
                                                                                                                                       => ! [X961: $i,X962: $i] :
                                                                                                                                            ( ( X961 = X962 )
                                                                                                                                           => ( ( in @ X961 @ X959 )
                                                                                                                                             => ( in @ X962 @ X960 ) ) ) )
                                                                                                                                   => ( ! [X963: $i,X964: $i] :
                                                                                                                                          ( ( X963 = X964 )
                                                                                                                                         => ! [X965: $i,X966: $i] :
                                                                                                                                              ( ( X965 = X966 )
                                                                                                                                             => ( ( in @ X965 @ X963 )
                                                                                                                                              <=> ( in @ X966 @ X964 ) ) ) )
                                                                                                                                     => ( ! [X967: $i > $o] :
                                                                                                                                            ( ? [X968: $i] :
                                                                                                                                                ( ( X967 @ X968 )
                                                                                                                                                & ! [X969: $i] :
                                                                                                                                                    ( ( X967 @ X969 )
                                                                                                                                                   => ( X968 = X969 ) ) )
                                                                                                                                           => ! [X970: $i,X971: $i] :
                                                                                                                                                ( ( X967 @ X970 )
                                                                                                                                               => ( ( X967 @ X971 )
                                                                                                                                                 => ( X970 = X971 ) ) ) )
                                                                                                                                       => ( ! [X972: $i > $o,X973: $i > $o] :
                                                                                                                                              ( ! [X974: $i,X975: $i] :
                                                                                                                                                  ( ( X974 = X975 )
                                                                                                                                                 => ( ( X972 @ X974 )
                                                                                                                                                  <=> ( X973 @ X975 ) ) )
                                                                                                                                             => ( ? [X976: $i] :
                                                                                                                                                    ( ( X972 @ X976 )
                                                                                                                                                    & ! [X977: $i] :
                                                                                                                                                        ( ( X972 @ X977 )
                                                                                                                                                       => ( X976 = X977 ) ) )
                                                                                                                                              <=> ? [X978: $i] :
                                                                                                                                                    ( ( X973 @ X978 )
                                                                                                                                                    & ! [X979: $i] :
                                                                                                                                                        ( ( X973 @ X979 )
                                                                                                                                                       => ( X978 = X979 ) ) ) ) )
                                                                                                                                         => ( ( emptyset = emptyset )
                                                                                                                                           => ( ! [X980: $i,X981: $i] :
                                                                                                                                                  ( ( X980 = X981 )
                                                                                                                                                 => ! [X982: $i,X983: $i] :
                                                                                                                                                      ( ( X982 = X983 )
                                                                                                                                                     => ( ( setadjoin @ X980 @ X982 )
                                                                                                                                                        = ( setadjoin @ X981 @ X983 ) ) ) )
                                                                                                                                             => ( ! [X984: $i,X985: $i] :
                                                                                                                                                    ( ( X984 = X985 )
                                                                                                                                                   => ( ( powerset @ X984 )
                                                                                                                                                      = ( powerset @ X985 ) ) )
                                                                                                                                               => ( ! [X986: $i,X987: $i] :
                                                                                                                                                      ( ( X986 = X987 )
                                                                                                                                                     => ( ( setunion @ X986 )
                                                                                                                                                        = ( setunion @ X987 ) ) )
                                                                                                                                                 => ( ( omega = omega )
                                                                                                                                                   => ( ! [X988: $i > $o] :
                                                                                                                                                          ( ? [X989: $i] :
                                                                                                                                                              ( ( X988 @ X989 )
                                                                                                                                                              & ! [X990: $i] :
                                                                                                                                                                  ( ( X988 @ X990 )
                                                                                                                                                                 => ( X989 = X990 ) ) )
                                                                                                                                                         => ! [X991: $i,X992: $i] :
                                                                                                                                                              ( ( X988 @ X991 )
                                                                                                                                                             => ( ( X988 @ X992 )
                                                                                                                                                               => ( X991 = X992 ) ) ) )
                                                                                                                                                     => ( ! [X993: $i > $o,X994: $i > $o] :
                                                                                                                                                            ( ! [X995: $i,X996: $i] :
                                                                                                                                                                ( ( X995 = X996 )
                                                                                                                                                               => ( ( X993 @ X995 )
                                                                                                                                                                <=> ( X994 @ X996 ) ) )
                                                                                                                                                           => ( ? [X997: $i] :
                                                                                                                                                                  ( ( X993 @ X997 )
                                                                                                                                                                  & ! [X998: $i] :
                                                                                                                                                                      ( ( X993 @ X998 )
                                                                                                                                                                     => ( X997 = X998 ) ) )
                                                                                                                                                             => ( ? [X999: $i] :
                                                                                                                                                                    ( ( X994 @ X999 )
                                                                                                                                                                    & ! [X1000: $i] :
                                                                                                                                                                        ( ( X994 @ X1000 )
                                                                                                                                                                       => ( X999 = X1000 ) ) )
                                                                                                                                                               => ( ( descr @ X993 )
                                                                                                                                                                  = ( descr @ X994 ) ) ) ) )
                                                                                                                                                       => ( ! [X1001: $i,X1002: $i] :
                                                                                                                                                              ( ( X1001 = X1002 )
                                                                                                                                                             => ! [X1003: $i > $o,X1004: $i > $o] :
                                                                                                                                                                  ( ! [X1005: $i] :
                                                                                                                                                                      ( ( in @ X1005 @ X1001 )
                                                                                                                                                                     => ! [X1006: $i] :
                                                                                                                                                                          ( ( in @ X1006 @ X1002 )
                                                                                                                                                                         => ( ( X1005 = X1006 )
                                                                                                                                                                           => ( ( X1003 @ X1005 )
                                                                                                                                                                            <=> ( X1004 @ X1006 ) ) ) ) )
                                                                                                                                                                 => ( ( dsetconstr @ X1001 @ X1003 )
                                                                                                                                                                    = ( dsetconstr @ X1002 @ X1004 ) ) ) )
                                                                                                                                                         => ( ! [X1007: $i,X1008: $i] :
                                                                                                                                                                ( ! [X1009: $i] :
                                                                                                                                                                    ( ( in @ X1009 @ X1007 )
                                                                                                                                                                   => ( in @ X1009 @ X1008 ) )
                                                                                                                                                               => ( subset @ X1007 @ X1008 ) )
                                                                                                                                                           => ( ! [X1010: $i,X1011: $i] :
                                                                                                                                                                  ( ( X1010 = X1011 )
                                                                                                                                                                 => ( subset @ X1011 @ X1010 ) )
                                                                                                                                                             => ( ! [X1012: $i,X1013: $i] :
                                                                                                                                                                    ( ( X1012 = X1013 )
                                                                                                                                                                   => ( subset @ X1012 @ X1013 ) )
                                                                                                                                                               => ( ! [X1014: $i,X1015: $i] :
                                                                                                                                                                      ( ! [X1016: $i] :
                                                                                                                                                                          ( ( in @ X1016 @ X1014 )
                                                                                                                                                                         => ( in @ X1016 @ X1015 ) )
                                                                                                                                                                     => ( subset @ X1014 @ X1015 ) )
                                                                                                                                                                 => ( ! [X1017: $i] : ( subset @ emptyset @ X1017 )
                                                                                                                                                                   => ( ! [X1018: $i,X1019: $i,X1020: $i] :
                                                                                                                                                                          ( ( subset @ X1018 @ X1019 )
                                                                                                                                                                         => ( ( in @ X1020 @ X1018 )
                                                                                                                                                                           => ( in @ X1020 @ X1019 ) ) )
                                                                                                                                                                     => ( ! [X1021: $i,X1022: $i,X1023: $i] :
                                                                                                                                                                            ( ( subset @ X1021 @ X1022 )
                                                                                                                                                                           => ( ~ ( in @ X1023 @ X1022 )
                                                                                                                                                                             => ~ ( in @ X1023 @ X1021 ) ) )
                                                                                                                                                                       => ( ! [X1024: $i,X1025: $i,X1026: $i] :
                                                                                                                                                                              ( ( in @ X1026 @ X1024 )
                                                                                                                                                                             => ( ~ ( in @ X1026 @ X1025 )
                                                                                                                                                                               => ~ ( subset @ X1024 @ X1025 ) ) )
                                                                                                                                                                         => ( ! [X1027: $i,X1028: $i] :
                                                                                                                                                                                ( ~ ( subset @ X1027 @ X1028 )
                                                                                                                                                                               => ( X1027 != X1028 ) )
                                                                                                                                                                           => ( ! [X1029: $i,X1030: $i,X1031: $i] :
                                                                                                                                                                                  ( ( in @ X1031 @ X1029 )
                                                                                                                                                                                 => ( ~ ( in @ X1031 @ X1030 )
                                                                                                                                                                                   => ( X1029 != X1030 ) ) )
                                                                                                                                                                             => ( ! [X1032: $i] : ( subset @ X1032 @ X1032 )
                                                                                                                                                                               => ( ! [X1033: $i,X1034: $i,X1035: $i] :
                                                                                                                                                                                      ( ( subset @ X1033 @ X1034 )
                                                                                                                                                                                     => ( ( subset @ X1034 @ X1035 )
                                                                                                                                                                                       => ( subset @ X1033 @ X1035 ) ) )
                                                                                                                                                                                 => ( ! [X1036: $i,X1037: $i] : ( subset @ X1037 @ ( setadjoin @ X1036 @ X1037 ) )
                                                                                                                                                                                   => ( ! [X1038: $i,X1039: $i,X1040: $i] :
                                                                                                                                                                                          ( ( subset @ X1038 @ X1040 )
                                                                                                                                                                                         => ( subset @ X1038 @ ( setadjoin @ X1039 @ X1040 ) ) )
                                                                                                                                                                                     => ( ! [X1041: $i,X1042: $i] :
                                                                                                                                                                                            ( ( subset @ X1041 @ X1042 )
                                                                                                                                                                                           => ( in @ X1041 @ ( powerset @ X1042 ) ) )
                                                                                                                                                                                       => ( ! [X1043: $i,X1044: $i] :
                                                                                                                                                                                              ( ( subset @ X1043 @ X1044 )
                                                                                                                                                                                             => ( ( subset @ X1044 @ X1043 )
                                                                                                                                                                                               => ( X1043 = X1044 ) ) )
                                                                                                                                                                                         => ( ! [X1045: $i] :
                                                                                                                                                                                                ( ( subset @ X1045 @ emptyset )
                                                                                                                                                                                               => ( X1045 = emptyset ) )
                                                                                                                                                                                           => ( ! [X1046: $i,X1047: $i] :
                                                                                                                                                                                                  ( ( subset @ X1047 @ X1046 )
                                                                                                                                                                                                 => ( in @ X1047 @ ( powerset @ X1046 ) ) )
                                                                                                                                                                                             => ( ! [X1048: $i,X1049: $i] :
                                                                                                                                                                                                    ( ( in @ X1049 @ ( powerset @ X1048 ) )
                                                                                                                                                                                                   => ( subset @ X1049 @ X1048 ) )
                                                                                                                                                                                               => ( ! [X1050: $i] : ( in @ X1050 @ ( powerset @ X1050 ) )
                                                                                                                                                                                                 => ( ! [X1051: $i,X1052: $i] :
                                                                                                                                                                                                        ( ( subset @ X1051 @ X1052 )
                                                                                                                                                                                                       => ( subset @ ( powerset @ X1051 ) @ ( powerset @ X1052 ) ) )
                                                                                                                                                                                                   => ( ! [X1053: $i,X1054: $i > $o] : ( in @ ( dsetconstr @ X1053 @ X1054 ) @ ( powerset @ X1053 ) )
                                                                                                                                                                                                     => ( ! [X1055: $i,X1056: $i > $o] : ( subset @ ( dsetconstr @ X1055 @ X1056 ) @ X1055 )
                                                                                                                                                                                                       => ( ! [X1057: $i,X1058: $i,X1059: $i] :
                                                                                                                                                                                                              ( ( in @ X1059 @ X1057 )
                                                                                                                                                                                                             => ( in @ X1059 @ ( binunion @ X1057 @ X1058 ) ) )
                                                                                                                                                                                                         => ( ! [X1060: $i,X1061: $i] : ( in @ X1061 @ ( setadjoin @ X1060 @ ( setadjoin @ X1061 @ emptyset ) ) )
                                                                                                                                                                                                           => ( ! [X1062: $i,X1063: $i,X1064: $i] :
                                                                                                                                                                                                                  ( ( in @ X1064 @ X1063 )
                                                                                                                                                                                                                 => ( in @ X1064 @ ( binunion @ X1062 @ X1063 ) ) )
                                                                                                                                                                                                             => ( ! [X1065: $i,X1066: $i,X1067: $i,X1068: $o] :
                                                                                                                                                                                                                    ( ( in @ X1067 @ ( binunion @ X1065 @ X1066 ) )
                                                                                                                                                                                                                   => ( ( ( in @ X1067 @ X1065 )
                                                                                                                                                                                                                       => X1068 )
                                                                                                                                                                                                                     => ( ( ( in @ X1067 @ X1066 )
                                                                                                                                                                                                                         => X1068 )
                                                                                                                                                                                                                       => X1068 ) ) )
                                                                                                                                                                                                               => ( ! [X1069: $i,X1070: $i,X1071: $i] :
                                                                                                                                                                                                                      ( ( in @ X1071 @ ( binunion @ X1069 @ X1070 ) )
                                                                                                                                                                                                                     => ( ( in @ X1071 @ X1069 )
                                                                                                                                                                                                                        | ( in @ X1071 @ X1070 ) ) )
                                                                                                                                                                                                                 => ( ! [X1072: $i,X1073: $i] : ( subset @ X1072 @ ( binunion @ X1072 @ X1073 ) )
                                                                                                                                                                                                                   => ( ! [X1074: $i,X1075: $i] : ( subset @ X1075 @ ( binunion @ X1074 @ X1075 ) )
                                                                                                                                                                                                                     => ( ! [X1076: $i,X1077: $i,X1078: $i] :
                                                                                                                                                                                                                            ( ( in @ X1078 @ X1076 )
                                                                                                                                                                                                                           => ( ( in @ X1078 @ X1077 )
                                                                                                                                                                                                                             => ( in @ X1078 @ ( binintersect @ X1076 @ X1077 ) ) ) )
                                                                                                                                                                                                                       => ( ! [X1079: $i,X1080: $i,X1081: $i] :
                                                                                                                                                                                                                              ( ( subset @ X1081 @ X1079 )
                                                                                                                                                                                                                             => ( ( subset @ X1081 @ X1080 )
                                                                                                                                                                                                                               => ( subset @ X1081 @ ( binintersect @ X1079 @ X1080 ) ) ) )
                                                                                                                                                                                                                         => ( ! [X1082: $i,X1083: $i,X1084: $i] :
                                                                                                                                                                                                                                ( ( in @ X1084 @ ( binintersect @ X1082 @ X1083 ) )
                                                                                                                                                                                                                               => ( in @ X1084 @ X1082 ) )
                                                                                                                                                                                                                           => ( ! [X1085: $i,X1086: $i] : ( subset @ ( binintersect @ X1085 @ X1086 ) @ X1085 )
                                                                                                                                                                                                                             => ( ! [X1087: $i,X1088: $i] :
                                                                                                                                                                                                                                    ( ( subset @ X1087 @ X1088 )
                                                                                                                                                                                                                                   => ( ( binintersect @ X1087 @ X1088 )
                                                                                                                                                                                                                                      = X1087 ) )
                                                                                                                                                                                                                               => ( ! [X1089: $i,X1090: $i] :
                                                                                                                                                                                                                                      ( ( ( binintersect @ X1089 @ X1090 )
                                                                                                                                                                                                                                        = X1090 )
                                                                                                                                                                                                                                     => ( subset @ X1090 @ X1089 ) )
                                                                                                                                                                                                                                 => ( ! [X1091: $i,X1092: $i,X1093: $i] :
                                                                                                                                                                                                                                        ( ( in @ X1093 @ ( binintersect @ X1091 @ X1092 ) )
                                                                                                                                                                                                                                       => ( in @ X1093 @ X1092 ) )
                                                                                                                                                                                                                                   => ( ! [X1094: $i,X1095: $i] :
                                                                                                                                                                                                                                          ( ~ ? [X1096: $i] :
                                                                                                                                                                                                                                                ( ( in @ X1096 @ X1094 )
                                                                                                                                                                                                                                                & ( in @ X1096 @ X1095 ) )
                                                                                                                                                                                                                                         => ( ( binintersect @ X1094 @ X1095 )
                                                                                                                                                                                                                                            = emptyset ) )
                                                                                                                                                                                                                                     => ( ! [X1097: $i,X1098: $i] : ( subset @ ( binintersect @ X1097 @ X1098 ) @ X1098 )
                                                                                                                                                                                                                                       => ( ! [X1099: $i,X1100: $i] :
                                                                                                                                                                                                                                              ( ( subset @ X1100 @ X1099 )
                                                                                                                                                                                                                                             => ( ( binintersect @ X1099 @ X1100 )
                                                                                                                                                                                                                                                = X1100 ) )
                                                                                                                                                                                                                                         => ( ! [X1101: $i,X1102: $i] :
                                                                                                                                                                                                                                                ( ( ( binintersect @ X1101 @ X1102 )
                                                                                                                                                                                                                                                  = X1101 )
                                                                                                                                                                                                                                               => ( subset @ X1101 @ X1102 ) )
                                                                                                                                                                                                                                           => ( ! [X1103: $i,X1104: $i,X1105: $i] :
                                                                                                                                                                                                                                                  ( ( binintersect @ X1103 @ ( binunion @ X1104 @ X1105 ) )
                                                                                                                                                                                                                                                  = ( binunion @ ( binintersect @ X1103 @ X1104 ) @ ( binintersect @ X1103 @ X1105 ) ) )
                                                                                                                                                                                                                                             => ( ! [X1106: $i,X1107: $i,X1108: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X1108 @ X1106 )
                                                                                                                                                                                                                                                   => ( ~ ( in @ X1108 @ X1107 )
                                                                                                                                                                                                                                                     => ( in @ X1108 @ ( setminus @ X1106 @ X1107 ) ) ) )
                                                                                                                                                                                                                                               => ( ! [X1109: $i,X1110: $i,X1111: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X1111 @ ( setminus @ X1109 @ X1110 ) )
                                                                                                                                                                                                                                                     => ( in @ X1111 @ X1109 ) )
                                                                                                                                                                                                                                                 => ( ! [X1112: $i,X1113: $i,X1114: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X1114 @ ( setminus @ X1112 @ X1113 ) )
                                                                                                                                                                                                                                                       => ~ ( in @ X1114 @ X1113 ) )
                                                                                                                                                                                                                                                   => ( ! [X1115: $i,X1116: $i] :
                                                                                                                                                                                                                                                          ( ( subset @ X1115 @ X1116 )
                                                                                                                                                                                                                                                         => ( ( setminus @ X1115 @ X1116 )
                                                                                                                                                                                                                                                            = emptyset ) )
                                                                                                                                                                                                                                                     => ( ! [X1117: $i,X1118: $i,X1119: $i] :
                                                                                                                                                                                                                                                            ( ~ ( in @ X1119 @ ( setminus @ X1117 @ X1118 ) )
                                                                                                                                                                                                                                                           => ( ( in @ X1119 @ X1117 )
                                                                                                                                                                                                                                                             => ( in @ X1119 @ X1118 ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1120: $i,X1121: $i,X1122: $i] :
                                                                                                                                                                                                                                                              ( ~ ( in @ X1122 @ ( setminus @ X1120 @ X1121 ) )
                                                                                                                                                                                                                                                             => ( ~ ( in @ X1122 @ X1121 )
                                                                                                                                                                                                                                                               => ~ ( in @ X1122 @ X1120 ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1123: $i,X1124: $i,X1125: $i] :
                                                                                                                                                                                                                                                                ( ~ ( in @ X1125 @ X1123 )
                                                                                                                                                                                                                                                               => ~ ( in @ X1125 @ ( setminus @ X1123 @ X1124 ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1126: $i,X1127: $i,X1128: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X1128 @ X1127 )
                                                                                                                                                                                                                                                                 => ~ ( in @ X1128 @ ( setminus @ X1126 @ X1127 ) ) )
                                                                                                                                                                                                                                                             => ( ! [X1129: $i,X1130: $i] : ( subset @ ( setminus @ X1129 @ X1130 ) @ X1129 )
                                                                                                                                                                                                                                                               => ( ! [X1131: $i,X1132: $i] :
                                                                                                                                                                                                                                                                      ( ( ( setminus @ X1131 @ X1132 )
                                                                                                                                                                                                                                                                        = emptyset )
                                                                                                                                                                                                                                                                     => ( subset @ X1131 @ X1132 ) )
                                                                                                                                                                                                                                                                 => ( ! [X1133: $i,X1134: $i,X1135: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X1135 @ ( symdiff @ X1133 @ X1134 ) )
                                                                                                                                                                                                                                                                       => ! [X1136: $o] :
                                                                                                                                                                                                                                                                            ( ( ( in @ X1135 @ X1133 )
                                                                                                                                                                                                                                                                             => ( ~ ( in @ X1135 @ X1134 )
                                                                                                                                                                                                                                                                               => X1136 ) )
                                                                                                                                                                                                                                                                           => ( ( ~ ( in @ X1135 @ X1133 )
                                                                                                                                                                                                                                                                               => ( ( in @ X1135 @ X1134 )
                                                                                                                                                                                                                                                                                 => X1136 ) )
                                                                                                                                                                                                                                                                             => X1136 ) ) )
                                                                                                                                                                                                                                                                   => ( ! [X1137: $i,X1138: $i,X1139: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X1139 @ X1137 )
                                                                                                                                                                                                                                                                         => ( ~ ( in @ X1139 @ X1138 )
                                                                                                                                                                                                                                                                           => ( in @ X1139 @ ( symdiff @ X1137 @ X1138 ) ) ) )
                                                                                                                                                                                                                                                                     => ( ! [X1140: $i,X1141: $i,X1142: $i] :
                                                                                                                                                                                                                                                                            ( ~ ( in @ X1142 @ X1140 )
                                                                                                                                                                                                                                                                           => ( ( in @ X1142 @ X1141 )
                                                                                                                                                                                                                                                                             => ( in @ X1142 @ ( symdiff @ X1140 @ X1141 ) ) ) )
                                                                                                                                                                                                                                                                       => ( ! [X1143: $i,X1144: $i,X1145: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X1145 @ X1143 )
                                                                                                                                                                                                                                                                             => ( ( in @ X1145 @ X1144 )
                                                                                                                                                                                                                                                                               => ~ ( in @ X1145 @ ( symdiff @ X1143 @ X1144 ) ) ) )
                                                                                                                                                                                                                                                                         => ( ! [X1146: $i,X1147: $i,X1148: $i] :
                                                                                                                                                                                                                                                                                ( ~ ( in @ X1148 @ X1146 )
                                                                                                                                                                                                                                                                               => ( ~ ( in @ X1148 @ X1147 )
                                                                                                                                                                                                                                                                                 => ~ ( in @ X1148 @ ( symdiff @ X1146 @ X1147 ) ) ) )
                                                                                                                                                                                                                                                                           => ( ! [X1149: $i,X1150: $i] : ( in @ X1150 @ ( setadjoin @ X1149 @ ( setadjoin @ X1150 @ emptyset ) ) )
                                                                                                                                                                                                                                                                             => ( ! [X1151: $i,X1152: $i] : ( in @ X1151 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1151 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1151 @ ( setadjoin @ X1152 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                               => ( ! [X1153: $i,X1154: $i] : ( in @ X1154 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1153 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1153 @ ( setadjoin @ X1154 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1155: $i,X1156: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1155 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1155 @ ( setadjoin @ X1156 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1157: $i,X1158: $i] : ( iskpair @ ( kpair @ X1157 @ X1158 ) )
                                                                                                                                                                                                                                                                                     => ( ! [X1159: $i,X1160: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X1160 @ X1159 )
                                                                                                                                                                                                                                                                                           => ( subset @ ( setadjoin @ X1160 @ emptyset ) @ X1159 ) )
                                                                                                                                                                                                                                                                                       => ( ! [X1161: $i,X1162: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X1162 @ X1161 )
                                                                                                                                                                                                                                                                                             => ( in @ ( setadjoin @ X1162 @ emptyset ) @ ( powerset @ X1161 ) ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1163: $i,X1164: $i,X1165: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X1165 @ X1163 )
                                                                                                                                                                                                                                                                                               => ( in @ ( setadjoin @ X1165 @ emptyset ) @ ( powerset @ ( binunion @ X1163 @ X1164 ) ) ) )
                                                                                                                                                                                                                                                                                           => ( ! [X1166: $i,X1167: $i,X1168: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X1168 @ ( setadjoin @ X1166 @ ( setadjoin @ X1167 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                 => ( ( X1168 = X1166 )
                                                                                                                                                                                                                                                                                                    | ( X1168 = X1167 ) ) )
                                                                                                                                                                                                                                                                                             => ( ! [X1169: $i,X1170: $i,X1171: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X1171 @ X1169 )
                                                                                                                                                                                                                                                                                                   => ! [X1172: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X1172 @ X1170 )
                                                                                                                                                                                                                                                                                                       => ( subset @ ( setadjoin @ X1171 @ ( setadjoin @ X1172 @ emptyset ) ) @ ( binunion @ X1169 @ X1170 ) ) ) )
                                                                                                                                                                                                                                                                                               => ( ! [X1173: $i,X1174: $i,X1175: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ X1175 @ X1173 )
                                                                                                                                                                                                                                                                                                     => ! [X1176: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X1176 @ X1174 )
                                                                                                                                                                                                                                                                                                         => ( in @ ( setadjoin @ X1175 @ ( setadjoin @ X1176 @ emptyset ) ) @ ( powerset @ ( binunion @ X1173 @ X1174 ) ) ) ) )
                                                                                                                                                                                                                                                                                                 => ( ! [X1177: $i,X1178: $i,X1179: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X1179 @ X1177 )
                                                                                                                                                                                                                                                                                                       => ! [X1180: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X1180 @ X1178 )
                                                                                                                                                                                                                                                                                                           => ( subset @ ( setadjoin @ ( setadjoin @ X1179 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1179 @ ( setadjoin @ X1180 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1177 @ X1178 ) ) ) ) )
                                                                                                                                                                                                                                                                                                   => ( ! [X1181: $i,X1182: $i,X1183: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X1183 @ X1181 )
                                                                                                                                                                                                                                                                                                         => ! [X1184: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X1184 @ X1182 )
                                                                                                                                                                                                                                                                                                             => ( in @ ( setadjoin @ ( setadjoin @ X1183 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1183 @ ( setadjoin @ X1184 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1181 @ X1182 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                     => ( ! [X1185: $i,X1186: $i,X1187: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X1187 @ X1185 )
                                                                                                                                                                                                                                                                                                           => ! [X1188: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X1188 @ X1186 )
                                                                                                                                                                                                                                                                                                               => ( in @ ( kpair @ X1187 @ X1188 ) @ ( powerset @ ( powerset @ ( binunion @ X1185 @ X1186 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                       => ( ! [X1189: $i,X1190: $i,X1191: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X1191 @ X1189 )
                                                                                                                                                                                                                                                                                                             => ! [X1192: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ X1192 @ X1190 )
                                                                                                                                                                                                                                                                                                                 => ( in @ ( kpair @ X1191 @ X1192 ) @ ( cartprod @ X1189 @ X1190 ) ) ) )
                                                                                                                                                                                                                                                                                                         => ( ! [X1193: $i,X1194: $i,X1195: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X1195 @ ( cartprod @ X1193 @ X1194 ) )
                                                                                                                                                                                                                                                                                                               => ? [X1196: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X1196 @ X1193 )
                                                                                                                                                                                                                                                                                                                    & ? [X1197: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( in @ X1197 @ X1194 )
                                                                                                                                                                                                                                                                                                                        & ( X1195
                                                                                                                                                                                                                                                                                                                          = ( kpair @ X1196 @ X1197 ) ) ) ) )
                                                                                                                                                                                                                                                                                                           => ( ! [X1198: $i,X1199: $i,X1200: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ X1200 @ ( cartprod @ X1198 @ X1199 ) )
                                                                                                                                                                                                                                                                                                                 => ( iskpair @ X1200 ) )
                                                                                                                                                                                                                                                                                                             => ( ! [X1201: $i,X1202: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X1202 @ ( setunion @ X1201 ) )
                                                                                                                                                                                                                                                                                                                   => ? [X1203: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( in @ X1203 @ X1201 )
                                                                                                                                                                                                                                                                                                                        & ( in @ X1202 @ X1203 ) ) )
                                                                                                                                                                                                                                                                                                               => ( ! [X1204: $i] : ( subset @ ( setunion @ ( setadjoin @ X1204 @ emptyset ) ) @ X1204 )
                                                                                                                                                                                                                                                                                                                 => ( ! [X1205: $i] : ( subset @ X1205 @ ( setunion @ ( setadjoin @ X1205 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                   => ( ! [X1206: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( setunion @ ( setadjoin @ X1206 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                          = X1206 )
                                                                                                                                                                                                                                                                                                                     => ( ! [X1207: $i,X1208: $i > $o] :
                                                                                                                                                                                                                                                                                                                            ( ! [X1209: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( in @ X1209 @ X1207 )
                                                                                                                                                                                                                                                                                                                               => ! [X1210: $i] :
                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1210 @ X1207 )
                                                                                                                                                                                                                                                                                                                                   => ( ( X1208 @ X1209 )
                                                                                                                                                                                                                                                                                                                                     => ( ( X1208 @ X1210 )
                                                                                                                                                                                                                                                                                                                                       => ( X1209 = X1210 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                           => ( ? [X1211: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1211 @ X1207 )
                                                                                                                                                                                                                                                                                                                                  & ( X1208 @ X1211 ) )
                                                                                                                                                                                                                                                                                                                             => ? [X1212: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1212 @ ( dsetconstr @ X1207 @ X1208 ) )
                                                                                                                                                                                                                                                                                                                                  & ( ( dsetconstr @ X1207 @ X1208 )
                                                                                                                                                                                                                                                                                                                                    = ( setadjoin @ X1212 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                                       => ( ! [X1213: $i,X1214: $i > $o] :
                                                                                                                                                                                                                                                                                                                              ( ? [X1215: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1215 @ ( dsetconstr @ X1213 @ X1214 ) )
                                                                                                                                                                                                                                                                                                                                  & ( ( dsetconstr @ X1213 @ X1214 )
                                                                                                                                                                                                                                                                                                                                    = ( setadjoin @ X1215 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                             => ? [X1216: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1216 @ X1213 )
                                                                                                                                                                                                                                                                                                                                  & ( X1214 @ X1216 ) ) )
                                                                                                                                                                                                                                                                                                                         => ( ! [X1217: $i,X1218: $i > $o,X1219: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( in @ X1219 @ X1217 )
                                                                                                                                                                                                                                                                                                                               => ( ( X1218 @ X1219 )
                                                                                                                                                                                                                                                                                                                                 => ( ! [X1220: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1220 @ X1217 )
                                                                                                                                                                                                                                                                                                                                       => ( ( X1218 @ X1220 )
                                                                                                                                                                                                                                                                                                                                         => ( X1220 = X1219 ) ) )
                                                                                                                                                                                                                                                                                                                                   => ? [X1221: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1221 @ ( dsetconstr @ X1217 @ X1218 ) )
                                                                                                                                                                                                                                                                                                                                        & ( ( dsetconstr @ X1217 @ X1218 )
                                                                                                                                                                                                                                                                                                                                          = ( setadjoin @ X1221 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                           => ( ! [X1222: $i,X1223: $i > $o] :
                                                                                                                                                                                                                                                                                                                                  ( ! [X1224: $i] :
                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1224 @ X1222 )
                                                                                                                                                                                                                                                                                                                                     => ! [X1225: $i] :
                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1225 @ X1222 )
                                                                                                                                                                                                                                                                                                                                         => ( ( X1223 @ X1224 )
                                                                                                                                                                                                                                                                                                                                           => ( ( X1223 @ X1225 )
                                                                                                                                                                                                                                                                                                                                             => ( X1224 = X1225 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                 => ( ? [X1226: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1226 @ X1222 )
                                                                                                                                                                                                                                                                                                                                        & ( X1223 @ X1226 ) )
                                                                                                                                                                                                                                                                                                                                   => ? [X1227: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1227 @ ( dsetconstr @ X1222 @ X1223 ) )
                                                                                                                                                                                                                                                                                                                                        & ( ( dsetconstr @ X1222 @ X1223 )
                                                                                                                                                                                                                                                                                                                                          = ( setadjoin @ X1227 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                                             => ( ! [X1228: $i,X1229: $i] :
                                                                                                                                                                                                                                                                                                                                    ( ( ( setadjoin @ X1228 @ emptyset )
                                                                                                                                                                                                                                                                                                                                      = ( setadjoin @ X1229 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                   => ( X1228 = X1229 ) )
                                                                                                                                                                                                                                                                                                                               => ( ! [X1230: $i,X1231: $i,X1232: $i] :
                                                                                                                                                                                                                                                                                                                                      ( ( in @ ( setadjoin @ X1232 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1230 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1230 @ ( setadjoin @ X1231 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                     => ( X1230 = X1232 ) )
                                                                                                                                                                                                                                                                                                                                 => ( ! [X1233: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( iskpair @ X1233 )
                                                                                                                                                                                                                                                                                                                                       => ? [X1234: $i] :
                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1234
                                                                                                                                                                                                                                                                                                                                              @ ( dsetconstr @ ( setunion @ X1233 )
                                                                                                                                                                                                                                                                                                                                                @ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1233 ) ) )
                                                                                                                                                                                                                                                                                                                                            & ( ( dsetconstr @ ( setunion @ X1233 )
                                                                                                                                                                                                                                                                                                                                                @ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1233 ) )
                                                                                                                                                                                                                                                                                                                                              = ( setadjoin @ X1234 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                                                   => ( ! [X1235: $i] :
                                                                                                                                                                                                                                                                                                                                          ( ? [X1236: $i] :
                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1236 @ X1235 )
                                                                                                                                                                                                                                                                                                                                              & ( X1235
                                                                                                                                                                                                                                                                                                                                                = ( setadjoin @ X1236 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                         => ( in @ ( setunion @ X1235 ) @ X1235 ) )
                                                                                                                                                                                                                                                                                                                                     => ( ! [X1237: $i,X1238: $i] :
                                                                                                                                                                                                                                                                                                                                            ( ( kfst @ ( kpair @ X1237 @ X1238 ) )
                                                                                                                                                                                                                                                                                                                                            = X1237 )
                                                                                                                                                                                                                                                                                                                                       => ( ! [X1239: $i,X1240: $i,X1241: $i] :
                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1241 @ ( cartprod @ X1239 @ X1240 ) )
                                                                                                                                                                                                                                                                                                                                             => ( in @ ( kfst @ X1241 ) @ X1239 ) )
                                                                                                                                                                                                                                                                                                                                         => ( ! [X1242: $i,X1243: $i,X1244: $i,X1245: $i] :
                                                                                                                                                                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1242 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1242 @ ( setadjoin @ X1243 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X1244 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1244 @ ( setadjoin @ X1245 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                               => ( X1242 = X1244 ) )
                                                                                                                                                                                                                                                                                                                                           => ( ! [X1246: $i,X1247: $i,X1248: $i,X1249: $i] :
                                                                                                                                                                                                                                                                                                                                                  ( ( ( kpair @ X1246 @ X1247 )
                                                                                                                                                                                                                                                                                                                                                    = ( kpair @ X1248 @ X1249 ) )
                                                                                                                                                                                                                                                                                                                                                 => ( X1246 = X1248 ) )
                                                                                                                                                                                                                                                                                                                                             => ( ! [X1250: $i,X1251: $i] :
                                                                                                                                                                                                                                                                                                                                                    ( ( X1250 = X1251 )
                                                                                                                                                                                                                                                                                                                                                   => ( ( setadjoin @ X1250 @ ( setadjoin @ X1251 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                      = ( setadjoin @ X1250 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                               => ( ! [X1252: $i,X1253: $i] :
                                                                                                                                                                                                                                                                                                                                                      ( ( X1252 = X1253 )
                                                                                                                                                                                                                                                                                                                                                     => ( ( setadjoin @ ( setadjoin @ X1252 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1252 @ ( setadjoin @ X1253 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X1252 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1254: $i,X1255: $i,X1256: $i,X1257: $i] :
                                                                                                                                                                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1254 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1254 @ ( setadjoin @ X1255 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X1256 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1256 @ ( setadjoin @ X1257 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                                       => ( ( X1256 = X1257 )
                                                                                                                                                                                                                                                                                                                                                         => ( X1255 = X1257 ) ) )
                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1258: $i,X1259: $i,X1260: $i] :
                                                                                                                                                                                                                                                                                                                                                          ( ( ( setadjoin @ X1258 @ ( setadjoin @ X1259 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                            = ( setadjoin @ X1260 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                         => ( X1258 = X1259 ) )
                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1261: $i,X1262: $i,X1263: $i,X1264: $i] :
                                                                                                                                                                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1261 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1261 @ ( setadjoin @ X1262 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X1263 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1263 @ ( setadjoin @ X1264 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                                           => ( X1262 = X1264 ) )
                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1265: $i,X1266: $i,X1267: $i,X1268: $i] :
                                                                                                                                                                                                                                                                                                                                                              ( ( ( kpair @ X1265 @ X1266 )
                                                                                                                                                                                                                                                                                                                                                                = ( kpair @ X1267 @ X1268 ) )
                                                                                                                                                                                                                                                                                                                                                             => ( X1266 = X1268 ) )
                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1269: $i] :
                                                                                                                                                                                                                                                                                                                                                                ( ( iskpair @ X1269 )
                                                                                                                                                                                                                                                                                                                                                               => ? [X1270: $i] :
                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1270
                                                                                                                                                                                                                                                                                                                                                                      @ ( dsetconstr @ ( setunion @ X1269 )
                                                                                                                                                                                                                                                                                                                                                                        @ ^ [Z0: $i] :
                                                                                                                                                                                                                                                                                                                                                                            ( X1269
                                                                                                                                                                                                                                                                                                                                                                            = ( kpair @ ( kfst @ X1269 ) @ Z0 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                    & ( ( dsetconstr @ ( setunion @ X1269 )
                                                                                                                                                                                                                                                                                                                                                                        @ ^ [Z0: $i] :
                                                                                                                                                                                                                                                                                                                                                                            ( X1269
                                                                                                                                                                                                                                                                                                                                                                            = ( kpair @ ( kfst @ X1269 ) @ Z0 ) ) )
                                                                                                                                                                                                                                                                                                                                                                      = ( setadjoin @ X1270 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1271: $i,X1272: $i] :
                                                                                                                                                                                                                                                                                                                                                                  ( ( ksnd @ ( kpair @ X1271 @ X1272 ) )
                                                                                                                                                                                                                                                                                                                                                                  = X1272 )
                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1273: $i] :
                                                                                                                                                                                                                                                                                                                                                                    ( ( iskpair @ X1273 )
                                                                                                                                                                                                                                                                                                                                                                   => ( ( kpair @ ( kfst @ X1273 ) @ ( ksnd @ X1273 ) )
                                                                                                                                                                                                                                                                                                                                                                      = X1273 ) )
                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1274: $i,X1275: $i,X1276: $i] :
                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1276 @ ( cartprod @ X1274 @ X1275 ) )
                                                                                                                                                                                                                                                                                                                                                                     => ( in @ ( ksnd @ X1276 ) @ X1275 ) )
                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1277: $i,X1278: $i,X1279: $i,X1280: $i] :
                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ ( kpair @ X1279 @ X1280 ) @ ( cartprod @ X1277 @ X1278 ) )
                                                                                                                                                                                                                                                                                                                                                                       => ( in @ X1279 @ X1277 ) )
                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1281: $i,X1282: $i,X1283: $i,X1284: $i] :
                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ ( kpair @ X1283 @ X1284 ) @ ( cartprod @ X1281 @ X1282 ) )
                                                                                                                                                                                                                                                                                                                                                                         => ( in @ X1284 @ X1282 ) )
                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1285: $i,X1286: $i,X1287: $i] :
                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1287 @ X1285 )
                                                                                                                                                                                                                                                                                                                                                                           => ! [X1288: $i] :
                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1288 @ X1286 )
                                                                                                                                                                                                                                                                                                                                                                               => ( ( kpair @ X1287 @ X1288 )
                                                                                                                                                                                                                                                                                                                                                                                  = ( kpair @ X1287 @ X1288 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1289: $i,X1290: $i,X1291: $i] :
                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1291 @ X1289 )
                                                                                                                                                                                                                                                                                                                                                                             => ! [X1292: $i] :
                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1292 @ X1290 )
                                                                                                                                                                                                                                                                                                                                                                                 => ( ( kfst @ ( kpair @ X1291 @ X1292 ) )
                                                                                                                                                                                                                                                                                                                                                                                    = X1291 ) ) )
                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1293: $i,X1294: $i,X1295: $i] :
                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1295 @ X1293 )
                                                                                                                                                                                                                                                                                                                                                                               => ! [X1296: $i] :
                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1296 @ X1294 )
                                                                                                                                                                                                                                                                                                                                                                                   => ( ( ksnd @ ( kpair @ X1295 @ X1296 ) )
                                                                                                                                                                                                                                                                                                                                                                                      = X1296 ) ) )
                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1297: $i,X1298: $i,X1299: $i] :
                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1299 @ ( cartprod @ X1297 @ X1298 ) )
                                                                                                                                                                                                                                                                                                                                                                                 => ( ( kpair @ ( kfst @ X1299 ) @ ( ksnd @ X1299 ) )
                                                                                                                                                                                                                                                                                                                                                                                    = X1299 ) )
                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1300: $i,X1301: $i,X1302: $i > $i > $o,X1303: $i] :
                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1303 @ X1300 )
                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1304: $i] :
                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1304 @ X1301 )
                                                                                                                                                                                                                                                                                                                                                                                       => ( ( X1302 @ X1303 @ X1304 )
                                                                                                                                                                                                                                                                                                                                                                                         => ( in @ ( kpair @ X1303 @ X1304 ) @ ( dpsetconstr @ X1300 @ X1301 @ X1302 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1305: $i,X1306: $i,X1307: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1305 @ X1306 @ X1307 ) @ ( cartprod @ X1305 @ X1306 ) )
                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1308: $i,X1309: $i,X1310: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1308 @ X1309 @ X1310 ) @ ( cartprod @ X1308 @ X1309 ) )
                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1311: $i,X1312: $i,X1313: $i > $i > $o,X1314: $i] :
                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1314 @ X1311 )
                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1315: $i] :
                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1315 @ X1312 )
                                                                                                                                                                                                                                                                                                                                                                                             => ( ( in @ ( kpair @ X1314 @ X1315 ) @ ( dpsetconstr @ X1311 @ X1312 @ X1313 ) )
                                                                                                                                                                                                                                                                                                                                                                                               => ( X1313 @ X1314 @ X1315 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1316: $i,X1317: $i,X1318: $i > $i > $o,X1319: $i,X1320: $i] :
                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ ( kpair @ X1319 @ X1320 ) @ ( dpsetconstr @ X1316 @ X1317 @ X1318 ) )
                                                                                                                                                                                                                                                                                                                                                                                           => ( in @ X1319 @ X1316 ) )
                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1321: $i,X1322: $i,X1323: $i > $i > $o,X1324: $i,X1325: $i] :
                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ ( kpair @ X1324 @ X1325 ) @ ( dpsetconstr @ X1321 @ X1322 @ X1323 ) )
                                                                                                                                                                                                                                                                                                                                                                                             => ( in @ X1325 @ X1322 ) )
                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1326: $i,X1327: $i,X1328: $i > $i > $o,X1329: $i,X1330: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ ( kpair @ X1329 @ X1330 ) @ ( dpsetconstr @ X1326 @ X1327 @ X1328 ) )
                                                                                                                                                                                                                                                                                                                                                                                               => ( X1328 @ X1329 @ X1330 ) )
                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1331: $i,X1332: $i,X1333: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                  ( ( func @ X1331 @ X1332 @ X1333 )
                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1334: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1334 @ X1331 )
                                                                                                                                                                                                                                                                                                                                                                                                     => ? [X1335: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1335
                                                                                                                                                                                                                                                                                                                                                                                                            @ ( dsetconstr @ X1332
                                                                                                                                                                                                                                                                                                                                                                                                              @ ^ [Z0: $i] : ( in @ ( kpair @ X1334 @ Z0 ) @ X1333 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                          & ( ( dsetconstr @ X1332
                                                                                                                                                                                                                                                                                                                                                                                                              @ ^ [Z0: $i] : ( in @ ( kpair @ X1334 @ Z0 ) @ X1333 ) )
                                                                                                                                                                                                                                                                                                                                                                                                            = ( setadjoin @ X1335 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1336: $i,X1337: $i,X1338: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                    ( ( func @ X1336 @ X1337 @ X1338 )
                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1339: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1339 @ X1336 )
                                                                                                                                                                                                                                                                                                                                                                                                       => ( in
                                                                                                                                                                                                                                                                                                                                                                                                          @ ( setunion
                                                                                                                                                                                                                                                                                                                                                                                                            @ ( dsetconstr @ X1337
                                                                                                                                                                                                                                                                                                                                                                                                              @ ^ [Z0: $i] : ( in @ ( kpair @ X1339 @ Z0 ) @ X1338 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                          @ X1337 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1340: $i,X1341: $i,X1342: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                      ( ( func @ X1340 @ X1341 @ X1342 )
                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1343: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1343 @ X1340 )
                                                                                                                                                                                                                                                                                                                                                                                                         => ( in @ ( ap @ X1340 @ X1341 @ X1342 @ X1343 ) @ X1341 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1344: $i,X1345: $i,X1346: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1346 @ ( funcSet @ X1344 @ X1345 ) )
                                                                                                                                                                                                                                                                                                                                                                                                       => ( func @ X1344 @ X1345 @ X1346 ) )
                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1347: $i,X1348: $i,X1349: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1349 @ ( funcSet @ X1347 @ X1348 ) )
                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1350: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1350 @ X1347 )
                                                                                                                                                                                                                                                                                                                                                                                                             => ( in @ ( ap @ X1347 @ X1348 @ X1349 @ X1350 ) @ X1348 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1351: $i,X1352: $i,X1353: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                            ( ( func @ X1351 @ X1352 @ X1353 )
                                                                                                                                                                                                                                                                                                                                                                                                           => ( in @ X1353 @ ( funcSet @ X1351 @ X1352 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1354: $i,X1355: $i,X1356: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                              ( ! [X1357: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1357 @ X1354 )
                                                                                                                                                                                                                                                                                                                                                                                                                 => ( in @ ( X1356 @ X1357 ) @ X1355 ) )
                                                                                                                                                                                                                                                                                                                                                                                                             => ( func @ X1354 @ X1355
                                                                                                                                                                                                                                                                                                                                                                                                                @ ( dpsetconstr @ X1354 @ X1355
                                                                                                                                                                                                                                                                                                                                                                                                                  @ ^ [Z0: $i] : ( $eq @ ( X1356 @ Z0 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1358: $i,X1359: $i,X1360: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                ( ! [X1361: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1361 @ X1358 )
                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ ( X1360 @ X1361 ) @ X1359 ) )
                                                                                                                                                                                                                                                                                                                                                                                                               => ( func @ X1358 @ X1359 @ ( lam @ X1358 @ X1359 @ X1360 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1362: $i,X1363: $i,X1364: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                  ( ! [X1365: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1365 @ X1362 )
                                                                                                                                                                                                                                                                                                                                                                                                                     => ( in @ ( X1364 @ X1365 ) @ X1363 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                 => ( in @ ( lam @ X1362 @ X1363 @ X1364 ) @ ( funcSet @ X1362 @ X1363 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1366: $i,X1367: $i,X1368: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( subset @ X1368 @ ( cartprod @ X1366 @ X1367 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1369: $i > $o] :
                                                                                                                                                                                                                                                                                                                                                                                                                        ( ! [X1370: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1370 @ X1366 )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1371: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1371 @ X1367 )
                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( in @ ( kpair @ X1370 @ X1371 ) @ X1368 )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( X1369 @ ( kpair @ X1370 @ X1371 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1372: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1372 @ X1368 )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ( X1369 @ X1372 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1373: $i,X1374: $i,X1375: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( subset @ X1375 @ ( cartprod @ X1373 @ X1374 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1376: $i > $o] :
                                                                                                                                                                                                                                                                                                                                                                                                                          ( ! [X1377: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1377 @ X1373 )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1378: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1378 @ X1374 )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( in @ ( kpair @ X1377 @ X1378 ) @ X1375 )
                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( X1376 @ ( kpair @ X1377 @ X1378 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1379: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1379 @ X1375 )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ( X1376 @ X1379 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1380: $i,X1381: $i > $o] :
                                                                                                                                                                                                                                                                                                                                                                                                                        ( ? [X1382: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1382 @ ( dsetconstr @ X1380 @ X1381 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                            & ( ( dsetconstr @ X1380 @ X1381 )
                                                                                                                                                                                                                                                                                                                                                                                                                              = ( setadjoin @ X1382 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1383: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1383 @ X1380 )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1384: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1384 @ X1380 )
                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( X1381 @ X1383 )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( X1381 @ X1384 )
                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( X1383 = X1384 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1385: $i,X1386: $i,X1387: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( func @ X1385 @ X1386 @ X1387 )
                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1388: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1388 @ X1385 )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ( in @ ( kpair @ X1388 @ ( ap @ X1385 @ X1386 @ X1387 @ X1388 ) ) @ X1387 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1389: $i,X1390: $i,X1391: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1391 @ ( funcSet @ X1389 @ X1390 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1392: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1392 @ X1389 )
                                                                                                                                                                                                                                                                                                                                                                                                                               => ( in @ ( kpair @ X1392 @ ( ap @ X1389 @ X1390 @ X1391 @ X1392 ) ) @ X1391 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1393: $i,X1394: $i,X1395: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( func @ X1393 @ X1394 @ X1395 )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1396: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1396 @ X1393 )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1397: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1397 @ X1394 )
                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( in @ ( kpair @ X1396 @ X1397 ) @ X1395 )
                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( ap @ X1393 @ X1394 @ X1395 @ X1396 )
                                                                                                                                                                                                                                                                                                                                                                                                                                          = X1397 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1398: $i,X1399: $i,X1400: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( func @ X1398 @ X1399 @ X1400 )
                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1401: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( func @ X1398 @ X1399 @ X1401 )
                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1402: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1402 @ X1398 )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( ap @ X1398 @ X1399 @ X1400 @ X1402 )
                                                                                                                                                                                                                                                                                                                                                                                                                                            = ( ap @ X1398 @ X1399 @ X1401 @ X1402 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1403: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1403 @ X1398 )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1404: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1404 @ X1399 )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ( in @ ( kpair @ X1403 @ X1404 ) @ X1401 )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( in @ ( kpair @ X1403 @ X1404 ) @ X1400 ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1405: $i,X1406: $i,X1407: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1407 @ ( funcSet @ X1405 @ X1406 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1408: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1408 @ X1405 )
                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1409: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1409 @ X1406 )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( in @ ( kpair @ X1408 @ X1409 ) @ X1407 )
                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ( ap @ X1405 @ X1406 @ X1407 @ X1408 )
                                                                                                                                                                                                                                                                                                                                                                                                                                              = X1409 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1410: $i,X1411: $i,X1412: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( subset @ X1412 @ ( cartprod @ X1410 @ X1411 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1413: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( subset @ X1413 @ ( cartprod @ X1410 @ X1411 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1414: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1414 @ X1410 )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1415: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1415 @ X1411 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( in @ ( kpair @ X1414 @ X1415 ) @ X1412 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ ( kpair @ X1414 @ X1415 ) @ X1413 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( subset @ X1412 @ X1413 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1416: $i,X1417: $i,X1418: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( subset @ X1418 @ ( cartprod @ X1416 @ X1417 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1419: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( subset @ X1419 @ ( cartprod @ X1416 @ X1417 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1420: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1420 @ X1416 )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1421: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1421 @ X1417 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( in @ ( kpair @ X1420 @ X1421 ) @ X1418 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( in @ ( kpair @ X1420 @ X1421 ) @ X1419 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1422: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1422 @ X1416 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1423: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1423 @ X1417 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( in @ ( kpair @ X1422 @ X1423 ) @ X1419 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ ( kpair @ X1422 @ X1423 ) @ X1418 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( X1418 = X1419 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1424: $i,X1425: $i,X1426: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( func @ X1424 @ X1425 @ X1426 )
                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1427: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( func @ X1424 @ X1425 @ X1427 )
                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1428: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1428 @ X1424 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( ap @ X1424 @ X1425 @ X1426 @ X1428 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                    = ( ap @ X1424 @ X1425 @ X1427 @ X1428 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( X1426 = X1427 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1429: $i,X1430: $i,X1431: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1431 @ ( funcSet @ X1429 @ X1430 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1432: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1432 @ ( funcSet @ X1429 @ X1430 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1433: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1433 @ X1429 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( ap @ X1429 @ X1430 @ X1431 @ X1433 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                      = ( ap @ X1429 @ X1430 @ X1432 @ X1433 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( X1431 = X1432 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1434: $i,X1435: $i,X1436: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1436 @ ( funcSet @ X1434 @ X1435 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1437: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1437 @ X1434 )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( ap @ X1434 @ X1435 @ X1436 @ X1437 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                  = ( ap @ X1434 @ X1435 @ X1436 @ X1437 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1438: $i,X1439: $i,X1440: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( func @ X1438 @ X1439 @ X1440 )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1441: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1441 @ X1438 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( ap @ X1438 @ X1439 @ X1440 @ X1441 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                    = ( ap @ X1438 @ X1439 @ X1440 @ X1441 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1442: $i,X1443: $i,X1444: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ! [X1445: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1445 @ X1442 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ ( X1444 @ X1445 ) @ X1443 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1446: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1446 @ X1442 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( ap @ X1442 @ X1443 @ ( lam @ X1442 @ X1443 @ X1444 ) @ X1446 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                      = ( X1444 @ X1446 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1447: $i,X1448: $i,X1449: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( func @ X1447 @ X1448 @ X1449 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( lam @ X1447 @ X1448 @ ( ap @ X1447 @ X1448 @ X1449 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                    = X1449 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1450: $i,X1451: $i,X1452: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ! [X1453: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1453 @ X1450 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ ( X1452 @ X1453 ) @ X1451 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( lam @ X1450 @ X1451 @ X1452 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                      = ( lam @ X1450 @ X1451 @ X1452 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1454: $i,X1455: $i,X1456: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ! [X1457: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1457 @ X1454 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( in @ ( X1456 @ X1457 ) @ X1455 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1458: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1458 @ X1454 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( ap @ X1454 @ X1455 @ ( lam @ X1454 @ X1455 @ X1456 ) @ X1458 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                            = ( X1456 @ X1458 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1459: $i,X1460: $i,X1461: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1461 @ ( funcSet @ X1459 @ X1460 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( lam @ X1459 @ X1460 @ ( ap @ X1459 @ X1460 @ X1461 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                          = X1461 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1462: $i,X1463: $o,X1464: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1464 @ X1462 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1465: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1465 @ X1462 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ~ X1463
                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( in @ X1465
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  @ ( dsetconstr @ X1462
                                                                                                                                                                                                                                                                                                                                                                                                                                                                    @ ^ [Z0: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( X1463
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          & ( Z0 = X1464 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        | ( ~ X1463
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          & ( Z0 = X1465 ) ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1466: $i,X1467: $o,X1468: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1468 @ X1466 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1469: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1469 @ X1466 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ~ X1467
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( dsetconstr @ X1466
                                                                                                                                                                                                                                                                                                                                                                                                                                                                      @ ^ [Z0: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( X1467
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            & ( Z0 = X1468 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          | ( ~ X1467
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            & ( Z0 = X1469 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                    = ( setadjoin @ X1469 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1470: $i,X1471: $o,X1472: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1472 @ X1470 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1473: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1473 @ X1470 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( X1471
                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ X1472
                                                                                                                                                                                                                                                                                                                                                                                                                                                                      @ ( dsetconstr @ X1470
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        @ ^ [Z0: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( X1471
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              & ( Z0 = X1472 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            | ( ~ X1471
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              & ( Z0 = X1473 ) ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1474: $i,X1475: $o,X1476: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1476 @ X1474 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1477: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1477 @ X1474 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( X1475
                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( dsetconstr @ X1474
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          @ ^ [Z0: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( X1475
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                & ( Z0 = X1476 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | ( ~ X1475
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                & ( Z0 = X1477 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        = ( setadjoin @ X1476 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1478: $i,X1479: $o,X1480: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1480 @ X1478 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1481: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1481 @ X1478 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ? [X1482: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1482
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            @ ( dsetconstr @ X1478
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              @ ^ [Z0: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( X1479
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    & ( Z0 = X1480 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  | ( ~ X1479
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    & ( Z0 = X1481 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          & ( ( dsetconstr @ X1478
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              @ ^ [Z0: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( X1479
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    & ( Z0 = X1480 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  | ( ~ X1479
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    & ( Z0 = X1481 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            = ( setadjoin @ X1482 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X4: $i,X45: $o,X2: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X2 @ X4 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X3: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X4 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( in @ ( if @ X4 @ X45 @ X2 @ X3 ) @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[ifp]),setextAx]),emptysetAx]),setadjoinAx]),powersetAx]),setunionAx]),omega0Ax]),omegaSAx]),omegaIndAx]),c_0_257]),foundationAx]),wellorderingAx]),c_0_258]),c_0_259]),c_0_260]),c_0_261]),c_0_262]),prop2setE]),emptysetE]),emptysetimpfalse]),notinemptyset]),c_0_263]),setext]),emptyI]),noeltsimpempty]),c_0_264]),c_0_265]),c_0_266]),c_0_267]),setadjoinIL]),emptyinunitempty]),setadjoinIR]),setadjoinE]),setadjoinOr]),c_0_268]),powersetI]),emptyinPowerset]),emptyInPowerset]),powersetE]),setunionI]),setunionE]),subPowSU]),c_0_269]),c_0_270]),uniqinunit]),notinsingleton]),eqinunit]),singletonsswitch]),upairsetE]),upairsetIL]),upairsetIR]),c_0_271]),vacuousDall]),quantDeMorgan1]),quantDeMorgan2]),quantDeMorgan3]),quantDeMorgan4]),prop2setI]),prop2set2propI]),notdexE]),notdallE]),c_0_272]),c_0_273]),c_0_274]),inCongP]),in__Cong]),c_0_275]),c_0_276]),emptyset__Cong]),setadjoin__Cong]),powerset__Cong]),setunion__Cong]),omega__Cong]),c_0_277]),c_0_278]),c_0_279]),subsetI1]),eqimpsubset2]),eqimpsubset1]),subsetI2]),emptysetsubset]),subsetE]),subsetE2]),notsubsetI]),notequalI1]),notequalI2]),subsetRefl]),subsetTrans]),setadjoinSub]),setadjoinSub2]),subset2powerset]),setextsub]),subsetemptysetimpeq]),powersetI1]),powersetE1]),inPowerset]),powersetsubset]),c_0_280]),c_0_281]),binunionIL]),upairset2IR]),binunionIR]),binunionEcases]),binunionE]),binunionLsub]),binunionRsub]),binintersectI]),binintersectSubset5]),binintersectEL]),binintersectLsub]),binintersectSubset2]),binintersectSubset3]),binintersectER]),disjointsetsI1]),binintersectRsub]),binintersectSubset4]),binintersectSubset1]),bs114d]),setminusI]),setminusEL]),setminusER]),setminusSubset2]),setminusERneg]),setminusELneg]),setminusILneg]),setminusIRneg]),setminusLsub]),setminusSubset1]),symdiffE]),symdiffI1]),symdiffI2]),symdiffIneg1]),symdiffIneg2]),secondinupair]),setukpairIL]),setukpairIR]),kpairiskpair]),kpairp]),singletonsubset]),singletoninpowerset]),singletoninpowunion]),upairset2E]),upairsubunion]),upairinpowunion]),ubforcartprodlem1]),ubforcartprodlem2]),ubforcartprodlem3]),cartprodpairin]),cartprodmempair1]),cartprodmempair]),setunionE2]),setunionsingleton1]),setunionsingleton2]),setunionsingleton]),c_0_282]),c_0_283]),c_0_284]),c_0_285]),singletonsuniq]),setukpairinjL1]),c_0_286]),c_0_287]),kfstpairEq]),cartprodfstin]),setukpairinjL2]),setukpairinjL]),setukpairinjR11]),setukpairinjR12]),setukpairinjR1]),upairequniteq]),setukpairinjR2]),setukpairinjR]),c_0_288]),ksndpairEq]),kpairsurjEq]),cartprodsndin]),cartprodpairmemEL]),cartprodpairmemER]),cartprodmempaircEq]),cartprodfstpairEq]),cartprodsndpairEq]),cartprodpairsurjEq]),c_0_289]),c_0_290]),c_0_291]),c_0_292]),c_0_293]),c_0_294]),c_0_295]),c_0_296]),c_0_297]),app]),infuncsetfunc]),ap2p]),funcinfuncset]),c_0_298]),c_0_299]),c_0_300]),c_0_301]),c_0_302]),c_0_303]),funcGraphProp1]),funcGraphProp3]),funcGraphProp2]),funcextLem]),funcGraphProp4]),c_0_304]),c_0_305]),funcext]),funcext2]),ap2apEq1]),ap2apEq2]),c_0_306]),c_0_307]),c_0_308]),c_0_309]),c_0_310]),c_0_311]),c_0_312]),c_0_313]),c_0_314]),c_0_315])])]),c_0_316]) ).

thf(c_0_318,plain,
    ! [X1483: $i,X1484: $o,X1485: $i,X1486: $i] :
      ( ( if @ X1483 @ X1484 @ X1485 @ X1486 )
      = ( setunion
        @ ( dsetconstr @ X1483
          @ ^ [Z0: $i] :
              ( ( X1484
                & ( Z0 = X1485 ) )
              | ( ~ X1484
                & ( Z0 = X1486 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[if])]) ).

thf(c_0_319,negated_conjecture,
    ! [X1491: $i,X1492: $i,X1494: $i,X1495: $i,X1496: $i,X1497: $i,X1498: $i,X1499: $i,X1500: $i,X1501: $i,X1502: $i,X1504: $i,X1505: $i,X1507: $i,X1508: $i,X1509: $i,X1510: $i,X1511: $i,X1513: $i,X1514: $i > $i > $o,X1515: $i,X1517: $i,X1520: $i,X1522: $i,X1523: $i,X1524: $i,X1525: $i,X1527: $i,X1528: $i > $o,X1529: $i,X1531: $i,X1532: $i > $o,X1533: $i,X1534: $i,X1535: $i > $o,X1536: $i,X1537: $i,X1538: $i > $o,X1539: $i,X1540: $i > $o,X1541: $i,X1544: $i,X1545: $o,X1546: $i,X1547: $i,X1548: $o,X1549: $i,X1550: $i,X1551: $i > $o,X1552: $i,X1555: $i,X1556: $i,X1559: $i,X1561: $i,X1563: $i,X1564: $i > $o,X1565: $i,X1566: $i,X1568: $i,X1569: $i > $o,X1570: $i,X1571: $i,X1572: $i,X1573: $i,X1574: $i,X1575: $i,X1576: $i,X1577: $i,X1578: $i,X1579: $i,X1580: $i,X1581: $o,X1582: $i,X1583: $i,X1584: $i,X1585: $i,X1586: $i,X1587: $i,X1589: $i,X1590: $i,X1591: $i,X1592: $i,X1593: $i,X1594: $i,X1595: $i,X1596: $i,X1597: $i,X1598: $i,X1599: $o,X1601: $i,X1602: $i,X1603: $i > $o,X1604: $i,X1607: $i,X1608: $i,X1609: $i,X1611: $i,X1612: $i,X1613: $i,X1614: $i,X1615: $i,X1616: $i,X1617: $i,X1618: $i,X1619: $i,X1620: $i,X1621: $i,X1622: $i,X1623: $i,X1624: $i,X1625: $i,X1626: $i,X1627: $i > $o,X1628: $i,X1629: $i > $o,X1630: $i,X1631: $i,X1632: $i > $o,X1633: $i,X1635: $i,X1636: $i > $o,X1638: $i,X1639: $i,X1640: $i > $o,X1642: $i,X1643: $i,X1644: $i > $o,X1645: $i,X1647: $o,X1648: $o,X1649: $i,X1650: $i > $o,X1652: $i,X1653: $i,X1654: $i > $o,X1655: $i,X1657: $i > $o,X1658: $i,X1661: $i,X1662: $i > $o,X1663: $i,X1667: $i,X1668: $i > $o,X1669: $i,X1672: $i,X1673: $i,X1674: $i,X1675: $i,X1676: $i,X1677: $i,X1678: $i,X1679: $i,X1680: $i,X1681: $i > $o,X1682: $i,X1684: $i,X1685: $i,X1686: $i > $o,X1687: $i > $o,X1690: $i,X1693: $i,X1694: $i,X1697: $i,X1698: $i,X1699: $i,X1700: $i,X1701: $i,X1702: $i,X1703: $i,X1704: $i,X1705: $i,X1706: $i > $o,X1707: $i,X1709: $i,X1710: $i,X1711: $i > $o,X1712: $i > $o,X1715: $i,X1717: $i,X1719: $i,X1720: $i,X1721: $i > $o,X1722: $i > $o,X1725: $i,X1726: $i,X1728: $i,X1729: $i,X1730: $i,X1731: $i,X1732: $i,X1733: $i,X1735: $i,X1736: $i,X1737: $i,X1738: $i,X1739: $i,X1740: $i,X1741: $i,X1742: $i,X1743: $i,X1744: $i,X1745: $i,X1746: $i,X1747: $i,X1748: $i,X1749: $i,X1750: $i,X1751: $i,X1752: $i,X1753: $i,X1754: $i,X1755: $i,X1756: $i,X1757: $i,X1758: $i,X1759: $i,X1760: $i,X1761: $i,X1762: $i,X1763: $i,X1764: $i,X1765: $i,X1766: $i,X1767: $i,X1768: $i,X1769: $i,X1770: $i,X1771: $i,X1772: $i > $o,X1773: $i,X1774: $i > $o,X1775: $i,X1776: $i,X1777: $i,X1778: $i,X1779: $i,X1780: $i,X1781: $i,X1782: $i,X1783: $i,X1784: $i,X1785: $i,X1786: $o,X1787: $i,X1788: $i,X1789: $i,X1790: $i,X1791: $i,X1792: $i,X1793: $i,X1794: $i,X1795: $i,X1796: $i,X1797: $i,X1798: $i,X1799: $i,X1800: $i,X1801: $i,X1802: $i,X1803: $i,X1804: $i,X1805: $i,X1806: $i,X1807: $i,X1808: $i,X1809: $i,X1810: $i,X1811: $i,X1812: $i,X1813: $i,X1815: $i,X1816: $i,X1817: $i,X1818: $i,X1819: $i,X1820: $i,X1821: $i,X1822: $i,X1823: $i,X1824: $i,X1825: $i,X1826: $i,X1827: $i,X1828: $i,X1829: $i,X1830: $i,X1831: $i,X1832: $i,X1833: $i,X1834: $i,X1835: $i,X1836: $i,X1837: $i,X1838: $i,X1839: $i,X1840: $i,X1841: $i,X1842: $i,X1843: $i,X1844: $i,X1845: $i,X1846: $i,X1847: $i,X1848: $i,X1849: $i,X1850: $i,X1851: $i,X1852: $i,X1853: $i,X1854: $o,X1855: $i,X1856: $i,X1857: $i,X1858: $i,X1859: $i,X1860: $i,X1861: $i,X1862: $i,X1863: $i,X1864: $i,X1865: $i,X1866: $i,X1867: $i,X1868: $i,X1869: $i,X1870: $i,X1871: $i,X1872: $i,X1873: $i,X1874: $i,X1875: $i,X1876: $i,X1877: $i,X1878: $i,X1879: $i,X1880: $i,X1881: $i,X1882: $i,X1883: $i,X1884: $i,X1885: $i,X1886: $i,X1887: $i,X1888: $i,X1889: $i,X1890: $i,X1891: $i,X1892: $i,X1893: $i,X1894: $i,X1895: $i,X1896: $i,X1897: $i,X1898: $i,X1899: $i,X1900: $i,X1901: $i,X1902: $i,X1903: $i,X1904: $i,X1905: $i,X1906: $i,X1907: $i,X1908: $i,X1909: $i,X1910: $i,X1911: $i,X1912: $i,X1913: $i,X1916: $i,X1917: $i,X1918: $i,X1919: $i,X1920: $i,X1922: $i,X1923: $i,X1924: $i,X1925: $i,X1926: $i > $o,X1929: $i,X1931: $i,X1932: $i > $o,X1933: $i,X1935: $i,X1936: $i > $o,X1937: $i,X1940: $i,X1941: $i > $o,X1944: $i,X1946: $i,X1947: $i,X1948: $i,X1949: $i,X1950: $i,X1951: $i,X1953: $i,X1954: $i,X1955: $i,X1956: $i,X1957: $i,X1958: $i,X1959: $i,X1960: $i,X1961: $i,X1962: $i,X1963: $i,X1964: $i,X1965: $i,X1966: $i,X1967: $i,X1968: $i,X1969: $i,X1970: $i,X1971: $i,X1972: $i,X1973: $i,X1974: $i,X1975: $i,X1976: $i,X1977: $i,X1978: $i,X1979: $i,X1980: $i,X1981: $i,X1982: $i,X1983: $i,X1984: $i,X1985: $i,X1986: $i,X1987: $i,X1989: $i,X1990: $i,X1991: $i,X1992: $i,X1993: $i,X1994: $i,X1995: $i,X1996: $i,X1997: $i,X1998: $i,X1999: $i,X2000: $i,X2001: $i,X2002: $i,X2003: $i,X2004: $i,X2005: $i,X2006: $i,X2007: $i,X2008: $i,X2009: $i,X2010: $i,X2011: $i,X2012: $i,X2013: $i,X2014: $i,X2015: $i,X2016: $i,X2017: $i,X2018: $i,X2019: $i,X2020: $i > $i > $o,X2021: $i,X2022: $i,X2023: $i,X2024: $i,X2025: $i > $i > $o,X2026: $i,X2027: $i,X2028: $i > $i > $o,X2029: $i,X2030: $i,X2031: $i > $i > $o,X2032: $i,X2033: $i,X2034: $i,X2035: $i,X2036: $i > $i > $o,X2037: $i,X2038: $i,X2039: $i,X2040: $i,X2041: $i > $i > $o,X2042: $i,X2043: $i,X2044: $i,X2045: $i,X2046: $i > $i > $o,X2047: $i,X2048: $i,X2049: $i,X2050: $i,X2051: $i,X2052: $i,X2054: $i,X2055: $i,X2056: $i,X2057: $i,X2058: $i,X2059: $i,X2060: $i,X2061: $i,X2062: $i,X2063: $i,X2064: $i,X2065: $i,X2066: $i,X2067: $i,X2068: $i,X2069: $i,X2070: $i,X2071: $i,X2072: $i,X2073: $i,X2074: $i > $i,X2076: $i,X2077: $i,X2078: $i > $i,X2080: $i,X2081: $i,X2082: $i > $i,X2084: $i,X2085: $i,X2086: $i,X2087: $i > $o,X2090: $i,X2091: $i,X2092: $i,X2093: $i,X2094: $i > $o,X2097: $i,X2098: $i,X2099: $i > $o,X2100: $i,X2101: $i,X2102: $i,X2103: $i,X2104: $i,X2105: $i,X2106: $i,X2107: $i,X2108: $i,X2109: $i,X2110: $i,X2111: $i,X2112: $i,X2113: $i,X2114: $i,X2115: $i,X2116: $i,X2117: $i,X2118: $i,X2119: $i,X2121: $i,X2122: $i,X2123: $i,X2124: $i,X2125: $i,X2126: $i,X2127: $i,X2128: $i,X2129: $i,X2130: $i,X2131: $i,X2134: $i,X2135: $i,X2136: $i,X2137: $i,X2142: $i,X2143: $i,X2144: $i,X2145: $i,X2147: $i,X2148: $i,X2149: $i,X2150: $i,X2152: $i,X2153: $i,X2154: $i,X2155: $i,X2156: $i,X2157: $i,X2158: $i,X2159: $i,X2160: $i,X2161: $i,X2162: $i > $i,X2164: $i,X2165: $i,X2166: $i,X2167: $i,X2168: $i,X2169: $i,X2170: $i > $i,X2172: $i,X2173: $i,X2174: $i > $i,X2176: $i,X2177: $i,X2178: $i,X2179: $i,X2180: $i,X2181: $o,X2182: $i,X2183: $i,X2184: $i,X2185: $o,X2186: $i,X2187: $i,X2188: $i,X2189: $o,X2190: $i,X2191: $i,X2192: $i,X2193: $o,X2194: $i,X2195: $i,X2196: $i,X2197: $o,X2198: $i,X2199: $i] :
      ( ( ~ ( in @ ( esk1_2 @ X1491 @ X1492 ) @ X1491 )
        | ~ ( in @ ( esk1_2 @ X1491 @ X1492 ) @ X1492 )
        | ( X1491 = X1492 ) )
      & ( ( in @ ( esk1_2 @ X1491 @ X1492 ) @ X1491 )
        | ( in @ ( esk1_2 @ X1491 @ X1492 ) @ X1492 )
        | ( X1491 = X1492 ) )
      & ~ ( in @ X1494 @ emptyset )
      & ( ~ ( in @ X1497 @ ( setadjoin @ X1495 @ X1496 ) )
        | ( X1497 = X1495 )
        | ( in @ X1497 @ X1496 ) )
      & ( ( X1497 != X1495 )
        | ( in @ X1497 @ ( setadjoin @ X1495 @ X1496 ) ) )
      & ( ~ ( in @ X1497 @ X1496 )
        | ( in @ X1497 @ ( setadjoin @ X1495 @ X1496 ) ) )
      & ( ~ ( in @ X1499 @ ( powerset @ X1498 ) )
        | ~ ( in @ X1500 @ X1499 )
        | ( in @ X1500 @ X1498 ) )
      & ( ( in @ ( esk2_2 @ X1501 @ X1502 ) @ X1502 )
        | ( in @ X1502 @ ( powerset @ X1501 ) ) )
      & ( ~ ( in @ ( esk2_2 @ X1501 @ X1502 ) @ X1501 )
        | ( in @ X1502 @ ( powerset @ X1501 ) ) )
      & ( ( in @ X1505 @ ( esk3_2 @ X1504 @ X1505 ) )
        | ~ ( in @ X1505 @ ( setunion @ X1504 ) ) )
      & ( ( in @ ( esk3_2 @ X1504 @ X1505 ) @ X1504 )
        | ~ ( in @ X1505 @ ( setunion @ X1504 ) ) )
      & ( ~ ( in @ X1508 @ X1509 )
        | ~ ( in @ X1509 @ X1507 )
        | ( in @ X1508 @ ( setunion @ X1507 ) ) )
      & ( in @ emptyset @ omega )
      & ( ~ ( in @ X1510 @ omega )
        | ( in @ ( setadjoin @ X1510 @ X1510 ) @ omega ) )
      & ( ( in @ ( esk4_1 @ X1511 ) @ omega )
        | ~ ( in @ emptyset @ X1511 )
        | ~ ( in @ X1513 @ omega )
        | ( in @ X1513 @ X1511 ) )
      & ( ( in @ ( esk4_1 @ X1511 ) @ X1511 )
        | ~ ( in @ emptyset @ X1511 )
        | ~ ( in @ X1513 @ omega )
        | ( in @ X1513 @ X1511 ) )
      & ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X1511 ) @ ( esk4_1 @ X1511 ) ) @ X1511 )
        | ~ ( in @ emptyset @ X1511 )
        | ~ ( in @ X1513 @ omega )
        | ( in @ X1513 @ X1511 ) )
      & ( ( in @ ( esk8_3 @ X1514 @ X1515 @ X1520 ) @ X1515 )
        | ~ ( in @ X1520 @ ( esk7_2 @ X1514 @ X1515 ) )
        | ( in @ ( esk5_2 @ X1514 @ X1515 ) @ X1515 ) )
      & ( ( X1514 @ ( esk8_3 @ X1514 @ X1515 @ X1520 ) @ X1520 )
        | ~ ( in @ X1520 @ ( esk7_2 @ X1514 @ X1515 ) )
        | ( in @ ( esk5_2 @ X1514 @ X1515 ) @ X1515 ) )
      & ( ~ ( in @ X1523 @ X1515 )
        | ~ ( X1514 @ X1523 @ X1522 )
        | ( in @ X1522 @ ( esk7_2 @ X1514 @ X1515 ) )
        | ( in @ ( esk5_2 @ X1514 @ X1515 ) @ X1515 ) )
      & ( ( in @ ( esk8_3 @ X1514 @ X1515 @ X1520 ) @ X1515 )
        | ~ ( in @ X1520 @ ( esk7_2 @ X1514 @ X1515 ) )
        | ( X1514 @ ( esk5_2 @ X1514 @ X1515 ) @ ( esk6_3 @ X1514 @ X1515 @ X1517 ) )
        | ~ ( X1514 @ ( esk5_2 @ X1514 @ X1515 ) @ X1517 ) )
      & ( ( X1514 @ ( esk8_3 @ X1514 @ X1515 @ X1520 ) @ X1520 )
        | ~ ( in @ X1520 @ ( esk7_2 @ X1514 @ X1515 ) )
        | ( X1514 @ ( esk5_2 @ X1514 @ X1515 ) @ ( esk6_3 @ X1514 @ X1515 @ X1517 ) )
        | ~ ( X1514 @ ( esk5_2 @ X1514 @ X1515 ) @ X1517 ) )
      & ( ~ ( in @ X1523 @ X1515 )
        | ~ ( X1514 @ X1523 @ X1522 )
        | ( in @ X1522 @ ( esk7_2 @ X1514 @ X1515 ) )
        | ( X1514 @ ( esk5_2 @ X1514 @ X1515 ) @ ( esk6_3 @ X1514 @ X1515 @ X1517 ) )
        | ~ ( X1514 @ ( esk5_2 @ X1514 @ X1515 ) @ X1517 ) )
      & ( ( in @ ( esk8_3 @ X1514 @ X1515 @ X1520 ) @ X1515 )
        | ~ ( in @ X1520 @ ( esk7_2 @ X1514 @ X1515 ) )
        | ( X1517
         != ( esk6_3 @ X1514 @ X1515 @ X1517 ) )
        | ~ ( X1514 @ ( esk5_2 @ X1514 @ X1515 ) @ X1517 ) )
      & ( ( X1514 @ ( esk8_3 @ X1514 @ X1515 @ X1520 ) @ X1520 )
        | ~ ( in @ X1520 @ ( esk7_2 @ X1514 @ X1515 ) )
        | ( X1517
         != ( esk6_3 @ X1514 @ X1515 @ X1517 ) )
        | ~ ( X1514 @ ( esk5_2 @ X1514 @ X1515 ) @ X1517 ) )
      & ( ~ ( in @ X1523 @ X1515 )
        | ~ ( X1514 @ X1523 @ X1522 )
        | ( in @ X1522 @ ( esk7_2 @ X1514 @ X1515 ) )
        | ( X1517
         != ( esk6_3 @ X1514 @ X1515 @ X1517 ) )
        | ~ ( X1514 @ ( esk5_2 @ X1514 @ X1515 ) @ X1517 ) )
      & ( ( in @ ( esk9_1 @ X1524 ) @ X1524 )
        | ~ ( in @ X1525 @ X1524 ) )
      & ( ~ ( in @ X1527 @ ( esk9_1 @ X1524 ) )
        | ~ ( in @ X1527 @ X1524 )
        | ~ ( in @ X1525 @ X1524 ) )
      & epred1_0
      & ( ( X1528 @ ( esk10_2 @ X1528 @ X1529 ) )
        | ~ ( X1528 @ X1529 )
        | ( X1528 @ ( descr @ X1528 ) ) )
      & ( ( X1529
         != ( esk10_2 @ X1528 @ X1529 ) )
        | ~ ( X1528 @ X1529 )
        | ( X1528 @ ( descr @ X1528 ) ) )
      & ( ~ ( in @ X1533 @ X1531 )
        | ~ ( X1532 @ X1533 )
        | ( in @ X1533 @ ( dsetconstr @ X1531 @ X1532 ) ) )
      & ( ~ ( in @ X1536 @ ( dsetconstr @ X1534 @ X1535 ) )
        | ( in @ X1536 @ X1534 ) )
      & ( ~ ( in @ X1539 @ ( dsetconstr @ X1537 @ X1538 ) )
        | ( X1538 @ X1539 ) )
      & ( ( X1540 @ ( esk12_1 @ X1540 ) )
        | ( X1540 @ ( esk11_2 @ X1540 @ X1541 ) )
        | ~ ( X1540 @ X1541 ) )
      & ( ~ ( X1540 @ X1544 )
        | ( ( esk12_1 @ X1540 )
          = X1544 )
        | ( X1540 @ ( esk11_2 @ X1540 @ X1541 ) )
        | ~ ( X1540 @ X1541 ) )
      & ( ( X1540 @ ( esk12_1 @ X1540 ) )
        | ( X1541
         != ( esk11_2 @ X1540 @ X1541 ) )
        | ~ ( X1540 @ X1541 ) )
      & ( ~ ( X1540 @ X1544 )
        | ( ( esk12_1 @ X1540 )
          = X1544 )
        | ( X1541
         != ( esk11_2 @ X1540 @ X1541 ) )
        | ~ ( X1540 @ X1541 ) )
      & ( ~ ( in @ X1546 @ ( prop2set @ X1545 ) )
        | X1545 )
      & ( ~ ( in @ X1547 @ emptyset )
        | X1548 )
      & ( ~ ( in @ X1549 @ emptyset )
        | ~ $true )
      & ~ ( in @ X1550 @ emptyset )
      & ( ( X1551 @ ( esk13_2 @ X1551 @ X1552 ) )
        | ~ ( X1551 @ X1552 )
        | ( X1551 @ ( esk14_1 @ X1551 ) ) )
      & ( ( X1552
         != ( esk13_2 @ X1551 @ X1552 ) )
        | ~ ( X1551 @ X1552 )
        | ( X1551 @ ( esk14_1 @ X1551 ) ) )
      & ( ( in @ ( esk16_2 @ X1555 @ X1556 ) @ X1556 )
        | ( X1555 = X1556 )
        | ( in @ ( esk15_2 @ X1555 @ X1556 ) @ X1555 ) )
      & ( ~ ( in @ ( esk16_2 @ X1555 @ X1556 ) @ X1555 )
        | ( X1555 = X1556 )
        | ( in @ ( esk15_2 @ X1555 @ X1556 ) @ X1555 ) )
      & ( ( in @ ( esk16_2 @ X1555 @ X1556 ) @ X1556 )
        | ( X1555 = X1556 )
        | ~ ( in @ ( esk15_2 @ X1555 @ X1556 ) @ X1556 ) )
      & ( ~ ( in @ ( esk16_2 @ X1555 @ X1556 ) @ X1555 )
        | ( X1555 = X1556 )
        | ~ ( in @ ( esk15_2 @ X1555 @ X1556 ) @ X1556 ) )
      & ( ( in @ ( esk17_1 @ X1559 ) @ X1559 )
        | ( X1559 = emptyset ) )
      & ( ( in @ ( esk18_1 @ X1561 ) @ X1561 )
        | ( X1561 = emptyset ) )
      & ( ~ ( in @ X1565 @ ( dsetconstr @ X1563 @ X1564 ) )
        | ( X1564 @ X1565 )
        | ~ ( in @ X1565 @ X1563 ) )
      & ( ~ ( X1564 @ X1565 )
        | ( in @ X1565 @ ( dsetconstr @ X1563 @ X1564 ) )
        | ~ ( in @ X1565 @ X1563 ) )
      & ( ( X1566 = emptyset )
        | ( in @ ( esk19_1 @ X1566 ) @ X1566 ) )
      & ( ~ ( in @ X1570 @ X1568 )
        | ~ ( X1569 @ X1570 )
        | ( ( dsetconstr @ X1568 @ X1569 )
         != emptyset ) )
      & ( ~ ( in @ X1572 @ X1571 )
        | ( X1571 != emptyset ) )
      & ( in @ X1573 @ ( setadjoin @ X1573 @ X1574 ) )
      & ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
      & ( ~ ( in @ X1577 @ X1576 )
        | ( in @ X1577 @ ( setadjoin @ X1575 @ X1576 ) ) )
      & ( ( in @ X1580 @ X1579 )
        | X1581
        | ( X1580 = X1578 )
        | ~ ( in @ X1580 @ ( setadjoin @ X1578 @ X1579 ) ) )
      & ( ~ X1581
        | X1581
        | ( X1580 = X1578 )
        | ~ ( in @ X1580 @ ( setadjoin @ X1578 @ X1579 ) ) )
      & ( ( in @ X1580 @ X1579 )
        | X1581
        | ~ X1581
        | ~ ( in @ X1580 @ ( setadjoin @ X1578 @ X1579 ) ) )
      & ( ~ X1581
        | X1581
        | ~ X1581
        | ~ ( in @ X1580 @ ( setadjoin @ X1578 @ X1579 ) ) )
      & ( ~ ( in @ X1584 @ ( setadjoin @ X1582 @ X1583 ) )
        | ( X1584 = X1582 )
        | ( in @ X1584 @ X1583 ) )
      & ( ( dsetconstr @ X1585
          @ ^ [Z0: $i] : $true )
        = X1585 )
      & ( ( in @ ( esk20_2 @ X1586 @ X1587 ) @ X1587 )
        | ( in @ X1587 @ ( powerset @ X1586 ) ) )
      & ( ~ ( in @ ( esk20_2 @ X1586 @ X1587 ) @ X1586 )
        | ( in @ X1587 @ ( powerset @ X1586 ) ) )
      & ( in @ emptyset @ ( powerset @ X1589 ) )
      & ( in @ emptyset @ ( powerset @ X1590 ) )
      & ( ~ ( in @ X1592 @ ( powerset @ X1591 ) )
        | ~ ( in @ X1593 @ X1592 )
        | ( in @ X1593 @ X1591 ) )
      & ( ~ ( in @ X1595 @ X1596 )
        | ~ ( in @ X1596 @ X1594 )
        | ( in @ X1595 @ ( setunion @ X1594 ) ) )
      & ( ( in @ X1598 @ ( esk21_3 @ X1597 @ X1598 @ X1599 ) )
        | X1599
        | ~ ( in @ X1598 @ ( setunion @ X1597 ) ) )
      & ( ( in @ ( esk21_3 @ X1597 @ X1598 @ X1599 ) @ X1597 )
        | X1599
        | ~ ( in @ X1598 @ ( setunion @ X1597 ) ) )
      & ( ~ X1599
        | X1599
        | ~ ( in @ X1598 @ ( setunion @ X1597 ) ) )
      & ( ~ ( in @ X1602 @ X1601 )
        | ( in @ X1602 @ ( powerset @ ( setunion @ X1601 ) ) ) )
      & ( ~ ( X1603 @ X1607 )
        | ( X1607
          = ( esk23_1 @ X1603 ) )
        | ( X1603 @ ( esk22_2 @ X1603 @ X1604 ) )
        | ~ ( X1603 @ X1604 ) )
      & ( ( X1608
         != ( esk23_1 @ X1603 ) )
        | ( X1603 @ X1608 )
        | ( X1603 @ ( esk22_2 @ X1603 @ X1604 ) )
        | ~ ( X1603 @ X1604 ) )
      & ( ~ ( X1603 @ X1607 )
        | ( X1607
          = ( esk23_1 @ X1603 ) )
        | ( X1604
         != ( esk22_2 @ X1603 @ X1604 ) )
        | ~ ( X1603 @ X1604 ) )
      & ( ( X1608
         != ( esk23_1 @ X1603 ) )
        | ( X1603 @ X1608 )
        | ( X1604
         != ( esk22_2 @ X1603 @ X1604 ) )
        | ~ ( X1603 @ X1604 ) )
      & ( ( in @ ( esk24_1 @ X1609 ) @ X1609 )
        | ( X1609 = emptyset ) )
      & ( $true
        | ( X1609 = emptyset ) )
      & ( ~ ( in @ X1611 @ ( setadjoin @ X1612 @ emptyset ) )
        | ( X1611 = X1612 ) )
      & ( ( X1613 = X1614 )
        | ~ ( in @ X1614 @ ( setadjoin @ X1613 @ emptyset ) ) )
      & ( ( X1615 != X1616 )
        | ( in @ X1615 @ ( setadjoin @ X1616 @ emptyset ) ) )
      & ( ~ ( in @ X1617 @ ( setadjoin @ X1618 @ emptyset ) )
        | ( in @ X1618 @ ( setadjoin @ X1617 @ emptyset ) ) )
      & ( ~ ( in @ X1621 @ ( setadjoin @ X1619 @ ( setadjoin @ X1620 @ emptyset ) ) )
        | ( X1621 = X1619 )
        | ( X1621 = X1620 ) )
      & ( in @ X1622 @ ( setadjoin @ X1622 @ ( setadjoin @ X1623 @ emptyset ) ) )
      & ( in @ X1625 @ ( setadjoin @ X1624 @ ( setadjoin @ X1625 @ emptyset ) ) )
      & ( ~ ( in @ X1628 @ X1626 )
        | ~ ( X1627 @ X1628 )
        | ( ( dsetconstr @ X1626 @ X1627 )
         != emptyset )
        | ~ $true )
      & ( ~ ( in @ X1630 @ emptyset )
        | ( X1629 @ X1630 ) )
      & ( ( in @ ( esk25_2 @ X1631 @ X1632 ) @ X1631 )
        | ~ ( in @ X1633 @ X1631 )
        | ( X1632 @ X1633 ) )
      & ( ~ ( X1632 @ ( esk25_2 @ X1631 @ X1632 ) )
        | ~ ( in @ X1633 @ X1631 )
        | ( X1632 @ X1633 ) )
      & ( ( in @ ( esk26_2 @ X1635 @ X1636 ) @ X1635 )
        | ~ ( in @ X1638 @ X1635 )
        | ~ ( X1636 @ X1638 ) )
      & ( ( X1636 @ ( esk26_2 @ X1635 @ X1636 ) )
        | ~ ( in @ X1638 @ X1635 )
        | ~ ( X1636 @ X1638 ) )
      & ( ( in @ ( esk27_2 @ X1639 @ X1640 ) @ X1639 )
        | ~ ( in @ X1642 @ X1639 )
        | ~ ( X1640 @ X1642 ) )
      & ( ( X1640 @ ( esk27_2 @ X1639 @ X1640 ) )
        | ~ ( in @ X1642 @ X1639 )
        | ~ ( X1640 @ X1642 ) )
      & ( ( in @ ( esk28_2 @ X1643 @ X1644 ) @ X1643 )
        | ~ ( in @ X1645 @ X1643 )
        | ( X1644 @ X1645 ) )
      & ( ~ ( X1644 @ ( esk28_2 @ X1643 @ X1644 ) )
        | ~ ( in @ X1645 @ X1643 )
        | ( X1644 @ X1645 ) )
      & ( ~ X1647
        | ( in @ emptyset @ ( prop2set @ X1647 ) ) )
      & ( ~ X1648
        | ( set2prop @ ( prop2set @ X1648 ) ) )
      & ( ( in @ ( esk29_2 @ X1649 @ X1650 ) @ X1649 )
        | ~ ( in @ X1652 @ X1649 )
        | ~ ( X1650 @ X1652 ) )
      & ( ( X1650 @ ( esk29_2 @ X1649 @ X1650 ) )
        | ~ ( in @ X1652 @ X1649 )
        | ~ ( X1650 @ X1652 ) )
      & ( ( in @ ( esk30_2 @ X1653 @ X1654 ) @ X1653 )
        | ~ ( in @ X1655 @ X1653 )
        | ( X1654 @ X1655 ) )
      & ( ~ ( X1654 @ ( esk30_2 @ X1653 @ X1654 ) )
        | ~ ( in @ X1655 @ X1653 )
        | ( X1654 @ X1655 ) )
      & ( ( X1657 @ ( esk32_1 @ X1657 ) )
        | ( X1657 @ ( esk31_2 @ X1657 @ X1658 ) )
        | ~ ( X1657 @ X1658 ) )
      & ( ~ ( X1657 @ X1661 )
        | ( ( esk32_1 @ X1657 )
          = X1661 )
        | ( X1657 @ ( esk31_2 @ X1657 @ X1658 ) )
        | ~ ( X1657 @ X1658 ) )
      & ( ( X1657 @ ( esk32_1 @ X1657 ) )
        | ( X1658
         != ( esk31_2 @ X1657 @ X1658 ) )
        | ~ ( X1657 @ X1658 ) )
      & ( ~ ( X1657 @ X1661 )
        | ( ( esk32_1 @ X1657 )
          = X1661 )
        | ( X1658
         != ( esk31_2 @ X1657 @ X1658 ) )
        | ~ ( X1657 @ X1658 ) )
      & ( ( X1662 @ ( esk35_1 @ X1662 ) )
        | ( X1662 @ ( esk33_1 @ X1662 ) )
        | ~ ( X1662 @ X1663 ) )
      & ( ~ ( X1662 @ X1667 )
        | ( ( esk35_1 @ X1662 )
          = X1667 )
        | ( X1662 @ ( esk33_1 @ X1662 ) )
        | ~ ( X1662 @ X1663 ) )
      & ( ( X1662 @ ( esk35_1 @ X1662 ) )
        | ( X1662 @ ( esk34_1 @ X1662 ) )
        | ~ ( X1662 @ X1663 ) )
      & ( ~ ( X1662 @ X1667 )
        | ( ( esk35_1 @ X1662 )
          = X1667 )
        | ( X1662 @ ( esk34_1 @ X1662 ) )
        | ~ ( X1662 @ X1663 ) )
      & ( ( X1662 @ ( esk35_1 @ X1662 ) )
        | ( ( esk33_1 @ X1662 )
         != ( esk34_1 @ X1662 ) )
        | ~ ( X1662 @ X1663 ) )
      & ( ~ ( X1662 @ X1667 )
        | ( ( esk35_1 @ X1662 )
          = X1667 )
        | ( ( esk33_1 @ X1662 )
         != ( esk34_1 @ X1662 ) )
        | ~ ( X1662 @ X1663 ) )
      & ( ( X1668 @ ( esk37_1 @ X1668 ) )
        | ~ ( X1668 @ ( esk36_2 @ X1668 @ X1669 ) )
        | ( ( esk36_2 @ X1668 @ X1669 )
         != X1669 ) )
      & ( ~ ( X1668 @ X1672 )
        | ( ( esk37_1 @ X1668 )
          = X1672 )
        | ~ ( X1668 @ ( esk36_2 @ X1668 @ X1669 ) )
        | ( ( esk36_2 @ X1668 @ X1669 )
         != X1669 ) )
      & ( ( X1668 @ ( esk37_1 @ X1668 ) )
        | ( X1668 @ ( esk36_2 @ X1668 @ X1669 ) )
        | ( ( esk36_2 @ X1668 @ X1669 )
          = X1669 ) )
      & ( ~ ( X1668 @ X1672 )
        | ( ( esk37_1 @ X1668 )
          = X1672 )
        | ( X1668 @ ( esk36_2 @ X1668 @ X1669 ) )
        | ( ( esk36_2 @ X1668 @ X1669 )
          = X1669 ) )
      & ( ( X1673 != X1674 )
        | ( X1675 != X1676 )
        | ~ ( in @ X1675 @ X1673 )
        | ( in @ X1676 @ X1674 ) )
      & ( ~ ( in @ X1679 @ X1677 )
        | ( in @ X1680 @ X1678 )
        | ( X1679 != X1680 )
        | ( X1677 != X1678 ) )
      & ( ~ ( in @ X1680 @ X1678 )
        | ( in @ X1679 @ X1677 )
        | ( X1679 != X1680 )
        | ( X1677 != X1678 ) )
      & ( ( X1681 @ ( esk38_2 @ X1681 @ X1682 ) )
        | ~ ( X1681 @ X1682 )
        | ~ ( X1681 @ X1684 )
        | ~ ( X1681 @ X1685 )
        | ( X1684 = X1685 ) )
      & ( ( X1682
         != ( esk38_2 @ X1681 @ X1682 ) )
        | ~ ( X1681 @ X1682 )
        | ~ ( X1681 @ X1684 )
        | ~ ( X1681 @ X1685 )
        | ( X1684 = X1685 ) )
      & ( ( X1687 @ ( esk42_2 @ X1686 @ X1687 ) )
        | ( X1686 @ ( esk41_3 @ X1686 @ X1687 @ X1690 ) )
        | ~ ( X1686 @ X1690 )
        | ( ( esk39_2 @ X1686 @ X1687 )
          = ( esk40_2 @ X1686 @ X1687 ) ) )
      & ( ~ ( X1687 @ X1693 )
        | ( ( esk42_2 @ X1686 @ X1687 )
          = X1693 )
        | ( X1686 @ ( esk41_3 @ X1686 @ X1687 @ X1690 ) )
        | ~ ( X1686 @ X1690 )
        | ( ( esk39_2 @ X1686 @ X1687 )
          = ( esk40_2 @ X1686 @ X1687 ) ) )
      & ( ( X1687 @ ( esk42_2 @ X1686 @ X1687 ) )
        | ( X1690
         != ( esk41_3 @ X1686 @ X1687 @ X1690 ) )
        | ~ ( X1686 @ X1690 )
        | ( ( esk39_2 @ X1686 @ X1687 )
          = ( esk40_2 @ X1686 @ X1687 ) ) )
      & ( ~ ( X1687 @ X1693 )
        | ( ( esk42_2 @ X1686 @ X1687 )
          = X1693 )
        | ( X1690
         != ( esk41_3 @ X1686 @ X1687 @ X1690 ) )
        | ~ ( X1686 @ X1690 )
        | ( ( esk39_2 @ X1686 @ X1687 )
          = ( esk40_2 @ X1686 @ X1687 ) ) )
      & ( ( X1686 @ ( esk44_2 @ X1686 @ X1687 ) )
        | ( X1687 @ ( esk43_3 @ X1686 @ X1687 @ X1694 ) )
        | ~ ( X1687 @ X1694 )
        | ( ( esk39_2 @ X1686 @ X1687 )
          = ( esk40_2 @ X1686 @ X1687 ) ) )
      & ( ~ ( X1686 @ X1697 )
        | ( ( esk44_2 @ X1686 @ X1687 )
          = X1697 )
        | ( X1687 @ ( esk43_3 @ X1686 @ X1687 @ X1694 ) )
        | ~ ( X1687 @ X1694 )
        | ( ( esk39_2 @ X1686 @ X1687 )
          = ( esk40_2 @ X1686 @ X1687 ) ) )
      & ( ( X1686 @ ( esk44_2 @ X1686 @ X1687 ) )
        | ( X1694
         != ( esk43_3 @ X1686 @ X1687 @ X1694 ) )
        | ~ ( X1687 @ X1694 )
        | ( ( esk39_2 @ X1686 @ X1687 )
          = ( esk40_2 @ X1686 @ X1687 ) ) )
      & ( ~ ( X1686 @ X1697 )
        | ( ( esk44_2 @ X1686 @ X1687 )
          = X1697 )
        | ( X1694
         != ( esk43_3 @ X1686 @ X1687 @ X1694 ) )
        | ~ ( X1687 @ X1694 )
        | ( ( esk39_2 @ X1686 @ X1687 )
          = ( esk40_2 @ X1686 @ X1687 ) ) )
      & ( ( X1687 @ ( esk42_2 @ X1686 @ X1687 ) )
        | ( X1686 @ ( esk41_3 @ X1686 @ X1687 @ X1690 ) )
        | ~ ( X1686 @ X1690 )
        | ~ ( X1686 @ ( esk39_2 @ X1686 @ X1687 ) )
        | ~ ( X1687 @ ( esk40_2 @ X1686 @ X1687 ) ) )
      & ( ~ ( X1687 @ X1693 )
        | ( ( esk42_2 @ X1686 @ X1687 )
          = X1693 )
        | ( X1686 @ ( esk41_3 @ X1686 @ X1687 @ X1690 ) )
        | ~ ( X1686 @ X1690 )
        | ~ ( X1686 @ ( esk39_2 @ X1686 @ X1687 ) )
        | ~ ( X1687 @ ( esk40_2 @ X1686 @ X1687 ) ) )
      & ( ( X1687 @ ( esk42_2 @ X1686 @ X1687 ) )
        | ( X1690
         != ( esk41_3 @ X1686 @ X1687 @ X1690 ) )
        | ~ ( X1686 @ X1690 )
        | ~ ( X1686 @ ( esk39_2 @ X1686 @ X1687 ) )
        | ~ ( X1687 @ ( esk40_2 @ X1686 @ X1687 ) ) )
      & ( ~ ( X1687 @ X1693 )
        | ( ( esk42_2 @ X1686 @ X1687 )
          = X1693 )
        | ( X1690
         != ( esk41_3 @ X1686 @ X1687 @ X1690 ) )
        | ~ ( X1686 @ X1690 )
        | ~ ( X1686 @ ( esk39_2 @ X1686 @ X1687 ) )
        | ~ ( X1687 @ ( esk40_2 @ X1686 @ X1687 ) ) )
      & ( ( X1686 @ ( esk44_2 @ X1686 @ X1687 ) )
        | ( X1687 @ ( esk43_3 @ X1686 @ X1687 @ X1694 ) )
        | ~ ( X1687 @ X1694 )
        | ~ ( X1686 @ ( esk39_2 @ X1686 @ X1687 ) )
        | ~ ( X1687 @ ( esk40_2 @ X1686 @ X1687 ) ) )
      & ( ~ ( X1686 @ X1697 )
        | ( ( esk44_2 @ X1686 @ X1687 )
          = X1697 )
        | ( X1687 @ ( esk43_3 @ X1686 @ X1687 @ X1694 ) )
        | ~ ( X1687 @ X1694 )
        | ~ ( X1686 @ ( esk39_2 @ X1686 @ X1687 ) )
        | ~ ( X1687 @ ( esk40_2 @ X1686 @ X1687 ) ) )
      & ( ( X1686 @ ( esk44_2 @ X1686 @ X1687 ) )
        | ( X1694
         != ( esk43_3 @ X1686 @ X1687 @ X1694 ) )
        | ~ ( X1687 @ X1694 )
        | ~ ( X1686 @ ( esk39_2 @ X1686 @ X1687 ) )
        | ~ ( X1687 @ ( esk40_2 @ X1686 @ X1687 ) ) )
      & ( ~ ( X1686 @ X1697 )
        | ( ( esk44_2 @ X1686 @ X1687 )
          = X1697 )
        | ( X1694
         != ( esk43_3 @ X1686 @ X1687 @ X1694 ) )
        | ~ ( X1687 @ X1694 )
        | ~ ( X1686 @ ( esk39_2 @ X1686 @ X1687 ) )
        | ~ ( X1687 @ ( esk40_2 @ X1686 @ X1687 ) ) )
      & ( ( X1687 @ ( esk42_2 @ X1686 @ X1687 ) )
        | ( X1686 @ ( esk41_3 @ X1686 @ X1687 @ X1690 ) )
        | ~ ( X1686 @ X1690 )
        | ( X1686 @ ( esk39_2 @ X1686 @ X1687 ) )
        | ( X1687 @ ( esk40_2 @ X1686 @ X1687 ) ) )
      & ( ~ ( X1687 @ X1693 )
        | ( ( esk42_2 @ X1686 @ X1687 )
          = X1693 )
        | ( X1686 @ ( esk41_3 @ X1686 @ X1687 @ X1690 ) )
        | ~ ( X1686 @ X1690 )
        | ( X1686 @ ( esk39_2 @ X1686 @ X1687 ) )
        | ( X1687 @ ( esk40_2 @ X1686 @ X1687 ) ) )
      & ( ( X1687 @ ( esk42_2 @ X1686 @ X1687 ) )
        | ( X1690
         != ( esk41_3 @ X1686 @ X1687 @ X1690 ) )
        | ~ ( X1686 @ X1690 )
        | ( X1686 @ ( esk39_2 @ X1686 @ X1687 ) )
        | ( X1687 @ ( esk40_2 @ X1686 @ X1687 ) ) )
      & ( ~ ( X1687 @ X1693 )
        | ( ( esk42_2 @ X1686 @ X1687 )
          = X1693 )
        | ( X1690
         != ( esk41_3 @ X1686 @ X1687 @ X1690 ) )
        | ~ ( X1686 @ X1690 )
        | ( X1686 @ ( esk39_2 @ X1686 @ X1687 ) )
        | ( X1687 @ ( esk40_2 @ X1686 @ X1687 ) ) )
      & ( ( X1686 @ ( esk44_2 @ X1686 @ X1687 ) )
        | ( X1687 @ ( esk43_3 @ X1686 @ X1687 @ X1694 ) )
        | ~ ( X1687 @ X1694 )
        | ( X1686 @ ( esk39_2 @ X1686 @ X1687 ) )
        | ( X1687 @ ( esk40_2 @ X1686 @ X1687 ) ) )
      & ( ~ ( X1686 @ X1697 )
        | ( ( esk44_2 @ X1686 @ X1687 )
          = X1697 )
        | ( X1687 @ ( esk43_3 @ X1686 @ X1687 @ X1694 ) )
        | ~ ( X1687 @ X1694 )
        | ( X1686 @ ( esk39_2 @ X1686 @ X1687 ) )
        | ( X1687 @ ( esk40_2 @ X1686 @ X1687 ) ) )
      & ( ( X1686 @ ( esk44_2 @ X1686 @ X1687 ) )
        | ( X1694
         != ( esk43_3 @ X1686 @ X1687 @ X1694 ) )
        | ~ ( X1687 @ X1694 )
        | ( X1686 @ ( esk39_2 @ X1686 @ X1687 ) )
        | ( X1687 @ ( esk40_2 @ X1686 @ X1687 ) ) )
      & ( ~ ( X1686 @ X1697 )
        | ( ( esk44_2 @ X1686 @ X1687 )
          = X1697 )
        | ( X1694
         != ( esk43_3 @ X1686 @ X1687 @ X1694 ) )
        | ~ ( X1687 @ X1694 )
        | ( X1686 @ ( esk39_2 @ X1686 @ X1687 ) )
        | ( X1687 @ ( esk40_2 @ X1686 @ X1687 ) ) )
      & ( emptyset = emptyset )
      & ( ( X1698 != X1699 )
        | ( X1700 != X1701 )
        | ( ( setadjoin @ X1698 @ X1700 )
          = ( setadjoin @ X1699 @ X1701 ) ) )
      & ( ( X1702 != X1703 )
        | ( ( powerset @ X1702 )
          = ( powerset @ X1703 ) ) )
      & ( ( X1704 != X1705 )
        | ( ( setunion @ X1704 )
          = ( setunion @ X1705 ) ) )
      & ( omega = omega )
      & ( ( X1706 @ ( esk45_2 @ X1706 @ X1707 ) )
        | ~ ( X1706 @ X1707 )
        | ~ ( X1706 @ X1709 )
        | ~ ( X1706 @ X1710 )
        | ( X1709 = X1710 ) )
      & ( ( X1707
         != ( esk45_2 @ X1706 @ X1707 ) )
        | ~ ( X1706 @ X1707 )
        | ~ ( X1706 @ X1709 )
        | ~ ( X1706 @ X1710 )
        | ( X1709 = X1710 ) )
      & ( ( X1712 @ ( esk49_3 @ X1711 @ X1712 @ X1717 ) )
        | ~ ( X1712 @ X1717 )
        | ( ( descr @ X1711 )
          = ( descr @ X1712 ) )
        | ( X1711 @ ( esk48_3 @ X1711 @ X1712 @ X1715 ) )
        | ~ ( X1711 @ X1715 )
        | ( ( esk46_2 @ X1711 @ X1712 )
          = ( esk47_2 @ X1711 @ X1712 ) ) )
      & ( ( X1717
         != ( esk49_3 @ X1711 @ X1712 @ X1717 ) )
        | ~ ( X1712 @ X1717 )
        | ( ( descr @ X1711 )
          = ( descr @ X1712 ) )
        | ( X1711 @ ( esk48_3 @ X1711 @ X1712 @ X1715 ) )
        | ~ ( X1711 @ X1715 )
        | ( ( esk46_2 @ X1711 @ X1712 )
          = ( esk47_2 @ X1711 @ X1712 ) ) )
      & ( ( X1712 @ ( esk49_3 @ X1711 @ X1712 @ X1717 ) )
        | ~ ( X1712 @ X1717 )
        | ( ( descr @ X1711 )
          = ( descr @ X1712 ) )
        | ( X1715
         != ( esk48_3 @ X1711 @ X1712 @ X1715 ) )
        | ~ ( X1711 @ X1715 )
        | ( ( esk46_2 @ X1711 @ X1712 )
          = ( esk47_2 @ X1711 @ X1712 ) ) )
      & ( ( X1717
         != ( esk49_3 @ X1711 @ X1712 @ X1717 ) )
        | ~ ( X1712 @ X1717 )
        | ( ( descr @ X1711 )
          = ( descr @ X1712 ) )
        | ( X1715
         != ( esk48_3 @ X1711 @ X1712 @ X1715 ) )
        | ~ ( X1711 @ X1715 )
        | ( ( esk46_2 @ X1711 @ X1712 )
          = ( esk47_2 @ X1711 @ X1712 ) ) )
      & ( ( X1712 @ ( esk49_3 @ X1711 @ X1712 @ X1717 ) )
        | ~ ( X1712 @ X1717 )
        | ( ( descr @ X1711 )
          = ( descr @ X1712 ) )
        | ( X1711 @ ( esk48_3 @ X1711 @ X1712 @ X1715 ) )
        | ~ ( X1711 @ X1715 )
        | ~ ( X1711 @ ( esk46_2 @ X1711 @ X1712 ) )
        | ~ ( X1712 @ ( esk47_2 @ X1711 @ X1712 ) ) )
      & ( ( X1717
         != ( esk49_3 @ X1711 @ X1712 @ X1717 ) )
        | ~ ( X1712 @ X1717 )
        | ( ( descr @ X1711 )
          = ( descr @ X1712 ) )
        | ( X1711 @ ( esk48_3 @ X1711 @ X1712 @ X1715 ) )
        | ~ ( X1711 @ X1715 )
        | ~ ( X1711 @ ( esk46_2 @ X1711 @ X1712 ) )
        | ~ ( X1712 @ ( esk47_2 @ X1711 @ X1712 ) ) )
      & ( ( X1712 @ ( esk49_3 @ X1711 @ X1712 @ X1717 ) )
        | ~ ( X1712 @ X1717 )
        | ( ( descr @ X1711 )
          = ( descr @ X1712 ) )
        | ( X1715
         != ( esk48_3 @ X1711 @ X1712 @ X1715 ) )
        | ~ ( X1711 @ X1715 )
        | ~ ( X1711 @ ( esk46_2 @ X1711 @ X1712 ) )
        | ~ ( X1712 @ ( esk47_2 @ X1711 @ X1712 ) ) )
      & ( ( X1717
         != ( esk49_3 @ X1711 @ X1712 @ X1717 ) )
        | ~ ( X1712 @ X1717 )
        | ( ( descr @ X1711 )
          = ( descr @ X1712 ) )
        | ( X1715
         != ( esk48_3 @ X1711 @ X1712 @ X1715 ) )
        | ~ ( X1711 @ X1715 )
        | ~ ( X1711 @ ( esk46_2 @ X1711 @ X1712 ) )
        | ~ ( X1712 @ ( esk47_2 @ X1711 @ X1712 ) ) )
      & ( ( X1712 @ ( esk49_3 @ X1711 @ X1712 @ X1717 ) )
        | ~ ( X1712 @ X1717 )
        | ( ( descr @ X1711 )
          = ( descr @ X1712 ) )
        | ( X1711 @ ( esk48_3 @ X1711 @ X1712 @ X1715 ) )
        | ~ ( X1711 @ X1715 )
        | ( X1711 @ ( esk46_2 @ X1711 @ X1712 ) )
        | ( X1712 @ ( esk47_2 @ X1711 @ X1712 ) ) )
      & ( ( X1717
         != ( esk49_3 @ X1711 @ X1712 @ X1717 ) )
        | ~ ( X1712 @ X1717 )
        | ( ( descr @ X1711 )
          = ( descr @ X1712 ) )
        | ( X1711 @ ( esk48_3 @ X1711 @ X1712 @ X1715 ) )
        | ~ ( X1711 @ X1715 )
        | ( X1711 @ ( esk46_2 @ X1711 @ X1712 ) )
        | ( X1712 @ ( esk47_2 @ X1711 @ X1712 ) ) )
      & ( ( X1712 @ ( esk49_3 @ X1711 @ X1712 @ X1717 ) )
        | ~ ( X1712 @ X1717 )
        | ( ( descr @ X1711 )
          = ( descr @ X1712 ) )
        | ( X1715
         != ( esk48_3 @ X1711 @ X1712 @ X1715 ) )
        | ~ ( X1711 @ X1715 )
        | ( X1711 @ ( esk46_2 @ X1711 @ X1712 ) )
        | ( X1712 @ ( esk47_2 @ X1711 @ X1712 ) ) )
      & ( ( X1717
         != ( esk49_3 @ X1711 @ X1712 @ X1717 ) )
        | ~ ( X1712 @ X1717 )
        | ( ( descr @ X1711 )
          = ( descr @ X1712 ) )
        | ( X1715
         != ( esk48_3 @ X1711 @ X1712 @ X1715 ) )
        | ~ ( X1711 @ X1715 )
        | ( X1711 @ ( esk46_2 @ X1711 @ X1712 ) )
        | ( X1712 @ ( esk47_2 @ X1711 @ X1712 ) ) )
      & ( ( in @ ( esk50_4 @ X1719 @ X1720 @ X1721 @ X1722 ) @ X1719 )
        | ( ( dsetconstr @ X1719 @ X1721 )
          = ( dsetconstr @ X1720 @ X1722 ) )
        | ( X1719 != X1720 ) )
      & ( ( in @ ( esk51_4 @ X1719 @ X1720 @ X1721 @ X1722 ) @ X1720 )
        | ( ( dsetconstr @ X1719 @ X1721 )
          = ( dsetconstr @ X1720 @ X1722 ) )
        | ( X1719 != X1720 ) )
      & ( ( ( esk50_4 @ X1719 @ X1720 @ X1721 @ X1722 )
          = ( esk51_4 @ X1719 @ X1720 @ X1721 @ X1722 ) )
        | ( ( dsetconstr @ X1719 @ X1721 )
          = ( dsetconstr @ X1720 @ X1722 ) )
        | ( X1719 != X1720 ) )
      & ( ~ ( X1721 @ ( esk50_4 @ X1719 @ X1720 @ X1721 @ X1722 ) )
        | ~ ( X1722 @ ( esk51_4 @ X1719 @ X1720 @ X1721 @ X1722 ) )
        | ( ( dsetconstr @ X1719 @ X1721 )
          = ( dsetconstr @ X1720 @ X1722 ) )
        | ( X1719 != X1720 ) )
      & ( ( X1721 @ ( esk50_4 @ X1719 @ X1720 @ X1721 @ X1722 ) )
        | ( X1722 @ ( esk51_4 @ X1719 @ X1720 @ X1721 @ X1722 ) )
        | ( ( dsetconstr @ X1719 @ X1721 )
          = ( dsetconstr @ X1720 @ X1722 ) )
        | ( X1719 != X1720 ) )
      & ( ( in @ ( esk52_2 @ X1725 @ X1726 ) @ X1725 )
        | ( subset @ X1725 @ X1726 ) )
      & ( ~ ( in @ ( esk52_2 @ X1725 @ X1726 ) @ X1726 )
        | ( subset @ X1725 @ X1726 ) )
      & ( ( X1728 != X1729 )
        | ( subset @ X1729 @ X1728 ) )
      & ( ( X1730 != X1731 )
        | ( subset @ X1730 @ X1731 ) )
      & ( ( in @ ( esk53_2 @ X1732 @ X1733 ) @ X1732 )
        | ( subset @ X1732 @ X1733 ) )
      & ( ~ ( in @ ( esk53_2 @ X1732 @ X1733 ) @ X1733 )
        | ( subset @ X1732 @ X1733 ) )
      & ( subset @ emptyset @ X1735 )
      & ( ~ ( subset @ X1736 @ X1737 )
        | ~ ( in @ X1738 @ X1736 )
        | ( in @ X1738 @ X1737 ) )
      & ( ~ ( subset @ X1739 @ X1740 )
        | ( in @ X1741 @ X1740 )
        | ~ ( in @ X1741 @ X1739 ) )
      & ( ~ ( in @ X1744 @ X1742 )
        | ( in @ X1744 @ X1743 )
        | ~ ( subset @ X1742 @ X1743 ) )
      & ( ( subset @ X1745 @ X1746 )
        | ( X1745 != X1746 ) )
      & ( ~ ( in @ X1749 @ X1747 )
        | ( in @ X1749 @ X1748 )
        | ( X1747 != X1748 ) )
      & ( subset @ X1750 @ X1750 )
      & ( ~ ( subset @ X1751 @ X1752 )
        | ~ ( subset @ X1752 @ X1753 )
        | ( subset @ X1751 @ X1753 ) )
      & ( subset @ X1755 @ ( setadjoin @ X1754 @ X1755 ) )
      & ( ~ ( subset @ X1756 @ X1758 )
        | ( subset @ X1756 @ ( setadjoin @ X1757 @ X1758 ) ) )
      & ( ~ ( subset @ X1759 @ X1760 )
        | ( in @ X1759 @ ( powerset @ X1760 ) ) )
      & ( ~ ( subset @ X1761 @ X1762 )
        | ~ ( subset @ X1762 @ X1761 )
        | ( X1761 = X1762 ) )
      & ( ~ ( subset @ X1763 @ emptyset )
        | ( X1763 = emptyset ) )
      & ( ~ ( subset @ X1765 @ X1764 )
        | ( in @ X1765 @ ( powerset @ X1764 ) ) )
      & ( ~ ( in @ X1767 @ ( powerset @ X1766 ) )
        | ( subset @ X1767 @ X1766 ) )
      & ( in @ X1768 @ ( powerset @ X1768 ) )
      & ( ~ ( subset @ X1769 @ X1770 )
        | ( subset @ ( powerset @ X1769 ) @ ( powerset @ X1770 ) ) )
      & ( in @ ( dsetconstr @ X1771 @ X1772 ) @ ( powerset @ X1771 ) )
      & ( subset @ ( dsetconstr @ X1773 @ X1774 ) @ X1773 )
      & ( ~ ( in @ X1777 @ X1775 )
        | ( in @ X1777 @ ( binunion @ X1775 @ X1776 ) ) )
      & ( in @ X1779 @ ( setadjoin @ X1778 @ ( setadjoin @ X1779 @ emptyset ) ) )
      & ( ~ ( in @ X1782 @ X1781 )
        | ( in @ X1782 @ ( binunion @ X1780 @ X1781 ) ) )
      & ( ( in @ X1785 @ X1784 )
        | X1786
        | ( in @ X1785 @ X1783 )
        | ~ ( in @ X1785 @ ( binunion @ X1783 @ X1784 ) ) )
      & ( ~ X1786
        | X1786
        | ( in @ X1785 @ X1783 )
        | ~ ( in @ X1785 @ ( binunion @ X1783 @ X1784 ) ) )
      & ( ( in @ X1785 @ X1784 )
        | X1786
        | ~ X1786
        | ~ ( in @ X1785 @ ( binunion @ X1783 @ X1784 ) ) )
      & ( ~ X1786
        | X1786
        | ~ X1786
        | ~ ( in @ X1785 @ ( binunion @ X1783 @ X1784 ) ) )
      & ( ~ ( in @ X1789 @ ( binunion @ X1787 @ X1788 ) )
        | ( in @ X1789 @ X1787 )
        | ( in @ X1789 @ X1788 ) )
      & ( subset @ X1790 @ ( binunion @ X1790 @ X1791 ) )
      & ( subset @ X1793 @ ( binunion @ X1792 @ X1793 ) )
      & ( ~ ( in @ X1796 @ X1794 )
        | ~ ( in @ X1796 @ X1795 )
        | ( in @ X1796 @ ( binintersect @ X1794 @ X1795 ) ) )
      & ( ~ ( subset @ X1799 @ X1797 )
        | ~ ( subset @ X1799 @ X1798 )
        | ( subset @ X1799 @ ( binintersect @ X1797 @ X1798 ) ) )
      & ( ~ ( in @ X1802 @ ( binintersect @ X1800 @ X1801 ) )
        | ( in @ X1802 @ X1800 ) )
      & ( subset @ ( binintersect @ X1803 @ X1804 ) @ X1803 )
      & ( ~ ( subset @ X1805 @ X1806 )
        | ( ( binintersect @ X1805 @ X1806 )
          = X1805 ) )
      & ( ( ( binintersect @ X1807 @ X1808 )
         != X1808 )
        | ( subset @ X1808 @ X1807 ) )
      & ( ~ ( in @ X1811 @ ( binintersect @ X1809 @ X1810 ) )
        | ( in @ X1811 @ X1810 ) )
      & ( ( in @ ( esk54_2 @ X1812 @ X1813 ) @ X1812 )
        | ( ( binintersect @ X1812 @ X1813 )
          = emptyset ) )
      & ( ( in @ ( esk54_2 @ X1812 @ X1813 ) @ X1813 )
        | ( ( binintersect @ X1812 @ X1813 )
          = emptyset ) )
      & ( subset @ ( binintersect @ X1815 @ X1816 ) @ X1816 )
      & ( ~ ( subset @ X1818 @ X1817 )
        | ( ( binintersect @ X1817 @ X1818 )
          = X1818 ) )
      & ( ( ( binintersect @ X1819 @ X1820 )
         != X1819 )
        | ( subset @ X1819 @ X1820 ) )
      & ( ( binintersect @ X1821 @ ( binunion @ X1822 @ X1823 ) )
        = ( binunion @ ( binintersect @ X1821 @ X1822 ) @ ( binintersect @ X1821 @ X1823 ) ) )
      & ( ~ ( in @ X1826 @ X1824 )
        | ( in @ X1826 @ X1825 )
        | ( in @ X1826 @ ( setminus @ X1824 @ X1825 ) ) )
      & ( ~ ( in @ X1829 @ ( setminus @ X1827 @ X1828 ) )
        | ( in @ X1829 @ X1827 ) )
      & ( ~ ( in @ X1832 @ ( setminus @ X1830 @ X1831 ) )
        | ~ ( in @ X1832 @ X1831 ) )
      & ( ~ ( subset @ X1833 @ X1834 )
        | ( ( setminus @ X1833 @ X1834 )
          = emptyset ) )
      & ( ( in @ X1837 @ ( setminus @ X1835 @ X1836 ) )
        | ~ ( in @ X1837 @ X1835 )
        | ( in @ X1837 @ X1836 ) )
      & ( ( in @ X1840 @ ( setminus @ X1838 @ X1839 ) )
        | ( in @ X1840 @ X1839 )
        | ~ ( in @ X1840 @ X1838 ) )
      & ( ( in @ X1843 @ X1841 )
        | ~ ( in @ X1843 @ ( setminus @ X1841 @ X1842 ) ) )
      & ( ~ ( in @ X1846 @ X1845 )
        | ~ ( in @ X1846 @ ( setminus @ X1844 @ X1845 ) ) )
      & ( subset @ ( setminus @ X1847 @ X1848 ) @ X1847 )
      & ( ( ( setminus @ X1849 @ X1850 )
         != emptyset )
        | ( subset @ X1849 @ X1850 ) )
      & ( ~ ( in @ X1853 @ X1851 )
        | X1854
        | ( in @ X1853 @ X1851 )
        | ~ ( in @ X1853 @ ( symdiff @ X1851 @ X1852 ) ) )
      & ( ( in @ X1853 @ X1852 )
        | X1854
        | ( in @ X1853 @ X1851 )
        | ~ ( in @ X1853 @ ( symdiff @ X1851 @ X1852 ) ) )
      & ( ~ X1854
        | X1854
        | ( in @ X1853 @ X1851 )
        | ~ ( in @ X1853 @ ( symdiff @ X1851 @ X1852 ) ) )
      & ( ~ ( in @ X1853 @ X1851 )
        | X1854
        | ~ ( in @ X1853 @ X1852 )
        | ~ ( in @ X1853 @ ( symdiff @ X1851 @ X1852 ) ) )
      & ( ( in @ X1853 @ X1852 )
        | X1854
        | ~ ( in @ X1853 @ X1852 )
        | ~ ( in @ X1853 @ ( symdiff @ X1851 @ X1852 ) ) )
      & ( ~ X1854
        | X1854
        | ~ ( in @ X1853 @ X1852 )
        | ~ ( in @ X1853 @ ( symdiff @ X1851 @ X1852 ) ) )
      & ( ~ ( in @ X1853 @ X1851 )
        | X1854
        | ~ X1854
        | ~ ( in @ X1853 @ ( symdiff @ X1851 @ X1852 ) ) )
      & ( ( in @ X1853 @ X1852 )
        | X1854
        | ~ X1854
        | ~ ( in @ X1853 @ ( symdiff @ X1851 @ X1852 ) ) )
      & ( ~ X1854
        | X1854
        | ~ X1854
        | ~ ( in @ X1853 @ ( symdiff @ X1851 @ X1852 ) ) )
      & ( ~ ( in @ X1857 @ X1855 )
        | ( in @ X1857 @ X1856 )
        | ( in @ X1857 @ ( symdiff @ X1855 @ X1856 ) ) )
      & ( ( in @ X1860 @ X1858 )
        | ~ ( in @ X1860 @ X1859 )
        | ( in @ X1860 @ ( symdiff @ X1858 @ X1859 ) ) )
      & ( ~ ( in @ X1863 @ X1861 )
        | ~ ( in @ X1863 @ X1862 )
        | ~ ( in @ X1863 @ ( symdiff @ X1861 @ X1862 ) ) )
      & ( ( in @ X1866 @ X1864 )
        | ( in @ X1866 @ X1865 )
        | ~ ( in @ X1866 @ ( symdiff @ X1864 @ X1865 ) ) )
      & ( in @ X1868 @ ( setadjoin @ X1867 @ ( setadjoin @ X1868 @ emptyset ) ) )
      & ( in @ X1869 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1869 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1869 @ ( setadjoin @ X1870 @ emptyset ) ) @ emptyset ) ) ) )
      & ( in @ X1872 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1871 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1871 @ ( setadjoin @ X1872 @ emptyset ) ) @ emptyset ) ) ) )
      & ( iskpair @ ( setadjoin @ ( setadjoin @ X1873 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1873 @ ( setadjoin @ X1874 @ emptyset ) ) @ emptyset ) ) )
      & ( iskpair @ ( kpair @ X1875 @ X1876 ) )
      & ( ~ ( in @ X1878 @ X1877 )
        | ( subset @ ( setadjoin @ X1878 @ emptyset ) @ X1877 ) )
      & ( ~ ( in @ X1880 @ X1879 )
        | ( in @ ( setadjoin @ X1880 @ emptyset ) @ ( powerset @ X1879 ) ) )
      & ( ~ ( in @ X1883 @ X1881 )
        | ( in @ ( setadjoin @ X1883 @ emptyset ) @ ( powerset @ ( binunion @ X1881 @ X1882 ) ) ) )
      & ( ~ ( in @ X1886 @ ( setadjoin @ X1884 @ ( setadjoin @ X1885 @ emptyset ) ) )
        | ( X1886 = X1884 )
        | ( X1886 = X1885 ) )
      & ( ~ ( in @ X1889 @ X1887 )
        | ~ ( in @ X1890 @ X1888 )
        | ( subset @ ( setadjoin @ X1889 @ ( setadjoin @ X1890 @ emptyset ) ) @ ( binunion @ X1887 @ X1888 ) ) )
      & ( ~ ( in @ X1893 @ X1891 )
        | ~ ( in @ X1894 @ X1892 )
        | ( in @ ( setadjoin @ X1893 @ ( setadjoin @ X1894 @ emptyset ) ) @ ( powerset @ ( binunion @ X1891 @ X1892 ) ) ) )
      & ( ~ ( in @ X1897 @ X1895 )
        | ~ ( in @ X1898 @ X1896 )
        | ( subset @ ( setadjoin @ ( setadjoin @ X1897 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1897 @ ( setadjoin @ X1898 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1895 @ X1896 ) ) ) )
      & ( ~ ( in @ X1901 @ X1899 )
        | ~ ( in @ X1902 @ X1900 )
        | ( in @ ( setadjoin @ ( setadjoin @ X1901 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1901 @ ( setadjoin @ X1902 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1899 @ X1900 ) ) ) ) )
      & ( ~ ( in @ X1905 @ X1903 )
        | ~ ( in @ X1906 @ X1904 )
        | ( in @ ( kpair @ X1905 @ X1906 ) @ ( powerset @ ( powerset @ ( binunion @ X1903 @ X1904 ) ) ) ) )
      & ( ~ ( in @ X1909 @ X1907 )
        | ~ ( in @ X1910 @ X1908 )
        | ( in @ ( kpair @ X1909 @ X1910 ) @ ( cartprod @ X1907 @ X1908 ) ) )
      & ( ( in @ ( esk55_3 @ X1911 @ X1912 @ X1913 ) @ X1911 )
        | ~ ( in @ X1913 @ ( cartprod @ X1911 @ X1912 ) ) )
      & ( ( in @ ( esk56_3 @ X1911 @ X1912 @ X1913 ) @ X1912 )
        | ~ ( in @ X1913 @ ( cartprod @ X1911 @ X1912 ) ) )
      & ( ( X1913
          = ( kpair @ ( esk55_3 @ X1911 @ X1912 @ X1913 ) @ ( esk56_3 @ X1911 @ X1912 @ X1913 ) ) )
        | ~ ( in @ X1913 @ ( cartprod @ X1911 @ X1912 ) ) )
      & ( ~ ( in @ X1918 @ ( cartprod @ X1916 @ X1917 ) )
        | ( iskpair @ X1918 ) )
      & ( ( in @ ( esk57_2 @ X1919 @ X1920 ) @ X1919 )
        | ~ ( in @ X1920 @ ( setunion @ X1919 ) ) )
      & ( ( in @ X1920 @ ( esk57_2 @ X1919 @ X1920 ) )
        | ~ ( in @ X1920 @ ( setunion @ X1919 ) ) )
      & ( subset @ ( setunion @ ( setadjoin @ X1922 @ emptyset ) ) @ X1922 )
      & ( subset @ X1923 @ ( setunion @ ( setadjoin @ X1923 @ emptyset ) ) )
      & ( ( setunion @ ( setadjoin @ X1924 @ emptyset ) )
        = X1924 )
      & ( ( in @ ( esk60_2 @ X1925 @ X1926 ) @ ( dsetconstr @ X1925 @ X1926 ) )
        | ~ ( in @ X1929 @ X1925 )
        | ~ ( X1926 @ X1929 )
        | ( in @ ( esk58_2 @ X1925 @ X1926 ) @ X1925 ) )
      & ( ( ( dsetconstr @ X1925 @ X1926 )
          = ( setadjoin @ ( esk60_2 @ X1925 @ X1926 ) @ emptyset ) )
        | ~ ( in @ X1929 @ X1925 )
        | ~ ( X1926 @ X1929 )
        | ( in @ ( esk58_2 @ X1925 @ X1926 ) @ X1925 ) )
      & ( ( in @ ( esk60_2 @ X1925 @ X1926 ) @ ( dsetconstr @ X1925 @ X1926 ) )
        | ~ ( in @ X1929 @ X1925 )
        | ~ ( X1926 @ X1929 )
        | ( in @ ( esk59_2 @ X1925 @ X1926 ) @ X1925 ) )
      & ( ( ( dsetconstr @ X1925 @ X1926 )
          = ( setadjoin @ ( esk60_2 @ X1925 @ X1926 ) @ emptyset ) )
        | ~ ( in @ X1929 @ X1925 )
        | ~ ( X1926 @ X1929 )
        | ( in @ ( esk59_2 @ X1925 @ X1926 ) @ X1925 ) )
      & ( ( in @ ( esk60_2 @ X1925 @ X1926 ) @ ( dsetconstr @ X1925 @ X1926 ) )
        | ~ ( in @ X1929 @ X1925 )
        | ~ ( X1926 @ X1929 )
        | ( X1926 @ ( esk58_2 @ X1925 @ X1926 ) ) )
      & ( ( ( dsetconstr @ X1925 @ X1926 )
          = ( setadjoin @ ( esk60_2 @ X1925 @ X1926 ) @ emptyset ) )
        | ~ ( in @ X1929 @ X1925 )
        | ~ ( X1926 @ X1929 )
        | ( X1926 @ ( esk58_2 @ X1925 @ X1926 ) ) )
      & ( ( in @ ( esk60_2 @ X1925 @ X1926 ) @ ( dsetconstr @ X1925 @ X1926 ) )
        | ~ ( in @ X1929 @ X1925 )
        | ~ ( X1926 @ X1929 )
        | ( X1926 @ ( esk59_2 @ X1925 @ X1926 ) ) )
      & ( ( ( dsetconstr @ X1925 @ X1926 )
          = ( setadjoin @ ( esk60_2 @ X1925 @ X1926 ) @ emptyset ) )
        | ~ ( in @ X1929 @ X1925 )
        | ~ ( X1926 @ X1929 )
        | ( X1926 @ ( esk59_2 @ X1925 @ X1926 ) ) )
      & ( ( in @ ( esk60_2 @ X1925 @ X1926 ) @ ( dsetconstr @ X1925 @ X1926 ) )
        | ~ ( in @ X1929 @ X1925 )
        | ~ ( X1926 @ X1929 )
        | ( ( esk58_2 @ X1925 @ X1926 )
         != ( esk59_2 @ X1925 @ X1926 ) ) )
      & ( ( ( dsetconstr @ X1925 @ X1926 )
          = ( setadjoin @ ( esk60_2 @ X1925 @ X1926 ) @ emptyset ) )
        | ~ ( in @ X1929 @ X1925 )
        | ~ ( X1926 @ X1929 )
        | ( ( esk58_2 @ X1925 @ X1926 )
         != ( esk59_2 @ X1925 @ X1926 ) ) )
      & ( ( in @ ( esk61_2 @ X1931 @ X1932 ) @ X1931 )
        | ~ ( in @ X1933 @ ( dsetconstr @ X1931 @ X1932 ) )
        | ( ( dsetconstr @ X1931 @ X1932 )
         != ( setadjoin @ X1933 @ emptyset ) ) )
      & ( ( X1932 @ ( esk61_2 @ X1931 @ X1932 ) )
        | ~ ( in @ X1933 @ ( dsetconstr @ X1931 @ X1932 ) )
        | ( ( dsetconstr @ X1931 @ X1932 )
         != ( setadjoin @ X1933 @ emptyset ) ) )
      & ( ( in @ ( esk63_3 @ X1935 @ X1936 @ X1937 ) @ ( dsetconstr @ X1935 @ X1936 ) )
        | ( in @ ( esk62_3 @ X1935 @ X1936 @ X1937 ) @ X1935 )
        | ~ ( X1936 @ X1937 )
        | ~ ( in @ X1937 @ X1935 ) )
      & ( ( ( dsetconstr @ X1935 @ X1936 )
          = ( setadjoin @ ( esk63_3 @ X1935 @ X1936 @ X1937 ) @ emptyset ) )
        | ( in @ ( esk62_3 @ X1935 @ X1936 @ X1937 ) @ X1935 )
        | ~ ( X1936 @ X1937 )
        | ~ ( in @ X1937 @ X1935 ) )
      & ( ( in @ ( esk63_3 @ X1935 @ X1936 @ X1937 ) @ ( dsetconstr @ X1935 @ X1936 ) )
        | ( X1936 @ ( esk62_3 @ X1935 @ X1936 @ X1937 ) )
        | ~ ( X1936 @ X1937 )
        | ~ ( in @ X1937 @ X1935 ) )
      & ( ( ( dsetconstr @ X1935 @ X1936 )
          = ( setadjoin @ ( esk63_3 @ X1935 @ X1936 @ X1937 ) @ emptyset ) )
        | ( X1936 @ ( esk62_3 @ X1935 @ X1936 @ X1937 ) )
        | ~ ( X1936 @ X1937 )
        | ~ ( in @ X1937 @ X1935 ) )
      & ( ( in @ ( esk63_3 @ X1935 @ X1936 @ X1937 ) @ ( dsetconstr @ X1935 @ X1936 ) )
        | ( ( esk62_3 @ X1935 @ X1936 @ X1937 )
         != X1937 )
        | ~ ( X1936 @ X1937 )
        | ~ ( in @ X1937 @ X1935 ) )
      & ( ( ( dsetconstr @ X1935 @ X1936 )
          = ( setadjoin @ ( esk63_3 @ X1935 @ X1936 @ X1937 ) @ emptyset ) )
        | ( ( esk62_3 @ X1935 @ X1936 @ X1937 )
         != X1937 )
        | ~ ( X1936 @ X1937 )
        | ~ ( in @ X1937 @ X1935 ) )
      & ( ( in @ ( esk66_2 @ X1940 @ X1941 ) @ ( dsetconstr @ X1940 @ X1941 ) )
        | ~ ( in @ X1944 @ X1940 )
        | ~ ( X1941 @ X1944 )
        | ( in @ ( esk64_2 @ X1940 @ X1941 ) @ X1940 ) )
      & ( ( ( dsetconstr @ X1940 @ X1941 )
          = ( setadjoin @ ( esk66_2 @ X1940 @ X1941 ) @ emptyset ) )
        | ~ ( in @ X1944 @ X1940 )
        | ~ ( X1941 @ X1944 )
        | ( in @ ( esk64_2 @ X1940 @ X1941 ) @ X1940 ) )
      & ( ( in @ ( esk66_2 @ X1940 @ X1941 ) @ ( dsetconstr @ X1940 @ X1941 ) )
        | ~ ( in @ X1944 @ X1940 )
        | ~ ( X1941 @ X1944 )
        | ( in @ ( esk65_2 @ X1940 @ X1941 ) @ X1940 ) )
      & ( ( ( dsetconstr @ X1940 @ X1941 )
          = ( setadjoin @ ( esk66_2 @ X1940 @ X1941 ) @ emptyset ) )
        | ~ ( in @ X1944 @ X1940 )
        | ~ ( X1941 @ X1944 )
        | ( in @ ( esk65_2 @ X1940 @ X1941 ) @ X1940 ) )
      & ( ( in @ ( esk66_2 @ X1940 @ X1941 ) @ ( dsetconstr @ X1940 @ X1941 ) )
        | ~ ( in @ X1944 @ X1940 )
        | ~ ( X1941 @ X1944 )
        | ( X1941 @ ( esk64_2 @ X1940 @ X1941 ) ) )
      & ( ( ( dsetconstr @ X1940 @ X1941 )
          = ( setadjoin @ ( esk66_2 @ X1940 @ X1941 ) @ emptyset ) )
        | ~ ( in @ X1944 @ X1940 )
        | ~ ( X1941 @ X1944 )
        | ( X1941 @ ( esk64_2 @ X1940 @ X1941 ) ) )
      & ( ( in @ ( esk66_2 @ X1940 @ X1941 ) @ ( dsetconstr @ X1940 @ X1941 ) )
        | ~ ( in @ X1944 @ X1940 )
        | ~ ( X1941 @ X1944 )
        | ( X1941 @ ( esk65_2 @ X1940 @ X1941 ) ) )
      & ( ( ( dsetconstr @ X1940 @ X1941 )
          = ( setadjoin @ ( esk66_2 @ X1940 @ X1941 ) @ emptyset ) )
        | ~ ( in @ X1944 @ X1940 )
        | ~ ( X1941 @ X1944 )
        | ( X1941 @ ( esk65_2 @ X1940 @ X1941 ) ) )
      & ( ( in @ ( esk66_2 @ X1940 @ X1941 ) @ ( dsetconstr @ X1940 @ X1941 ) )
        | ~ ( in @ X1944 @ X1940 )
        | ~ ( X1941 @ X1944 )
        | ( ( esk64_2 @ X1940 @ X1941 )
         != ( esk65_2 @ X1940 @ X1941 ) ) )
      & ( ( ( dsetconstr @ X1940 @ X1941 )
          = ( setadjoin @ ( esk66_2 @ X1940 @ X1941 ) @ emptyset ) )
        | ~ ( in @ X1944 @ X1940 )
        | ~ ( X1941 @ X1944 )
        | ( ( esk64_2 @ X1940 @ X1941 )
         != ( esk65_2 @ X1940 @ X1941 ) ) )
      & ( ( ( setadjoin @ X1946 @ emptyset )
         != ( setadjoin @ X1947 @ emptyset ) )
        | ( X1946 = X1947 ) )
      & ( ~ ( in @ ( setadjoin @ X1950 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1948 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1948 @ ( setadjoin @ X1949 @ emptyset ) ) @ emptyset ) ) )
        | ( X1948 = X1950 ) )
      & ( ( in @ ( esk67_1 @ X1951 )
          @ ( dsetconstr @ ( setunion @ X1951 )
            @ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1951 ) ) )
        | ~ ( iskpair @ X1951 ) )
      & ( ( ( dsetconstr @ ( setunion @ X1951 )
            @ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1951 ) )
          = ( setadjoin @ ( esk67_1 @ X1951 ) @ emptyset ) )
        | ~ ( iskpair @ X1951 ) )
      & ( ~ ( in @ X1954 @ X1953 )
        | ( X1953
         != ( setadjoin @ X1954 @ emptyset ) )
        | ( in @ ( setunion @ X1953 ) @ X1953 ) )
      & ( ( kfst @ ( kpair @ X1955 @ X1956 ) )
        = X1955 )
      & ( ~ ( in @ X1959 @ ( cartprod @ X1957 @ X1958 ) )
        | ( in @ ( kfst @ X1959 ) @ X1957 ) )
      & ( ( ( setadjoin @ ( setadjoin @ X1960 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1960 @ ( setadjoin @ X1961 @ emptyset ) ) @ emptyset ) )
         != ( setadjoin @ ( setadjoin @ X1962 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1962 @ ( setadjoin @ X1963 @ emptyset ) ) @ emptyset ) ) )
        | ( X1960 = X1962 ) )
      & ( ( ( kpair @ X1964 @ X1965 )
         != ( kpair @ X1966 @ X1967 ) )
        | ( X1964 = X1966 ) )
      & ( ( X1968 != X1969 )
        | ( ( setadjoin @ X1968 @ ( setadjoin @ X1969 @ emptyset ) )
          = ( setadjoin @ X1968 @ emptyset ) ) )
      & ( ( X1970 != X1971 )
        | ( ( setadjoin @ ( setadjoin @ X1970 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1970 @ ( setadjoin @ X1971 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ X1970 @ emptyset ) @ emptyset ) ) )
      & ( ( ( setadjoin @ ( setadjoin @ X1972 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1972 @ ( setadjoin @ X1973 @ emptyset ) ) @ emptyset ) )
         != ( setadjoin @ ( setadjoin @ X1974 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1974 @ ( setadjoin @ X1975 @ emptyset ) ) @ emptyset ) ) )
        | ( X1974 != X1975 )
        | ( X1973 = X1975 ) )
      & ( ( ( setadjoin @ X1976 @ ( setadjoin @ X1977 @ emptyset ) )
         != ( setadjoin @ X1978 @ emptyset ) )
        | ( X1976 = X1977 ) )
      & ( ( ( setadjoin @ ( setadjoin @ X1979 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1979 @ ( setadjoin @ X1980 @ emptyset ) ) @ emptyset ) )
         != ( setadjoin @ ( setadjoin @ X1981 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1981 @ ( setadjoin @ X1982 @ emptyset ) ) @ emptyset ) ) )
        | ( X1980 = X1982 ) )
      & ( ( ( kpair @ X1983 @ X1984 )
         != ( kpair @ X1985 @ X1986 ) )
        | ( X1984 = X1986 ) )
      & ( ( in @ ( esk68_1 @ X1987 )
          @ ( dsetconstr @ ( setunion @ X1987 )
            @ ^ [Z0: $i] :
                ( X1987
                = ( kpair @ ( kfst @ X1987 ) @ Z0 ) ) ) )
        | ~ ( iskpair @ X1987 ) )
      & ( ( ( dsetconstr @ ( setunion @ X1987 )
            @ ^ [Z0: $i] :
                ( X1987
                = ( kpair @ ( kfst @ X1987 ) @ Z0 ) ) )
          = ( setadjoin @ ( esk68_1 @ X1987 ) @ emptyset ) )
        | ~ ( iskpair @ X1987 ) )
      & ( ( ksnd @ ( kpair @ X1989 @ X1990 ) )
        = X1990 )
      & ( ~ ( iskpair @ X1991 )
        | ( ( kpair @ ( kfst @ X1991 ) @ ( ksnd @ X1991 ) )
          = X1991 ) )
      & ( ~ ( in @ X1994 @ ( cartprod @ X1992 @ X1993 ) )
        | ( in @ ( ksnd @ X1994 ) @ X1993 ) )
      & ( ~ ( in @ ( kpair @ X1997 @ X1998 ) @ ( cartprod @ X1995 @ X1996 ) )
        | ( in @ X1997 @ X1995 ) )
      & ( ~ ( in @ ( kpair @ X2001 @ X2002 ) @ ( cartprod @ X1999 @ X2000 ) )
        | ( in @ X2002 @ X2000 ) )
      & ( ~ ( in @ X2005 @ X2003 )
        | ~ ( in @ X2006 @ X2004 )
        | ( ( kpair @ X2005 @ X2006 )
          = ( kpair @ X2005 @ X2006 ) ) )
      & ( ~ ( in @ X2009 @ X2007 )
        | ~ ( in @ X2010 @ X2008 )
        | ( ( kfst @ ( kpair @ X2009 @ X2010 ) )
          = X2009 ) )
      & ( ~ ( in @ X2013 @ X2011 )
        | ~ ( in @ X2014 @ X2012 )
        | ( ( ksnd @ ( kpair @ X2013 @ X2014 ) )
          = X2014 ) )
      & ( ~ ( in @ X2017 @ ( cartprod @ X2015 @ X2016 ) )
        | ( ( kpair @ ( kfst @ X2017 ) @ ( ksnd @ X2017 ) )
          = X2017 ) )
      & ( ~ ( in @ X2021 @ X2018 )
        | ~ ( in @ X2022 @ X2019 )
        | ~ ( X2020 @ X2021 @ X2022 )
        | ( in @ ( kpair @ X2021 @ X2022 ) @ ( dpsetconstr @ X2018 @ X2019 @ X2020 ) ) )
      & ( subset @ ( dpsetconstr @ X2023 @ X2024 @ X2025 ) @ ( cartprod @ X2023 @ X2024 ) )
      & ( subset @ ( dpsetconstr @ X2026 @ X2027 @ X2028 ) @ ( cartprod @ X2026 @ X2027 ) )
      & ( ~ ( in @ X2032 @ X2029 )
        | ~ ( in @ X2033 @ X2030 )
        | ~ ( in @ ( kpair @ X2032 @ X2033 ) @ ( dpsetconstr @ X2029 @ X2030 @ X2031 ) )
        | ( X2031 @ X2032 @ X2033 ) )
      & ( ~ ( in @ ( kpair @ X2037 @ X2038 ) @ ( dpsetconstr @ X2034 @ X2035 @ X2036 ) )
        | ( in @ X2037 @ X2034 ) )
      & ( ~ ( in @ ( kpair @ X2042 @ X2043 ) @ ( dpsetconstr @ X2039 @ X2040 @ X2041 ) )
        | ( in @ X2043 @ X2040 ) )
      & ( ~ ( in @ ( kpair @ X2047 @ X2048 ) @ ( dpsetconstr @ X2044 @ X2045 @ X2046 ) )
        | ( X2046 @ X2047 @ X2048 ) )
      & ( ( in @ ( esk69_4 @ X2049 @ X2050 @ X2051 @ X2052 )
          @ ( dsetconstr @ X2050
            @ ^ [Z0: $i] : ( in @ ( kpair @ X2052 @ Z0 ) @ X2051 ) ) )
        | ~ ( in @ X2052 @ X2049 )
        | ~ ( func @ X2049 @ X2050 @ X2051 ) )
      & ( ( ( dsetconstr @ X2050
            @ ^ [Z0: $i] : ( in @ ( kpair @ X2052 @ Z0 ) @ X2051 ) )
          = ( setadjoin @ ( esk69_4 @ X2049 @ X2050 @ X2051 @ X2052 ) @ emptyset ) )
        | ~ ( in @ X2052 @ X2049 )
        | ~ ( func @ X2049 @ X2050 @ X2051 ) )
      & ( ~ ( func @ X2054 @ X2055 @ X2056 )
        | ~ ( in @ X2057 @ X2054 )
        | ( in
          @ ( setunion
            @ ( dsetconstr @ X2055
              @ ^ [Z0: $i] : ( in @ ( kpair @ X2057 @ Z0 ) @ X2056 ) ) )
          @ X2055 ) )
      & ( ~ ( func @ X2058 @ X2059 @ X2060 )
        | ~ ( in @ X2061 @ X2058 )
        | ( in @ ( ap @ X2058 @ X2059 @ X2060 @ X2061 ) @ X2059 ) )
      & ( ~ ( in @ X2064 @ ( funcSet @ X2062 @ X2063 ) )
        | ( func @ X2062 @ X2063 @ X2064 ) )
      & ( ~ ( in @ X2067 @ ( funcSet @ X2065 @ X2066 ) )
        | ~ ( in @ X2068 @ X2065 )
        | ( in @ ( ap @ X2065 @ X2066 @ X2067 @ X2068 ) @ X2066 ) )
      & ( ~ ( func @ X2069 @ X2070 @ X2071 )
        | ( in @ X2071 @ ( funcSet @ X2069 @ X2070 ) ) )
      & ( ( in @ ( esk70_3 @ X2072 @ X2073 @ X2074 ) @ X2072 )
        | ( func @ X2072 @ X2073
          @ ( dpsetconstr @ X2072 @ X2073
            @ ^ [Z0: $i] : ( $eq @ ( X2074 @ Z0 ) ) ) ) )
      & ( ~ ( in @ ( X2074 @ ( esk70_3 @ X2072 @ X2073 @ X2074 ) ) @ X2073 )
        | ( func @ X2072 @ X2073
          @ ( dpsetconstr @ X2072 @ X2073
            @ ^ [Z0: $i] : ( $eq @ ( X2074 @ Z0 ) ) ) ) )
      & ( ( in @ ( esk71_3 @ X2076 @ X2077 @ X2078 ) @ X2076 )
        | ( func @ X2076 @ X2077 @ ( lam @ X2076 @ X2077 @ X2078 ) ) )
      & ( ~ ( in @ ( X2078 @ ( esk71_3 @ X2076 @ X2077 @ X2078 ) ) @ X2077 )
        | ( func @ X2076 @ X2077 @ ( lam @ X2076 @ X2077 @ X2078 ) ) )
      & ( ( in @ ( esk72_3 @ X2080 @ X2081 @ X2082 ) @ X2080 )
        | ( in @ ( lam @ X2080 @ X2081 @ X2082 ) @ ( funcSet @ X2080 @ X2081 ) ) )
      & ( ~ ( in @ ( X2082 @ ( esk72_3 @ X2080 @ X2081 @ X2082 ) ) @ X2081 )
        | ( in @ ( lam @ X2080 @ X2081 @ X2082 ) @ ( funcSet @ X2080 @ X2081 ) ) )
      & ( ( in @ ( esk73_4 @ X2084 @ X2085 @ X2086 @ X2087 ) @ X2084 )
        | ~ ( in @ X2090 @ X2086 )
        | ( X2087 @ X2090 )
        | ~ ( subset @ X2086 @ ( cartprod @ X2084 @ X2085 ) ) )
      & ( ( in @ ( esk74_4 @ X2084 @ X2085 @ X2086 @ X2087 ) @ X2085 )
        | ~ ( in @ X2090 @ X2086 )
        | ( X2087 @ X2090 )
        | ~ ( subset @ X2086 @ ( cartprod @ X2084 @ X2085 ) ) )
      & ( ( in @ ( kpair @ ( esk73_4 @ X2084 @ X2085 @ X2086 @ X2087 ) @ ( esk74_4 @ X2084 @ X2085 @ X2086 @ X2087 ) ) @ X2086 )
        | ~ ( in @ X2090 @ X2086 )
        | ( X2087 @ X2090 )
        | ~ ( subset @ X2086 @ ( cartprod @ X2084 @ X2085 ) ) )
      & ( ~ ( X2087 @ ( kpair @ ( esk73_4 @ X2084 @ X2085 @ X2086 @ X2087 ) @ ( esk74_4 @ X2084 @ X2085 @ X2086 @ X2087 ) ) )
        | ~ ( in @ X2090 @ X2086 )
        | ( X2087 @ X2090 )
        | ~ ( subset @ X2086 @ ( cartprod @ X2084 @ X2085 ) ) )
      & ( ( in @ ( esk75_4 @ X2091 @ X2092 @ X2093 @ X2094 ) @ X2091 )
        | ~ ( in @ X2097 @ X2093 )
        | ( X2094 @ X2097 )
        | ~ ( subset @ X2093 @ ( cartprod @ X2091 @ X2092 ) ) )
      & ( ( in @ ( esk76_4 @ X2091 @ X2092 @ X2093 @ X2094 ) @ X2092 )
        | ~ ( in @ X2097 @ X2093 )
        | ( X2094 @ X2097 )
        | ~ ( subset @ X2093 @ ( cartprod @ X2091 @ X2092 ) ) )
      & ( ( in @ ( kpair @ ( esk75_4 @ X2091 @ X2092 @ X2093 @ X2094 ) @ ( esk76_4 @ X2091 @ X2092 @ X2093 @ X2094 ) ) @ X2093 )
        | ~ ( in @ X2097 @ X2093 )
        | ( X2094 @ X2097 )
        | ~ ( subset @ X2093 @ ( cartprod @ X2091 @ X2092 ) ) )
      & ( ~ ( X2094 @ ( kpair @ ( esk75_4 @ X2091 @ X2092 @ X2093 @ X2094 ) @ ( esk76_4 @ X2091 @ X2092 @ X2093 @ X2094 ) ) )
        | ~ ( in @ X2097 @ X2093 )
        | ( X2094 @ X2097 )
        | ~ ( subset @ X2093 @ ( cartprod @ X2091 @ X2092 ) ) )
      & ( ~ ( in @ X2100 @ ( dsetconstr @ X2098 @ X2099 ) )
        | ( ( dsetconstr @ X2098 @ X2099 )
         != ( setadjoin @ X2100 @ emptyset ) )
        | ~ ( in @ X2101 @ X2098 )
        | ~ ( in @ X2102 @ X2098 )
        | ~ ( X2099 @ X2101 )
        | ~ ( X2099 @ X2102 )
        | ( X2101 = X2102 ) )
      & ( ~ ( func @ X2103 @ X2104 @ X2105 )
        | ~ ( in @ X2106 @ X2103 )
        | ( in @ ( kpair @ X2106 @ ( ap @ X2103 @ X2104 @ X2105 @ X2106 ) ) @ X2105 ) )
      & ( ~ ( in @ X2109 @ ( funcSet @ X2107 @ X2108 ) )
        | ~ ( in @ X2110 @ X2107 )
        | ( in @ ( kpair @ X2110 @ ( ap @ X2107 @ X2108 @ X2109 @ X2110 ) ) @ X2109 ) )
      & ( ~ ( func @ X2111 @ X2112 @ X2113 )
        | ~ ( in @ X2114 @ X2111 )
        | ~ ( in @ X2115 @ X2112 )
        | ~ ( in @ ( kpair @ X2114 @ X2115 ) @ X2113 )
        | ( ( ap @ X2111 @ X2112 @ X2113 @ X2114 )
          = X2115 ) )
      & ( ( in @ ( esk77_4 @ X2116 @ X2117 @ X2118 @ X2119 ) @ X2116 )
        | ~ ( in @ X2121 @ X2116 )
        | ~ ( in @ X2122 @ X2117 )
        | ~ ( in @ ( kpair @ X2121 @ X2122 ) @ X2119 )
        | ( in @ ( kpair @ X2121 @ X2122 ) @ X2118 )
        | ~ ( func @ X2116 @ X2117 @ X2119 )
        | ~ ( func @ X2116 @ X2117 @ X2118 ) )
      & ( ( ( ap @ X2116 @ X2117 @ X2118 @ ( esk77_4 @ X2116 @ X2117 @ X2118 @ X2119 ) )
         != ( ap @ X2116 @ X2117 @ X2119 @ ( esk77_4 @ X2116 @ X2117 @ X2118 @ X2119 ) ) )
        | ~ ( in @ X2121 @ X2116 )
        | ~ ( in @ X2122 @ X2117 )
        | ~ ( in @ ( kpair @ X2121 @ X2122 ) @ X2119 )
        | ( in @ ( kpair @ X2121 @ X2122 ) @ X2118 )
        | ~ ( func @ X2116 @ X2117 @ X2119 )
        | ~ ( func @ X2116 @ X2117 @ X2118 ) )
      & ( ~ ( in @ X2125 @ ( funcSet @ X2123 @ X2124 ) )
        | ~ ( in @ X2126 @ X2123 )
        | ~ ( in @ X2127 @ X2124 )
        | ~ ( in @ ( kpair @ X2126 @ X2127 ) @ X2125 )
        | ( ( ap @ X2123 @ X2124 @ X2125 @ X2126 )
          = X2127 ) )
      & ( ( in @ ( esk78_4 @ X2128 @ X2129 @ X2130 @ X2131 ) @ X2128 )
        | ( subset @ X2130 @ X2131 )
        | ~ ( subset @ X2131 @ ( cartprod @ X2128 @ X2129 ) )
        | ~ ( subset @ X2130 @ ( cartprod @ X2128 @ X2129 ) ) )
      & ( ( in @ ( esk79_4 @ X2128 @ X2129 @ X2130 @ X2131 ) @ X2129 )
        | ( subset @ X2130 @ X2131 )
        | ~ ( subset @ X2131 @ ( cartprod @ X2128 @ X2129 ) )
        | ~ ( subset @ X2130 @ ( cartprod @ X2128 @ X2129 ) ) )
      & ( ( in @ ( kpair @ ( esk78_4 @ X2128 @ X2129 @ X2130 @ X2131 ) @ ( esk79_4 @ X2128 @ X2129 @ X2130 @ X2131 ) ) @ X2130 )
        | ( subset @ X2130 @ X2131 )
        | ~ ( subset @ X2131 @ ( cartprod @ X2128 @ X2129 ) )
        | ~ ( subset @ X2130 @ ( cartprod @ X2128 @ X2129 ) ) )
      & ( ~ ( in @ ( kpair @ ( esk78_4 @ X2128 @ X2129 @ X2130 @ X2131 ) @ ( esk79_4 @ X2128 @ X2129 @ X2130 @ X2131 ) ) @ X2131 )
        | ( subset @ X2130 @ X2131 )
        | ~ ( subset @ X2131 @ ( cartprod @ X2128 @ X2129 ) )
        | ~ ( subset @ X2130 @ ( cartprod @ X2128 @ X2129 ) ) )
      & ( ( in @ ( esk82_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ X2134 )
        | ( X2136 = X2137 )
        | ( in @ ( esk80_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ X2134 )
        | ~ ( subset @ X2137 @ ( cartprod @ X2134 @ X2135 ) )
        | ~ ( subset @ X2136 @ ( cartprod @ X2134 @ X2135 ) ) )
      & ( ( in @ ( esk83_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ X2135 )
        | ( X2136 = X2137 )
        | ( in @ ( esk80_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ X2134 )
        | ~ ( subset @ X2137 @ ( cartprod @ X2134 @ X2135 ) )
        | ~ ( subset @ X2136 @ ( cartprod @ X2134 @ X2135 ) ) )
      & ( ( in @ ( kpair @ ( esk82_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ ( esk83_4 @ X2134 @ X2135 @ X2136 @ X2137 ) ) @ X2137 )
        | ( X2136 = X2137 )
        | ( in @ ( esk80_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ X2134 )
        | ~ ( subset @ X2137 @ ( cartprod @ X2134 @ X2135 ) )
        | ~ ( subset @ X2136 @ ( cartprod @ X2134 @ X2135 ) ) )
      & ( ~ ( in @ ( kpair @ ( esk82_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ ( esk83_4 @ X2134 @ X2135 @ X2136 @ X2137 ) ) @ X2136 )
        | ( X2136 = X2137 )
        | ( in @ ( esk80_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ X2134 )
        | ~ ( subset @ X2137 @ ( cartprod @ X2134 @ X2135 ) )
        | ~ ( subset @ X2136 @ ( cartprod @ X2134 @ X2135 ) ) )
      & ( ( in @ ( esk82_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ X2134 )
        | ( X2136 = X2137 )
        | ( in @ ( esk81_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ X2135 )
        | ~ ( subset @ X2137 @ ( cartprod @ X2134 @ X2135 ) )
        | ~ ( subset @ X2136 @ ( cartprod @ X2134 @ X2135 ) ) )
      & ( ( in @ ( esk83_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ X2135 )
        | ( X2136 = X2137 )
        | ( in @ ( esk81_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ X2135 )
        | ~ ( subset @ X2137 @ ( cartprod @ X2134 @ X2135 ) )
        | ~ ( subset @ X2136 @ ( cartprod @ X2134 @ X2135 ) ) )
      & ( ( in @ ( kpair @ ( esk82_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ ( esk83_4 @ X2134 @ X2135 @ X2136 @ X2137 ) ) @ X2137 )
        | ( X2136 = X2137 )
        | ( in @ ( esk81_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ X2135 )
        | ~ ( subset @ X2137 @ ( cartprod @ X2134 @ X2135 ) )
        | ~ ( subset @ X2136 @ ( cartprod @ X2134 @ X2135 ) ) )
      & ( ~ ( in @ ( kpair @ ( esk82_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ ( esk83_4 @ X2134 @ X2135 @ X2136 @ X2137 ) ) @ X2136 )
        | ( X2136 = X2137 )
        | ( in @ ( esk81_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ X2135 )
        | ~ ( subset @ X2137 @ ( cartprod @ X2134 @ X2135 ) )
        | ~ ( subset @ X2136 @ ( cartprod @ X2134 @ X2135 ) ) )
      & ( ( in @ ( esk82_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ X2134 )
        | ( X2136 = X2137 )
        | ( in @ ( kpair @ ( esk80_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ ( esk81_4 @ X2134 @ X2135 @ X2136 @ X2137 ) ) @ X2136 )
        | ~ ( subset @ X2137 @ ( cartprod @ X2134 @ X2135 ) )
        | ~ ( subset @ X2136 @ ( cartprod @ X2134 @ X2135 ) ) )
      & ( ( in @ ( esk83_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ X2135 )
        | ( X2136 = X2137 )
        | ( in @ ( kpair @ ( esk80_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ ( esk81_4 @ X2134 @ X2135 @ X2136 @ X2137 ) ) @ X2136 )
        | ~ ( subset @ X2137 @ ( cartprod @ X2134 @ X2135 ) )
        | ~ ( subset @ X2136 @ ( cartprod @ X2134 @ X2135 ) ) )
      & ( ( in @ ( kpair @ ( esk82_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ ( esk83_4 @ X2134 @ X2135 @ X2136 @ X2137 ) ) @ X2137 )
        | ( X2136 = X2137 )
        | ( in @ ( kpair @ ( esk80_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ ( esk81_4 @ X2134 @ X2135 @ X2136 @ X2137 ) ) @ X2136 )
        | ~ ( subset @ X2137 @ ( cartprod @ X2134 @ X2135 ) )
        | ~ ( subset @ X2136 @ ( cartprod @ X2134 @ X2135 ) ) )
      & ( ~ ( in @ ( kpair @ ( esk82_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ ( esk83_4 @ X2134 @ X2135 @ X2136 @ X2137 ) ) @ X2136 )
        | ( X2136 = X2137 )
        | ( in @ ( kpair @ ( esk80_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ ( esk81_4 @ X2134 @ X2135 @ X2136 @ X2137 ) ) @ X2136 )
        | ~ ( subset @ X2137 @ ( cartprod @ X2134 @ X2135 ) )
        | ~ ( subset @ X2136 @ ( cartprod @ X2134 @ X2135 ) ) )
      & ( ( in @ ( esk82_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ X2134 )
        | ( X2136 = X2137 )
        | ~ ( in @ ( kpair @ ( esk80_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ ( esk81_4 @ X2134 @ X2135 @ X2136 @ X2137 ) ) @ X2137 )
        | ~ ( subset @ X2137 @ ( cartprod @ X2134 @ X2135 ) )
        | ~ ( subset @ X2136 @ ( cartprod @ X2134 @ X2135 ) ) )
      & ( ( in @ ( esk83_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ X2135 )
        | ( X2136 = X2137 )
        | ~ ( in @ ( kpair @ ( esk80_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ ( esk81_4 @ X2134 @ X2135 @ X2136 @ X2137 ) ) @ X2137 )
        | ~ ( subset @ X2137 @ ( cartprod @ X2134 @ X2135 ) )
        | ~ ( subset @ X2136 @ ( cartprod @ X2134 @ X2135 ) ) )
      & ( ( in @ ( kpair @ ( esk82_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ ( esk83_4 @ X2134 @ X2135 @ X2136 @ X2137 ) ) @ X2137 )
        | ( X2136 = X2137 )
        | ~ ( in @ ( kpair @ ( esk80_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ ( esk81_4 @ X2134 @ X2135 @ X2136 @ X2137 ) ) @ X2137 )
        | ~ ( subset @ X2137 @ ( cartprod @ X2134 @ X2135 ) )
        | ~ ( subset @ X2136 @ ( cartprod @ X2134 @ X2135 ) ) )
      & ( ~ ( in @ ( kpair @ ( esk82_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ ( esk83_4 @ X2134 @ X2135 @ X2136 @ X2137 ) ) @ X2136 )
        | ( X2136 = X2137 )
        | ~ ( in @ ( kpair @ ( esk80_4 @ X2134 @ X2135 @ X2136 @ X2137 ) @ ( esk81_4 @ X2134 @ X2135 @ X2136 @ X2137 ) ) @ X2137 )
        | ~ ( subset @ X2137 @ ( cartprod @ X2134 @ X2135 ) )
        | ~ ( subset @ X2136 @ ( cartprod @ X2134 @ X2135 ) ) )
      & ( ( in @ ( esk84_4 @ X2142 @ X2143 @ X2144 @ X2145 ) @ X2142 )
        | ( X2144 = X2145 )
        | ~ ( func @ X2142 @ X2143 @ X2145 )
        | ~ ( func @ X2142 @ X2143 @ X2144 ) )
      & ( ( ( ap @ X2142 @ X2143 @ X2144 @ ( esk84_4 @ X2142 @ X2143 @ X2144 @ X2145 ) )
         != ( ap @ X2142 @ X2143 @ X2145 @ ( esk84_4 @ X2142 @ X2143 @ X2144 @ X2145 ) ) )
        | ( X2144 = X2145 )
        | ~ ( func @ X2142 @ X2143 @ X2145 )
        | ~ ( func @ X2142 @ X2143 @ X2144 ) )
      & ( ( in @ ( esk85_4 @ X2147 @ X2148 @ X2149 @ X2150 ) @ X2147 )
        | ( X2149 = X2150 )
        | ~ ( in @ X2150 @ ( funcSet @ X2147 @ X2148 ) )
        | ~ ( in @ X2149 @ ( funcSet @ X2147 @ X2148 ) ) )
      & ( ( ( ap @ X2147 @ X2148 @ X2149 @ ( esk85_4 @ X2147 @ X2148 @ X2149 @ X2150 ) )
         != ( ap @ X2147 @ X2148 @ X2150 @ ( esk85_4 @ X2147 @ X2148 @ X2149 @ X2150 ) ) )
        | ( X2149 = X2150 )
        | ~ ( in @ X2150 @ ( funcSet @ X2147 @ X2148 ) )
        | ~ ( in @ X2149 @ ( funcSet @ X2147 @ X2148 ) ) )
      & ( ~ ( in @ X2154 @ ( funcSet @ X2152 @ X2153 ) )
        | ~ ( in @ X2155 @ X2152 )
        | ( ( ap @ X2152 @ X2153 @ X2154 @ X2155 )
          = ( ap @ X2152 @ X2153 @ X2154 @ X2155 ) ) )
      & ( ~ ( func @ X2156 @ X2157 @ X2158 )
        | ~ ( in @ X2159 @ X2156 )
        | ( ( ap @ X2156 @ X2157 @ X2158 @ X2159 )
          = ( ap @ X2156 @ X2157 @ X2158 @ X2159 ) ) )
      & ( ( in @ ( esk86_3 @ X2160 @ X2161 @ X2162 ) @ X2160 )
        | ~ ( in @ X2164 @ X2160 )
        | ( ( ap @ X2160 @ X2161 @ ( lam @ X2160 @ X2161 @ X2162 ) @ X2164 )
          = ( X2162 @ X2164 ) ) )
      & ( ~ ( in @ ( X2162 @ ( esk86_3 @ X2160 @ X2161 @ X2162 ) ) @ X2161 )
        | ~ ( in @ X2164 @ X2160 )
        | ( ( ap @ X2160 @ X2161 @ ( lam @ X2160 @ X2161 @ X2162 ) @ X2164 )
          = ( X2162 @ X2164 ) ) )
      & ( ~ ( func @ X2165 @ X2166 @ X2167 )
        | ( ( lam @ X2165 @ X2166 @ ( ap @ X2165 @ X2166 @ X2167 ) )
          = X2167 ) )
      & ( ( in @ ( esk87_3 @ X2168 @ X2169 @ X2170 ) @ X2168 )
        | ( ( lam @ X2168 @ X2169 @ X2170 )
          = ( lam @ X2168 @ X2169 @ X2170 ) ) )
      & ( ~ ( in @ ( X2170 @ ( esk87_3 @ X2168 @ X2169 @ X2170 ) ) @ X2169 )
        | ( ( lam @ X2168 @ X2169 @ X2170 )
          = ( lam @ X2168 @ X2169 @ X2170 ) ) )
      & ( ( in @ ( esk88_3 @ X2172 @ X2173 @ X2174 ) @ X2172 )
        | ~ ( in @ X2176 @ X2172 )
        | ( ( ap @ X2172 @ X2173 @ ( lam @ X2172 @ X2173 @ X2174 ) @ X2176 )
          = ( X2174 @ X2176 ) ) )
      & ( ~ ( in @ ( X2174 @ ( esk88_3 @ X2172 @ X2173 @ X2174 ) ) @ X2173 )
        | ~ ( in @ X2176 @ X2172 )
        | ( ( ap @ X2172 @ X2173 @ ( lam @ X2172 @ X2173 @ X2174 ) @ X2176 )
          = ( X2174 @ X2176 ) ) )
      & ( ~ ( in @ X2179 @ ( funcSet @ X2177 @ X2178 ) )
        | ( ( lam @ X2177 @ X2178 @ ( ap @ X2177 @ X2178 @ X2179 ) )
          = X2179 ) )
      & ( ~ ( in @ X2182 @ X2180 )
        | ~ ( in @ X2183 @ X2180 )
        | X2181
        | ( in @ X2183
          @ ( dsetconstr @ X2180
            @ ^ [Z0: $i] :
                ( ( X2181
                  & ( Z0 = X2182 ) )
                | ( ~ X2181
                  & ( Z0 = X2183 ) ) ) ) ) )
      & ( ~ ( in @ X2186 @ X2184 )
        | ~ ( in @ X2187 @ X2184 )
        | X2185
        | ( ( dsetconstr @ X2184
            @ ^ [Z0: $i] :
                ( ( X2185
                  & ( Z0 = X2186 ) )
                | ( ~ X2185
                  & ( Z0 = X2187 ) ) ) )
          = ( setadjoin @ X2187 @ emptyset ) ) )
      & ( ~ ( in @ X2190 @ X2188 )
        | ~ ( in @ X2191 @ X2188 )
        | ~ X2189
        | ( in @ X2190
          @ ( dsetconstr @ X2188
            @ ^ [Z0: $i] :
                ( ( X2189
                  & ( Z0 = X2190 ) )
                | ( ~ X2189
                  & ( Z0 = X2191 ) ) ) ) ) )
      & ( ~ ( in @ X2194 @ X2192 )
        | ~ ( in @ X2195 @ X2192 )
        | ~ X2193
        | ( ( dsetconstr @ X2192
            @ ^ [Z0: $i] :
                ( ( X2193
                  & ( Z0 = X2194 ) )
                | ( ~ X2193
                  & ( Z0 = X2195 ) ) ) )
          = ( setadjoin @ X2194 @ emptyset ) ) )
      & ( ( in @ ( esk89_4 @ X2196 @ X2197 @ X2198 @ X2199 )
          @ ( dsetconstr @ X2196
            @ ^ [Z0: $i] :
                ( ( X2197
                  & ( Z0 = X2198 ) )
                | ( ~ X2197
                  & ( Z0 = X2199 ) ) ) ) )
        | ~ ( in @ X2199 @ X2196 )
        | ~ ( in @ X2198 @ X2196 ) )
      & ( ( ( dsetconstr @ X2196
            @ ^ [Z0: $i] :
                ( ( X2197
                  & ( Z0 = X2198 ) )
                | ( ~ X2197
                  & ( Z0 = X2199 ) ) ) )
          = ( setadjoin @ ( esk89_4 @ X2196 @ X2197 @ X2198 @ X2199 ) @ emptyset ) )
        | ~ ( in @ X2199 @ X2196 )
        | ~ ( in @ X2198 @ X2196 ) )
      & ( in @ esk91_0 @ esk90_0 )
      & ( in @ esk92_0 @ esk90_0 )
      & ( ~ epred2_0
        | epred2_0 )
      & ( ~ ( in @ ( if @ esk90_0 @ $false @ esk91_0 @ esk92_0 ) @ esk90_0 )
        | epred2_0 )
      & ( ~ epred2_0
        | ~ ( in @ ( if @ esk90_0 @ $true @ esk91_0 @ esk92_0 ) @ esk90_0 ) )
      & ( ~ ( in @ ( if @ esk90_0 @ $false @ esk91_0 @ esk92_0 ) @ esk90_0 )
        | ~ ( in @ ( if @ esk90_0 @ $true @ esk91_0 @ esk92_0 ) @ esk90_0 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_317])])])])])])])]) ).

thf(c_0_320,plain,
    ! [X1487: $i,X1488: $o,X1489: $i,X1490: $i] :
      ( ( if @ X1487 @ X1488 @ X1489 @ X1490 )
      = ( setunion
        @ ( dsetconstr @ X1487
          @ ^ [Z0: $i] :
              ( ( X1488
                & ( Z0 = X1489 ) )
              | ( ~ X1488
                & ( Z0 = X1490 ) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[c_0_318]) ).

thf(c_0_321,negated_conjecture,
    ( ~ epred2_0
    | ~ ( in @ ( if @ esk90_0 @ $true @ esk91_0 @ esk92_0 ) @ esk90_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_319]) ).

thf(c_0_322,plain,
    ! [X2: $i,X3: $i,X10: $o,X4: $i] :
      ( ( if @ X2 @ X10 @ X3 @ X4 )
      = ( setunion
        @ ( dsetconstr @ X2
          @ ^ [Z0: $i] :
              ( ( X10
                & ( Z0 = X3 ) )
              | ( ~ X10
                & ( Z0 = X4 ) ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_320]) ).

thf(c_0_323,negated_conjecture,
    ! [X2: $i,X4: $i,X3: $i] :
      ( ( ( dsetconstr @ X3
          @ ^ [Z0: $i] :
              ( ( ~ $true
                & ( Z0 = X2 ) )
              | ( ~ ~ $true
                & ( Z0 = X4 ) ) ) )
        = ( setadjoin @ X4 @ emptyset ) )
      | ~ ( in @ X2 @ X3 )
      | ~ ( in @ X4 @ X3 ) ),
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_319])])]) ).

thf(c_0_324,negated_conjecture,
    ( epred2_0
    | ~ ( in @ ( if @ esk90_0 @ ~ $true @ esk91_0 @ esk92_0 ) @ esk90_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_319]) ).

thf(c_0_325,negated_conjecture,
    ( ~ epred2_0
    | ~ ( in
        @ ( setunion
          @ ( dsetconstr @ esk90_0
            @ ^ [Z0: $i] :
                ( ( $true
                  & ( Z0 = esk91_0 ) )
                | ( ~ $true
                  & ( Z0 = esk92_0 ) ) ) ) )
        @ esk90_0 ) ),
    inference(rw,[status(thm)],[c_0_321,c_0_322]) ).

thf(c_0_326,negated_conjecture,
    ! [X4: $i,X3: $i,X2: $i] :
      ( ( ( dsetconstr @ X2
          @ ^ [Z0: $i] : ( Z0 = X3 ) )
        = ( setadjoin @ X3 @ emptyset ) )
      | ~ ( in @ X3 @ X2 )
      | ~ ( in @ X4 @ X2 ) ),
    inference(cn,[status(thm)],[c_0_323]) ).

thf(c_0_327,negated_conjecture,
    in @ esk92_0 @ esk90_0,
    inference(split_conjunct,[status(thm)],[c_0_319]) ).

thf(c_0_328,negated_conjecture,
    ( epred2_0
    | ~ ( in
        @ ( setunion
          @ ( dsetconstr @ esk90_0
            @ ^ [Z0: $i] :
                ( ( ~ $true
                  & ( Z0 = esk91_0 ) )
                | ( ~ ~ $true
                  & ( Z0 = esk92_0 ) ) ) ) )
        @ esk90_0 ) ),
    inference(rw,[status(thm)],[c_0_324,c_0_322]) ).

thf(c_0_329,negated_conjecture,
    ( ~ ( in
        @ ( setunion
          @ ( dsetconstr @ esk90_0
            @ ^ [Z0: $i] : ( Z0 = esk91_0 ) ) )
        @ esk90_0 )
    | ~ epred2_0 ),
    inference(cn,[status(thm)],[c_0_325]) ).

thf(c_0_330,negated_conjecture,
    ! [X2: $i] :
      ( ( ( dsetconstr @ esk90_0
          @ ^ [Z0: $i] : ( Z0 = X2 ) )
        = ( setadjoin @ X2 @ emptyset ) )
      | ~ ( in @ X2 @ esk90_0 ) ),
    inference(spm,[status(thm)],[c_0_326,c_0_327]) ).

thf(c_0_331,negated_conjecture,
    ! [X2: $i] :
      ( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
      = X2 ),
    inference(split_conjunct,[status(thm)],[c_0_319]) ).

thf(c_0_332,negated_conjecture,
    in @ esk91_0 @ esk90_0,
    inference(split_conjunct,[status(thm)],[c_0_319]) ).

thf(c_0_333,negated_conjecture,
    ( epred2_0
    | ~ ( in
        @ ( setunion
          @ ( dsetconstr @ esk90_0
            @ ^ [Z0: $i] : ( Z0 = esk92_0 ) ) )
        @ esk90_0 ) ),
    inference(cn,[status(thm)],[c_0_328]) ).

thf(c_0_334,negated_conjecture,
    ~ epred2_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_329,c_0_330]),c_0_331]),c_0_332]),c_0_332])]) ).

thf(c_0_335,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_333,c_0_330]),c_0_331]),c_0_327]),c_0_327])]),c_0_334]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SEU705^1 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n028.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sun May 19 18:05:22 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.19/0.47  Running higher-order theorem proving
% 0.19/0.47  Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 138.39/18.00  # Version: 3.1.0-ho
% 138.39/18.00  # Preprocessing class: HSLMSLSSLLLCHFA.
% 138.39/18.00  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 138.39/18.00  # Starting ehoh_best5 with 300s (1) cores
% 138.39/18.00  # Starting almost_fo_3_lam with 300s (1) cores
% 138.39/18.00  # Starting new_bool_5 with 300s (1) cores
% 138.39/18.00  # Starting pre_casc_3 with 300s (1) cores
% 138.39/18.00  # Starting ho_unfolding_8 with 300s (1) cores
% 138.39/18.00  # Starting new_ho_10_cnf2 with 300s (1) cores
% 138.39/18.00  # Starting new_bool_3 with 300s (1) cores
% 138.39/18.00  # Starting new_ho_5 with 300s (1) cores
% 138.39/18.00  # ho_unfolding_8 with pid 21240 completed with status 0
% 138.39/18.00  # Result found by ho_unfolding_8
% 138.39/18.00  # Preprocessing class: HSLMSLSSLLLCHFA.
% 138.39/18.00  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 138.39/18.00  # Starting ehoh_best5 with 300s (1) cores
% 138.39/18.00  # Starting almost_fo_3_lam with 300s (1) cores
% 138.39/18.00  # Starting new_bool_5 with 300s (1) cores
% 138.39/18.00  # Starting pre_casc_3 with 300s (1) cores
% 138.39/18.00  # Starting ho_unfolding_8 with 300s (1) cores
% 138.39/18.00  # No SInE strategy applied
% 138.39/18.00  # Search class: HGHSM-FSLM32-DHFMMSBN
% 138.39/18.00  # partial match(1): HGHSM-FSLM32-MHFMMSBN
% 138.39/18.00  # Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 138.39/18.00  # Starting ho_unfolding_8 with 61s (1) cores
% 138.39/18.00  # ho_unfolding_8 with pid 21250 completed with status 0
% 138.39/18.00  # Result found by ho_unfolding_8
% 138.39/18.00  # Preprocessing class: HSLMSLSSLLLCHFA.
% 138.39/18.00  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 138.39/18.00  # Starting ehoh_best5 with 300s (1) cores
% 138.39/18.00  # Starting almost_fo_3_lam with 300s (1) cores
% 138.39/18.00  # Starting new_bool_5 with 300s (1) cores
% 138.39/18.00  # Starting pre_casc_3 with 300s (1) cores
% 138.39/18.00  # Starting ho_unfolding_8 with 300s (1) cores
% 138.39/18.00  # No SInE strategy applied
% 138.39/18.00  # Search class: HGHSM-FSLM32-DHFMMSBN
% 138.39/18.00  # partial match(1): HGHSM-FSLM32-MHFMMSBN
% 138.39/18.00  # Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 138.39/18.00  # Starting ho_unfolding_8 with 61s (1) cores
% 138.39/18.00  # Preprocessing time       : 0.150 s
% 138.39/18.00  # Presaturation interreduction done
% 138.39/18.00  
% 138.39/18.00  # Proof found!
% 138.39/18.00  # SZS status Theorem
% 138.39/18.00  # SZS output start CNFRefutation
% See solution above
% 138.39/18.00  # Parsed axioms                        : 487
% 138.39/18.00  # Removed by relevancy pruning/SinE    : 0
% 138.39/18.00  # Initial clauses                      : 673
% 138.39/18.00  # Removed in clause preprocessing      : 290
% 138.39/18.00  # Initial clauses in saturation        : 383
% 138.39/18.00  # Processed clauses                    : 8558
% 138.39/18.00  # ...of these trivial                  : 43
% 138.39/18.00  # ...subsumed                          : 4863
% 138.39/18.00  # ...remaining for further processing  : 3651
% 138.39/18.00  # Other redundant clauses eliminated   : 188
% 138.39/18.00  # Clauses deleted for lack of memory   : 0
% 138.39/18.00  # Backward-subsumed                    : 371
% 138.39/18.00  # Backward-rewritten                   : 7
% 138.39/18.00  # Generated clauses                    : 612075
% 138.39/18.00  # ...of the previous two non-redundant : 606420
% 138.39/18.00  # ...aggressively subsumed             : 0
% 138.39/18.00  # Contextual simplify-reflections      : 89
% 138.39/18.00  # Paramodulations                      : 611465
% 138.39/18.00  # Factorizations                       : 120
% 138.39/18.00  # NegExts                              : 131
% 138.39/18.00  # Equation resolutions                 : 202
% 138.39/18.00  # Disequality decompositions           : 0
% 138.39/18.00  # Total rewrite steps                  : 59483
% 138.39/18.00  # ...of those cached                   : 59155
% 138.39/18.00  # Propositional unsat checks           : 0
% 138.39/18.00  #    Propositional check models        : 0
% 138.39/18.00  #    Propositional check unsatisfiable : 0
% 138.39/18.00  #    Propositional clauses             : 0
% 138.39/18.00  #    Propositional clauses after purity: 0
% 138.39/18.00  #    Propositional unsat core size     : 0
% 138.39/18.00  #    Propositional preprocessing time  : 0.000
% 138.39/18.00  #    Propositional encoding time       : 0.000
% 138.39/18.00  #    Propositional solver time         : 0.000
% 138.39/18.00  #    Success case prop preproc time    : 0.000
% 138.39/18.00  #    Success case prop encoding time   : 0.000
% 138.39/18.00  #    Success case prop solver time     : 0.000
% 138.39/18.00  # Current number of processed clauses  : 2884
% 138.39/18.00  #    Positive orientable unit clauses  : 54
% 138.39/18.00  #    Positive unorientable unit clauses: 0
% 138.39/18.00  #    Negative unit clauses             : 48
% 138.39/18.00  #    Non-unit-clauses                  : 2782
% 138.39/18.00  # Current number of unprocessed clauses: 598256
% 138.39/18.00  # ...number of literals in the above   : 2747506
% 138.39/18.00  # Current number of archived formulas  : 0
% 138.39/18.00  # Current number of archived clauses   : 752
% 138.39/18.00  # Clause-clause subsumption calls (NU) : 1358675
% 138.39/18.00  # Rec. Clause-clause subsumption calls : 595776
% 138.39/18.00  # Non-unit clause-clause subsumptions  : 3102
% 138.39/18.00  # Unit Clause-clause subsumption calls : 5694
% 138.39/18.00  # Rewrite failures with RHS unbound    : 0
% 138.39/18.00  # BW rewrite match attempts            : 33
% 138.39/18.00  # BW rewrite match successes           : 7
% 138.39/18.00  # Condensation attempts                : 0
% 138.39/18.00  # Condensation successes               : 0
% 138.39/18.00  # Termbank termtop insertions          : 14342457
% 138.39/18.00  # Search garbage collected termcells   : 24764
% 138.39/18.00  
% 138.39/18.00  # -------------------------------------------------
% 138.39/18.00  # User time                : 16.391 s
% 138.39/18.00  # System time              : 0.525 s
% 138.39/18.00  # Total time               : 16.915 s
% 138.39/18.00  # Maximum resident set size: 7544 pages
% 138.39/18.00  
% 138.39/18.00  # -------------------------------------------------
% 138.39/18.00  # User time                : 16.403 s
% 138.39/18.00  # System time              : 0.529 s
% 138.39/18.00  # Total time               : 16.932 s
% 138.39/18.00  # Maximum resident set size: 2344 pages
% 138.39/18.00  % E---3.1 exiting
% 138.39/18.00  % E exiting
%------------------------------------------------------------------------------