TSTP Solution File: SEU710^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU710^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n019.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 03:29:22 EDT 2024

% Result   : Theorem 6.73s 1.63s
% Output   : CNFRefutation 7.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :  573
% Syntax   : Number of formulae    :  666 (  40 unt; 342 typ;   0 def)
%            Number of atoms       : 2888 ( 616 equ;   0 cnn)
%            Maximal formula atoms :  871 (   8 avg)
%            Number of connectives : 11646 ( 779   ~; 857   |; 533   &;7736   @)
%                                         ( 319 <=>;1422  =>;   0  <=;   0 <~>)
%            Maximal formula depth : 1026 (  13 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  582 ( 582   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  346 ( 342 usr; 235 con; 0-4 aty)
%            Number of variables   : 2561 ( 182   ^2256   !; 123   ?;2561   :)

% 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_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,
    ifp: $o ).

thf(decl_282,type,
    theeq: $o ).

thf(decl_283,type,
    iftrue: $o ).

thf(decl_284,type,
    iffalse: $o ).

thf(decl_285,type,
    iftrueorfalse: $o ).

thf(decl_286,type,
    epred1_0: $o ).

thf(decl_287,type,
    esk1_2: $i > $i > $i ).

thf(decl_288,type,
    esk2_2: $i > $i > $i ).

thf(decl_289,type,
    esk3_2: $i > $i > $i ).

thf(decl_290,type,
    esk4_1: $i > $i ).

thf(decl_291,type,
    esk5_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_292,type,
    esk6_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_293,type,
    esk7_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_294,type,
    esk8_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_295,type,
    esk9_1: $i > $i ).

thf(decl_296,type,
    esk10_2: ( $i > $o ) > $i > $i ).

thf(decl_297,type,
    esk11_2: ( $i > $o ) > $i > $i ).

thf(decl_298,type,
    esk12_1: ( $i > $o ) > $i ).

thf(decl_299,type,
    esk13_2: ( $i > $o ) > $i > $i ).

thf(decl_300,type,
    esk14_1: ( $i > $o ) > $i ).

thf(decl_301,type,
    esk15_2: $i > $i > $i ).

thf(decl_302,type,
    esk16_2: $i > $i > $i ).

thf(decl_303,type,
    esk17_1: $i > $i ).

thf(decl_304,type,
    esk18_1: $i > $i ).

thf(decl_305,type,
    esk19_1: $i > $i ).

thf(decl_306,type,
    esk20_2: $i > $i > $i ).

thf(decl_307,type,
    esk21_3: $i > $i > $o > $i ).

thf(decl_308,type,
    esk22_2: ( $i > $o ) > $i > $i ).

thf(decl_309,type,
    esk23_1: ( $i > $o ) > $i ).

thf(decl_310,type,
    esk24_1: $i > $i ).

thf(decl_311,type,
    esk25_2: $i > ( $i > $o ) > $i ).

thf(decl_312,type,
    esk26_2: $i > ( $i > $o ) > $i ).

thf(decl_313,type,
    esk27_2: $i > ( $i > $o ) > $i ).

thf(decl_314,type,
    esk28_2: $i > ( $i > $o ) > $i ).

thf(decl_315,type,
    esk29_2: $i > ( $i > $o ) > $i ).

thf(decl_316,type,
    esk30_2: $i > ( $i > $o ) > $i ).

thf(decl_317,type,
    esk31_2: ( $i > $o ) > $i > $i ).

thf(decl_318,type,
    esk32_1: ( $i > $o ) > $i ).

thf(decl_319,type,
    esk33_1: ( $i > $o ) > $i ).

thf(decl_320,type,
    esk34_1: ( $i > $o ) > $i ).

thf(decl_321,type,
    esk35_1: ( $i > $o ) > $i ).

thf(decl_322,type,
    esk36_2: ( $i > $o ) > $i > $i ).

thf(decl_323,type,
    esk37_1: ( $i > $o ) > $i ).

thf(decl_324,type,
    esk38_2: ( $i > $o ) > $i > $i ).

thf(decl_325,type,
    esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_326,type,
    esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_327,type,
    esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_328,type,
    esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_329,type,
    esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_330,type,
    esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_331,type,
    esk45_2: ( $i > $o ) > $i > $i ).

thf(decl_332,type,
    esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_333,type,
    esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_334,type,
    esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_335,type,
    esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_336,type,
    esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_337,type,
    esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_338,type,
    esk52_2: $i > $i > $i ).

thf(decl_339,type,
    esk53_2: $i > $i > $i ).

thf(decl_340,type,
    esk54_2: $i > $i > $i ).

thf(decl_341,type,
    esk55_3: $i > $i > $i > $i ).

thf(decl_342,type,
    esk56_3: $i > $i > $i > $i ).

thf(decl_343,type,
    esk57_2: $i > $i > $i ).

thf(decl_344,type,
    esk58_2: $i > ( $i > $o ) > $i ).

thf(decl_345,type,
    esk59_2: $i > ( $i > $o ) > $i ).

thf(decl_346,type,
    esk60_2: $i > ( $i > $o ) > $i ).

thf(decl_347,type,
    esk61_3: $i > ( $i > $o ) > $i > $i ).

thf(decl_348,type,
    esk62_2: $i > ( $i > $o ) > $i ).

thf(decl_349,type,
    esk63_2: $i > ( $i > $o ) > $i ).

thf(decl_350,type,
    esk64_3: $i > $i > ( $i > $i ) > $i ).

thf(decl_351,type,
    esk65_3: $i > $i > ( $i > $i ) > $i ).

thf(decl_352,type,
    esk66_3: $i > $i > ( $i > $i ) > $i ).

thf(decl_353,type,
    esk67_4: $i > $i > $i > ( $i > $o ) > $i ).

thf(decl_354,type,
    esk68_4: $i > $i > $i > ( $i > $o ) > $i ).

thf(decl_355,type,
    esk69_4: $i > $i > $i > ( $i > $o ) > $i ).

thf(decl_356,type,
    esk70_4: $i > $i > $i > ( $i > $o ) > $i ).

thf(decl_357,type,
    esk71_4: $i > $i > $i > $i > $i ).

thf(decl_358,type,
    esk72_4: $i > $i > $i > $i > $i ).

thf(decl_359,type,
    esk73_4: $i > $i > $i > $i > $i ).

thf(decl_360,type,
    esk74_4: $i > $i > $i > $i > $i ).

thf(decl_361,type,
    esk75_4: $i > $i > $i > $i > $i ).

thf(decl_362,type,
    esk76_4: $i > $i > $i > $i > $i ).

thf(decl_363,type,
    esk77_4: $i > $i > $i > $i > $i ).

thf(decl_364,type,
    esk78_4: $i > $i > $i > $i > $i ).

thf(decl_365,type,
    esk79_4: $i > $i > $i > $i > $i ).

thf(decl_366,type,
    esk80_3: $i > $i > ( $i > $i ) > $i ).

thf(decl_367,type,
    esk81_3: $i > $i > ( $i > $i ) > $i ).

thf(decl_368,type,
    esk82_3: $i > $i > ( $i > $i ) > $i ).

thf(decl_369,type,
    esk83_0: $i ).

thf(decl_370,type,
    esk84_0: $i ).

thf(decl_371,type,
    esk85_0: $i ).

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

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

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

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

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

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

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

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

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(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(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(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(binintersectT_lem,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
                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ifp
                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( theeq
                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( iftrue
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( iffalse
                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( iftrueorfalse
                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X4: $i,X21: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X21 @ ( powerset @ X4 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X48: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X48 @ ( powerset @ X4 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( in @ ( binintersect @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectT_lem) ).

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

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(iftrueorfalse,axiom,
    ( iftrueorfalse
  <=> ! [X4: $i,X47: $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X4 )
           => ( in @ ( if @ X4 @ X47 @ X2 @ X3 ) @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueorfalse) ).

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

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

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(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(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(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(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(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(ifp,axiom,
    ( ifp
  <=> ! [X4: $i,X44: $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X4 )
           => ( in @ ( if @ X4 @ X44 @ X2 @ X3 ) @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifp) ).

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

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

thf(iftrue,axiom,
    ( iftrue
  <=> ! [X4: $i,X45: $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X4 )
           => ( X45
             => ( ( if @ X4 @ X45 @ X2 @ X3 )
                = X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrue) ).

thf(iffalse,axiom,
    ( iffalse
  <=> ! [X4: $i,X46: $o,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X4 )
           => ( ~ X46
             => ( ( if @ X4 @ X46 @ X2 @ X3 )
                = X3 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalse) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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(c_0_230,plain,
    ( breln
    = ( ^ [Z0: $i,Z1: $i,Z2: $i] : ( subset @ Z2 @ ( cartprod @ Z0 @ Z1 ) ) ) ),
    inference(fof_simplification,[status(thm)],[breln]) ).

thf(c_0_231,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_232,plain,
    ( ex1
    = ( ^ [Z0: $i,Z1: $i > $o] :
          ( singleton
          @ ( dsetconstr @ Z0
            @ ^ [Z2: $i] : ( Z1 @ Z2 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[ex1]) ).

thf(c_0_233,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_234,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_235,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_236,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_237,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_238,plain,
    ( exu
    = ( ^ [Z0: $i > $o] :
        ? [X2: $i] :
          ( ( Z0 @ X2 )
          & ! [X3: $i] :
              ( ( Z0 @ X3 )
             => ( X2 = X3 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[exu]) ).

thf(c_0_239,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_240,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_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,
    ( 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_243,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_244,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_245,plain,
    ( nonempty
    = ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
    inference(fof_simplification,[status(thm)],[nonempty]) ).

thf(c_0_246,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_247,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_248,plain,
    ( exuE3e
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ? [X2: $i] : ( X1 @ X2 ) ) ),
    inference(fof_simplification,[status(thm)],[exuE3e]) ).

thf(c_0_249,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_250,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_251,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_252,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_253,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_254,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_255,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_256,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_230]) ).

thf(c_0_257,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_230]) ).

thf(c_0_258,plain,
    ( ex1E2
    = ( ! [X4: $i,X1: $i > $o] :
          ( ( singleton
            @ ( dsetconstr @ X4
              @ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
         => ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ! [X3: $i] :
                  ( ( in @ X3 @ X4 )
                 => ( ( X1 @ X2 )
                   => ( ( X1 @ X3 )
                     => ( X2 = X3 ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_231,c_0_232]) ).

thf(c_0_259,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_230]) ).

thf(c_0_260,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_230]) ).

thf(c_0_261,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_262,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_263,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_264,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_265,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_266,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_267,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_268,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_269,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_270,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_271,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_272,plain,
    ( sepSubset
  <=> ! [X4: $i,X1: $i > $o] :
        ( subset
        @ ( dsetconstr @ X4
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
        @ X4 ) ),
    inference(fof_simplification,[status(thm)],[sepSubset]) ).

thf(c_0_273,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_274,plain,
    ( ex1E1
    = ( ! [X4: $i,X1: $i > $o] :
          ( ( singleton
            @ ( dsetconstr @ X4
              @ ^ [Z0: $i] : ( X1 @ Z0 ) ) )
         => ? [X2: $i] :
              ( ( in @ X2 @ X4 )
              & ( X1 @ X2 ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_233,c_0_232]) ).

thf(c_0_275,plain,
    ( ex1I
    = ( ! [X4: $i,X1: $i > $o,X2: $i] :
          ( ( in @ X2 @ X4 )
         => ( ( X1 @ X2 )
           => ( ! [X3: $i] :
                  ( ( in @ X3 @ X4 )
                 => ( ( X1 @ X3 )
                   => ( X3 = X2 ) ) )
             => ( singleton
                @ ( dsetconstr @ X4
                  @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_234,c_0_232]) ).

thf(c_0_276,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 ) )
           => ( singleton
              @ ( dsetconstr @ X4
                @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_235,c_0_232]) ).

thf(c_0_277,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_278,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_279,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_280,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_281,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_236,c_0_230]) ).

thf(c_0_282,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_283,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_284,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_285,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_286,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_287,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_288,plain,
    ( descr__Cong
    = ( ! [X1: $i > $o,X17: $i > $o] :
          ( ! [X2: $i,X3: $i] :
              ( ( X2 = X3 )
             => ( ( X1 @ X2 )
              <=> ( X17 @ X3 ) ) )
         => ( ? [X771: $i] :
                ( ( X1 @ X771 )
                & ! [X772: $i] :
                    ( ( X1 @ X772 )
                   => ( X771 = X772 ) ) )
           => ( ? [X773: $i] :
                  ( ( X17 @ X773 )
                  & ! [X774: $i] :
                      ( ( X17 @ X774 )
                     => ( X773 = X774 ) ) )
             => ( ( descr
                  @ ^ [Z0: $i] : ( X1 @ Z0 ) )
                = ( descr
                  @ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_237,c_0_238]) ).

thf(c_0_289,plain,
    ( exuEu
    = ( ! [X1: $i > $o] :
          ( ? [X769: $i] :
              ( ( X1 @ X769 )
              & ! [X770: $i] :
                  ( ( X1 @ X770 )
                 => ( X769 = X770 ) ) )
         => ! [X2: $i,X3: $i] :
              ( ( X1 @ X2 )
             => ( ( X1 @ X3 )
               => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_239,c_0_238]) ).

thf(c_0_290,plain,
    ( exu__Cong
    = ( ! [X1: $i > $o,X17: $i > $o] :
          ( ! [X2: $i,X3: $i] :
              ( ( X2 = X3 )
             => ( ( X1 @ X2 )
              <=> ( X17 @ X3 ) ) )
         => ( ? [X765: $i] :
                ( ( X1 @ X765 )
                & ! [X766: $i] :
                    ( ( X1 @ X766 )
                   => ( X765 = X766 ) ) )
          <=> ? [X767: $i] :
                ( ( X17 @ X767 )
                & ! [X768: $i] :
                    ( ( X17 @ X768 )
                   => ( X767 = X768 ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_240,c_0_238]) ).

thf(c_0_291,plain,
    ( exuE3u
    = ( ! [X1: $i > $o] :
          ( ? [X763: $i] :
              ( ( X1 @ X763 )
              & ! [X764: $i] :
                  ( ( X1 @ X764 )
                 => ( X763 = X764 ) ) )
         => ! [X2: $i,X3: $i] :
              ( ( X1 @ X2 )
             => ( ( X1 @ X3 )
               => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_241,c_0_238]) ).

thf(c_0_292,plain,
    ( exuI2
    = ( ! [X1: $i > $o] :
          ( ? [X2: $i] :
            ! [X3: $i] :
              ( ( X1 @ X3 )
            <=> ( X3 = X2 ) )
         => ? [X761: $i] :
              ( ( X1 @ X761 )
              & ! [X762: $i] :
                  ( ( X1 @ X762 )
                 => ( X761 = X762 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_242,c_0_238]) ).

thf(c_0_293,plain,
    ( exuI3
    = ( ! [X1: $i > $o] :
          ( ? [X2: $i] : ( X1 @ X2 )
         => ( ! [X2: $i,X3: $i] :
                ( ( X1 @ X2 )
               => ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) )
           => ? [X759: $i] :
                ( ( X1 @ X759 )
                & ! [X760: $i] :
                    ( ( X1 @ X760 )
                   => ( X759 = X760 ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_243,c_0_238]) ).

thf(c_0_294,plain,
    ( exuI1
    = ( ! [X1: $i > $o] :
          ( ? [X2: $i] :
              ( ( X1 @ X2 )
              & ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) )
         => ? [X757: $i] :
              ( ( X1 @ X757 )
              & ! [X758: $i] :
                  ( ( X1 @ X758 )
                 => ( X757 = X758 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_244,c_0_238]) ).

thf(c_0_295,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_296,axiom,
    ( nonemptyImpWitness
    = ( ! [X4: $i] :
          ( ( X4 != emptyset )
         => ? [X2: $i] :
              ( ( in @ X2 @ X4 )
              & $true ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_245]) ).

thf(c_0_297,plain,
    ( exuE2
    = ( ! [X1: $i > $o] :
          ( ? [X755: $i] :
              ( ( X1 @ X755 )
              & ! [X756: $i] :
                  ( ( X1 @ X756 )
                 => ( X755 = X756 ) ) )
         => ? [X2: $i] :
            ! [X3: $i] :
              ( ( X1 @ X3 )
            <=> ( X3 = X2 ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_246,c_0_238]) ).

thf(c_0_298,plain,
    ( setoftrueEq
  <=> ! [X4: $i] :
        ( ( dsetconstr @ X4
          @ ^ [Z0: $i] : $true )
        = X4 ) ),
    inference(fof_simplification,[status(thm)],[setoftrueEq]) ).

thf(c_0_299,axiom,
    ( nonemptyI1
    = ( ! [X4: $i] :
          ( ? [X2: $i] : ( in @ X2 @ X4 )
         => ( X4 != emptyset ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyI1,c_0_245]) ).

thf(c_0_300,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_247,c_0_245]) ).

thf(c_0_301,axiom,
    ( nonemptyE1
    = ( ! [X4: $i] :
          ( ( X4 != emptyset )
         => ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyE1,c_0_245]) ).

thf(c_0_302,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_303,plain,
    ( exuE3e
    = ( ! [X1: $i > $o] :
          ( ? [X753: $i] :
              ( ( X1 @ X753 )
              & ! [X754: $i] :
                  ( ( X1 @ X754 )
                 => ( X753 = X754 ) ) )
         => ? [X2: $i] : ( X1 @ X2 ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_248,c_0_238]) ).

thf(c_0_304,plain,
    ( exuE1
    = ( ! [X1: $i > $o] :
          ( ? [X751: $i] :
              ( ( X1 @ X751 )
              & ! [X752: $i] :
                  ( ( X1 @ X752 )
                 => ( X751 = X752 ) ) )
         => ? [X2: $i] :
              ( ( X1 @ X2 )
              & ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_249,c_0_238]) ).

thf(c_0_305,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_306,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_307,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_308,plain,
    ( descrp
    = ( ! [X1: $i > $o] :
          ( ? [X749: $i] :
              ( ( X1 @ X749 )
              & ! [X750: $i] :
                  ( ( X1 @ X750 )
                 => ( X749 = X750 ) ) )
         => ( X1
            @ ( descr
              @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_250,c_0_238]) ).

thf(c_0_309,plain,
    ( replAx
    = ( ! [X6: $i > $i > $o,X4: $i] :
          ( ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ? [X747: $i] :
                  ( ( X6 @ X2 @ X747 )
                  & ! [X748: $i] :
                      ( ( X6 @ X2 @ X748 )
                     => ( X747 = X748 ) ) ) )
         => ? [X5: $i] :
            ! [X2: $i] :
              ( ( in @ X2 @ X5 )
            <=> ? [X3: $i] :
                  ( ( in @ X3 @ X4 )
                  & ( X6 @ X3 @ X2 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_251,c_0_238]) ).

thf(c_0_310,plain,
    ( epred1_0
  <=> ! [X804: $i] :
      ? [X805: $i] :
        ( ! [X806: $i] :
            ( ( in @ X806 @ X805 )
           => ! [X807: $i] :
                ( ( in @ X807 @ X806 )
               => ( in @ X807 @ X804 ) ) )
        & ! [X808: $i,X809: $i] :
            ( ( ( in @ X808 @ X804 )
              & ( in @ X809 @ X804 ) )
           => ( ! [X810: $i] :
                  ( ( in @ X810 @ X805 )
                 => ( ( in @ X808 @ X810 )
                  <=> ( in @ X809 @ X810 ) ) )
             => ( X808 = X809 ) ) )
        & ! [X811: $i,X812: $i] :
            ( ( ( in @ X811 @ X805 )
              & ( in @ X812 @ X805 ) )
           => ( ! [X813: $i] :
                  ( ( in @ X813 @ X811 )
                 => ( in @ X813 @ X812 ) )
              | ! [X814: $i] :
                  ( ( in @ X814 @ X812 )
                 => ( in @ X814 @ X811 ) ) ) )
        & ! [X815: $i] :
            ( ( ! [X816: $i] :
                  ( ( in @ X816 @ X815 )
                 => ( in @ X816 @ X804 ) )
              & ? [X817: $i] : ( in @ X817 @ X815 ) )
           => ? [X818: $i,X819: $i] :
                ( ( in @ X818 @ X805 )
                & ( in @ X819 @ X815 )
                & ~ ? [X820: $i] :
                      ( ( in @ X820 @ X818 )
                      & ( in @ X820 @ X815 ) )
                & ! [X821: $i] :
                    ( ( in @ X821 @ X805 )
                   => ( ! [X822: $i] :
                          ( ( in @ X822 @ X821 )
                         => ( in @ X822 @ X818 ) )
                      | ( in @ X819 @ X821 ) ) ) ) ) ) ),
    introduced(definition) ).

thf(c_0_311,negated_conjecture,
    ~ ( ! [X775: $i,X776: $i] :
          ( ! [X777: $i] :
              ( ( in @ X777 @ X775 )
            <=> ( in @ X777 @ X776 ) )
         => ( X775 = X776 ) )
     => ( ! [X778: $i] :
            ~ ( in @ X778 @ emptyset )
       => ( ! [X779: $i,X780: $i,X781: $i] :
              ( ( in @ X781 @ ( setadjoin @ X779 @ X780 ) )
            <=> ( ( X781 = X779 )
                | ( in @ X781 @ X780 ) ) )
         => ( ! [X782: $i,X783: $i] :
                ( ( in @ X783 @ ( powerset @ X782 ) )
              <=> ! [X784: $i] :
                    ( ( in @ X784 @ X783 )
                   => ( in @ X784 @ X782 ) ) )
           => ( ! [X785: $i,X786: $i] :
                  ( ( in @ X786 @ ( setunion @ X785 ) )
                <=> ? [X787: $i] :
                      ( ( in @ X786 @ X787 )
                      & ( in @ X787 @ X785 ) ) )
             => ( ( in @ emptyset @ omega )
               => ( ! [X788: $i] :
                      ( ( in @ X788 @ omega )
                     => ( in @ ( setadjoin @ X788 @ X788 ) @ omega ) )
                 => ( ! [X789: $i] :
                        ( ( ( in @ emptyset @ X789 )
                          & ! [X790: $i] :
                              ( ( ( in @ X790 @ omega )
                                & ( in @ X790 @ X789 ) )
                             => ( in @ ( setadjoin @ X790 @ X790 ) @ X789 ) ) )
                       => ! [X791: $i] :
                            ( ( in @ X791 @ omega )
                           => ( in @ X791 @ X789 ) ) )
                   => ( ! [X792: $i > $i > $o,X793: $i] :
                          ( ! [X794: $i] :
                              ( ( in @ X794 @ X793 )
                             => ? [X795: $i] :
                                  ( ( X792 @ X794 @ X795 )
                                  & ! [X796: $i] :
                                      ( ( X792 @ X794 @ X796 )
                                     => ( X795 = X796 ) ) ) )
                         => ? [X797: $i] :
                            ! [X798: $i] :
                              ( ( in @ X798 @ X797 )
                            <=> ? [X799: $i] :
                                  ( ( in @ X799 @ X793 )
                                  & ( X792 @ X799 @ X798 ) ) ) )
                     => ( ! [X800: $i] :
                            ( ? [X801: $i] : ( in @ X801 @ X800 )
                           => ? [X802: $i] :
                                ( ( in @ X802 @ X800 )
                                & ~ ? [X803: $i] :
                                      ( ( in @ X803 @ X802 )
                                      & ( in @ X803 @ X800 ) ) ) )
                       => ( epred1_0
                         => ( ! [X823: $i > $o] :
                                ( ? [X824: $i] :
                                    ( ( X823 @ X824 )
                                    & ! [X825: $i] :
                                        ( ( X823 @ X825 )
                                       => ( X824 = X825 ) ) )
                               => ( X823
                                  @ ( descr
                                    @ ^ [Z0: $i] : ( X823 @ Z0 ) ) ) )
                           => ( ! [X826: $i,X827: $i > $o,X828: $i] :
                                  ( ( in @ X828 @ X826 )
                                 => ( ( X827 @ X828 )
                                   => ( in @ X828 @ ( dsetconstr @ X826 @ X827 ) ) ) )
                             => ( ! [X829: $i,X830: $i > $o,X831: $i] :
                                    ( ( in @ X831 @ ( dsetconstr @ X829 @ X830 ) )
                                   => ( in @ X831 @ X829 ) )
                               => ( ! [X832: $i,X833: $i > $o,X834: $i] :
                                      ( ( in @ X834 @ ( dsetconstr @ X832 @ X833 ) )
                                     => ( X833 @ X834 ) )
                                 => ( ! [X835: $i > $o] :
                                        ( ? [X836: $i] :
                                            ( ( X835 @ X836 )
                                            & ! [X837: $i] :
                                                ( ( X835 @ X837 )
                                               => ( X836 = X837 ) ) )
                                       => ? [X838: $i] :
                                            ( ( X835 @ X838 )
                                            & ! [X839: $i] :
                                                ( ( X835 @ X839 )
                                               => ( X838 = X839 ) ) ) )
                                   => ( ! [X840: $o,X841: $i] :
                                          ( ( in @ X841 @ ( prop2set @ X840 ) )
                                         => X840 )
                                     => ( ! [X842: $i] :
                                            ( ( in @ X842 @ emptyset )
                                           => ! [X843: $o] : X843 )
                                       => ( ! [X844: $i] :
                                              ( ( in @ X844 @ emptyset )
                                             => ~ $true )
                                         => ( ! [X845: $i] :
                                                ~ ( in @ X845 @ emptyset )
                                           => ( ! [X846: $i > $o] :
                                                  ( ? [X847: $i] :
                                                      ( ( X846 @ X847 )
                                                      & ! [X848: $i] :
                                                          ( ( X846 @ X848 )
                                                         => ( X847 = X848 ) ) )
                                                 => ? [X849: $i] : ( X846 @ X849 ) )
                                             => ( ! [X850: $i,X851: $i] :
                                                    ( ! [X852: $i] :
                                                        ( ( in @ X852 @ X850 )
                                                       => ( in @ X852 @ X851 ) )
                                                   => ( ! [X853: $i] :
                                                          ( ( in @ X853 @ X851 )
                                                         => ( in @ X853 @ X850 ) )
                                                     => ( X850 = X851 ) ) )
                                               => ( ! [X854: $i] :
                                                      ( ! [X855: $i] :
                                                          ~ ( in @ X855 @ X854 )
                                                     => ( X854 = emptyset ) )
                                                 => ( ! [X856: $i] :
                                                        ( ! [X857: $i] :
                                                            ~ ( in @ X857 @ X856 )
                                                       => ( X856 = emptyset ) )
                                                   => ( ! [X858: $i,X859: $i > $o,X860: $i] :
                                                          ( ( in @ X860 @ X858 )
                                                         => ( ( in @ X860 @ ( dsetconstr @ X858 @ X859 ) )
                                                          <=> ( X859 @ X860 ) ) )
                                                     => ( ! [X861: $i] :
                                                            ( ( X861 != emptyset )
                                                           => ? [X862: $i] : ( in @ X862 @ X861 ) )
                                                       => ( ! [X863: $i,X864: $i > $o,X865: $i] :
                                                              ( ( in @ X865 @ X863 )
                                                             => ( ( X864 @ X865 )
                                                               => ( ( dsetconstr @ X863 @ X864 )
                                                                 != emptyset ) ) )
                                                         => ( ! [X866: $i] :
                                                                ( ? [X867: $i] : ( in @ X867 @ X866 )
                                                               => ( X866 != emptyset ) )
                                                           => ( ! [X868: $i,X869: $i] : ( in @ X868 @ ( setadjoin @ X868 @ X869 ) )
                                                             => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                               => ( ! [X870: $i,X871: $i,X872: $i] :
                                                                      ( ( in @ X872 @ X871 )
                                                                     => ( in @ X872 @ ( setadjoin @ X870 @ X871 ) ) )
                                                                 => ( ! [X873: $i,X874: $i,X875: $i] :
                                                                        ( ( in @ X875 @ ( setadjoin @ X873 @ X874 ) )
                                                                       => ! [X876: $o] :
                                                                            ( ( ( X875 = X873 )
                                                                             => X876 )
                                                                           => ( ( ( in @ X875 @ X874 )
                                                                               => X876 )
                                                                             => X876 ) ) )
                                                                   => ( ! [X877: $i,X878: $i,X879: $i] :
                                                                          ( ( in @ X879 @ ( setadjoin @ X877 @ X878 ) )
                                                                         => ( ( X879 = X877 )
                                                                            | ( in @ X879 @ X878 ) ) )
                                                                     => ( ! [X880: $i] :
                                                                            ( ( dsetconstr @ X880
                                                                              @ ^ [Z0: $i] : $true )
                                                                            = X880 )
                                                                       => ( ! [X881: $i,X882: $i] :
                                                                              ( ! [X883: $i] :
                                                                                  ( ( in @ X883 @ X882 )
                                                                                 => ( in @ X883 @ X881 ) )
                                                                             => ( in @ X882 @ ( powerset @ X881 ) ) )
                                                                         => ( ! [X884: $i] : ( in @ emptyset @ ( powerset @ X884 ) )
                                                                           => ( ! [X885: $i] : ( in @ emptyset @ ( powerset @ X885 ) )
                                                                             => ( ! [X886: $i,X887: $i,X888: $i] :
                                                                                    ( ( in @ X887 @ ( powerset @ X886 ) )
                                                                                   => ( ( in @ X888 @ X887 )
                                                                                     => ( in @ X888 @ X886 ) ) )
                                                                               => ( ! [X889: $i,X890: $i,X891: $i] :
                                                                                      ( ( in @ X890 @ X891 )
                                                                                     => ( ( in @ X891 @ X889 )
                                                                                       => ( in @ X890 @ ( setunion @ X889 ) ) ) )
                                                                                 => ( ! [X892: $i,X893: $i] :
                                                                                        ( ( in @ X893 @ ( setunion @ X892 ) )
                                                                                       => ! [X894: $o] :
                                                                                            ( ! [X895: $i] :
                                                                                                ( ( in @ X893 @ X895 )
                                                                                               => ( ( in @ X895 @ X892 )
                                                                                                 => X894 ) )
                                                                                           => X894 ) )
                                                                                   => ( ! [X896: $i,X897: $i] :
                                                                                          ( ( in @ X897 @ X896 )
                                                                                         => ( in @ X897 @ ( powerset @ ( setunion @ X896 ) ) ) )
                                                                                     => ( ! [X898: $i > $o] :
                                                                                            ( ? [X899: $i] :
                                                                                                ( ( X898 @ X899 )
                                                                                                & ! [X900: $i] :
                                                                                                    ( ( X898 @ X900 )
                                                                                                   => ( X899 = X900 ) ) )
                                                                                           => ? [X901: $i] :
                                                                                              ! [X902: $i] :
                                                                                                ( ( X898 @ X902 )
                                                                                              <=> ( X902 = X901 ) ) )
                                                                                       => ( ! [X903: $i] :
                                                                                              ( ( X903 != emptyset )
                                                                                             => ? [X904: $i] :
                                                                                                  ( ( in @ X904 @ X903 )
                                                                                                  & $true ) )
                                                                                         => ( ! [X905: $i,X906: $i] :
                                                                                                ( ( in @ X905 @ ( setadjoin @ X906 @ emptyset ) )
                                                                                               => ( X905 = X906 ) )
                                                                                           => ( ! [X907: $i,X908: $i] :
                                                                                                  ( ( X907 != X908 )
                                                                                                 => ~ ( in @ X908 @ ( setadjoin @ X907 @ emptyset ) ) )
                                                                                             => ( ! [X909: $i,X910: $i] :
                                                                                                    ( ( X909 = X910 )
                                                                                                   => ( in @ X909 @ ( setadjoin @ X910 @ emptyset ) ) )
                                                                                               => ( ! [X911: $i,X912: $i] :
                                                                                                      ( ( in @ X911 @ ( setadjoin @ X912 @ emptyset ) )
                                                                                                     => ( in @ X912 @ ( setadjoin @ X911 @ emptyset ) ) )
                                                                                                 => ( ! [X913: $i,X914: $i,X915: $i] :
                                                                                                        ( ( in @ X915 @ ( setadjoin @ X913 @ ( setadjoin @ X914 @ emptyset ) ) )
                                                                                                       => ( ( X915 = X913 )
                                                                                                          | ( X915 = X914 ) ) )
                                                                                                   => ( ! [X916: $i,X917: $i] : ( in @ X916 @ ( setadjoin @ X916 @ ( setadjoin @ X917 @ emptyset ) ) )
                                                                                                     => ( ! [X918: $i,X919: $i] : ( in @ X919 @ ( setadjoin @ X918 @ ( setadjoin @ X919 @ emptyset ) ) )
                                                                                                       => ( ! [X920: $i,X921: $i > $o] :
                                                                                                              ( ? [X922: $i] :
                                                                                                                  ( ( in @ X922 @ X920 )
                                                                                                                  & ( X921 @ X922 ) )
                                                                                                             => ( ( ( dsetconstr @ X920 @ X921 )
                                                                                                                  = emptyset )
                                                                                                               => ~ $true ) )
                                                                                                         => ( ! [X923: $i > $o,X924: $i] :
                                                                                                                ( ( in @ X924 @ emptyset )
                                                                                                               => ( X923 @ 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: $i,X934: $i > $o] :
                                                                                                                      ( ~ ? [X935: $i] :
                                                                                                                            ( ( in @ X935 @ X933 )
                                                                                                                            & ( X934 @ X935 ) )
                                                                                                                     => ! [X936: $i] :
                                                                                                                          ( ( in @ X936 @ X933 )
                                                                                                                         => ~ ( X934 @ X936 ) ) )
                                                                                                                 => ( ! [X937: $i,X938: $i > $o] :
                                                                                                                        ( ? [X939: $i] :
                                                                                                                            ( ( in @ X939 @ X937 )
                                                                                                                            & ~ ( X938 @ X939 ) )
                                                                                                                       => ~ ! [X940: $i] :
                                                                                                                              ( ( in @ X940 @ X937 )
                                                                                                                             => ( X938 @ X940 ) ) )
                                                                                                                   => ( ! [X941: $o] :
                                                                                                                          ( X941
                                                                                                                         => ( in @ emptyset @ ( prop2set @ X941 ) ) )
                                                                                                                     => ( prop2set2propI
                                                                                                                       => ( ! [X942: $i,X943: $i > $o] :
                                                                                                                              ( ~ ? [X944: $i] :
                                                                                                                                    ( ( in @ X944 @ X942 )
                                                                                                                                    & ( X943 @ X944 ) )
                                                                                                                             => ! [X945: $i] :
                                                                                                                                  ( ( in @ X945 @ X942 )
                                                                                                                                 => ~ ( X943 @ X945 ) ) )
                                                                                                                         => ( ! [X946: $i,X947: $i > $o] :
                                                                                                                                ( ~ ! [X948: $i] :
                                                                                                                                      ( ( in @ X948 @ X946 )
                                                                                                                                     => ( X947 @ X948 ) )
                                                                                                                               => ? [X949: $i] :
                                                                                                                                    ( ( in @ X949 @ X946 )
                                                                                                                                    & ~ ( X947 @ X949 ) ) )
                                                                                                                           => ( ! [X950: $i > $o] :
                                                                                                                                  ( ? [X951: $i] :
                                                                                                                                      ( ( X950 @ X951 )
                                                                                                                                      & ! [X952: $i] :
                                                                                                                                          ( ( X950 @ X952 )
                                                                                                                                         => ( X951 = X952 ) ) )
                                                                                                                                 => ? [X953: $i] :
                                                                                                                                      ( ( X950 @ X953 )
                                                                                                                                      & ! [X954: $i] :
                                                                                                                                          ( ( X950 @ X954 )
                                                                                                                                         => ( X953 = X954 ) ) ) )
                                                                                                                             => ( ! [X955: $i > $o] :
                                                                                                                                    ( ? [X956: $i] : ( X955 @ X956 )
                                                                                                                                   => ( ! [X957: $i,X958: $i] :
                                                                                                                                          ( ( X955 @ X957 )
                                                                                                                                         => ( ( X955 @ X958 )
                                                                                                                                           => ( X957 = X958 ) ) )
                                                                                                                                     => ? [X959: $i] :
                                                                                                                                          ( ( X955 @ X959 )
                                                                                                                                          & ! [X960: $i] :
                                                                                                                                              ( ( X955 @ X960 )
                                                                                                                                             => ( X959 = X960 ) ) ) ) )
                                                                                                                               => ( ! [X961: $i > $o] :
                                                                                                                                      ( ? [X962: $i] :
                                                                                                                                        ! [X963: $i] :
                                                                                                                                          ( ( X961 @ X963 )
                                                                                                                                        <=> ( X963 = X962 ) )
                                                                                                                                     => ? [X964: $i] :
                                                                                                                                          ( ( X961 @ X964 )
                                                                                                                                          & ! [X965: $i] :
                                                                                                                                              ( ( X961 @ X965 )
                                                                                                                                             => ( X964 = X965 ) ) ) )
                                                                                                                                 => ( ! [X966: $i,X967: $i] :
                                                                                                                                        ( ( X966 = X967 )
                                                                                                                                       => ! [X968: $i,X969: $i] :
                                                                                                                                            ( ( X968 = X969 )
                                                                                                                                           => ( ( in @ X968 @ X966 )
                                                                                                                                             => ( in @ X969 @ X967 ) ) ) )
                                                                                                                                   => ( ! [X970: $i,X971: $i] :
                                                                                                                                          ( ( X970 = X971 )
                                                                                                                                         => ! [X972: $i,X973: $i] :
                                                                                                                                              ( ( X972 = X973 )
                                                                                                                                             => ( ( in @ X972 @ X970 )
                                                                                                                                              <=> ( in @ X973 @ X971 ) ) ) )
                                                                                                                                     => ( ! [X974: $i > $o] :
                                                                                                                                            ( ? [X975: $i] :
                                                                                                                                                ( ( X974 @ X975 )
                                                                                                                                                & ! [X976: $i] :
                                                                                                                                                    ( ( X974 @ X976 )
                                                                                                                                                   => ( X975 = X976 ) ) )
                                                                                                                                           => ! [X977: $i,X978: $i] :
                                                                                                                                                ( ( X974 @ X977 )
                                                                                                                                               => ( ( X974 @ X978 )
                                                                                                                                                 => ( X977 = X978 ) ) ) )
                                                                                                                                       => ( ! [X979: $i > $o,X980: $i > $o] :
                                                                                                                                              ( ! [X981: $i,X982: $i] :
                                                                                                                                                  ( ( X981 = X982 )
                                                                                                                                                 => ( ( X979 @ X981 )
                                                                                                                                                  <=> ( X980 @ X982 ) ) )
                                                                                                                                             => ( ? [X983: $i] :
                                                                                                                                                    ( ( X979 @ X983 )
                                                                                                                                                    & ! [X984: $i] :
                                                                                                                                                        ( ( X979 @ X984 )
                                                                                                                                                       => ( X983 = X984 ) ) )
                                                                                                                                              <=> ? [X985: $i] :
                                                                                                                                                    ( ( X980 @ X985 )
                                                                                                                                                    & ! [X986: $i] :
                                                                                                                                                        ( ( X980 @ X986 )
                                                                                                                                                       => ( X985 = X986 ) ) ) ) )
                                                                                                                                         => ( ( emptyset = emptyset )
                                                                                                                                           => ( ! [X987: $i,X988: $i] :
                                                                                                                                                  ( ( X987 = X988 )
                                                                                                                                                 => ! [X989: $i,X990: $i] :
                                                                                                                                                      ( ( X989 = X990 )
                                                                                                                                                     => ( ( setadjoin @ X987 @ X989 )
                                                                                                                                                        = ( setadjoin @ X988 @ X990 ) ) ) )
                                                                                                                                             => ( ! [X991: $i,X992: $i] :
                                                                                                                                                    ( ( X991 = X992 )
                                                                                                                                                   => ( ( powerset @ X991 )
                                                                                                                                                      = ( powerset @ X992 ) ) )
                                                                                                                                               => ( ! [X993: $i,X994: $i] :
                                                                                                                                                      ( ( X993 = X994 )
                                                                                                                                                     => ( ( setunion @ X993 )
                                                                                                                                                        = ( setunion @ X994 ) ) )
                                                                                                                                                 => ( ( omega = omega )
                                                                                                                                                   => ( ! [X995: $i > $o] :
                                                                                                                                                          ( ? [X996: $i] :
                                                                                                                                                              ( ( X995 @ X996 )
                                                                                                                                                              & ! [X997: $i] :
                                                                                                                                                                  ( ( X995 @ X997 )
                                                                                                                                                                 => ( X996 = X997 ) ) )
                                                                                                                                                         => ! [X998: $i,X999: $i] :
                                                                                                                                                              ( ( X995 @ X998 )
                                                                                                                                                             => ( ( X995 @ X999 )
                                                                                                                                                               => ( X998 = X999 ) ) ) )
                                                                                                                                                     => ( ! [X1000: $i > $o,X1001: $i > $o] :
                                                                                                                                                            ( ! [X1002: $i,X1003: $i] :
                                                                                                                                                                ( ( X1002 = X1003 )
                                                                                                                                                               => ( ( X1000 @ X1002 )
                                                                                                                                                                <=> ( X1001 @ X1003 ) ) )
                                                                                                                                                           => ( ? [X1004: $i] :
                                                                                                                                                                  ( ( X1000 @ X1004 )
                                                                                                                                                                  & ! [X1005: $i] :
                                                                                                                                                                      ( ( X1000 @ X1005 )
                                                                                                                                                                     => ( X1004 = X1005 ) ) )
                                                                                                                                                             => ( ? [X1006: $i] :
                                                                                                                                                                    ( ( X1001 @ X1006 )
                                                                                                                                                                    & ! [X1007: $i] :
                                                                                                                                                                        ( ( X1001 @ X1007 )
                                                                                                                                                                       => ( X1006 = X1007 ) ) )
                                                                                                                                                               => ( ( descr @ X1000 )
                                                                                                                                                                  = ( descr @ X1001 ) ) ) ) )
                                                                                                                                                       => ( ! [X1008: $i,X1009: $i] :
                                                                                                                                                              ( ( X1008 = X1009 )
                                                                                                                                                             => ! [X1010: $i > $o,X1011: $i > $o] :
                                                                                                                                                                  ( ! [X1012: $i] :
                                                                                                                                                                      ( ( in @ X1012 @ X1008 )
                                                                                                                                                                     => ! [X1013: $i] :
                                                                                                                                                                          ( ( in @ X1013 @ X1009 )
                                                                                                                                                                         => ( ( X1012 = X1013 )
                                                                                                                                                                           => ( ( X1010 @ X1012 )
                                                                                                                                                                            <=> ( X1011 @ X1013 ) ) ) ) )
                                                                                                                                                                 => ( ( dsetconstr @ X1008 @ X1010 )
                                                                                                                                                                    = ( dsetconstr @ X1009 @ X1011 ) ) ) )
                                                                                                                                                         => ( ! [X1014: $i,X1015: $i] :
                                                                                                                                                                ( ! [X1016: $i] :
                                                                                                                                                                    ( ( in @ X1016 @ X1014 )
                                                                                                                                                                   => ( in @ X1016 @ X1015 ) )
                                                                                                                                                               => ( subset @ X1014 @ X1015 ) )
                                                                                                                                                           => ( ! [X1017: $i,X1018: $i] :
                                                                                                                                                                  ( ( X1017 = X1018 )
                                                                                                                                                                 => ( subset @ X1018 @ X1017 ) )
                                                                                                                                                             => ( ! [X1019: $i,X1020: $i] :
                                                                                                                                                                    ( ( X1019 = X1020 )
                                                                                                                                                                   => ( subset @ X1019 @ X1020 ) )
                                                                                                                                                               => ( ! [X1021: $i,X1022: $i] :
                                                                                                                                                                      ( ! [X1023: $i] :
                                                                                                                                                                          ( ( in @ X1023 @ X1021 )
                                                                                                                                                                         => ( in @ X1023 @ X1022 ) )
                                                                                                                                                                     => ( subset @ X1021 @ X1022 ) )
                                                                                                                                                                 => ( ! [X1024: $i] : ( subset @ emptyset @ X1024 )
                                                                                                                                                                   => ( ! [X1025: $i,X1026: $i,X1027: $i] :
                                                                                                                                                                          ( ( subset @ X1025 @ X1026 )
                                                                                                                                                                         => ( ( in @ X1027 @ X1025 )
                                                                                                                                                                           => ( in @ X1027 @ X1026 ) ) )
                                                                                                                                                                     => ( ! [X1028: $i,X1029: $i,X1030: $i] :
                                                                                                                                                                            ( ( subset @ X1028 @ X1029 )
                                                                                                                                                                           => ( ~ ( in @ X1030 @ X1029 )
                                                                                                                                                                             => ~ ( in @ X1030 @ X1028 ) ) )
                                                                                                                                                                       => ( ! [X1031: $i,X1032: $i,X1033: $i] :
                                                                                                                                                                              ( ( in @ X1033 @ X1031 )
                                                                                                                                                                             => ( ~ ( in @ X1033 @ X1032 )
                                                                                                                                                                               => ~ ( subset @ X1031 @ X1032 ) ) )
                                                                                                                                                                         => ( ! [X1034: $i,X1035: $i] :
                                                                                                                                                                                ( ~ ( subset @ X1034 @ X1035 )
                                                                                                                                                                               => ( X1034 != X1035 ) )
                                                                                                                                                                           => ( ! [X1036: $i,X1037: $i,X1038: $i] :
                                                                                                                                                                                  ( ( in @ X1038 @ X1036 )
                                                                                                                                                                                 => ( ~ ( in @ X1038 @ X1037 )
                                                                                                                                                                                   => ( X1036 != X1037 ) ) )
                                                                                                                                                                             => ( ! [X1039: $i] : ( subset @ X1039 @ X1039 )
                                                                                                                                                                               => ( ! [X1040: $i,X1041: $i,X1042: $i] :
                                                                                                                                                                                      ( ( subset @ X1040 @ X1041 )
                                                                                                                                                                                     => ( ( subset @ X1041 @ X1042 )
                                                                                                                                                                                       => ( subset @ X1040 @ X1042 ) ) )
                                                                                                                                                                                 => ( ! [X1043: $i,X1044: $i] : ( subset @ X1044 @ ( setadjoin @ X1043 @ X1044 ) )
                                                                                                                                                                                   => ( ! [X1045: $i,X1046: $i,X1047: $i] :
                                                                                                                                                                                          ( ( subset @ X1045 @ X1047 )
                                                                                                                                                                                         => ( subset @ X1045 @ ( setadjoin @ X1046 @ X1047 ) ) )
                                                                                                                                                                                     => ( ! [X1048: $i,X1049: $i] :
                                                                                                                                                                                            ( ( subset @ X1048 @ X1049 )
                                                                                                                                                                                           => ( in @ X1048 @ ( powerset @ X1049 ) ) )
                                                                                                                                                                                       => ( ! [X1050: $i,X1051: $i] :
                                                                                                                                                                                              ( ( subset @ X1050 @ X1051 )
                                                                                                                                                                                             => ( ( subset @ X1051 @ X1050 )
                                                                                                                                                                                               => ( X1050 = X1051 ) ) )
                                                                                                                                                                                         => ( ! [X1052: $i] :
                                                                                                                                                                                                ( ( subset @ X1052 @ emptyset )
                                                                                                                                                                                               => ( X1052 = emptyset ) )
                                                                                                                                                                                           => ( ! [X1053: $i,X1054: $i] :
                                                                                                                                                                                                  ( ( subset @ X1054 @ X1053 )
                                                                                                                                                                                                 => ( in @ X1054 @ ( powerset @ X1053 ) ) )
                                                                                                                                                                                             => ( ! [X1055: $i,X1056: $i] :
                                                                                                                                                                                                    ( ( in @ X1056 @ ( powerset @ X1055 ) )
                                                                                                                                                                                                   => ( subset @ X1056 @ X1055 ) )
                                                                                                                                                                                               => ( ! [X1057: $i] : ( in @ X1057 @ ( powerset @ X1057 ) )
                                                                                                                                                                                                 => ( ! [X1058: $i,X1059: $i] :
                                                                                                                                                                                                        ( ( subset @ X1058 @ X1059 )
                                                                                                                                                                                                       => ( subset @ ( powerset @ X1058 ) @ ( powerset @ X1059 ) ) )
                                                                                                                                                                                                   => ( ! [X1060: $i,X1061: $i > $o] : ( in @ ( dsetconstr @ X1060 @ X1061 ) @ ( powerset @ X1060 ) )
                                                                                                                                                                                                     => ( ! [X1062: $i,X1063: $i > $o] : ( subset @ ( dsetconstr @ X1062 @ X1063 ) @ X1062 )
                                                                                                                                                                                                       => ( ! [X1064: $i,X1065: $i,X1066: $i] :
                                                                                                                                                                                                              ( ( in @ X1066 @ X1064 )
                                                                                                                                                                                                             => ( in @ X1066 @ ( binunion @ X1064 @ X1065 ) ) )
                                                                                                                                                                                                         => ( ! [X1067: $i,X1068: $i] : ( in @ X1068 @ ( setadjoin @ X1067 @ ( setadjoin @ X1068 @ emptyset ) ) )
                                                                                                                                                                                                           => ( ! [X1069: $i,X1070: $i,X1071: $i] :
                                                                                                                                                                                                                  ( ( in @ X1071 @ X1070 )
                                                                                                                                                                                                                 => ( in @ X1071 @ ( binunion @ X1069 @ X1070 ) ) )
                                                                                                                                                                                                             => ( ! [X1072: $i,X1073: $i,X1074: $i,X1075: $o] :
                                                                                                                                                                                                                    ( ( in @ X1074 @ ( binunion @ X1072 @ X1073 ) )
                                                                                                                                                                                                                   => ( ( ( in @ X1074 @ X1072 )
                                                                                                                                                                                                                       => X1075 )
                                                                                                                                                                                                                     => ( ( ( in @ X1074 @ X1073 )
                                                                                                                                                                                                                         => X1075 )
                                                                                                                                                                                                                       => X1075 ) ) )
                                                                                                                                                                                                               => ( ! [X1076: $i,X1077: $i,X1078: $i] :
                                                                                                                                                                                                                      ( ( in @ X1078 @ ( binunion @ X1076 @ X1077 ) )
                                                                                                                                                                                                                     => ( ( in @ X1078 @ X1076 )
                                                                                                                                                                                                                        | ( in @ X1078 @ X1077 ) ) )
                                                                                                                                                                                                                 => ( ! [X1079: $i,X1080: $i] : ( subset @ X1079 @ ( binunion @ X1079 @ X1080 ) )
                                                                                                                                                                                                                   => ( ! [X1081: $i,X1082: $i] : ( subset @ X1082 @ ( binunion @ X1081 @ X1082 ) )
                                                                                                                                                                                                                     => ( ! [X1083: $i,X1084: $i,X1085: $i] :
                                                                                                                                                                                                                            ( ( in @ X1085 @ X1083 )
                                                                                                                                                                                                                           => ( ( in @ X1085 @ X1084 )
                                                                                                                                                                                                                             => ( in @ X1085 @ ( binintersect @ X1083 @ X1084 ) ) ) )
                                                                                                                                                                                                                       => ( ! [X1086: $i,X1087: $i,X1088: $i] :
                                                                                                                                                                                                                              ( ( subset @ X1088 @ X1086 )
                                                                                                                                                                                                                             => ( ( subset @ X1088 @ X1087 )
                                                                                                                                                                                                                               => ( subset @ X1088 @ ( binintersect @ X1086 @ X1087 ) ) ) )
                                                                                                                                                                                                                         => ( ! [X1089: $i,X1090: $i,X1091: $i] :
                                                                                                                                                                                                                                ( ( in @ X1091 @ ( binintersect @ X1089 @ X1090 ) )
                                                                                                                                                                                                                               => ( in @ X1091 @ X1089 ) )
                                                                                                                                                                                                                           => ( ! [X1092: $i,X1093: $i] : ( subset @ ( binintersect @ X1092 @ X1093 ) @ X1092 )
                                                                                                                                                                                                                             => ( ! [X1094: $i,X1095: $i] :
                                                                                                                                                                                                                                    ( ( subset @ X1094 @ X1095 )
                                                                                                                                                                                                                                   => ( ( binintersect @ X1094 @ X1095 )
                                                                                                                                                                                                                                      = X1094 ) )
                                                                                                                                                                                                                               => ( ! [X1096: $i,X1097: $i] :
                                                                                                                                                                                                                                      ( ( ( binintersect @ X1096 @ X1097 )
                                                                                                                                                                                                                                        = X1097 )
                                                                                                                                                                                                                                     => ( subset @ X1097 @ X1096 ) )
                                                                                                                                                                                                                                 => ( ! [X1098: $i,X1099: $i,X1100: $i] :
                                                                                                                                                                                                                                        ( ( in @ X1100 @ ( binintersect @ X1098 @ X1099 ) )
                                                                                                                                                                                                                                       => ( in @ X1100 @ X1099 ) )
                                                                                                                                                                                                                                   => ( ! [X1101: $i,X1102: $i] :
                                                                                                                                                                                                                                          ( ~ ? [X1103: $i] :
                                                                                                                                                                                                                                                ( ( in @ X1103 @ X1101 )
                                                                                                                                                                                                                                                & ( in @ X1103 @ X1102 ) )
                                                                                                                                                                                                                                         => ( ( binintersect @ X1101 @ X1102 )
                                                                                                                                                                                                                                            = emptyset ) )
                                                                                                                                                                                                                                     => ( ! [X1104: $i,X1105: $i] : ( subset @ ( binintersect @ X1104 @ X1105 ) @ X1105 )
                                                                                                                                                                                                                                       => ( ! [X1106: $i,X1107: $i] :
                                                                                                                                                                                                                                              ( ( subset @ X1107 @ X1106 )
                                                                                                                                                                                                                                             => ( ( binintersect @ X1106 @ X1107 )
                                                                                                                                                                                                                                                = X1107 ) )
                                                                                                                                                                                                                                         => ( ! [X1108: $i,X1109: $i] :
                                                                                                                                                                                                                                                ( ( ( binintersect @ X1108 @ X1109 )
                                                                                                                                                                                                                                                  = X1108 )
                                                                                                                                                                                                                                               => ( subset @ X1108 @ X1109 ) )
                                                                                                                                                                                                                                           => ( ! [X1110: $i,X1111: $i,X1112: $i] :
                                                                                                                                                                                                                                                  ( ( binintersect @ X1110 @ ( binunion @ X1111 @ X1112 ) )
                                                                                                                                                                                                                                                  = ( binunion @ ( binintersect @ X1110 @ X1111 ) @ ( binintersect @ X1110 @ X1112 ) ) )
                                                                                                                                                                                                                                             => ( ! [X1113: $i,X1114: $i,X1115: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X1115 @ X1113 )
                                                                                                                                                                                                                                                   => ( ~ ( in @ X1115 @ X1114 )
                                                                                                                                                                                                                                                     => ( in @ X1115 @ ( setminus @ X1113 @ X1114 ) ) ) )
                                                                                                                                                                                                                                               => ( ! [X1116: $i,X1117: $i,X1118: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X1118 @ ( setminus @ X1116 @ X1117 ) )
                                                                                                                                                                                                                                                     => ( in @ X1118 @ X1116 ) )
                                                                                                                                                                                                                                                 => ( ! [X1119: $i,X1120: $i,X1121: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X1121 @ ( setminus @ X1119 @ X1120 ) )
                                                                                                                                                                                                                                                       => ~ ( in @ X1121 @ X1120 ) )
                                                                                                                                                                                                                                                   => ( ! [X1122: $i,X1123: $i] :
                                                                                                                                                                                                                                                          ( ( subset @ X1122 @ X1123 )
                                                                                                                                                                                                                                                         => ( ( setminus @ X1122 @ X1123 )
                                                                                                                                                                                                                                                            = emptyset ) )
                                                                                                                                                                                                                                                     => ( ! [X1124: $i,X1125: $i,X1126: $i] :
                                                                                                                                                                                                                                                            ( ~ ( in @ X1126 @ ( setminus @ X1124 @ X1125 ) )
                                                                                                                                                                                                                                                           => ( ( in @ X1126 @ X1124 )
                                                                                                                                                                                                                                                             => ( in @ X1126 @ X1125 ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1127: $i,X1128: $i,X1129: $i] :
                                                                                                                                                                                                                                                              ( ~ ( in @ X1129 @ ( setminus @ X1127 @ X1128 ) )
                                                                                                                                                                                                                                                             => ( ~ ( in @ X1129 @ X1128 )
                                                                                                                                                                                                                                                               => ~ ( in @ X1129 @ X1127 ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1130: $i,X1131: $i,X1132: $i] :
                                                                                                                                                                                                                                                                ( ~ ( in @ X1132 @ X1130 )
                                                                                                                                                                                                                                                               => ~ ( in @ X1132 @ ( setminus @ X1130 @ X1131 ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1133: $i,X1134: $i,X1135: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X1135 @ X1134 )
                                                                                                                                                                                                                                                                 => ~ ( in @ X1135 @ ( setminus @ X1133 @ X1134 ) ) )
                                                                                                                                                                                                                                                             => ( ! [X1136: $i,X1137: $i] : ( subset @ ( setminus @ X1136 @ X1137 ) @ X1136 )
                                                                                                                                                                                                                                                               => ( ! [X1138: $i,X1139: $i] :
                                                                                                                                                                                                                                                                      ( ( ( setminus @ X1138 @ X1139 )
                                                                                                                                                                                                                                                                        = emptyset )
                                                                                                                                                                                                                                                                     => ( subset @ X1138 @ X1139 ) )
                                                                                                                                                                                                                                                                 => ( ! [X1140: $i,X1141: $i,X1142: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X1142 @ ( symdiff @ X1140 @ X1141 ) )
                                                                                                                                                                                                                                                                       => ! [X1143: $o] :
                                                                                                                                                                                                                                                                            ( ( ( in @ X1142 @ X1140 )
                                                                                                                                                                                                                                                                             => ( ~ ( in @ X1142 @ X1141 )
                                                                                                                                                                                                                                                                               => X1143 ) )
                                                                                                                                                                                                                                                                           => ( ( ~ ( in @ X1142 @ X1140 )
                                                                                                                                                                                                                                                                               => ( ( in @ X1142 @ X1141 )
                                                                                                                                                                                                                                                                                 => X1143 ) )
                                                                                                                                                                                                                                                                             => X1143 ) ) )
                                                                                                                                                                                                                                                                   => ( ! [X1144: $i,X1145: $i,X1146: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X1146 @ X1144 )
                                                                                                                                                                                                                                                                         => ( ~ ( in @ X1146 @ X1145 )
                                                                                                                                                                                                                                                                           => ( in @ X1146 @ ( symdiff @ X1144 @ X1145 ) ) ) )
                                                                                                                                                                                                                                                                     => ( ! [X1147: $i,X1148: $i,X1149: $i] :
                                                                                                                                                                                                                                                                            ( ~ ( in @ X1149 @ X1147 )
                                                                                                                                                                                                                                                                           => ( ( in @ X1149 @ X1148 )
                                                                                                                                                                                                                                                                             => ( in @ X1149 @ ( symdiff @ X1147 @ X1148 ) ) ) )
                                                                                                                                                                                                                                                                       => ( ! [X1150: $i,X1151: $i,X1152: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X1152 @ X1150 )
                                                                                                                                                                                                                                                                             => ( ( in @ X1152 @ X1151 )
                                                                                                                                                                                                                                                                               => ~ ( in @ X1152 @ ( symdiff @ X1150 @ X1151 ) ) ) )
                                                                                                                                                                                                                                                                         => ( ! [X1153: $i,X1154: $i,X1155: $i] :
                                                                                                                                                                                                                                                                                ( ~ ( in @ X1155 @ X1153 )
                                                                                                                                                                                                                                                                               => ( ~ ( in @ X1155 @ X1154 )
                                                                                                                                                                                                                                                                                 => ~ ( in @ X1155 @ ( symdiff @ X1153 @ X1154 ) ) ) )
                                                                                                                                                                                                                                                                           => ( ! [X1156: $i,X1157: $i] : ( in @ X1157 @ ( setadjoin @ X1156 @ ( setadjoin @ X1157 @ emptyset ) ) )
                                                                                                                                                                                                                                                                             => ( ! [X1158: $i,X1159: $i] : ( in @ X1158 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1158 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1158 @ ( setadjoin @ X1159 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                               => ( ! [X1160: $i,X1161: $i] : ( in @ X1161 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1160 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1160 @ ( setadjoin @ X1161 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1162: $i,X1163: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1162 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1162 @ ( setadjoin @ X1163 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1164: $i,X1165: $i] : ( iskpair @ ( kpair @ X1164 @ X1165 ) )
                                                                                                                                                                                                                                                                                     => ( ! [X1166: $i,X1167: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X1167 @ X1166 )
                                                                                                                                                                                                                                                                                           => ( subset @ ( setadjoin @ X1167 @ emptyset ) @ X1166 ) )
                                                                                                                                                                                                                                                                                       => ( ! [X1168: $i,X1169: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X1169 @ X1168 )
                                                                                                                                                                                                                                                                                             => ( in @ ( setadjoin @ X1169 @ emptyset ) @ ( powerset @ X1168 ) ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1170: $i,X1171: $i,X1172: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X1172 @ X1170 )
                                                                                                                                                                                                                                                                                               => ( in @ ( setadjoin @ X1172 @ emptyset ) @ ( powerset @ ( binunion @ X1170 @ X1171 ) ) ) )
                                                                                                                                                                                                                                                                                           => ( ! [X1173: $i,X1174: $i,X1175: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X1175 @ ( setadjoin @ X1173 @ ( setadjoin @ X1174 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                 => ( ( X1175 = X1173 )
                                                                                                                                                                                                                                                                                                    | ( X1175 = X1174 ) ) )
                                                                                                                                                                                                                                                                                             => ( ! [X1176: $i,X1177: $i,X1178: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X1178 @ X1176 )
                                                                                                                                                                                                                                                                                                   => ! [X1179: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X1179 @ X1177 )
                                                                                                                                                                                                                                                                                                       => ( subset @ ( setadjoin @ X1178 @ ( setadjoin @ X1179 @ emptyset ) ) @ ( binunion @ X1176 @ X1177 ) ) ) )
                                                                                                                                                                                                                                                                                               => ( ! [X1180: $i,X1181: $i,X1182: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ X1182 @ X1180 )
                                                                                                                                                                                                                                                                                                     => ! [X1183: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X1183 @ X1181 )
                                                                                                                                                                                                                                                                                                         => ( in @ ( setadjoin @ X1182 @ ( setadjoin @ X1183 @ emptyset ) ) @ ( powerset @ ( binunion @ X1180 @ X1181 ) ) ) ) )
                                                                                                                                                                                                                                                                                                 => ( ! [X1184: $i,X1185: $i,X1186: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X1186 @ X1184 )
                                                                                                                                                                                                                                                                                                       => ! [X1187: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X1187 @ X1185 )
                                                                                                                                                                                                                                                                                                           => ( subset @ ( setadjoin @ ( setadjoin @ X1186 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1186 @ ( setadjoin @ X1187 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1184 @ X1185 ) ) ) ) )
                                                                                                                                                                                                                                                                                                   => ( ! [X1188: $i,X1189: $i,X1190: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X1190 @ X1188 )
                                                                                                                                                                                                                                                                                                         => ! [X1191: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X1191 @ X1189 )
                                                                                                                                                                                                                                                                                                             => ( in @ ( setadjoin @ ( setadjoin @ X1190 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1190 @ ( setadjoin @ X1191 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1188 @ X1189 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                     => ( ! [X1192: $i,X1193: $i,X1194: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X1194 @ X1192 )
                                                                                                                                                                                                                                                                                                           => ! [X1195: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X1195 @ X1193 )
                                                                                                                                                                                                                                                                                                               => ( in @ ( kpair @ X1194 @ X1195 ) @ ( powerset @ ( powerset @ ( binunion @ X1192 @ X1193 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                       => ( ! [X1196: $i,X1197: $i,X1198: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X1198 @ X1196 )
                                                                                                                                                                                                                                                                                                             => ! [X1199: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ X1199 @ X1197 )
                                                                                                                                                                                                                                                                                                                 => ( in @ ( kpair @ X1198 @ X1199 ) @ ( cartprod @ X1196 @ X1197 ) ) ) )
                                                                                                                                                                                                                                                                                                         => ( ! [X1200: $i,X1201: $i,X1202: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X1202 @ ( cartprod @ X1200 @ X1201 ) )
                                                                                                                                                                                                                                                                                                               => ? [X1203: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X1203 @ X1200 )
                                                                                                                                                                                                                                                                                                                    & ? [X1204: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( in @ X1204 @ X1201 )
                                                                                                                                                                                                                                                                                                                        & ( X1202
                                                                                                                                                                                                                                                                                                                          = ( kpair @ X1203 @ X1204 ) ) ) ) )
                                                                                                                                                                                                                                                                                                           => ( ! [X1205: $i,X1206: $i,X1207: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ X1207 @ ( cartprod @ X1205 @ X1206 ) )
                                                                                                                                                                                                                                                                                                                 => ( iskpair @ X1207 ) )
                                                                                                                                                                                                                                                                                                             => ( ! [X1208: $i,X1209: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X1209 @ ( setunion @ X1208 ) )
                                                                                                                                                                                                                                                                                                                   => ? [X1210: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( in @ X1210 @ X1208 )
                                                                                                                                                                                                                                                                                                                        & ( in @ X1209 @ X1210 ) ) )
                                                                                                                                                                                                                                                                                                               => ( ! [X1211: $i] : ( subset @ ( setunion @ ( setadjoin @ X1211 @ emptyset ) ) @ X1211 )
                                                                                                                                                                                                                                                                                                                 => ( ! [X1212: $i] : ( subset @ X1212 @ ( setunion @ ( setadjoin @ X1212 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                   => ( ! [X1213: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( setunion @ ( setadjoin @ X1213 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                          = X1213 )
                                                                                                                                                                                                                                                                                                                     => ( ! [X1214: $i,X1215: $i > $o] :
                                                                                                                                                                                                                                                                                                                            ( ! [X1216: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( in @ X1216 @ X1214 )
                                                                                                                                                                                                                                                                                                                               => ! [X1217: $i] :
                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1217 @ X1214 )
                                                                                                                                                                                                                                                                                                                                   => ( ( X1215 @ X1216 )
                                                                                                                                                                                                                                                                                                                                     => ( ( X1215 @ X1217 )
                                                                                                                                                                                                                                                                                                                                       => ( X1216 = X1217 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                           => ( ? [X1218: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1218 @ X1214 )
                                                                                                                                                                                                                                                                                                                                  & ( X1215 @ X1218 ) )
                                                                                                                                                                                                                                                                                                                             => ( singleton @ ( dsetconstr @ X1214 @ X1215 ) ) ) )
                                                                                                                                                                                                                                                                                                                       => ( ! [X1219: $i,X1220: $i > $o] :
                                                                                                                                                                                                                                                                                                                              ( ( singleton @ ( dsetconstr @ X1219 @ X1220 ) )
                                                                                                                                                                                                                                                                                                                             => ? [X1221: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1221 @ X1219 )
                                                                                                                                                                                                                                                                                                                                  & ( X1220 @ X1221 ) ) )
                                                                                                                                                                                                                                                                                                                         => ( ! [X1222: $i,X1223: $i > $o,X1224: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( in @ X1224 @ X1222 )
                                                                                                                                                                                                                                                                                                                               => ( ( X1223 @ X1224 )
                                                                                                                                                                                                                                                                                                                                 => ( ! [X1225: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1225 @ X1222 )
                                                                                                                                                                                                                                                                                                                                       => ( ( X1223 @ X1225 )
                                                                                                                                                                                                                                                                                                                                         => ( X1225 = X1224 ) ) )
                                                                                                                                                                                                                                                                                                                                   => ( singleton @ ( dsetconstr @ X1222 @ X1223 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                           => ( ! [X1226: $i,X1227: $i > $o] :
                                                                                                                                                                                                                                                                                                                                  ( ! [X1228: $i] :
                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1228 @ X1226 )
                                                                                                                                                                                                                                                                                                                                     => ! [X1229: $i] :
                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1229 @ X1226 )
                                                                                                                                                                                                                                                                                                                                         => ( ( X1227 @ X1228 )
                                                                                                                                                                                                                                                                                                                                           => ( ( X1227 @ X1229 )
                                                                                                                                                                                                                                                                                                                                             => ( X1228 = X1229 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                 => ( ? [X1230: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1230 @ X1226 )
                                                                                                                                                                                                                                                                                                                                        & ( X1227 @ X1230 ) )
                                                                                                                                                                                                                                                                                                                                   => ( singleton @ ( dsetconstr @ X1226 @ X1227 ) ) ) )
                                                                                                                                                                                                                                                                                                                             => ( ! [X1231: $i,X1232: $i] :
                                                                                                                                                                                                                                                                                                                                    ( ( ( setadjoin @ X1231 @ emptyset )
                                                                                                                                                                                                                                                                                                                                      = ( setadjoin @ X1232 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                   => ( X1231 = X1232 ) )
                                                                                                                                                                                                                                                                                                                               => ( ! [X1233: $i,X1234: $i,X1235: $i] :
                                                                                                                                                                                                                                                                                                                                      ( ( in @ ( setadjoin @ X1235 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1233 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1233 @ ( setadjoin @ X1234 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                     => ( X1233 = X1235 ) )
                                                                                                                                                                                                                                                                                                                                 => ( ! [X1236: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( iskpair @ X1236 )
                                                                                                                                                                                                                                                                                                                                       => ( singleton
                                                                                                                                                                                                                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1236 )
                                                                                                                                                                                                                                                                                                                                            @ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1236 ) ) ) )
                                                                                                                                                                                                                                                                                                                                   => ( ! [X1237: $i] :
                                                                                                                                                                                                                                                                                                                                          ( ( singleton @ X1237 )
                                                                                                                                                                                                                                                                                                                                         => ( in @ ( setunion @ X1237 ) @ X1237 ) )
                                                                                                                                                                                                                                                                                                                                     => ( ! [X1238: $i,X1239: $i] :
                                                                                                                                                                                                                                                                                                                                            ( ( kfst @ ( kpair @ X1238 @ X1239 ) )
                                                                                                                                                                                                                                                                                                                                            = X1238 )
                                                                                                                                                                                                                                                                                                                                       => ( ! [X1240: $i,X1241: $i,X1242: $i] :
                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1242 @ ( cartprod @ X1240 @ X1241 ) )
                                                                                                                                                                                                                                                                                                                                             => ( in @ ( kfst @ X1242 ) @ X1240 ) )
                                                                                                                                                                                                                                                                                                                                         => ( ! [X1243: $i,X1244: $i,X1245: $i,X1246: $i] :
                                                                                                                                                                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1243 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1243 @ ( setadjoin @ X1244 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X1245 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1245 @ ( setadjoin @ X1246 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                               => ( X1243 = X1245 ) )
                                                                                                                                                                                                                                                                                                                                           => ( ! [X1247: $i,X1248: $i,X1249: $i,X1250: $i] :
                                                                                                                                                                                                                                                                                                                                                  ( ( ( kpair @ X1247 @ X1248 )
                                                                                                                                                                                                                                                                                                                                                    = ( kpair @ X1249 @ X1250 ) )
                                                                                                                                                                                                                                                                                                                                                 => ( X1247 = X1249 ) )
                                                                                                                                                                                                                                                                                                                                             => ( ! [X1251: $i,X1252: $i] :
                                                                                                                                                                                                                                                                                                                                                    ( ( X1251 = X1252 )
                                                                                                                                                                                                                                                                                                                                                   => ( ( setadjoin @ X1251 @ ( setadjoin @ X1252 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                      = ( setadjoin @ X1251 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                               => ( ! [X1253: $i,X1254: $i] :
                                                                                                                                                                                                                                                                                                                                                      ( ( X1253 = X1254 )
                                                                                                                                                                                                                                                                                                                                                     => ( ( setadjoin @ ( setadjoin @ X1253 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1253 @ ( setadjoin @ X1254 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X1253 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1255: $i,X1256: $i,X1257: $i,X1258: $i] :
                                                                                                                                                                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1255 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1255 @ ( setadjoin @ X1256 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X1257 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1257 @ ( setadjoin @ X1258 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                                       => ( ( X1257 = X1258 )
                                                                                                                                                                                                                                                                                                                                                         => ( X1256 = X1258 ) ) )
                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1259: $i,X1260: $i,X1261: $i] :
                                                                                                                                                                                                                                                                                                                                                          ( ( ( setadjoin @ X1259 @ ( setadjoin @ X1260 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                            = ( setadjoin @ X1261 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                         => ( X1259 = X1260 ) )
                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1262: $i,X1263: $i,X1264: $i,X1265: $i] :
                                                                                                                                                                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1262 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1262 @ ( setadjoin @ X1263 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X1264 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1264 @ ( setadjoin @ X1265 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                                           => ( X1263 = X1265 ) )
                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1266: $i,X1267: $i,X1268: $i,X1269: $i] :
                                                                                                                                                                                                                                                                                                                                                              ( ( ( kpair @ X1266 @ X1267 )
                                                                                                                                                                                                                                                                                                                                                                = ( kpair @ X1268 @ X1269 ) )
                                                                                                                                                                                                                                                                                                                                                             => ( X1267 = X1269 ) )
                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1270: $i] :
                                                                                                                                                                                                                                                                                                                                                                ( ( iskpair @ X1270 )
                                                                                                                                                                                                                                                                                                                                                               => ( singleton
                                                                                                                                                                                                                                                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1270 )
                                                                                                                                                                                                                                                                                                                                                                    @ ^ [Z0: $i] :
                                                                                                                                                                                                                                                                                                                                                                        ( X1270
                                                                                                                                                                                                                                                                                                                                                                        = ( kpair @ ( kfst @ X1270 ) @ Z0 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                           => ( ! [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 )
                                                                                                                                                                                                                                                                                                                                                                                                     => ( singleton
                                                                                                                                                                                                                                                                                                                                                                                                        @ ( dsetconstr @ X1332
                                                                                                                                                                                                                                                                                                                                                                                                          @ ^ [Z0: $i] : ( in @ ( kpair @ X1334 @ Z0 ) @ X1333 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1335: $i,X1336: $i,X1337: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                    ( ( func @ X1335 @ X1336 @ X1337 )
                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1338: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1338 @ X1335 )
                                                                                                                                                                                                                                                                                                                                                                                                       => ( in
                                                                                                                                                                                                                                                                                                                                                                                                          @ ( setunion
                                                                                                                                                                                                                                                                                                                                                                                                            @ ( dsetconstr @ X1336
                                                                                                                                                                                                                                                                                                                                                                                                              @ ^ [Z0: $i] : ( in @ ( kpair @ X1338 @ Z0 ) @ X1337 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                          @ X1336 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1339: $i,X1340: $i,X1341: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                      ( ( func @ X1339 @ X1340 @ X1341 )
                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1342: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1342 @ X1339 )
                                                                                                                                                                                                                                                                                                                                                                                                         => ( in @ ( ap @ X1339 @ X1340 @ X1341 @ X1342 ) @ X1340 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1343: $i,X1344: $i,X1345: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1345 @ ( funcSet @ X1343 @ X1344 ) )
                                                                                                                                                                                                                                                                                                                                                                                                       => ( func @ X1343 @ X1344 @ X1345 ) )
                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1346: $i,X1347: $i,X1348: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1348 @ ( funcSet @ X1346 @ X1347 ) )
                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1349: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1349 @ X1346 )
                                                                                                                                                                                                                                                                                                                                                                                                             => ( in @ ( ap @ X1346 @ X1347 @ X1348 @ X1349 ) @ X1347 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1350: $i,X1351: $i,X1352: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                            ( ( func @ X1350 @ X1351 @ X1352 )
                                                                                                                                                                                                                                                                                                                                                                                                           => ( in @ X1352 @ ( funcSet @ X1350 @ X1351 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1353: $i,X1354: $i,X1355: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                              ( ! [X1356: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1356 @ X1353 )
                                                                                                                                                                                                                                                                                                                                                                                                                 => ( in @ ( X1355 @ X1356 ) @ X1354 ) )
                                                                                                                                                                                                                                                                                                                                                                                                             => ( func @ X1353 @ X1354
                                                                                                                                                                                                                                                                                                                                                                                                                @ ( dpsetconstr @ X1353 @ X1354
                                                                                                                                                                                                                                                                                                                                                                                                                  @ ^ [Z0: $i] : ( $eq @ ( X1355 @ Z0 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1357: $i,X1358: $i,X1359: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                ( ! [X1360: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1360 @ X1357 )
                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ ( X1359 @ X1360 ) @ X1358 ) )
                                                                                                                                                                                                                                                                                                                                                                                                               => ( func @ X1357 @ X1358 @ ( lam @ X1357 @ X1358 @ X1359 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1361: $i,X1362: $i,X1363: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                  ( ! [X1364: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1364 @ X1361 )
                                                                                                                                                                                                                                                                                                                                                                                                                     => ( in @ ( X1363 @ X1364 ) @ X1362 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                 => ( in @ ( lam @ X1361 @ X1362 @ X1363 ) @ ( funcSet @ X1361 @ X1362 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1365: $i,X1366: $i,X1367: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( subset @ X1367 @ ( cartprod @ X1365 @ X1366 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1368: $i > $o] :
                                                                                                                                                                                                                                                                                                                                                                                                                        ( ! [X1369: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1369 @ X1365 )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1370: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1370 @ X1366 )
                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( in @ ( kpair @ X1369 @ X1370 ) @ X1367 )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( X1368 @ ( kpair @ X1369 @ X1370 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1371: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1371 @ X1367 )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ( X1368 @ X1371 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1372: $i,X1373: $i,X1374: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( subset @ X1374 @ ( cartprod @ X1372 @ X1373 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1375: $i > $o] :
                                                                                                                                                                                                                                                                                                                                                                                                                          ( ! [X1376: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1376 @ X1372 )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1377: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1377 @ X1373 )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( in @ ( kpair @ X1376 @ X1377 ) @ X1374 )
                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( X1375 @ ( kpair @ X1376 @ X1377 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1378: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1378 @ X1374 )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ( X1375 @ X1378 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1379: $i,X1380: $i > $o] :
                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( singleton @ ( dsetconstr @ X1379 @ X1380 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1381: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1381 @ X1379 )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1382: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1382 @ X1379 )
                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( X1380 @ X1381 )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( X1380 @ X1382 )
                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( X1381 = X1382 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1383: $i,X1384: $i,X1385: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( func @ X1383 @ X1384 @ X1385 )
                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1386: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1386 @ X1383 )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ( in @ ( kpair @ X1386 @ ( ap @ X1383 @ X1384 @ X1385 @ X1386 ) ) @ X1385 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1387: $i,X1388: $i,X1389: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1389 @ ( funcSet @ X1387 @ X1388 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1390: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1390 @ X1387 )
                                                                                                                                                                                                                                                                                                                                                                                                                               => ( in @ ( kpair @ X1390 @ ( ap @ X1387 @ X1388 @ X1389 @ X1390 ) ) @ X1389 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1391: $i,X1392: $i,X1393: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( func @ X1391 @ X1392 @ X1393 )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1394: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1394 @ X1391 )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1395: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1395 @ X1392 )
                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( in @ ( kpair @ X1394 @ X1395 ) @ X1393 )
                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( ap @ X1391 @ X1392 @ X1393 @ X1394 )
                                                                                                                                                                                                                                                                                                                                                                                                                                          = X1395 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1396: $i,X1397: $i,X1398: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( func @ X1396 @ X1397 @ X1398 )
                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1399: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( func @ X1396 @ X1397 @ X1399 )
                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1400: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1400 @ X1396 )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( ap @ X1396 @ X1397 @ X1398 @ X1400 )
                                                                                                                                                                                                                                                                                                                                                                                                                                            = ( ap @ X1396 @ X1397 @ X1399 @ X1400 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1401: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1401 @ X1396 )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1402: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1402 @ X1397 )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ( in @ ( kpair @ X1401 @ X1402 ) @ X1399 )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( in @ ( kpair @ X1401 @ X1402 ) @ X1398 ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1403: $i,X1404: $i,X1405: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1405 @ ( funcSet @ X1403 @ X1404 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1406: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1406 @ X1403 )
                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1407: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1407 @ X1404 )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( in @ ( kpair @ X1406 @ X1407 ) @ X1405 )
                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ( ap @ X1403 @ X1404 @ X1405 @ X1406 )
                                                                                                                                                                                                                                                                                                                                                                                                                                              = X1407 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1408: $i,X1409: $i,X1410: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( subset @ X1410 @ ( cartprod @ X1408 @ X1409 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1411: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( subset @ X1411 @ ( cartprod @ X1408 @ X1409 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1412: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1412 @ X1408 )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1413: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1413 @ X1409 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( in @ ( kpair @ X1412 @ X1413 ) @ X1410 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ ( kpair @ X1412 @ X1413 ) @ X1411 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( subset @ X1410 @ X1411 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1414: $i,X1415: $i,X1416: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( subset @ X1416 @ ( cartprod @ X1414 @ X1415 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1417: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( subset @ X1417 @ ( cartprod @ X1414 @ X1415 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1418: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1418 @ X1414 )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1419: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1419 @ X1415 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( in @ ( kpair @ X1418 @ X1419 ) @ X1416 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( in @ ( kpair @ X1418 @ X1419 ) @ X1417 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1420: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1420 @ X1414 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1421: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1421 @ X1415 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( in @ ( kpair @ X1420 @ X1421 ) @ X1417 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ ( kpair @ X1420 @ X1421 ) @ X1416 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( X1416 = X1417 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1422: $i,X1423: $i,X1424: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( func @ X1422 @ X1423 @ X1424 )
                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1425: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( func @ X1422 @ X1423 @ X1425 )
                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1426: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1426 @ X1422 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( ap @ X1422 @ X1423 @ X1424 @ X1426 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                    = ( ap @ X1422 @ X1423 @ X1425 @ X1426 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( X1424 = X1425 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1427: $i,X1428: $i,X1429: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1429 @ ( funcSet @ X1427 @ X1428 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1430: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1430 @ ( funcSet @ X1427 @ X1428 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1431: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1431 @ X1427 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( ap @ X1427 @ X1428 @ X1429 @ X1431 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                      = ( ap @ X1427 @ X1428 @ X1430 @ X1431 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( X1429 = X1430 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1432: $i,X1433: $i,X1434: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1434 @ ( funcSet @ X1432 @ X1433 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1435: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1435 @ X1432 )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( ap @ X1432 @ X1433 @ X1434 @ X1435 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                  = ( ap @ X1432 @ X1433 @ X1434 @ X1435 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1436: $i,X1437: $i,X1438: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( func @ X1436 @ X1437 @ X1438 )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1439: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1439 @ X1436 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( ap @ X1436 @ X1437 @ X1438 @ X1439 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                    = ( ap @ X1436 @ X1437 @ X1438 @ X1439 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1440: $i,X1441: $i,X1442: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ! [X1443: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1443 @ X1440 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ ( X1442 @ X1443 ) @ X1441 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1444: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1444 @ X1440 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( ap @ X1440 @ X1441 @ ( lam @ X1440 @ X1441 @ X1442 ) @ X1444 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                      = ( X1442 @ X1444 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1445: $i,X1446: $i,X1447: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( func @ X1445 @ X1446 @ X1447 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( lam @ X1445 @ X1446 @ ( ap @ X1445 @ X1446 @ X1447 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                    = X1447 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1448: $i,X1449: $i,X1450: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ! [X1451: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1451 @ X1448 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ ( X1450 @ X1451 ) @ X1449 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( lam @ X1448 @ X1449 @ X1450 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                      = ( lam @ X1448 @ X1449 @ X1450 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1452: $i,X1453: $i,X1454: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ! [X1455: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1455 @ X1452 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( in @ ( X1454 @ X1455 ) @ X1453 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1456: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1456 @ X1452 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( ap @ X1452 @ X1453 @ ( lam @ X1452 @ X1453 @ X1454 ) @ X1456 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                            = ( X1454 @ X1456 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1457: $i,X1458: $i,X1459: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1459 @ ( funcSet @ X1457 @ X1458 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( lam @ X1457 @ X1458 @ ( ap @ X1457 @ X1458 @ X1459 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                          = X1459 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1460: $i,X1461: $o,X1462: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1462 @ X1460 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1463: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1463 @ X1460 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ~ X1461
                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( in @ X1463
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  @ ( dsetconstr @ X1460
                                                                                                                                                                                                                                                                                                                                                                                                                                                                    @ ^ [Z0: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( X1461
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          & ( Z0 = X1462 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        | ( ~ X1461
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          & ( Z0 = X1463 ) ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1464: $i,X1465: $o,X1466: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1466 @ X1464 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1467: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1467 @ X1464 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ~ X1465
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( dsetconstr @ X1464
                                                                                                                                                                                                                                                                                                                                                                                                                                                                      @ ^ [Z0: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( X1465
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            & ( Z0 = X1466 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          | ( ~ X1465
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            & ( Z0 = X1467 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                    = ( setadjoin @ X1467 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1468: $i,X1469: $o,X1470: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1470 @ X1468 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1471: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1471 @ X1468 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( X1469
                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ X1470
                                                                                                                                                                                                                                                                                                                                                                                                                                                                      @ ( dsetconstr @ X1468
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        @ ^ [Z0: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( X1469
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              & ( Z0 = X1470 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            | ( ~ X1469
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              & ( Z0 = X1471 ) ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1472: $i,X1473: $o,X1474: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1474 @ X1472 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1475: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1475 @ X1472 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( X1473
                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( dsetconstr @ X1472
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          @ ^ [Z0: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( X1473
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                & ( Z0 = X1474 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | ( ~ X1473
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                & ( Z0 = X1475 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        = ( setadjoin @ X1474 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1476: $i,X1477: $o,X1478: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1478 @ X1476 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1479: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1479 @ X1476 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( singleton
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        @ ( dsetconstr @ X1476
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          @ ^ [Z0: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( X1477
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                & ( Z0 = X1478 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | ( ~ X1477
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                & ( Z0 = X1479 ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1480: $i,X1481: $o,X1482: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1482 @ X1480 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1483: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1483 @ X1480 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ ( if @ X1480 @ X1481 @ X1482 @ X1483 ) @ X1480 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1484: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( singleton @ X1484 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1485: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1485 @ X1484 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( setunion @ X1484 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            = X1485 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1486: $i,X1487: $o,X1488: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1488 @ X1486 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1489: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1489 @ X1486 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( X1487
                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ( if @ X1486 @ X1487 @ X1488 @ X1489 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                = X1488 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1490: $i,X1491: $o,X1492: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1492 @ X1490 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1493: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1493 @ X1490 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ~ X1491
                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( if @ X1490 @ X1491 @ X1492 @ X1493 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  = X1493 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1494: $i,X1495: $o,X1496: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1496 @ X1494 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1497: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1497 @ X1494 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( in @ ( if @ X1494 @ X1495 @ X1496 @ X1497 ) @ ( setadjoin @ X1496 @ ( setadjoin @ X1497 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X4: $i,X21: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X21 @ ( powerset @ X4 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X48: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X48 @ ( powerset @ X4 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( in @ ( binintersect @ X21 @ X48 ) @ ( powerset @ 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(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[binintersectT_lem]),subset2powerset]),ap2apEq1]),iftrueorfalse]),c_0_252]),subsetE]),app]),infuncsetfunc]),ap2p]),subsetE2]),funcinfuncset]),c_0_253]),notsubsetI]),c_0_254]),c_0_255]),notequalI1]),c_0_256]),c_0_257]),notequalI2]),c_0_258]),funcGraphProp1]),subsetRefl]),funcGraphProp3]),funcGraphProp2]),subsetTrans]),funcextLem]),funcGraphProp4]),setadjoinSub]),c_0_259]),c_0_260]),funcext]),setadjoinSub2]),funcext2]),binintersectEL]),ap2apEq2]),c_0_261]),c_0_262]),setextsub]),c_0_263]),c_0_264]),subsetemptysetimpeq]),c_0_265]),c_0_266]),powersetI1]),c_0_267]),c_0_268]),c_0_269]),c_0_270]),powersetE1]),ifp]),theeq]),inPowerset]),iftrue]),iffalse]),powersetsubset]),c_0_271]),c_0_272]),binunionIL]),upairset2IR]),binunionIR]),binunionEcases]),binunionE]),binunionLsub]),binunionRsub]),binintersectI]),binintersectSubset5]),ubforcartprodlem1]),ubforcartprodlem2]),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]),eqimpsubset1]),singletonsubset]),subsetI2]),singletoninpowerset]),singletoninpowunion]),emptysetsubset]),upairset2E]),upairsubunion]),upairinpowunion]),ubforcartprodlem3]),cartprodpairin]),cartprodmempair1]),cartprodmempair]),setunionE2]),setunionsingleton1]),setunionsingleton2]),setunionsingleton]),c_0_273]),c_0_274]),c_0_275]),c_0_276]),singletonsuniq]),setukpairinjL1]),c_0_277]),theprop]),kfstpairEq]),cartprodfstin]),setukpairinjL2]),setukpairinjL]),setukpairinjR11]),setukpairinjR12]),setukpairinjR1]),upairequniteq]),setukpairinjR2]),setukpairinjR]),c_0_278]),ksndpairEq]),kpairsurjEq]),cartprodsndin]),cartprodpairmemEL]),cartprodpairmemER]),cartprodmempaircEq]),cartprodfstpairEq]),cartprodsndpairEq]),cartprodpairsurjEq]),c_0_279]),c_0_280]),c_0_281]),c_0_282]),c_0_283]),c_0_284]),c_0_285]),c_0_286]),eqimpsubset2]),subsetI1]),c_0_287]),c_0_288]),c_0_289]),omega__Cong]),setunion__Cong]),powerset__Cong]),setadjoin__Cong]),emptyset__Cong]),c_0_290]),c_0_291]),in__Cong]),inCongP]),c_0_292]),c_0_293]),c_0_294]),notdallE]),notdexE]),prop2setI]),quantDeMorgan4]),quantDeMorgan3]),quantDeMorgan2]),quantDeMorgan1]),vacuousDall]),c_0_295]),upairsetIR]),upairsetIL]),upairsetE]),singletonsswitch]),eqinunit]),notinsingleton]),uniqinunit]),c_0_296]),c_0_297]),subPowSU]),setunionE]),setunionI]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_298]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),c_0_299]),c_0_300]),c_0_301]),c_0_302]),noeltsimpempty]),emptyI]),setext]),c_0_303]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_304]),c_0_305]),c_0_306]),c_0_307]),c_0_308]),wellorderingAx]),foundationAx]),c_0_309]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_310]) ).

thf(c_0_312,negated_conjecture,
    ! [X1498: $i,X1499: $i,X1501: $i,X1502: $i,X1503: $i,X1504: $i,X1505: $i,X1506: $i,X1507: $i,X1508: $i,X1509: $i,X1511: $i,X1512: $i,X1514: $i,X1515: $i,X1516: $i,X1517: $i,X1518: $i,X1520: $i,X1521: $i > $i > $o,X1522: $i,X1524: $i,X1527: $i,X1529: $i,X1530: $i,X1531: $i,X1532: $i,X1534: $i,X1535: $i > $o,X1536: $i,X1538: $i,X1539: $i > $o,X1540: $i,X1541: $i,X1542: $i > $o,X1543: $i,X1544: $i,X1545: $i > $o,X1546: $i,X1547: $i > $o,X1548: $i,X1551: $i,X1552: $o,X1553: $i,X1554: $i,X1555: $o,X1556: $i,X1557: $i,X1558: $i > $o,X1559: $i,X1562: $i,X1563: $i,X1566: $i,X1568: $i,X1570: $i,X1571: $i > $o,X1572: $i,X1573: $i,X1575: $i,X1576: $i > $o,X1577: $i,X1578: $i,X1579: $i,X1580: $i,X1581: $i,X1582: $i,X1583: $i,X1584: $i,X1585: $i,X1586: $i,X1587: $i,X1588: $o,X1589: $i,X1590: $i,X1591: $i,X1592: $i,X1593: $i,X1594: $i,X1596: $i,X1597: $i,X1598: $i,X1599: $i,X1600: $i,X1601: $i,X1602: $i,X1603: $i,X1604: $i,X1605: $i,X1606: $o,X1608: $i,X1609: $i,X1610: $i > $o,X1611: $i,X1614: $i,X1615: $i,X1616: $i,X1618: $i,X1619: $i,X1620: $i,X1621: $i,X1622: $i,X1623: $i,X1624: $i,X1625: $i,X1626: $i,X1627: $i,X1628: $i,X1629: $i,X1630: $i,X1631: $i,X1632: $i,X1633: $i,X1634: $i > $o,X1635: $i,X1636: $i > $o,X1637: $i,X1638: $i,X1639: $i > $o,X1640: $i,X1642: $i,X1643: $i > $o,X1645: $i,X1646: $i,X1647: $i > $o,X1649: $i,X1650: $i,X1651: $i > $o,X1652: $i,X1654: $o,X1655: $i,X1656: $i > $o,X1658: $i,X1659: $i,X1660: $i > $o,X1661: $i,X1663: $i > $o,X1664: $i,X1667: $i,X1668: $i > $o,X1669: $i,X1673: $i,X1674: $i > $o,X1675: $i,X1678: $i,X1679: $i,X1680: $i,X1681: $i,X1682: $i,X1683: $i,X1684: $i,X1685: $i,X1686: $i,X1687: $i > $o,X1688: $i,X1690: $i,X1691: $i,X1692: $i > $o,X1693: $i > $o,X1696: $i,X1699: $i,X1700: $i,X1703: $i,X1704: $i,X1705: $i,X1706: $i,X1707: $i,X1708: $i,X1709: $i,X1710: $i,X1711: $i,X1712: $i > $o,X1713: $i,X1715: $i,X1716: $i,X1717: $i > $o,X1718: $i > $o,X1721: $i,X1723: $i,X1725: $i,X1726: $i,X1727: $i > $o,X1728: $i > $o,X1731: $i,X1732: $i,X1734: $i,X1735: $i,X1736: $i,X1737: $i,X1738: $i,X1739: $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,X1773: $i,X1774: $i,X1775: $i,X1776: $i,X1777: $i,X1778: $i > $o,X1779: $i,X1780: $i > $o,X1781: $i,X1782: $i,X1783: $i,X1784: $i,X1785: $i,X1786: $i,X1787: $i,X1788: $i,X1789: $i,X1790: $i,X1791: $i,X1792: $o,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,X1814: $i,X1815: $i,X1816: $i,X1817: $i,X1818: $i,X1819: $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: $i,X1855: $i,X1856: $i,X1857: $i,X1858: $i,X1859: $i,X1860: $o,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,X1914: $i,X1915: $i,X1916: $i,X1917: $i,X1918: $i,X1919: $i,X1922: $i,X1923: $i,X1924: $i,X1925: $i,X1926: $i,X1928: $i,X1929: $i,X1930: $i,X1931: $i,X1932: $i > $o,X1935: $i,X1936: $i,X1937: $i > $o,X1939: $i,X1940: $i > $o,X1941: $i,X1943: $i,X1944: $i > $o,X1947: $i,X1948: $i,X1949: $i,X1950: $i,X1951: $i,X1952: $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,X1988: $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 > $i > $o,X2020: $i,X2021: $i,X2022: $i,X2023: $i,X2024: $i > $i > $o,X2025: $i,X2026: $i,X2027: $i > $i > $o,X2028: $i,X2029: $i,X2030: $i > $i > $o,X2031: $i,X2032: $i,X2033: $i,X2034: $i,X2035: $i > $i > $o,X2036: $i,X2037: $i,X2038: $i,X2039: $i,X2040: $i > $i > $o,X2041: $i,X2042: $i,X2043: $i,X2044: $i,X2045: $i > $i > $o,X2046: $i,X2047: $i,X2048: $i,X2049: $i,X2050: $i,X2051: $i,X2052: $i,X2053: $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 > $i,X2074: $i,X2075: $i,X2076: $i > $i,X2078: $i,X2079: $i,X2080: $i > $i,X2082: $i,X2083: $i,X2084: $i,X2085: $i > $o,X2088: $i,X2089: $i,X2090: $i,X2091: $i,X2092: $i > $o,X2095: $i,X2096: $i,X2097: $i > $o,X2098: $i,X2099: $i,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,X2118: $i,X2119: $i,X2120: $i,X2121: $i,X2122: $i,X2123: $i,X2124: $i,X2125: $i,X2126: $i,X2127: $i,X2128: $i,X2131: $i,X2132: $i,X2133: $i,X2134: $i,X2139: $i,X2140: $i,X2141: $i,X2142: $i,X2144: $i,X2145: $i,X2146: $i,X2147: $i,X2149: $i,X2150: $i,X2151: $i,X2152: $i,X2153: $i,X2154: $i,X2155: $i,X2156: $i,X2157: $i,X2158: $i,X2159: $i > $i,X2161: $i,X2162: $i,X2163: $i,X2164: $i,X2165: $i,X2166: $i,X2167: $i > $i,X2169: $i,X2170: $i,X2171: $i > $i,X2173: $i,X2174: $i,X2175: $i,X2176: $i,X2177: $i,X2178: $o,X2179: $i,X2180: $i,X2181: $i,X2182: $o,X2183: $i,X2184: $i,X2185: $i,X2186: $o,X2187: $i,X2188: $i,X2189: $i,X2190: $o,X2191: $i,X2192: $i,X2193: $i,X2194: $o,X2195: $i,X2196: $i,X2197: $i,X2198: $o,X2199: $i,X2200: $i,X2201: $i,X2202: $i,X2203: $i,X2204: $o,X2205: $i,X2206: $i,X2207: $i,X2208: $o,X2209: $i,X2210: $i,X2211: $i,X2212: $o,X2213: $i,X2214: $i] :
      ( ( ~ ( in @ ( esk1_2 @ X1498 @ X1499 ) @ X1498 )
        | ~ ( in @ ( esk1_2 @ X1498 @ X1499 ) @ X1499 )
        | ( X1498 = X1499 ) )
      & ( ( in @ ( esk1_2 @ X1498 @ X1499 ) @ X1498 )
        | ( in @ ( esk1_2 @ X1498 @ X1499 ) @ X1499 )
        | ( X1498 = X1499 ) )
      & ~ ( in @ X1501 @ emptyset )
      & ( ~ ( in @ X1504 @ ( setadjoin @ X1502 @ X1503 ) )
        | ( X1504 = X1502 )
        | ( in @ X1504 @ X1503 ) )
      & ( ( X1504 != X1502 )
        | ( in @ X1504 @ ( setadjoin @ X1502 @ X1503 ) ) )
      & ( ~ ( in @ X1504 @ X1503 )
        | ( in @ X1504 @ ( setadjoin @ X1502 @ X1503 ) ) )
      & ( ~ ( in @ X1506 @ ( powerset @ X1505 ) )
        | ~ ( in @ X1507 @ X1506 )
        | ( in @ X1507 @ X1505 ) )
      & ( ( in @ ( esk2_2 @ X1508 @ X1509 ) @ X1509 )
        | ( in @ X1509 @ ( powerset @ X1508 ) ) )
      & ( ~ ( in @ ( esk2_2 @ X1508 @ X1509 ) @ X1508 )
        | ( in @ X1509 @ ( powerset @ X1508 ) ) )
      & ( ( in @ X1512 @ ( esk3_2 @ X1511 @ X1512 ) )
        | ~ ( in @ X1512 @ ( setunion @ X1511 ) ) )
      & ( ( in @ ( esk3_2 @ X1511 @ X1512 ) @ X1511 )
        | ~ ( in @ X1512 @ ( setunion @ X1511 ) ) )
      & ( ~ ( in @ X1515 @ X1516 )
        | ~ ( in @ X1516 @ X1514 )
        | ( in @ X1515 @ ( setunion @ X1514 ) ) )
      & ( in @ emptyset @ omega )
      & ( ~ ( in @ X1517 @ omega )
        | ( in @ ( setadjoin @ X1517 @ X1517 ) @ omega ) )
      & ( ( in @ ( esk4_1 @ X1518 ) @ omega )
        | ~ ( in @ emptyset @ X1518 )
        | ~ ( in @ X1520 @ omega )
        | ( in @ X1520 @ X1518 ) )
      & ( ( in @ ( esk4_1 @ X1518 ) @ X1518 )
        | ~ ( in @ emptyset @ X1518 )
        | ~ ( in @ X1520 @ omega )
        | ( in @ X1520 @ X1518 ) )
      & ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X1518 ) @ ( esk4_1 @ X1518 ) ) @ X1518 )
        | ~ ( in @ emptyset @ X1518 )
        | ~ ( in @ X1520 @ omega )
        | ( in @ X1520 @ X1518 ) )
      & ( ( in @ ( esk8_3 @ X1521 @ X1522 @ X1527 ) @ X1522 )
        | ~ ( in @ X1527 @ ( esk7_2 @ X1521 @ X1522 ) )
        | ( in @ ( esk5_2 @ X1521 @ X1522 ) @ X1522 ) )
      & ( ( X1521 @ ( esk8_3 @ X1521 @ X1522 @ X1527 ) @ X1527 )
        | ~ ( in @ X1527 @ ( esk7_2 @ X1521 @ X1522 ) )
        | ( in @ ( esk5_2 @ X1521 @ X1522 ) @ X1522 ) )
      & ( ~ ( in @ X1530 @ X1522 )
        | ~ ( X1521 @ X1530 @ X1529 )
        | ( in @ X1529 @ ( esk7_2 @ X1521 @ X1522 ) )
        | ( in @ ( esk5_2 @ X1521 @ X1522 ) @ X1522 ) )
      & ( ( in @ ( esk8_3 @ X1521 @ X1522 @ X1527 ) @ X1522 )
        | ~ ( in @ X1527 @ ( esk7_2 @ X1521 @ X1522 ) )
        | ( X1521 @ ( esk5_2 @ X1521 @ X1522 ) @ ( esk6_3 @ X1521 @ X1522 @ X1524 ) )
        | ~ ( X1521 @ ( esk5_2 @ X1521 @ X1522 ) @ X1524 ) )
      & ( ( X1521 @ ( esk8_3 @ X1521 @ X1522 @ X1527 ) @ X1527 )
        | ~ ( in @ X1527 @ ( esk7_2 @ X1521 @ X1522 ) )
        | ( X1521 @ ( esk5_2 @ X1521 @ X1522 ) @ ( esk6_3 @ X1521 @ X1522 @ X1524 ) )
        | ~ ( X1521 @ ( esk5_2 @ X1521 @ X1522 ) @ X1524 ) )
      & ( ~ ( in @ X1530 @ X1522 )
        | ~ ( X1521 @ X1530 @ X1529 )
        | ( in @ X1529 @ ( esk7_2 @ X1521 @ X1522 ) )
        | ( X1521 @ ( esk5_2 @ X1521 @ X1522 ) @ ( esk6_3 @ X1521 @ X1522 @ X1524 ) )
        | ~ ( X1521 @ ( esk5_2 @ X1521 @ X1522 ) @ X1524 ) )
      & ( ( in @ ( esk8_3 @ X1521 @ X1522 @ X1527 ) @ X1522 )
        | ~ ( in @ X1527 @ ( esk7_2 @ X1521 @ X1522 ) )
        | ( X1524
         != ( esk6_3 @ X1521 @ X1522 @ X1524 ) )
        | ~ ( X1521 @ ( esk5_2 @ X1521 @ X1522 ) @ X1524 ) )
      & ( ( X1521 @ ( esk8_3 @ X1521 @ X1522 @ X1527 ) @ X1527 )
        | ~ ( in @ X1527 @ ( esk7_2 @ X1521 @ X1522 ) )
        | ( X1524
         != ( esk6_3 @ X1521 @ X1522 @ X1524 ) )
        | ~ ( X1521 @ ( esk5_2 @ X1521 @ X1522 ) @ X1524 ) )
      & ( ~ ( in @ X1530 @ X1522 )
        | ~ ( X1521 @ X1530 @ X1529 )
        | ( in @ X1529 @ ( esk7_2 @ X1521 @ X1522 ) )
        | ( X1524
         != ( esk6_3 @ X1521 @ X1522 @ X1524 ) )
        | ~ ( X1521 @ ( esk5_2 @ X1521 @ X1522 ) @ X1524 ) )
      & ( ( in @ ( esk9_1 @ X1531 ) @ X1531 )
        | ~ ( in @ X1532 @ X1531 ) )
      & ( ~ ( in @ X1534 @ ( esk9_1 @ X1531 ) )
        | ~ ( in @ X1534 @ X1531 )
        | ~ ( in @ X1532 @ X1531 ) )
      & epred1_0
      & ( ( X1535 @ ( esk10_2 @ X1535 @ X1536 ) )
        | ~ ( X1535 @ X1536 )
        | ( X1535 @ ( descr @ X1535 ) ) )
      & ( ( X1536
         != ( esk10_2 @ X1535 @ X1536 ) )
        | ~ ( X1535 @ X1536 )
        | ( X1535 @ ( descr @ X1535 ) ) )
      & ( ~ ( in @ X1540 @ X1538 )
        | ~ ( X1539 @ X1540 )
        | ( in @ X1540 @ ( dsetconstr @ X1538 @ X1539 ) ) )
      & ( ~ ( in @ X1543 @ ( dsetconstr @ X1541 @ X1542 ) )
        | ( in @ X1543 @ X1541 ) )
      & ( ~ ( in @ X1546 @ ( dsetconstr @ X1544 @ X1545 ) )
        | ( X1545 @ X1546 ) )
      & ( ( X1547 @ ( esk12_1 @ X1547 ) )
        | ( X1547 @ ( esk11_2 @ X1547 @ X1548 ) )
        | ~ ( X1547 @ X1548 ) )
      & ( ~ ( X1547 @ X1551 )
        | ( ( esk12_1 @ X1547 )
          = X1551 )
        | ( X1547 @ ( esk11_2 @ X1547 @ X1548 ) )
        | ~ ( X1547 @ X1548 ) )
      & ( ( X1547 @ ( esk12_1 @ X1547 ) )
        | ( X1548
         != ( esk11_2 @ X1547 @ X1548 ) )
        | ~ ( X1547 @ X1548 ) )
      & ( ~ ( X1547 @ X1551 )
        | ( ( esk12_1 @ X1547 )
          = X1551 )
        | ( X1548
         != ( esk11_2 @ X1547 @ X1548 ) )
        | ~ ( X1547 @ X1548 ) )
      & ( ~ ( in @ X1553 @ ( prop2set @ X1552 ) )
        | X1552 )
      & ( ~ ( in @ X1554 @ emptyset )
        | X1555 )
      & ( ~ ( in @ X1556 @ emptyset )
        | ~ $true )
      & ~ ( in @ X1557 @ emptyset )
      & ( ( X1558 @ ( esk13_2 @ X1558 @ X1559 ) )
        | ~ ( X1558 @ X1559 )
        | ( X1558 @ ( esk14_1 @ X1558 ) ) )
      & ( ( X1559
         != ( esk13_2 @ X1558 @ X1559 ) )
        | ~ ( X1558 @ X1559 )
        | ( X1558 @ ( esk14_1 @ X1558 ) ) )
      & ( ( in @ ( esk16_2 @ X1562 @ X1563 ) @ X1563 )
        | ( X1562 = X1563 )
        | ( in @ ( esk15_2 @ X1562 @ X1563 ) @ X1562 ) )
      & ( ~ ( in @ ( esk16_2 @ X1562 @ X1563 ) @ X1562 )
        | ( X1562 = X1563 )
        | ( in @ ( esk15_2 @ X1562 @ X1563 ) @ X1562 ) )
      & ( ( in @ ( esk16_2 @ X1562 @ X1563 ) @ X1563 )
        | ( X1562 = X1563 )
        | ~ ( in @ ( esk15_2 @ X1562 @ X1563 ) @ X1563 ) )
      & ( ~ ( in @ ( esk16_2 @ X1562 @ X1563 ) @ X1562 )
        | ( X1562 = X1563 )
        | ~ ( in @ ( esk15_2 @ X1562 @ X1563 ) @ X1563 ) )
      & ( ( in @ ( esk17_1 @ X1566 ) @ X1566 )
        | ( X1566 = emptyset ) )
      & ( ( in @ ( esk18_1 @ X1568 ) @ X1568 )
        | ( X1568 = emptyset ) )
      & ( ~ ( in @ X1572 @ ( dsetconstr @ X1570 @ X1571 ) )
        | ( X1571 @ X1572 )
        | ~ ( in @ X1572 @ X1570 ) )
      & ( ~ ( X1571 @ X1572 )
        | ( in @ X1572 @ ( dsetconstr @ X1570 @ X1571 ) )
        | ~ ( in @ X1572 @ X1570 ) )
      & ( ( X1573 = emptyset )
        | ( in @ ( esk19_1 @ X1573 ) @ X1573 ) )
      & ( ~ ( in @ X1577 @ X1575 )
        | ~ ( X1576 @ X1577 )
        | ( ( dsetconstr @ X1575 @ X1576 )
         != emptyset ) )
      & ( ~ ( in @ X1579 @ X1578 )
        | ( X1578 != emptyset ) )
      & ( in @ X1580 @ ( setadjoin @ X1580 @ X1581 ) )
      & ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
      & ( ~ ( in @ X1584 @ X1583 )
        | ( in @ X1584 @ ( setadjoin @ X1582 @ X1583 ) ) )
      & ( ( in @ X1587 @ X1586 )
        | X1588
        | ( X1587 = X1585 )
        | ~ ( in @ X1587 @ ( setadjoin @ X1585 @ X1586 ) ) )
      & ( ~ X1588
        | X1588
        | ( X1587 = X1585 )
        | ~ ( in @ X1587 @ ( setadjoin @ X1585 @ X1586 ) ) )
      & ( ( in @ X1587 @ X1586 )
        | X1588
        | ~ X1588
        | ~ ( in @ X1587 @ ( setadjoin @ X1585 @ X1586 ) ) )
      & ( ~ X1588
        | X1588
        | ~ X1588
        | ~ ( in @ X1587 @ ( setadjoin @ X1585 @ X1586 ) ) )
      & ( ~ ( in @ X1591 @ ( setadjoin @ X1589 @ X1590 ) )
        | ( X1591 = X1589 )
        | ( in @ X1591 @ X1590 ) )
      & ( ( dsetconstr @ X1592
          @ ^ [Z0: $i] : $true )
        = X1592 )
      & ( ( in @ ( esk20_2 @ X1593 @ X1594 ) @ X1594 )
        | ( in @ X1594 @ ( powerset @ X1593 ) ) )
      & ( ~ ( in @ ( esk20_2 @ X1593 @ X1594 ) @ X1593 )
        | ( in @ X1594 @ ( powerset @ X1593 ) ) )
      & ( in @ emptyset @ ( powerset @ X1596 ) )
      & ( in @ emptyset @ ( powerset @ X1597 ) )
      & ( ~ ( in @ X1599 @ ( powerset @ X1598 ) )
        | ~ ( in @ X1600 @ X1599 )
        | ( in @ X1600 @ X1598 ) )
      & ( ~ ( in @ X1602 @ X1603 )
        | ~ ( in @ X1603 @ X1601 )
        | ( in @ X1602 @ ( setunion @ X1601 ) ) )
      & ( ( in @ X1605 @ ( esk21_3 @ X1604 @ X1605 @ X1606 ) )
        | X1606
        | ~ ( in @ X1605 @ ( setunion @ X1604 ) ) )
      & ( ( in @ ( esk21_3 @ X1604 @ X1605 @ X1606 ) @ X1604 )
        | X1606
        | ~ ( in @ X1605 @ ( setunion @ X1604 ) ) )
      & ( ~ X1606
        | X1606
        | ~ ( in @ X1605 @ ( setunion @ X1604 ) ) )
      & ( ~ ( in @ X1609 @ X1608 )
        | ( in @ X1609 @ ( powerset @ ( setunion @ X1608 ) ) ) )
      & ( ~ ( X1610 @ X1614 )
        | ( X1614
          = ( esk23_1 @ X1610 ) )
        | ( X1610 @ ( esk22_2 @ X1610 @ X1611 ) )
        | ~ ( X1610 @ X1611 ) )
      & ( ( X1615
         != ( esk23_1 @ X1610 ) )
        | ( X1610 @ X1615 )
        | ( X1610 @ ( esk22_2 @ X1610 @ X1611 ) )
        | ~ ( X1610 @ X1611 ) )
      & ( ~ ( X1610 @ X1614 )
        | ( X1614
          = ( esk23_1 @ X1610 ) )
        | ( X1611
         != ( esk22_2 @ X1610 @ X1611 ) )
        | ~ ( X1610 @ X1611 ) )
      & ( ( X1615
         != ( esk23_1 @ X1610 ) )
        | ( X1610 @ X1615 )
        | ( X1611
         != ( esk22_2 @ X1610 @ X1611 ) )
        | ~ ( X1610 @ X1611 ) )
      & ( ( in @ ( esk24_1 @ X1616 ) @ X1616 )
        | ( X1616 = emptyset ) )
      & ( $true
        | ( X1616 = emptyset ) )
      & ( ~ ( in @ X1618 @ ( setadjoin @ X1619 @ emptyset ) )
        | ( X1618 = X1619 ) )
      & ( ( X1620 = X1621 )
        | ~ ( in @ X1621 @ ( setadjoin @ X1620 @ emptyset ) ) )
      & ( ( X1622 != X1623 )
        | ( in @ X1622 @ ( setadjoin @ X1623 @ emptyset ) ) )
      & ( ~ ( in @ X1624 @ ( setadjoin @ X1625 @ emptyset ) )
        | ( in @ X1625 @ ( setadjoin @ X1624 @ emptyset ) ) )
      & ( ~ ( in @ X1628 @ ( setadjoin @ X1626 @ ( setadjoin @ X1627 @ emptyset ) ) )
        | ( X1628 = X1626 )
        | ( X1628 = X1627 ) )
      & ( in @ X1629 @ ( setadjoin @ X1629 @ ( setadjoin @ X1630 @ emptyset ) ) )
      & ( in @ X1632 @ ( setadjoin @ X1631 @ ( setadjoin @ X1632 @ emptyset ) ) )
      & ( ~ ( in @ X1635 @ X1633 )
        | ~ ( X1634 @ X1635 )
        | ( ( dsetconstr @ X1633 @ X1634 )
         != emptyset )
        | ~ $true )
      & ( ~ ( in @ X1637 @ emptyset )
        | ( X1636 @ X1637 ) )
      & ( ( in @ ( esk25_2 @ X1638 @ X1639 ) @ X1638 )
        | ~ ( in @ X1640 @ X1638 )
        | ( X1639 @ X1640 ) )
      & ( ~ ( X1639 @ ( esk25_2 @ X1638 @ X1639 ) )
        | ~ ( in @ X1640 @ X1638 )
        | ( X1639 @ X1640 ) )
      & ( ( in @ ( esk26_2 @ X1642 @ X1643 ) @ X1642 )
        | ~ ( in @ X1645 @ X1642 )
        | ~ ( X1643 @ X1645 ) )
      & ( ( X1643 @ ( esk26_2 @ X1642 @ X1643 ) )
        | ~ ( in @ X1645 @ X1642 )
        | ~ ( X1643 @ X1645 ) )
      & ( ( in @ ( esk27_2 @ X1646 @ X1647 ) @ X1646 )
        | ~ ( in @ X1649 @ X1646 )
        | ~ ( X1647 @ X1649 ) )
      & ( ( X1647 @ ( esk27_2 @ X1646 @ X1647 ) )
        | ~ ( in @ X1649 @ X1646 )
        | ~ ( X1647 @ X1649 ) )
      & ( ( in @ ( esk28_2 @ X1650 @ X1651 ) @ X1650 )
        | ~ ( in @ X1652 @ X1650 )
        | ( X1651 @ X1652 ) )
      & ( ~ ( X1651 @ ( esk28_2 @ X1650 @ X1651 ) )
        | ~ ( in @ X1652 @ X1650 )
        | ( X1651 @ X1652 ) )
      & ( ~ X1654
        | ( in @ emptyset @ ( prop2set @ X1654 ) ) )
      & prop2set2propI
      & ( ( in @ ( esk29_2 @ X1655 @ X1656 ) @ X1655 )
        | ~ ( in @ X1658 @ X1655 )
        | ~ ( X1656 @ X1658 ) )
      & ( ( X1656 @ ( esk29_2 @ X1655 @ X1656 ) )
        | ~ ( in @ X1658 @ X1655 )
        | ~ ( X1656 @ X1658 ) )
      & ( ( in @ ( esk30_2 @ X1659 @ X1660 ) @ X1659 )
        | ~ ( in @ X1661 @ X1659 )
        | ( X1660 @ X1661 ) )
      & ( ~ ( X1660 @ ( esk30_2 @ X1659 @ X1660 ) )
        | ~ ( in @ X1661 @ X1659 )
        | ( X1660 @ X1661 ) )
      & ( ( X1663 @ ( esk32_1 @ X1663 ) )
        | ( X1663 @ ( esk31_2 @ X1663 @ X1664 ) )
        | ~ ( X1663 @ X1664 ) )
      & ( ~ ( X1663 @ X1667 )
        | ( ( esk32_1 @ X1663 )
          = X1667 )
        | ( X1663 @ ( esk31_2 @ X1663 @ X1664 ) )
        | ~ ( X1663 @ X1664 ) )
      & ( ( X1663 @ ( esk32_1 @ X1663 ) )
        | ( X1664
         != ( esk31_2 @ X1663 @ X1664 ) )
        | ~ ( X1663 @ X1664 ) )
      & ( ~ ( X1663 @ X1667 )
        | ( ( esk32_1 @ X1663 )
          = X1667 )
        | ( X1664
         != ( esk31_2 @ X1663 @ X1664 ) )
        | ~ ( X1663 @ X1664 ) )
      & ( ( X1668 @ ( esk35_1 @ X1668 ) )
        | ( X1668 @ ( esk33_1 @ X1668 ) )
        | ~ ( X1668 @ X1669 ) )
      & ( ~ ( X1668 @ X1673 )
        | ( ( esk35_1 @ X1668 )
          = X1673 )
        | ( X1668 @ ( esk33_1 @ X1668 ) )
        | ~ ( X1668 @ X1669 ) )
      & ( ( X1668 @ ( esk35_1 @ X1668 ) )
        | ( X1668 @ ( esk34_1 @ X1668 ) )
        | ~ ( X1668 @ X1669 ) )
      & ( ~ ( X1668 @ X1673 )
        | ( ( esk35_1 @ X1668 )
          = X1673 )
        | ( X1668 @ ( esk34_1 @ X1668 ) )
        | ~ ( X1668 @ X1669 ) )
      & ( ( X1668 @ ( esk35_1 @ X1668 ) )
        | ( ( esk33_1 @ X1668 )
         != ( esk34_1 @ X1668 ) )
        | ~ ( X1668 @ X1669 ) )
      & ( ~ ( X1668 @ X1673 )
        | ( ( esk35_1 @ X1668 )
          = X1673 )
        | ( ( esk33_1 @ X1668 )
         != ( esk34_1 @ X1668 ) )
        | ~ ( X1668 @ X1669 ) )
      & ( ( X1674 @ ( esk37_1 @ X1674 ) )
        | ~ ( X1674 @ ( esk36_2 @ X1674 @ X1675 ) )
        | ( ( esk36_2 @ X1674 @ X1675 )
         != X1675 ) )
      & ( ~ ( X1674 @ X1678 )
        | ( ( esk37_1 @ X1674 )
          = X1678 )
        | ~ ( X1674 @ ( esk36_2 @ X1674 @ X1675 ) )
        | ( ( esk36_2 @ X1674 @ X1675 )
         != X1675 ) )
      & ( ( X1674 @ ( esk37_1 @ X1674 ) )
        | ( X1674 @ ( esk36_2 @ X1674 @ X1675 ) )
        | ( ( esk36_2 @ X1674 @ X1675 )
          = X1675 ) )
      & ( ~ ( X1674 @ X1678 )
        | ( ( esk37_1 @ X1674 )
          = X1678 )
        | ( X1674 @ ( esk36_2 @ X1674 @ X1675 ) )
        | ( ( esk36_2 @ X1674 @ X1675 )
          = X1675 ) )
      & ( ( X1679 != X1680 )
        | ( X1681 != X1682 )
        | ~ ( in @ X1681 @ X1679 )
        | ( in @ X1682 @ X1680 ) )
      & ( ~ ( in @ X1685 @ X1683 )
        | ( in @ X1686 @ X1684 )
        | ( X1685 != X1686 )
        | ( X1683 != X1684 ) )
      & ( ~ ( in @ X1686 @ X1684 )
        | ( in @ X1685 @ X1683 )
        | ( X1685 != X1686 )
        | ( X1683 != X1684 ) )
      & ( ( X1687 @ ( esk38_2 @ X1687 @ X1688 ) )
        | ~ ( X1687 @ X1688 )
        | ~ ( X1687 @ X1690 )
        | ~ ( X1687 @ X1691 )
        | ( X1690 = X1691 ) )
      & ( ( X1688
         != ( esk38_2 @ X1687 @ X1688 ) )
        | ~ ( X1687 @ X1688 )
        | ~ ( X1687 @ X1690 )
        | ~ ( X1687 @ X1691 )
        | ( X1690 = X1691 ) )
      & ( ( X1693 @ ( esk42_2 @ X1692 @ X1693 ) )
        | ( X1692 @ ( esk41_3 @ X1692 @ X1693 @ X1696 ) )
        | ~ ( X1692 @ X1696 )
        | ( ( esk39_2 @ X1692 @ X1693 )
          = ( esk40_2 @ X1692 @ X1693 ) ) )
      & ( ~ ( X1693 @ X1699 )
        | ( ( esk42_2 @ X1692 @ X1693 )
          = X1699 )
        | ( X1692 @ ( esk41_3 @ X1692 @ X1693 @ X1696 ) )
        | ~ ( X1692 @ X1696 )
        | ( ( esk39_2 @ X1692 @ X1693 )
          = ( esk40_2 @ X1692 @ X1693 ) ) )
      & ( ( X1693 @ ( esk42_2 @ X1692 @ X1693 ) )
        | ( X1696
         != ( esk41_3 @ X1692 @ X1693 @ X1696 ) )
        | ~ ( X1692 @ X1696 )
        | ( ( esk39_2 @ X1692 @ X1693 )
          = ( esk40_2 @ X1692 @ X1693 ) ) )
      & ( ~ ( X1693 @ X1699 )
        | ( ( esk42_2 @ X1692 @ X1693 )
          = X1699 )
        | ( X1696
         != ( esk41_3 @ X1692 @ X1693 @ X1696 ) )
        | ~ ( X1692 @ X1696 )
        | ( ( esk39_2 @ X1692 @ X1693 )
          = ( esk40_2 @ X1692 @ X1693 ) ) )
      & ( ( X1692 @ ( esk44_2 @ X1692 @ X1693 ) )
        | ( X1693 @ ( esk43_3 @ X1692 @ X1693 @ X1700 ) )
        | ~ ( X1693 @ X1700 )
        | ( ( esk39_2 @ X1692 @ X1693 )
          = ( esk40_2 @ X1692 @ X1693 ) ) )
      & ( ~ ( X1692 @ X1703 )
        | ( ( esk44_2 @ X1692 @ X1693 )
          = X1703 )
        | ( X1693 @ ( esk43_3 @ X1692 @ X1693 @ X1700 ) )
        | ~ ( X1693 @ X1700 )
        | ( ( esk39_2 @ X1692 @ X1693 )
          = ( esk40_2 @ X1692 @ X1693 ) ) )
      & ( ( X1692 @ ( esk44_2 @ X1692 @ X1693 ) )
        | ( X1700
         != ( esk43_3 @ X1692 @ X1693 @ X1700 ) )
        | ~ ( X1693 @ X1700 )
        | ( ( esk39_2 @ X1692 @ X1693 )
          = ( esk40_2 @ X1692 @ X1693 ) ) )
      & ( ~ ( X1692 @ X1703 )
        | ( ( esk44_2 @ X1692 @ X1693 )
          = X1703 )
        | ( X1700
         != ( esk43_3 @ X1692 @ X1693 @ X1700 ) )
        | ~ ( X1693 @ X1700 )
        | ( ( esk39_2 @ X1692 @ X1693 )
          = ( esk40_2 @ X1692 @ X1693 ) ) )
      & ( ( X1693 @ ( esk42_2 @ X1692 @ X1693 ) )
        | ( X1692 @ ( esk41_3 @ X1692 @ X1693 @ X1696 ) )
        | ~ ( X1692 @ X1696 )
        | ~ ( X1692 @ ( esk39_2 @ X1692 @ X1693 ) )
        | ~ ( X1693 @ ( esk40_2 @ X1692 @ X1693 ) ) )
      & ( ~ ( X1693 @ X1699 )
        | ( ( esk42_2 @ X1692 @ X1693 )
          = X1699 )
        | ( X1692 @ ( esk41_3 @ X1692 @ X1693 @ X1696 ) )
        | ~ ( X1692 @ X1696 )
        | ~ ( X1692 @ ( esk39_2 @ X1692 @ X1693 ) )
        | ~ ( X1693 @ ( esk40_2 @ X1692 @ X1693 ) ) )
      & ( ( X1693 @ ( esk42_2 @ X1692 @ X1693 ) )
        | ( X1696
         != ( esk41_3 @ X1692 @ X1693 @ X1696 ) )
        | ~ ( X1692 @ X1696 )
        | ~ ( X1692 @ ( esk39_2 @ X1692 @ X1693 ) )
        | ~ ( X1693 @ ( esk40_2 @ X1692 @ X1693 ) ) )
      & ( ~ ( X1693 @ X1699 )
        | ( ( esk42_2 @ X1692 @ X1693 )
          = X1699 )
        | ( X1696
         != ( esk41_3 @ X1692 @ X1693 @ X1696 ) )
        | ~ ( X1692 @ X1696 )
        | ~ ( X1692 @ ( esk39_2 @ X1692 @ X1693 ) )
        | ~ ( X1693 @ ( esk40_2 @ X1692 @ X1693 ) ) )
      & ( ( X1692 @ ( esk44_2 @ X1692 @ X1693 ) )
        | ( X1693 @ ( esk43_3 @ X1692 @ X1693 @ X1700 ) )
        | ~ ( X1693 @ X1700 )
        | ~ ( X1692 @ ( esk39_2 @ X1692 @ X1693 ) )
        | ~ ( X1693 @ ( esk40_2 @ X1692 @ X1693 ) ) )
      & ( ~ ( X1692 @ X1703 )
        | ( ( esk44_2 @ X1692 @ X1693 )
          = X1703 )
        | ( X1693 @ ( esk43_3 @ X1692 @ X1693 @ X1700 ) )
        | ~ ( X1693 @ X1700 )
        | ~ ( X1692 @ ( esk39_2 @ X1692 @ X1693 ) )
        | ~ ( X1693 @ ( esk40_2 @ X1692 @ X1693 ) ) )
      & ( ( X1692 @ ( esk44_2 @ X1692 @ X1693 ) )
        | ( X1700
         != ( esk43_3 @ X1692 @ X1693 @ X1700 ) )
        | ~ ( X1693 @ X1700 )
        | ~ ( X1692 @ ( esk39_2 @ X1692 @ X1693 ) )
        | ~ ( X1693 @ ( esk40_2 @ X1692 @ X1693 ) ) )
      & ( ~ ( X1692 @ X1703 )
        | ( ( esk44_2 @ X1692 @ X1693 )
          = X1703 )
        | ( X1700
         != ( esk43_3 @ X1692 @ X1693 @ X1700 ) )
        | ~ ( X1693 @ X1700 )
        | ~ ( X1692 @ ( esk39_2 @ X1692 @ X1693 ) )
        | ~ ( X1693 @ ( esk40_2 @ X1692 @ X1693 ) ) )
      & ( ( X1693 @ ( esk42_2 @ X1692 @ X1693 ) )
        | ( X1692 @ ( esk41_3 @ X1692 @ X1693 @ X1696 ) )
        | ~ ( X1692 @ X1696 )
        | ( X1692 @ ( esk39_2 @ X1692 @ X1693 ) )
        | ( X1693 @ ( esk40_2 @ X1692 @ X1693 ) ) )
      & ( ~ ( X1693 @ X1699 )
        | ( ( esk42_2 @ X1692 @ X1693 )
          = X1699 )
        | ( X1692 @ ( esk41_3 @ X1692 @ X1693 @ X1696 ) )
        | ~ ( X1692 @ X1696 )
        | ( X1692 @ ( esk39_2 @ X1692 @ X1693 ) )
        | ( X1693 @ ( esk40_2 @ X1692 @ X1693 ) ) )
      & ( ( X1693 @ ( esk42_2 @ X1692 @ X1693 ) )
        | ( X1696
         != ( esk41_3 @ X1692 @ X1693 @ X1696 ) )
        | ~ ( X1692 @ X1696 )
        | ( X1692 @ ( esk39_2 @ X1692 @ X1693 ) )
        | ( X1693 @ ( esk40_2 @ X1692 @ X1693 ) ) )
      & ( ~ ( X1693 @ X1699 )
        | ( ( esk42_2 @ X1692 @ X1693 )
          = X1699 )
        | ( X1696
         != ( esk41_3 @ X1692 @ X1693 @ X1696 ) )
        | ~ ( X1692 @ X1696 )
        | ( X1692 @ ( esk39_2 @ X1692 @ X1693 ) )
        | ( X1693 @ ( esk40_2 @ X1692 @ X1693 ) ) )
      & ( ( X1692 @ ( esk44_2 @ X1692 @ X1693 ) )
        | ( X1693 @ ( esk43_3 @ X1692 @ X1693 @ X1700 ) )
        | ~ ( X1693 @ X1700 )
        | ( X1692 @ ( esk39_2 @ X1692 @ X1693 ) )
        | ( X1693 @ ( esk40_2 @ X1692 @ X1693 ) ) )
      & ( ~ ( X1692 @ X1703 )
        | ( ( esk44_2 @ X1692 @ X1693 )
          = X1703 )
        | ( X1693 @ ( esk43_3 @ X1692 @ X1693 @ X1700 ) )
        | ~ ( X1693 @ X1700 )
        | ( X1692 @ ( esk39_2 @ X1692 @ X1693 ) )
        | ( X1693 @ ( esk40_2 @ X1692 @ X1693 ) ) )
      & ( ( X1692 @ ( esk44_2 @ X1692 @ X1693 ) )
        | ( X1700
         != ( esk43_3 @ X1692 @ X1693 @ X1700 ) )
        | ~ ( X1693 @ X1700 )
        | ( X1692 @ ( esk39_2 @ X1692 @ X1693 ) )
        | ( X1693 @ ( esk40_2 @ X1692 @ X1693 ) ) )
      & ( ~ ( X1692 @ X1703 )
        | ( ( esk44_2 @ X1692 @ X1693 )
          = X1703 )
        | ( X1700
         != ( esk43_3 @ X1692 @ X1693 @ X1700 ) )
        | ~ ( X1693 @ X1700 )
        | ( X1692 @ ( esk39_2 @ X1692 @ X1693 ) )
        | ( X1693 @ ( esk40_2 @ X1692 @ X1693 ) ) )
      & ( emptyset = emptyset )
      & ( ( X1704 != X1705 )
        | ( X1706 != X1707 )
        | ( ( setadjoin @ X1704 @ X1706 )
          = ( setadjoin @ X1705 @ X1707 ) ) )
      & ( ( X1708 != X1709 )
        | ( ( powerset @ X1708 )
          = ( powerset @ X1709 ) ) )
      & ( ( X1710 != X1711 )
        | ( ( setunion @ X1710 )
          = ( setunion @ X1711 ) ) )
      & ( omega = omega )
      & ( ( X1712 @ ( esk45_2 @ X1712 @ X1713 ) )
        | ~ ( X1712 @ X1713 )
        | ~ ( X1712 @ X1715 )
        | ~ ( X1712 @ X1716 )
        | ( X1715 = X1716 ) )
      & ( ( X1713
         != ( esk45_2 @ X1712 @ X1713 ) )
        | ~ ( X1712 @ X1713 )
        | ~ ( X1712 @ X1715 )
        | ~ ( X1712 @ X1716 )
        | ( X1715 = X1716 ) )
      & ( ( X1718 @ ( esk49_3 @ X1717 @ X1718 @ X1723 ) )
        | ~ ( X1718 @ X1723 )
        | ( ( descr @ X1717 )
          = ( descr @ X1718 ) )
        | ( X1717 @ ( esk48_3 @ X1717 @ X1718 @ X1721 ) )
        | ~ ( X1717 @ X1721 )
        | ( ( esk46_2 @ X1717 @ X1718 )
          = ( esk47_2 @ X1717 @ X1718 ) ) )
      & ( ( X1723
         != ( esk49_3 @ X1717 @ X1718 @ X1723 ) )
        | ~ ( X1718 @ X1723 )
        | ( ( descr @ X1717 )
          = ( descr @ X1718 ) )
        | ( X1717 @ ( esk48_3 @ X1717 @ X1718 @ X1721 ) )
        | ~ ( X1717 @ X1721 )
        | ( ( esk46_2 @ X1717 @ X1718 )
          = ( esk47_2 @ X1717 @ X1718 ) ) )
      & ( ( X1718 @ ( esk49_3 @ X1717 @ X1718 @ X1723 ) )
        | ~ ( X1718 @ X1723 )
        | ( ( descr @ X1717 )
          = ( descr @ X1718 ) )
        | ( X1721
         != ( esk48_3 @ X1717 @ X1718 @ X1721 ) )
        | ~ ( X1717 @ X1721 )
        | ( ( esk46_2 @ X1717 @ X1718 )
          = ( esk47_2 @ X1717 @ X1718 ) ) )
      & ( ( X1723
         != ( esk49_3 @ X1717 @ X1718 @ X1723 ) )
        | ~ ( X1718 @ X1723 )
        | ( ( descr @ X1717 )
          = ( descr @ X1718 ) )
        | ( X1721
         != ( esk48_3 @ X1717 @ X1718 @ X1721 ) )
        | ~ ( X1717 @ X1721 )
        | ( ( esk46_2 @ X1717 @ X1718 )
          = ( esk47_2 @ X1717 @ X1718 ) ) )
      & ( ( X1718 @ ( esk49_3 @ X1717 @ X1718 @ X1723 ) )
        | ~ ( X1718 @ X1723 )
        | ( ( descr @ X1717 )
          = ( descr @ X1718 ) )
        | ( X1717 @ ( esk48_3 @ X1717 @ X1718 @ X1721 ) )
        | ~ ( X1717 @ X1721 )
        | ~ ( X1717 @ ( esk46_2 @ X1717 @ X1718 ) )
        | ~ ( X1718 @ ( esk47_2 @ X1717 @ X1718 ) ) )
      & ( ( X1723
         != ( esk49_3 @ X1717 @ X1718 @ X1723 ) )
        | ~ ( X1718 @ X1723 )
        | ( ( descr @ X1717 )
          = ( descr @ X1718 ) )
        | ( X1717 @ ( esk48_3 @ X1717 @ X1718 @ X1721 ) )
        | ~ ( X1717 @ X1721 )
        | ~ ( X1717 @ ( esk46_2 @ X1717 @ X1718 ) )
        | ~ ( X1718 @ ( esk47_2 @ X1717 @ X1718 ) ) )
      & ( ( X1718 @ ( esk49_3 @ X1717 @ X1718 @ X1723 ) )
        | ~ ( X1718 @ X1723 )
        | ( ( descr @ X1717 )
          = ( descr @ X1718 ) )
        | ( X1721
         != ( esk48_3 @ X1717 @ X1718 @ X1721 ) )
        | ~ ( X1717 @ X1721 )
        | ~ ( X1717 @ ( esk46_2 @ X1717 @ X1718 ) )
        | ~ ( X1718 @ ( esk47_2 @ X1717 @ X1718 ) ) )
      & ( ( X1723
         != ( esk49_3 @ X1717 @ X1718 @ X1723 ) )
        | ~ ( X1718 @ X1723 )
        | ( ( descr @ X1717 )
          = ( descr @ X1718 ) )
        | ( X1721
         != ( esk48_3 @ X1717 @ X1718 @ X1721 ) )
        | ~ ( X1717 @ X1721 )
        | ~ ( X1717 @ ( esk46_2 @ X1717 @ X1718 ) )
        | ~ ( X1718 @ ( esk47_2 @ X1717 @ X1718 ) ) )
      & ( ( X1718 @ ( esk49_3 @ X1717 @ X1718 @ X1723 ) )
        | ~ ( X1718 @ X1723 )
        | ( ( descr @ X1717 )
          = ( descr @ X1718 ) )
        | ( X1717 @ ( esk48_3 @ X1717 @ X1718 @ X1721 ) )
        | ~ ( X1717 @ X1721 )
        | ( X1717 @ ( esk46_2 @ X1717 @ X1718 ) )
        | ( X1718 @ ( esk47_2 @ X1717 @ X1718 ) ) )
      & ( ( X1723
         != ( esk49_3 @ X1717 @ X1718 @ X1723 ) )
        | ~ ( X1718 @ X1723 )
        | ( ( descr @ X1717 )
          = ( descr @ X1718 ) )
        | ( X1717 @ ( esk48_3 @ X1717 @ X1718 @ X1721 ) )
        | ~ ( X1717 @ X1721 )
        | ( X1717 @ ( esk46_2 @ X1717 @ X1718 ) )
        | ( X1718 @ ( esk47_2 @ X1717 @ X1718 ) ) )
      & ( ( X1718 @ ( esk49_3 @ X1717 @ X1718 @ X1723 ) )
        | ~ ( X1718 @ X1723 )
        | ( ( descr @ X1717 )
          = ( descr @ X1718 ) )
        | ( X1721
         != ( esk48_3 @ X1717 @ X1718 @ X1721 ) )
        | ~ ( X1717 @ X1721 )
        | ( X1717 @ ( esk46_2 @ X1717 @ X1718 ) )
        | ( X1718 @ ( esk47_2 @ X1717 @ X1718 ) ) )
      & ( ( X1723
         != ( esk49_3 @ X1717 @ X1718 @ X1723 ) )
        | ~ ( X1718 @ X1723 )
        | ( ( descr @ X1717 )
          = ( descr @ X1718 ) )
        | ( X1721
         != ( esk48_3 @ X1717 @ X1718 @ X1721 ) )
        | ~ ( X1717 @ X1721 )
        | ( X1717 @ ( esk46_2 @ X1717 @ X1718 ) )
        | ( X1718 @ ( esk47_2 @ X1717 @ X1718 ) ) )
      & ( ( in @ ( esk50_4 @ X1725 @ X1726 @ X1727 @ X1728 ) @ X1725 )
        | ( ( dsetconstr @ X1725 @ X1727 )
          = ( dsetconstr @ X1726 @ X1728 ) )
        | ( X1725 != X1726 ) )
      & ( ( in @ ( esk51_4 @ X1725 @ X1726 @ X1727 @ X1728 ) @ X1726 )
        | ( ( dsetconstr @ X1725 @ X1727 )
          = ( dsetconstr @ X1726 @ X1728 ) )
        | ( X1725 != X1726 ) )
      & ( ( ( esk50_4 @ X1725 @ X1726 @ X1727 @ X1728 )
          = ( esk51_4 @ X1725 @ X1726 @ X1727 @ X1728 ) )
        | ( ( dsetconstr @ X1725 @ X1727 )
          = ( dsetconstr @ X1726 @ X1728 ) )
        | ( X1725 != X1726 ) )
      & ( ~ ( X1727 @ ( esk50_4 @ X1725 @ X1726 @ X1727 @ X1728 ) )
        | ~ ( X1728 @ ( esk51_4 @ X1725 @ X1726 @ X1727 @ X1728 ) )
        | ( ( dsetconstr @ X1725 @ X1727 )
          = ( dsetconstr @ X1726 @ X1728 ) )
        | ( X1725 != X1726 ) )
      & ( ( X1727 @ ( esk50_4 @ X1725 @ X1726 @ X1727 @ X1728 ) )
        | ( X1728 @ ( esk51_4 @ X1725 @ X1726 @ X1727 @ X1728 ) )
        | ( ( dsetconstr @ X1725 @ X1727 )
          = ( dsetconstr @ X1726 @ X1728 ) )
        | ( X1725 != X1726 ) )
      & ( ( in @ ( esk52_2 @ X1731 @ X1732 ) @ X1731 )
        | ( subset @ X1731 @ X1732 ) )
      & ( ~ ( in @ ( esk52_2 @ X1731 @ X1732 ) @ X1732 )
        | ( subset @ X1731 @ X1732 ) )
      & ( ( X1734 != X1735 )
        | ( subset @ X1735 @ X1734 ) )
      & ( ( X1736 != X1737 )
        | ( subset @ X1736 @ X1737 ) )
      & ( ( in @ ( esk53_2 @ X1738 @ X1739 ) @ X1738 )
        | ( subset @ X1738 @ X1739 ) )
      & ( ~ ( in @ ( esk53_2 @ X1738 @ X1739 ) @ X1739 )
        | ( subset @ X1738 @ X1739 ) )
      & ( subset @ emptyset @ X1741 )
      & ( ~ ( subset @ X1742 @ X1743 )
        | ~ ( in @ X1744 @ X1742 )
        | ( in @ X1744 @ X1743 ) )
      & ( ~ ( subset @ X1745 @ X1746 )
        | ( in @ X1747 @ X1746 )
        | ~ ( in @ X1747 @ X1745 ) )
      & ( ~ ( in @ X1750 @ X1748 )
        | ( in @ X1750 @ X1749 )
        | ~ ( subset @ X1748 @ X1749 ) )
      & ( ( subset @ X1751 @ X1752 )
        | ( X1751 != X1752 ) )
      & ( ~ ( in @ X1755 @ X1753 )
        | ( in @ X1755 @ X1754 )
        | ( X1753 != X1754 ) )
      & ( subset @ X1756 @ X1756 )
      & ( ~ ( subset @ X1757 @ X1758 )
        | ~ ( subset @ X1758 @ X1759 )
        | ( subset @ X1757 @ X1759 ) )
      & ( subset @ X1761 @ ( setadjoin @ X1760 @ X1761 ) )
      & ( ~ ( subset @ X1762 @ X1764 )
        | ( subset @ X1762 @ ( setadjoin @ X1763 @ X1764 ) ) )
      & ( ~ ( subset @ X1765 @ X1766 )
        | ( in @ X1765 @ ( powerset @ X1766 ) ) )
      & ( ~ ( subset @ X1767 @ X1768 )
        | ~ ( subset @ X1768 @ X1767 )
        | ( X1767 = X1768 ) )
      & ( ~ ( subset @ X1769 @ emptyset )
        | ( X1769 = emptyset ) )
      & ( ~ ( subset @ X1771 @ X1770 )
        | ( in @ X1771 @ ( powerset @ X1770 ) ) )
      & ( ~ ( in @ X1773 @ ( powerset @ X1772 ) )
        | ( subset @ X1773 @ X1772 ) )
      & ( in @ X1774 @ ( powerset @ X1774 ) )
      & ( ~ ( subset @ X1775 @ X1776 )
        | ( subset @ ( powerset @ X1775 ) @ ( powerset @ X1776 ) ) )
      & ( in @ ( dsetconstr @ X1777 @ X1778 ) @ ( powerset @ X1777 ) )
      & ( subset @ ( dsetconstr @ X1779 @ X1780 ) @ X1779 )
      & ( ~ ( in @ X1783 @ X1781 )
        | ( in @ X1783 @ ( binunion @ X1781 @ X1782 ) ) )
      & ( in @ X1785 @ ( setadjoin @ X1784 @ ( setadjoin @ X1785 @ emptyset ) ) )
      & ( ~ ( in @ X1788 @ X1787 )
        | ( in @ X1788 @ ( binunion @ X1786 @ X1787 ) ) )
      & ( ( in @ X1791 @ X1790 )
        | X1792
        | ( in @ X1791 @ X1789 )
        | ~ ( in @ X1791 @ ( binunion @ X1789 @ X1790 ) ) )
      & ( ~ X1792
        | X1792
        | ( in @ X1791 @ X1789 )
        | ~ ( in @ X1791 @ ( binunion @ X1789 @ X1790 ) ) )
      & ( ( in @ X1791 @ X1790 )
        | X1792
        | ~ X1792
        | ~ ( in @ X1791 @ ( binunion @ X1789 @ X1790 ) ) )
      & ( ~ X1792
        | X1792
        | ~ X1792
        | ~ ( in @ X1791 @ ( binunion @ X1789 @ X1790 ) ) )
      & ( ~ ( in @ X1795 @ ( binunion @ X1793 @ X1794 ) )
        | ( in @ X1795 @ X1793 )
        | ( in @ X1795 @ X1794 ) )
      & ( subset @ X1796 @ ( binunion @ X1796 @ X1797 ) )
      & ( subset @ X1799 @ ( binunion @ X1798 @ X1799 ) )
      & ( ~ ( in @ X1802 @ X1800 )
        | ~ ( in @ X1802 @ X1801 )
        | ( in @ X1802 @ ( binintersect @ X1800 @ X1801 ) ) )
      & ( ~ ( subset @ X1805 @ X1803 )
        | ~ ( subset @ X1805 @ X1804 )
        | ( subset @ X1805 @ ( binintersect @ X1803 @ X1804 ) ) )
      & ( ~ ( in @ X1808 @ ( binintersect @ X1806 @ X1807 ) )
        | ( in @ X1808 @ X1806 ) )
      & ( subset @ ( binintersect @ X1809 @ X1810 ) @ X1809 )
      & ( ~ ( subset @ X1811 @ X1812 )
        | ( ( binintersect @ X1811 @ X1812 )
          = X1811 ) )
      & ( ( ( binintersect @ X1813 @ X1814 )
         != X1814 )
        | ( subset @ X1814 @ X1813 ) )
      & ( ~ ( in @ X1817 @ ( binintersect @ X1815 @ X1816 ) )
        | ( in @ X1817 @ X1816 ) )
      & ( ( in @ ( esk54_2 @ X1818 @ X1819 ) @ X1818 )
        | ( ( binintersect @ X1818 @ X1819 )
          = emptyset ) )
      & ( ( in @ ( esk54_2 @ X1818 @ X1819 ) @ X1819 )
        | ( ( binintersect @ X1818 @ X1819 )
          = emptyset ) )
      & ( subset @ ( binintersect @ X1821 @ X1822 ) @ X1822 )
      & ( ~ ( subset @ X1824 @ X1823 )
        | ( ( binintersect @ X1823 @ X1824 )
          = X1824 ) )
      & ( ( ( binintersect @ X1825 @ X1826 )
         != X1825 )
        | ( subset @ X1825 @ X1826 ) )
      & ( ( binintersect @ X1827 @ ( binunion @ X1828 @ X1829 ) )
        = ( binunion @ ( binintersect @ X1827 @ X1828 ) @ ( binintersect @ X1827 @ X1829 ) ) )
      & ( ~ ( in @ X1832 @ X1830 )
        | ( in @ X1832 @ X1831 )
        | ( in @ X1832 @ ( setminus @ X1830 @ X1831 ) ) )
      & ( ~ ( in @ X1835 @ ( setminus @ X1833 @ X1834 ) )
        | ( in @ X1835 @ X1833 ) )
      & ( ~ ( in @ X1838 @ ( setminus @ X1836 @ X1837 ) )
        | ~ ( in @ X1838 @ X1837 ) )
      & ( ~ ( subset @ X1839 @ X1840 )
        | ( ( setminus @ X1839 @ X1840 )
          = emptyset ) )
      & ( ( in @ X1843 @ ( setminus @ X1841 @ X1842 ) )
        | ~ ( in @ X1843 @ X1841 )
        | ( in @ X1843 @ X1842 ) )
      & ( ( in @ X1846 @ ( setminus @ X1844 @ X1845 ) )
        | ( in @ X1846 @ X1845 )
        | ~ ( in @ X1846 @ X1844 ) )
      & ( ( in @ X1849 @ X1847 )
        | ~ ( in @ X1849 @ ( setminus @ X1847 @ X1848 ) ) )
      & ( ~ ( in @ X1852 @ X1851 )
        | ~ ( in @ X1852 @ ( setminus @ X1850 @ X1851 ) ) )
      & ( subset @ ( setminus @ X1853 @ X1854 ) @ X1853 )
      & ( ( ( setminus @ X1855 @ X1856 )
         != emptyset )
        | ( subset @ X1855 @ X1856 ) )
      & ( ~ ( in @ X1859 @ X1857 )
        | X1860
        | ( in @ X1859 @ X1857 )
        | ~ ( in @ X1859 @ ( symdiff @ X1857 @ X1858 ) ) )
      & ( ( in @ X1859 @ X1858 )
        | X1860
        | ( in @ X1859 @ X1857 )
        | ~ ( in @ X1859 @ ( symdiff @ X1857 @ X1858 ) ) )
      & ( ~ X1860
        | X1860
        | ( in @ X1859 @ X1857 )
        | ~ ( in @ X1859 @ ( symdiff @ X1857 @ X1858 ) ) )
      & ( ~ ( in @ X1859 @ X1857 )
        | X1860
        | ~ ( in @ X1859 @ X1858 )
        | ~ ( in @ X1859 @ ( symdiff @ X1857 @ X1858 ) ) )
      & ( ( in @ X1859 @ X1858 )
        | X1860
        | ~ ( in @ X1859 @ X1858 )
        | ~ ( in @ X1859 @ ( symdiff @ X1857 @ X1858 ) ) )
      & ( ~ X1860
        | X1860
        | ~ ( in @ X1859 @ X1858 )
        | ~ ( in @ X1859 @ ( symdiff @ X1857 @ X1858 ) ) )
      & ( ~ ( in @ X1859 @ X1857 )
        | X1860
        | ~ X1860
        | ~ ( in @ X1859 @ ( symdiff @ X1857 @ X1858 ) ) )
      & ( ( in @ X1859 @ X1858 )
        | X1860
        | ~ X1860
        | ~ ( in @ X1859 @ ( symdiff @ X1857 @ X1858 ) ) )
      & ( ~ X1860
        | X1860
        | ~ X1860
        | ~ ( in @ X1859 @ ( symdiff @ X1857 @ X1858 ) ) )
      & ( ~ ( in @ X1863 @ X1861 )
        | ( in @ X1863 @ X1862 )
        | ( in @ X1863 @ ( symdiff @ X1861 @ X1862 ) ) )
      & ( ( in @ X1866 @ X1864 )
        | ~ ( in @ X1866 @ X1865 )
        | ( in @ X1866 @ ( symdiff @ X1864 @ X1865 ) ) )
      & ( ~ ( in @ X1869 @ X1867 )
        | ~ ( in @ X1869 @ X1868 )
        | ~ ( in @ X1869 @ ( symdiff @ X1867 @ X1868 ) ) )
      & ( ( in @ X1872 @ X1870 )
        | ( in @ X1872 @ X1871 )
        | ~ ( in @ X1872 @ ( symdiff @ X1870 @ X1871 ) ) )
      & ( in @ X1874 @ ( setadjoin @ X1873 @ ( setadjoin @ X1874 @ emptyset ) ) )
      & ( in @ X1875 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1875 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1875 @ ( setadjoin @ X1876 @ emptyset ) ) @ emptyset ) ) ) )
      & ( in @ X1878 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1877 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1877 @ ( setadjoin @ X1878 @ emptyset ) ) @ emptyset ) ) ) )
      & ( iskpair @ ( setadjoin @ ( setadjoin @ X1879 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1879 @ ( setadjoin @ X1880 @ emptyset ) ) @ emptyset ) ) )
      & ( iskpair @ ( kpair @ X1881 @ X1882 ) )
      & ( ~ ( in @ X1884 @ X1883 )
        | ( subset @ ( setadjoin @ X1884 @ emptyset ) @ X1883 ) )
      & ( ~ ( in @ X1886 @ X1885 )
        | ( in @ ( setadjoin @ X1886 @ emptyset ) @ ( powerset @ X1885 ) ) )
      & ( ~ ( in @ X1889 @ X1887 )
        | ( in @ ( setadjoin @ X1889 @ emptyset ) @ ( powerset @ ( binunion @ X1887 @ X1888 ) ) ) )
      & ( ~ ( in @ X1892 @ ( setadjoin @ X1890 @ ( setadjoin @ X1891 @ emptyset ) ) )
        | ( X1892 = X1890 )
        | ( X1892 = X1891 ) )
      & ( ~ ( in @ X1895 @ X1893 )
        | ~ ( in @ X1896 @ X1894 )
        | ( subset @ ( setadjoin @ X1895 @ ( setadjoin @ X1896 @ emptyset ) ) @ ( binunion @ X1893 @ X1894 ) ) )
      & ( ~ ( in @ X1899 @ X1897 )
        | ~ ( in @ X1900 @ X1898 )
        | ( in @ ( setadjoin @ X1899 @ ( setadjoin @ X1900 @ emptyset ) ) @ ( powerset @ ( binunion @ X1897 @ X1898 ) ) ) )
      & ( ~ ( in @ X1903 @ X1901 )
        | ~ ( in @ X1904 @ X1902 )
        | ( subset @ ( setadjoin @ ( setadjoin @ X1903 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1903 @ ( setadjoin @ X1904 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1901 @ X1902 ) ) ) )
      & ( ~ ( in @ X1907 @ X1905 )
        | ~ ( in @ X1908 @ X1906 )
        | ( in @ ( setadjoin @ ( setadjoin @ X1907 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1907 @ ( setadjoin @ X1908 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1905 @ X1906 ) ) ) ) )
      & ( ~ ( in @ X1911 @ X1909 )
        | ~ ( in @ X1912 @ X1910 )
        | ( in @ ( kpair @ X1911 @ X1912 ) @ ( powerset @ ( powerset @ ( binunion @ X1909 @ X1910 ) ) ) ) )
      & ( ~ ( in @ X1915 @ X1913 )
        | ~ ( in @ X1916 @ X1914 )
        | ( in @ ( kpair @ X1915 @ X1916 ) @ ( cartprod @ X1913 @ X1914 ) ) )
      & ( ( in @ ( esk55_3 @ X1917 @ X1918 @ X1919 ) @ X1917 )
        | ~ ( in @ X1919 @ ( cartprod @ X1917 @ X1918 ) ) )
      & ( ( in @ ( esk56_3 @ X1917 @ X1918 @ X1919 ) @ X1918 )
        | ~ ( in @ X1919 @ ( cartprod @ X1917 @ X1918 ) ) )
      & ( ( X1919
          = ( kpair @ ( esk55_3 @ X1917 @ X1918 @ X1919 ) @ ( esk56_3 @ X1917 @ X1918 @ X1919 ) ) )
        | ~ ( in @ X1919 @ ( cartprod @ X1917 @ X1918 ) ) )
      & ( ~ ( in @ X1924 @ ( cartprod @ X1922 @ X1923 ) )
        | ( iskpair @ X1924 ) )
      & ( ( in @ ( esk57_2 @ X1925 @ X1926 ) @ X1925 )
        | ~ ( in @ X1926 @ ( setunion @ X1925 ) ) )
      & ( ( in @ X1926 @ ( esk57_2 @ X1925 @ X1926 ) )
        | ~ ( in @ X1926 @ ( setunion @ X1925 ) ) )
      & ( subset @ ( setunion @ ( setadjoin @ X1928 @ emptyset ) ) @ X1928 )
      & ( subset @ X1929 @ ( setunion @ ( setadjoin @ X1929 @ emptyset ) ) )
      & ( ( setunion @ ( setadjoin @ X1930 @ emptyset ) )
        = X1930 )
      & ( ( in @ ( esk58_2 @ X1931 @ X1932 ) @ X1931 )
        | ~ ( in @ X1935 @ X1931 )
        | ~ ( X1932 @ X1935 )
        | ( singleton @ ( dsetconstr @ X1931 @ X1932 ) ) )
      & ( ( in @ ( esk59_2 @ X1931 @ X1932 ) @ X1931 )
        | ~ ( in @ X1935 @ X1931 )
        | ~ ( X1932 @ X1935 )
        | ( singleton @ ( dsetconstr @ X1931 @ X1932 ) ) )
      & ( ( X1932 @ ( esk58_2 @ X1931 @ X1932 ) )
        | ~ ( in @ X1935 @ X1931 )
        | ~ ( X1932 @ X1935 )
        | ( singleton @ ( dsetconstr @ X1931 @ X1932 ) ) )
      & ( ( X1932 @ ( esk59_2 @ X1931 @ X1932 ) )
        | ~ ( in @ X1935 @ X1931 )
        | ~ ( X1932 @ X1935 )
        | ( singleton @ ( dsetconstr @ X1931 @ X1932 ) ) )
      & ( ( ( esk58_2 @ X1931 @ X1932 )
         != ( esk59_2 @ X1931 @ X1932 ) )
        | ~ ( in @ X1935 @ X1931 )
        | ~ ( X1932 @ X1935 )
        | ( singleton @ ( dsetconstr @ X1931 @ X1932 ) ) )
      & ( ( in @ ( esk60_2 @ X1936 @ X1937 ) @ X1936 )
        | ~ ( singleton @ ( dsetconstr @ X1936 @ X1937 ) ) )
      & ( ( X1937 @ ( esk60_2 @ X1936 @ X1937 ) )
        | ~ ( singleton @ ( dsetconstr @ X1936 @ X1937 ) ) )
      & ( ( in @ ( esk61_3 @ X1939 @ X1940 @ X1941 ) @ X1939 )
        | ( singleton @ ( dsetconstr @ X1939 @ X1940 ) )
        | ~ ( X1940 @ X1941 )
        | ~ ( in @ X1941 @ X1939 ) )
      & ( ( X1940 @ ( esk61_3 @ X1939 @ X1940 @ X1941 ) )
        | ( singleton @ ( dsetconstr @ X1939 @ X1940 ) )
        | ~ ( X1940 @ X1941 )
        | ~ ( in @ X1941 @ X1939 ) )
      & ( ( ( esk61_3 @ X1939 @ X1940 @ X1941 )
         != X1941 )
        | ( singleton @ ( dsetconstr @ X1939 @ X1940 ) )
        | ~ ( X1940 @ X1941 )
        | ~ ( in @ X1941 @ X1939 ) )
      & ( ( in @ ( esk62_2 @ X1943 @ X1944 ) @ X1943 )
        | ~ ( in @ X1947 @ X1943 )
        | ~ ( X1944 @ X1947 )
        | ( singleton @ ( dsetconstr @ X1943 @ X1944 ) ) )
      & ( ( in @ ( esk63_2 @ X1943 @ X1944 ) @ X1943 )
        | ~ ( in @ X1947 @ X1943 )
        | ~ ( X1944 @ X1947 )
        | ( singleton @ ( dsetconstr @ X1943 @ X1944 ) ) )
      & ( ( X1944 @ ( esk62_2 @ X1943 @ X1944 ) )
        | ~ ( in @ X1947 @ X1943 )
        | ~ ( X1944 @ X1947 )
        | ( singleton @ ( dsetconstr @ X1943 @ X1944 ) ) )
      & ( ( X1944 @ ( esk63_2 @ X1943 @ X1944 ) )
        | ~ ( in @ X1947 @ X1943 )
        | ~ ( X1944 @ X1947 )
        | ( singleton @ ( dsetconstr @ X1943 @ X1944 ) ) )
      & ( ( ( esk62_2 @ X1943 @ X1944 )
         != ( esk63_2 @ X1943 @ X1944 ) )
        | ~ ( in @ X1947 @ X1943 )
        | ~ ( X1944 @ X1947 )
        | ( singleton @ ( dsetconstr @ X1943 @ X1944 ) ) )
      & ( ( ( setadjoin @ X1948 @ emptyset )
         != ( setadjoin @ X1949 @ emptyset ) )
        | ( X1948 = X1949 ) )
      & ( ~ ( in @ ( setadjoin @ X1952 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1950 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1950 @ ( setadjoin @ X1951 @ emptyset ) ) @ emptyset ) ) )
        | ( X1950 = X1952 ) )
      & ( ~ ( iskpair @ X1953 )
        | ( singleton
          @ ( dsetconstr @ ( setunion @ X1953 )
            @ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1953 ) ) ) )
      & ( ~ ( singleton @ X1954 )
        | ( in @ ( setunion @ X1954 ) @ X1954 ) )
      & ( ( 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 ) )
      & ( ~ ( iskpair @ X1987 )
        | ( singleton
          @ ( dsetconstr @ ( setunion @ X1987 )
            @ ^ [Z0: $i] :
                ( X1987
                = ( kpair @ ( kfst @ X1987 ) @ Z0 ) ) ) ) )
      & ( ( ksnd @ ( kpair @ X1988 @ X1989 ) )
        = X1989 )
      & ( ~ ( iskpair @ X1990 )
        | ( ( kpair @ ( kfst @ X1990 ) @ ( ksnd @ X1990 ) )
          = X1990 ) )
      & ( ~ ( in @ X1993 @ ( cartprod @ X1991 @ X1992 ) )
        | ( in @ ( ksnd @ X1993 ) @ X1992 ) )
      & ( ~ ( in @ ( kpair @ X1996 @ X1997 ) @ ( cartprod @ X1994 @ X1995 ) )
        | ( in @ X1996 @ X1994 ) )
      & ( ~ ( in @ ( kpair @ X2000 @ X2001 ) @ ( cartprod @ X1998 @ X1999 ) )
        | ( in @ X2001 @ X1999 ) )
      & ( ~ ( in @ X2004 @ X2002 )
        | ~ ( in @ X2005 @ X2003 )
        | ( ( kpair @ X2004 @ X2005 )
          = ( kpair @ X2004 @ X2005 ) ) )
      & ( ~ ( in @ X2008 @ X2006 )
        | ~ ( in @ X2009 @ X2007 )
        | ( ( kfst @ ( kpair @ X2008 @ X2009 ) )
          = X2008 ) )
      & ( ~ ( in @ X2012 @ X2010 )
        | ~ ( in @ X2013 @ X2011 )
        | ( ( ksnd @ ( kpair @ X2012 @ X2013 ) )
          = X2013 ) )
      & ( ~ ( in @ X2016 @ ( cartprod @ X2014 @ X2015 ) )
        | ( ( kpair @ ( kfst @ X2016 ) @ ( ksnd @ X2016 ) )
          = X2016 ) )
      & ( ~ ( in @ X2020 @ X2017 )
        | ~ ( in @ X2021 @ X2018 )
        | ~ ( X2019 @ X2020 @ X2021 )
        | ( in @ ( kpair @ X2020 @ X2021 ) @ ( dpsetconstr @ X2017 @ X2018 @ X2019 ) ) )
      & ( subset @ ( dpsetconstr @ X2022 @ X2023 @ X2024 ) @ ( cartprod @ X2022 @ X2023 ) )
      & ( subset @ ( dpsetconstr @ X2025 @ X2026 @ X2027 ) @ ( cartprod @ X2025 @ X2026 ) )
      & ( ~ ( in @ X2031 @ X2028 )
        | ~ ( in @ X2032 @ X2029 )
        | ~ ( in @ ( kpair @ X2031 @ X2032 ) @ ( dpsetconstr @ X2028 @ X2029 @ X2030 ) )
        | ( X2030 @ X2031 @ X2032 ) )
      & ( ~ ( in @ ( kpair @ X2036 @ X2037 ) @ ( dpsetconstr @ X2033 @ X2034 @ X2035 ) )
        | ( in @ X2036 @ X2033 ) )
      & ( ~ ( in @ ( kpair @ X2041 @ X2042 ) @ ( dpsetconstr @ X2038 @ X2039 @ X2040 ) )
        | ( in @ X2042 @ X2039 ) )
      & ( ~ ( in @ ( kpair @ X2046 @ X2047 ) @ ( dpsetconstr @ X2043 @ X2044 @ X2045 ) )
        | ( X2045 @ X2046 @ X2047 ) )
      & ( ~ ( func @ X2048 @ X2049 @ X2050 )
        | ~ ( in @ X2051 @ X2048 )
        | ( singleton
          @ ( dsetconstr @ X2049
            @ ^ [Z0: $i] : ( in @ ( kpair @ X2051 @ Z0 ) @ X2050 ) ) ) )
      & ( ~ ( func @ X2052 @ X2053 @ X2054 )
        | ~ ( in @ X2055 @ X2052 )
        | ( in
          @ ( setunion
            @ ( dsetconstr @ X2053
              @ ^ [Z0: $i] : ( in @ ( kpair @ X2055 @ Z0 ) @ X2054 ) ) )
          @ X2053 ) )
      & ( ~ ( func @ X2056 @ X2057 @ X2058 )
        | ~ ( in @ X2059 @ X2056 )
        | ( in @ ( ap @ X2056 @ X2057 @ X2058 @ X2059 ) @ X2057 ) )
      & ( ~ ( in @ X2062 @ ( funcSet @ X2060 @ X2061 ) )
        | ( func @ X2060 @ X2061 @ X2062 ) )
      & ( ~ ( in @ X2065 @ ( funcSet @ X2063 @ X2064 ) )
        | ~ ( in @ X2066 @ X2063 )
        | ( in @ ( ap @ X2063 @ X2064 @ X2065 @ X2066 ) @ X2064 ) )
      & ( ~ ( func @ X2067 @ X2068 @ X2069 )
        | ( in @ X2069 @ ( funcSet @ X2067 @ X2068 ) ) )
      & ( ( in @ ( esk64_3 @ X2070 @ X2071 @ X2072 ) @ X2070 )
        | ( func @ X2070 @ X2071
          @ ( dpsetconstr @ X2070 @ X2071
            @ ^ [Z0: $i] : ( $eq @ ( X2072 @ Z0 ) ) ) ) )
      & ( ~ ( in @ ( X2072 @ ( esk64_3 @ X2070 @ X2071 @ X2072 ) ) @ X2071 )
        | ( func @ X2070 @ X2071
          @ ( dpsetconstr @ X2070 @ X2071
            @ ^ [Z0: $i] : ( $eq @ ( X2072 @ Z0 ) ) ) ) )
      & ( ( in @ ( esk65_3 @ X2074 @ X2075 @ X2076 ) @ X2074 )
        | ( func @ X2074 @ X2075 @ ( lam @ X2074 @ X2075 @ X2076 ) ) )
      & ( ~ ( in @ ( X2076 @ ( esk65_3 @ X2074 @ X2075 @ X2076 ) ) @ X2075 )
        | ( func @ X2074 @ X2075 @ ( lam @ X2074 @ X2075 @ X2076 ) ) )
      & ( ( in @ ( esk66_3 @ X2078 @ X2079 @ X2080 ) @ X2078 )
        | ( in @ ( lam @ X2078 @ X2079 @ X2080 ) @ ( funcSet @ X2078 @ X2079 ) ) )
      & ( ~ ( in @ ( X2080 @ ( esk66_3 @ X2078 @ X2079 @ X2080 ) ) @ X2079 )
        | ( in @ ( lam @ X2078 @ X2079 @ X2080 ) @ ( funcSet @ X2078 @ X2079 ) ) )
      & ( ( in @ ( esk67_4 @ X2082 @ X2083 @ X2084 @ X2085 ) @ X2082 )
        | ~ ( in @ X2088 @ X2084 )
        | ( X2085 @ X2088 )
        | ~ ( subset @ X2084 @ ( cartprod @ X2082 @ X2083 ) ) )
      & ( ( in @ ( esk68_4 @ X2082 @ X2083 @ X2084 @ X2085 ) @ X2083 )
        | ~ ( in @ X2088 @ X2084 )
        | ( X2085 @ X2088 )
        | ~ ( subset @ X2084 @ ( cartprod @ X2082 @ X2083 ) ) )
      & ( ( in @ ( kpair @ ( esk67_4 @ X2082 @ X2083 @ X2084 @ X2085 ) @ ( esk68_4 @ X2082 @ X2083 @ X2084 @ X2085 ) ) @ X2084 )
        | ~ ( in @ X2088 @ X2084 )
        | ( X2085 @ X2088 )
        | ~ ( subset @ X2084 @ ( cartprod @ X2082 @ X2083 ) ) )
      & ( ~ ( X2085 @ ( kpair @ ( esk67_4 @ X2082 @ X2083 @ X2084 @ X2085 ) @ ( esk68_4 @ X2082 @ X2083 @ X2084 @ X2085 ) ) )
        | ~ ( in @ X2088 @ X2084 )
        | ( X2085 @ X2088 )
        | ~ ( subset @ X2084 @ ( cartprod @ X2082 @ X2083 ) ) )
      & ( ( in @ ( esk69_4 @ X2089 @ X2090 @ X2091 @ X2092 ) @ X2089 )
        | ~ ( in @ X2095 @ X2091 )
        | ( X2092 @ X2095 )
        | ~ ( subset @ X2091 @ ( cartprod @ X2089 @ X2090 ) ) )
      & ( ( in @ ( esk70_4 @ X2089 @ X2090 @ X2091 @ X2092 ) @ X2090 )
        | ~ ( in @ X2095 @ X2091 )
        | ( X2092 @ X2095 )
        | ~ ( subset @ X2091 @ ( cartprod @ X2089 @ X2090 ) ) )
      & ( ( in @ ( kpair @ ( esk69_4 @ X2089 @ X2090 @ X2091 @ X2092 ) @ ( esk70_4 @ X2089 @ X2090 @ X2091 @ X2092 ) ) @ X2091 )
        | ~ ( in @ X2095 @ X2091 )
        | ( X2092 @ X2095 )
        | ~ ( subset @ X2091 @ ( cartprod @ X2089 @ X2090 ) ) )
      & ( ~ ( X2092 @ ( kpair @ ( esk69_4 @ X2089 @ X2090 @ X2091 @ X2092 ) @ ( esk70_4 @ X2089 @ X2090 @ X2091 @ X2092 ) ) )
        | ~ ( in @ X2095 @ X2091 )
        | ( X2092 @ X2095 )
        | ~ ( subset @ X2091 @ ( cartprod @ X2089 @ X2090 ) ) )
      & ( ~ ( singleton @ ( dsetconstr @ X2096 @ X2097 ) )
        | ~ ( in @ X2098 @ X2096 )
        | ~ ( in @ X2099 @ X2096 )
        | ~ ( X2097 @ X2098 )
        | ~ ( X2097 @ X2099 )
        | ( X2098 = X2099 ) )
      & ( ~ ( func @ X2100 @ X2101 @ X2102 )
        | ~ ( in @ X2103 @ X2100 )
        | ( in @ ( kpair @ X2103 @ ( ap @ X2100 @ X2101 @ X2102 @ X2103 ) ) @ X2102 ) )
      & ( ~ ( in @ X2106 @ ( funcSet @ X2104 @ X2105 ) )
        | ~ ( in @ X2107 @ X2104 )
        | ( in @ ( kpair @ X2107 @ ( ap @ X2104 @ X2105 @ X2106 @ X2107 ) ) @ X2106 ) )
      & ( ~ ( func @ X2108 @ X2109 @ X2110 )
        | ~ ( in @ X2111 @ X2108 )
        | ~ ( in @ X2112 @ X2109 )
        | ~ ( in @ ( kpair @ X2111 @ X2112 ) @ X2110 )
        | ( ( ap @ X2108 @ X2109 @ X2110 @ X2111 )
          = X2112 ) )
      & ( ( in @ ( esk71_4 @ X2113 @ X2114 @ X2115 @ X2116 ) @ X2113 )
        | ~ ( in @ X2118 @ X2113 )
        | ~ ( in @ X2119 @ X2114 )
        | ~ ( in @ ( kpair @ X2118 @ X2119 ) @ X2116 )
        | ( in @ ( kpair @ X2118 @ X2119 ) @ X2115 )
        | ~ ( func @ X2113 @ X2114 @ X2116 )
        | ~ ( func @ X2113 @ X2114 @ X2115 ) )
      & ( ( ( ap @ X2113 @ X2114 @ X2115 @ ( esk71_4 @ X2113 @ X2114 @ X2115 @ X2116 ) )
         != ( ap @ X2113 @ X2114 @ X2116 @ ( esk71_4 @ X2113 @ X2114 @ X2115 @ X2116 ) ) )
        | ~ ( in @ X2118 @ X2113 )
        | ~ ( in @ X2119 @ X2114 )
        | ~ ( in @ ( kpair @ X2118 @ X2119 ) @ X2116 )
        | ( in @ ( kpair @ X2118 @ X2119 ) @ X2115 )
        | ~ ( func @ X2113 @ X2114 @ X2116 )
        | ~ ( func @ X2113 @ X2114 @ X2115 ) )
      & ( ~ ( in @ X2122 @ ( funcSet @ X2120 @ X2121 ) )
        | ~ ( in @ X2123 @ X2120 )
        | ~ ( in @ X2124 @ X2121 )
        | ~ ( in @ ( kpair @ X2123 @ X2124 ) @ X2122 )
        | ( ( ap @ X2120 @ X2121 @ X2122 @ X2123 )
          = X2124 ) )
      & ( ( in @ ( esk72_4 @ X2125 @ X2126 @ X2127 @ X2128 ) @ X2125 )
        | ( subset @ X2127 @ X2128 )
        | ~ ( subset @ X2128 @ ( cartprod @ X2125 @ X2126 ) )
        | ~ ( subset @ X2127 @ ( cartprod @ X2125 @ X2126 ) ) )
      & ( ( in @ ( esk73_4 @ X2125 @ X2126 @ X2127 @ X2128 ) @ X2126 )
        | ( subset @ X2127 @ X2128 )
        | ~ ( subset @ X2128 @ ( cartprod @ X2125 @ X2126 ) )
        | ~ ( subset @ X2127 @ ( cartprod @ X2125 @ X2126 ) ) )
      & ( ( in @ ( kpair @ ( esk72_4 @ X2125 @ X2126 @ X2127 @ X2128 ) @ ( esk73_4 @ X2125 @ X2126 @ X2127 @ X2128 ) ) @ X2127 )
        | ( subset @ X2127 @ X2128 )
        | ~ ( subset @ X2128 @ ( cartprod @ X2125 @ X2126 ) )
        | ~ ( subset @ X2127 @ ( cartprod @ X2125 @ X2126 ) ) )
      & ( ~ ( in @ ( kpair @ ( esk72_4 @ X2125 @ X2126 @ X2127 @ X2128 ) @ ( esk73_4 @ X2125 @ X2126 @ X2127 @ X2128 ) ) @ X2128 )
        | ( subset @ X2127 @ X2128 )
        | ~ ( subset @ X2128 @ ( cartprod @ X2125 @ X2126 ) )
        | ~ ( subset @ X2127 @ ( cartprod @ X2125 @ X2126 ) ) )
      & ( ( in @ ( esk76_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ X2131 )
        | ( X2133 = X2134 )
        | ( in @ ( esk74_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ X2131 )
        | ~ ( subset @ X2134 @ ( cartprod @ X2131 @ X2132 ) )
        | ~ ( subset @ X2133 @ ( cartprod @ X2131 @ X2132 ) ) )
      & ( ( in @ ( esk77_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ X2132 )
        | ( X2133 = X2134 )
        | ( in @ ( esk74_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ X2131 )
        | ~ ( subset @ X2134 @ ( cartprod @ X2131 @ X2132 ) )
        | ~ ( subset @ X2133 @ ( cartprod @ X2131 @ X2132 ) ) )
      & ( ( in @ ( kpair @ ( esk76_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ ( esk77_4 @ X2131 @ X2132 @ X2133 @ X2134 ) ) @ X2134 )
        | ( X2133 = X2134 )
        | ( in @ ( esk74_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ X2131 )
        | ~ ( subset @ X2134 @ ( cartprod @ X2131 @ X2132 ) )
        | ~ ( subset @ X2133 @ ( cartprod @ X2131 @ X2132 ) ) )
      & ( ~ ( in @ ( kpair @ ( esk76_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ ( esk77_4 @ X2131 @ X2132 @ X2133 @ X2134 ) ) @ X2133 )
        | ( X2133 = X2134 )
        | ( in @ ( esk74_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ X2131 )
        | ~ ( subset @ X2134 @ ( cartprod @ X2131 @ X2132 ) )
        | ~ ( subset @ X2133 @ ( cartprod @ X2131 @ X2132 ) ) )
      & ( ( in @ ( esk76_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ X2131 )
        | ( X2133 = X2134 )
        | ( in @ ( esk75_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ X2132 )
        | ~ ( subset @ X2134 @ ( cartprod @ X2131 @ X2132 ) )
        | ~ ( subset @ X2133 @ ( cartprod @ X2131 @ X2132 ) ) )
      & ( ( in @ ( esk77_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ X2132 )
        | ( X2133 = X2134 )
        | ( in @ ( esk75_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ X2132 )
        | ~ ( subset @ X2134 @ ( cartprod @ X2131 @ X2132 ) )
        | ~ ( subset @ X2133 @ ( cartprod @ X2131 @ X2132 ) ) )
      & ( ( in @ ( kpair @ ( esk76_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ ( esk77_4 @ X2131 @ X2132 @ X2133 @ X2134 ) ) @ X2134 )
        | ( X2133 = X2134 )
        | ( in @ ( esk75_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ X2132 )
        | ~ ( subset @ X2134 @ ( cartprod @ X2131 @ X2132 ) )
        | ~ ( subset @ X2133 @ ( cartprod @ X2131 @ X2132 ) ) )
      & ( ~ ( in @ ( kpair @ ( esk76_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ ( esk77_4 @ X2131 @ X2132 @ X2133 @ X2134 ) ) @ X2133 )
        | ( X2133 = X2134 )
        | ( in @ ( esk75_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ X2132 )
        | ~ ( subset @ X2134 @ ( cartprod @ X2131 @ X2132 ) )
        | ~ ( subset @ X2133 @ ( cartprod @ X2131 @ X2132 ) ) )
      & ( ( in @ ( esk76_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ X2131 )
        | ( X2133 = X2134 )
        | ( in @ ( kpair @ ( esk74_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ ( esk75_4 @ X2131 @ X2132 @ X2133 @ X2134 ) ) @ X2133 )
        | ~ ( subset @ X2134 @ ( cartprod @ X2131 @ X2132 ) )
        | ~ ( subset @ X2133 @ ( cartprod @ X2131 @ X2132 ) ) )
      & ( ( in @ ( esk77_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ X2132 )
        | ( X2133 = X2134 )
        | ( in @ ( kpair @ ( esk74_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ ( esk75_4 @ X2131 @ X2132 @ X2133 @ X2134 ) ) @ X2133 )
        | ~ ( subset @ X2134 @ ( cartprod @ X2131 @ X2132 ) )
        | ~ ( subset @ X2133 @ ( cartprod @ X2131 @ X2132 ) ) )
      & ( ( in @ ( kpair @ ( esk76_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ ( esk77_4 @ X2131 @ X2132 @ X2133 @ X2134 ) ) @ X2134 )
        | ( X2133 = X2134 )
        | ( in @ ( kpair @ ( esk74_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ ( esk75_4 @ X2131 @ X2132 @ X2133 @ X2134 ) ) @ X2133 )
        | ~ ( subset @ X2134 @ ( cartprod @ X2131 @ X2132 ) )
        | ~ ( subset @ X2133 @ ( cartprod @ X2131 @ X2132 ) ) )
      & ( ~ ( in @ ( kpair @ ( esk76_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ ( esk77_4 @ X2131 @ X2132 @ X2133 @ X2134 ) ) @ X2133 )
        | ( X2133 = X2134 )
        | ( in @ ( kpair @ ( esk74_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ ( esk75_4 @ X2131 @ X2132 @ X2133 @ X2134 ) ) @ X2133 )
        | ~ ( subset @ X2134 @ ( cartprod @ X2131 @ X2132 ) )
        | ~ ( subset @ X2133 @ ( cartprod @ X2131 @ X2132 ) ) )
      & ( ( in @ ( esk76_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ X2131 )
        | ( X2133 = X2134 )
        | ~ ( in @ ( kpair @ ( esk74_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ ( esk75_4 @ X2131 @ X2132 @ X2133 @ X2134 ) ) @ X2134 )
        | ~ ( subset @ X2134 @ ( cartprod @ X2131 @ X2132 ) )
        | ~ ( subset @ X2133 @ ( cartprod @ X2131 @ X2132 ) ) )
      & ( ( in @ ( esk77_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ X2132 )
        | ( X2133 = X2134 )
        | ~ ( in @ ( kpair @ ( esk74_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ ( esk75_4 @ X2131 @ X2132 @ X2133 @ X2134 ) ) @ X2134 )
        | ~ ( subset @ X2134 @ ( cartprod @ X2131 @ X2132 ) )
        | ~ ( subset @ X2133 @ ( cartprod @ X2131 @ X2132 ) ) )
      & ( ( in @ ( kpair @ ( esk76_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ ( esk77_4 @ X2131 @ X2132 @ X2133 @ X2134 ) ) @ X2134 )
        | ( X2133 = X2134 )
        | ~ ( in @ ( kpair @ ( esk74_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ ( esk75_4 @ X2131 @ X2132 @ X2133 @ X2134 ) ) @ X2134 )
        | ~ ( subset @ X2134 @ ( cartprod @ X2131 @ X2132 ) )
        | ~ ( subset @ X2133 @ ( cartprod @ X2131 @ X2132 ) ) )
      & ( ~ ( in @ ( kpair @ ( esk76_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ ( esk77_4 @ X2131 @ X2132 @ X2133 @ X2134 ) ) @ X2133 )
        | ( X2133 = X2134 )
        | ~ ( in @ ( kpair @ ( esk74_4 @ X2131 @ X2132 @ X2133 @ X2134 ) @ ( esk75_4 @ X2131 @ X2132 @ X2133 @ X2134 ) ) @ X2134 )
        | ~ ( subset @ X2134 @ ( cartprod @ X2131 @ X2132 ) )
        | ~ ( subset @ X2133 @ ( cartprod @ X2131 @ X2132 ) ) )
      & ( ( in @ ( esk78_4 @ X2139 @ X2140 @ X2141 @ X2142 ) @ X2139 )
        | ( X2141 = X2142 )
        | ~ ( func @ X2139 @ X2140 @ X2142 )
        | ~ ( func @ X2139 @ X2140 @ X2141 ) )
      & ( ( ( ap @ X2139 @ X2140 @ X2141 @ ( esk78_4 @ X2139 @ X2140 @ X2141 @ X2142 ) )
         != ( ap @ X2139 @ X2140 @ X2142 @ ( esk78_4 @ X2139 @ X2140 @ X2141 @ X2142 ) ) )
        | ( X2141 = X2142 )
        | ~ ( func @ X2139 @ X2140 @ X2142 )
        | ~ ( func @ X2139 @ X2140 @ X2141 ) )
      & ( ( in @ ( esk79_4 @ X2144 @ X2145 @ X2146 @ X2147 ) @ X2144 )
        | ( X2146 = X2147 )
        | ~ ( in @ X2147 @ ( funcSet @ X2144 @ X2145 ) )
        | ~ ( in @ X2146 @ ( funcSet @ X2144 @ X2145 ) ) )
      & ( ( ( ap @ X2144 @ X2145 @ X2146 @ ( esk79_4 @ X2144 @ X2145 @ X2146 @ X2147 ) )
         != ( ap @ X2144 @ X2145 @ X2147 @ ( esk79_4 @ X2144 @ X2145 @ X2146 @ X2147 ) ) )
        | ( X2146 = X2147 )
        | ~ ( in @ X2147 @ ( funcSet @ X2144 @ X2145 ) )
        | ~ ( in @ X2146 @ ( funcSet @ X2144 @ X2145 ) ) )
      & ( ~ ( in @ X2151 @ ( funcSet @ X2149 @ X2150 ) )
        | ~ ( in @ X2152 @ X2149 )
        | ( ( ap @ X2149 @ X2150 @ X2151 @ X2152 )
          = ( ap @ X2149 @ X2150 @ X2151 @ X2152 ) ) )
      & ( ~ ( func @ X2153 @ X2154 @ X2155 )
        | ~ ( in @ X2156 @ X2153 )
        | ( ( ap @ X2153 @ X2154 @ X2155 @ X2156 )
          = ( ap @ X2153 @ X2154 @ X2155 @ X2156 ) ) )
      & ( ( in @ ( esk80_3 @ X2157 @ X2158 @ X2159 ) @ X2157 )
        | ~ ( in @ X2161 @ X2157 )
        | ( ( ap @ X2157 @ X2158 @ ( lam @ X2157 @ X2158 @ X2159 ) @ X2161 )
          = ( X2159 @ X2161 ) ) )
      & ( ~ ( in @ ( X2159 @ ( esk80_3 @ X2157 @ X2158 @ X2159 ) ) @ X2158 )
        | ~ ( in @ X2161 @ X2157 )
        | ( ( ap @ X2157 @ X2158 @ ( lam @ X2157 @ X2158 @ X2159 ) @ X2161 )
          = ( X2159 @ X2161 ) ) )
      & ( ~ ( func @ X2162 @ X2163 @ X2164 )
        | ( ( lam @ X2162 @ X2163 @ ( ap @ X2162 @ X2163 @ X2164 ) )
          = X2164 ) )
      & ( ( in @ ( esk81_3 @ X2165 @ X2166 @ X2167 ) @ X2165 )
        | ( ( lam @ X2165 @ X2166 @ X2167 )
          = ( lam @ X2165 @ X2166 @ X2167 ) ) )
      & ( ~ ( in @ ( X2167 @ ( esk81_3 @ X2165 @ X2166 @ X2167 ) ) @ X2166 )
        | ( ( lam @ X2165 @ X2166 @ X2167 )
          = ( lam @ X2165 @ X2166 @ X2167 ) ) )
      & ( ( in @ ( esk82_3 @ X2169 @ X2170 @ X2171 ) @ X2169 )
        | ~ ( in @ X2173 @ X2169 )
        | ( ( ap @ X2169 @ X2170 @ ( lam @ X2169 @ X2170 @ X2171 ) @ X2173 )
          = ( X2171 @ X2173 ) ) )
      & ( ~ ( in @ ( X2171 @ ( esk82_3 @ X2169 @ X2170 @ X2171 ) ) @ X2170 )
        | ~ ( in @ X2173 @ X2169 )
        | ( ( ap @ X2169 @ X2170 @ ( lam @ X2169 @ X2170 @ X2171 ) @ X2173 )
          = ( X2171 @ X2173 ) ) )
      & ( ~ ( in @ X2176 @ ( funcSet @ X2174 @ X2175 ) )
        | ( ( lam @ X2174 @ X2175 @ ( ap @ X2174 @ X2175 @ X2176 ) )
          = X2176 ) )
      & ( ~ ( in @ X2179 @ X2177 )
        | ~ ( in @ X2180 @ X2177 )
        | X2178
        | ( in @ X2180
          @ ( dsetconstr @ X2177
            @ ^ [Z0: $i] :
                ( ( X2178
                  & ( Z0 = X2179 ) )
                | ( ~ X2178
                  & ( Z0 = X2180 ) ) ) ) ) )
      & ( ~ ( in @ X2183 @ X2181 )
        | ~ ( in @ X2184 @ X2181 )
        | X2182
        | ( ( dsetconstr @ X2181
            @ ^ [Z0: $i] :
                ( ( X2182
                  & ( Z0 = X2183 ) )
                | ( ~ X2182
                  & ( Z0 = X2184 ) ) ) )
          = ( setadjoin @ X2184 @ emptyset ) ) )
      & ( ~ ( in @ X2187 @ X2185 )
        | ~ ( in @ X2188 @ X2185 )
        | ~ X2186
        | ( in @ X2187
          @ ( dsetconstr @ X2185
            @ ^ [Z0: $i] :
                ( ( X2186
                  & ( Z0 = X2187 ) )
                | ( ~ X2186
                  & ( Z0 = X2188 ) ) ) ) ) )
      & ( ~ ( in @ X2191 @ X2189 )
        | ~ ( in @ X2192 @ X2189 )
        | ~ X2190
        | ( ( dsetconstr @ X2189
            @ ^ [Z0: $i] :
                ( ( X2190
                  & ( Z0 = X2191 ) )
                | ( ~ X2190
                  & ( Z0 = X2192 ) ) ) )
          = ( setadjoin @ X2191 @ emptyset ) ) )
      & ( ~ ( in @ X2195 @ X2193 )
        | ~ ( in @ X2196 @ X2193 )
        | ( singleton
          @ ( dsetconstr @ X2193
            @ ^ [Z0: $i] :
                ( ( X2194
                  & ( Z0 = X2195 ) )
                | ( ~ X2194
                  & ( Z0 = X2196 ) ) ) ) ) )
      & ( ~ ( in @ X2199 @ X2197 )
        | ~ ( in @ X2200 @ X2197 )
        | ( in @ ( if @ X2197 @ X2198 @ X2199 @ X2200 ) @ X2197 ) )
      & ( ~ ( singleton @ X2201 )
        | ~ ( in @ X2202 @ X2201 )
        | ( ( setunion @ X2201 )
          = X2202 ) )
      & ( ~ ( in @ X2205 @ X2203 )
        | ~ ( in @ X2206 @ X2203 )
        | ~ X2204
        | ( ( if @ X2203 @ X2204 @ X2205 @ X2206 )
          = X2205 ) )
      & ( ~ ( in @ X2209 @ X2207 )
        | ~ ( in @ X2210 @ X2207 )
        | X2208
        | ( ( if @ X2207 @ X2208 @ X2209 @ X2210 )
          = X2210 ) )
      & ( ~ ( in @ X2213 @ X2211 )
        | ~ ( in @ X2214 @ X2211 )
        | ( in @ ( if @ X2211 @ X2212 @ X2213 @ X2214 ) @ ( setadjoin @ X2213 @ ( setadjoin @ X2214 @ emptyset ) ) ) )
      & ( in @ esk84_0 @ ( powerset @ esk83_0 ) )
      & ( in @ esk85_0 @ ( powerset @ esk83_0 ) )
      & ~ ( in @ ( binintersect @ esk84_0 @ esk85_0 ) @ ( powerset @ esk83_0 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[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_311])])])])])])]) ).

thf(c_0_313,negated_conjecture,
    ! [X2: $i,X3: $i] :
      ( ( subset @ X2 @ X3 )
      | ~ ( in @ X2 @ ( powerset @ X3 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_312]) ).

thf(c_0_314,negated_conjecture,
    in @ esk85_0 @ ( powerset @ esk83_0 ),
    inference(split_conjunct,[status(thm)],[c_0_312]) ).

thf(c_0_315,negated_conjecture,
    ! [X2: $i,X3: $i,X4: $i] :
      ( ( subset @ X2 @ X4 )
      | ~ ( subset @ X2 @ X3 )
      | ~ ( subset @ X3 @ X4 ) ),
    inference(split_conjunct,[status(thm)],[c_0_312]) ).

thf(c_0_316,negated_conjecture,
    subset @ esk85_0 @ esk83_0,
    inference(spm,[status(thm)],[c_0_313,c_0_314]) ).

thf(c_0_317,negated_conjecture,
    ~ ( in @ ( binintersect @ esk84_0 @ esk85_0 ) @ ( powerset @ esk83_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_312]) ).

thf(c_0_318,negated_conjecture,
    ! [X2: $i,X3: $i] :
      ( ( in @ X2 @ ( powerset @ X3 ) )
      | ~ ( subset @ X2 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_312]) ).

thf(c_0_319,negated_conjecture,
    ! [X2: $i] :
      ( ( subset @ X2 @ esk83_0 )
      | ~ ( subset @ X2 @ esk85_0 ) ),
    inference(spm,[status(thm)],[c_0_315,c_0_316]) ).

thf(c_0_320,negated_conjecture,
    ! [X2: $i,X3: $i] : ( subset @ ( binintersect @ X2 @ X3 ) @ X3 ),
    inference(split_conjunct,[status(thm)],[c_0_312]) ).

thf(c_0_321,negated_conjecture,
    ~ ( subset @ ( binintersect @ esk84_0 @ esk85_0 ) @ esk83_0 ),
    inference(spm,[status(thm)],[c_0_317,c_0_318]) ).

thf(c_0_322,negated_conjecture,
    ! [X2: $i] : ( subset @ ( binintersect @ X2 @ esk85_0 ) @ esk83_0 ),
    inference(spm,[status(thm)],[c_0_319,c_0_320]) ).

thf(c_0_323,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_321,c_0_322])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SEU710^1 : TPTP v8.2.0. Released v3.7.0.
% 0.12/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n019.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 16:49:53 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
% 6.73/1.63  # Version: 3.1.0-ho
% 6.73/1.63  # Preprocessing class: HSLMSLSSLLLCHFA.
% 6.73/1.63  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 6.73/1.63  # Starting ehoh_best5 with 300s (1) cores
% 6.73/1.63  # Starting almost_fo_3_lam with 300s (1) cores
% 6.73/1.63  # Starting new_bool_5 with 300s (1) cores
% 6.73/1.63  # Starting pre_casc_3 with 300s (1) cores
% 6.73/1.63  # Starting ho_unfolding_8 with 300s (1) cores
% 6.73/1.63  # Starting new_ho_10_cnf2 with 300s (1) cores
% 6.73/1.63  # Starting new_bool_3 with 300s (1) cores
% 6.73/1.63  # Starting new_ho_5 with 300s (1) cores
% 6.73/1.63  # new_ho_5 with pid 18595 completed with status 8
% 6.73/1.63  # pre_casc_3 with pid 18591 completed with status 8
% 6.73/1.63  # new_bool_3 with pid 18594 completed with status 0
% 6.73/1.63  # Result found by new_bool_3
% 6.73/1.63  # Preprocessing class: HSLMSLSSLLLCHFA.
% 6.73/1.63  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 6.73/1.63  # Starting ehoh_best5 with 300s (1) cores
% 6.73/1.63  # Starting almost_fo_3_lam with 300s (1) cores
% 6.73/1.63  # Starting new_bool_5 with 300s (1) cores
% 6.73/1.63  # Starting pre_casc_3 with 300s (1) cores
% 6.73/1.63  # Starting ho_unfolding_8 with 300s (1) cores
% 6.73/1.63  # Starting new_ho_10_cnf2 with 300s (1) cores
% 6.73/1.63  # Starting new_bool_3 with 300s (1) cores
% 6.73/1.63  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 6.73/1.63  # Search class: HGHSM-FSLM32-MHFMMSBN
% 6.73/1.63  # Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 6.73/1.63  # Starting ho_unfolding_8 with 61s (1) cores
% 6.73/1.63  # ho_unfolding_8 with pid 18627 completed with status 0
% 6.73/1.63  # Result found by ho_unfolding_8
% 6.73/1.63  # Preprocessing class: HSLMSLSSLLLCHFA.
% 6.73/1.63  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 6.73/1.63  # Starting ehoh_best5 with 300s (1) cores
% 6.73/1.63  # Starting almost_fo_3_lam with 300s (1) cores
% 6.73/1.63  # Starting new_bool_5 with 300s (1) cores
% 6.73/1.63  # Starting pre_casc_3 with 300s (1) cores
% 6.73/1.63  # Starting ho_unfolding_8 with 300s (1) cores
% 6.73/1.63  # Starting new_ho_10_cnf2 with 300s (1) cores
% 6.73/1.63  # Starting new_bool_3 with 300s (1) cores
% 6.73/1.63  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 6.73/1.63  # Search class: HGHSM-FSLM32-MHFMMSBN
% 6.73/1.63  # Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 6.73/1.63  # Starting ho_unfolding_8 with 61s (1) cores
% 6.73/1.63  # Preprocessing time       : 0.060 s
% 6.73/1.63  # Presaturation interreduction done
% 6.73/1.63  
% 6.73/1.63  # Proof found!
% 6.73/1.63  # SZS status Theorem
% 6.73/1.63  # SZS output start CNFRefutation
% See solution above
% 7.25/1.63  # Parsed axioms                        : 495
% 7.25/1.63  # Removed by relevancy pruning/SinE    : 265
% 7.25/1.63  # Initial clauses                      : 398
% 7.25/1.63  # Removed in clause preprocessing      : 29
% 7.25/1.63  # Initial clauses in saturation        : 369
% 7.25/1.63  # Processed clauses                    : 2622
% 7.25/1.63  # ...of these trivial                  : 23
% 7.25/1.63  # ...subsumed                          : 1077
% 7.25/1.63  # ...remaining for further processing  : 1522
% 7.25/1.63  # Other redundant clauses eliminated   : 67
% 7.25/1.63  # Clauses deleted for lack of memory   : 0
% 7.25/1.63  # Backward-subsumed                    : 82
% 7.25/1.63  # Backward-rewritten                   : 17
% 7.25/1.63  # Generated clauses                    : 49492
% 7.25/1.63  # ...of the previous two non-redundant : 47776
% 7.25/1.63  # ...aggressively subsumed             : 0
% 7.25/1.63  # Contextual simplify-reflections      : 1
% 7.25/1.63  # Paramodulations                      : 49377
% 7.25/1.63  # Factorizations                       : 22
% 7.25/1.63  # NegExts                              : 2
% 7.25/1.63  # Equation resolutions                 : 75
% 7.25/1.63  # Disequality decompositions           : 0
% 7.25/1.63  # Total rewrite steps                  : 5113
% 7.25/1.63  # ...of those cached                   : 4907
% 7.25/1.63  # Propositional unsat checks           : 0
% 7.25/1.63  #    Propositional check models        : 0
% 7.25/1.63  #    Propositional check unsatisfiable : 0
% 7.25/1.63  #    Propositional clauses             : 0
% 7.25/1.63  #    Propositional clauses after purity: 0
% 7.25/1.63  #    Propositional unsat core size     : 0
% 7.25/1.63  #    Propositional preprocessing time  : 0.000
% 7.25/1.63  #    Propositional encoding time       : 0.000
% 7.25/1.63  #    Propositional solver time         : 0.000
% 7.25/1.63  #    Success case prop preproc time    : 0.000
% 7.25/1.63  #    Success case prop encoding time   : 0.000
% 7.25/1.63  #    Success case prop solver time     : 0.000
% 7.25/1.63  # Current number of processed clauses  : 1084
% 7.25/1.63  #    Positive orientable unit clauses  : 55
% 7.25/1.63  #    Positive unorientable unit clauses: 0
% 7.25/1.63  #    Negative unit clauses             : 61
% 7.25/1.63  #    Non-unit-clauses                  : 968
% 7.25/1.63  # Current number of unprocessed clauses: 45744
% 7.25/1.63  # ...number of literals in the above   : 175259
% 7.25/1.63  # Current number of archived formulas  : 0
% 7.25/1.63  # Current number of archived clauses   : 423
% 7.25/1.63  # Clause-clause subsumption calls (NU) : 146697
% 7.25/1.63  # Rec. Clause-clause subsumption calls : 74638
% 7.25/1.63  # Non-unit clause-clause subsumptions  : 724
% 7.25/1.63  # Unit Clause-clause subsumption calls : 2610
% 7.25/1.63  # Rewrite failures with RHS unbound    : 0
% 7.25/1.63  # BW rewrite match attempts            : 44
% 7.25/1.63  # BW rewrite match successes           : 12
% 7.25/1.63  # Condensation attempts                : 0
% 7.25/1.63  # Condensation successes               : 0
% 7.25/1.63  # Termbank termtop insertions          : 979505
% 7.25/1.63  # Search garbage collected termcells   : 23022
% 7.25/1.63  
% 7.25/1.63  # -------------------------------------------------
% 7.25/1.63  # User time                : 1.038 s
% 7.25/1.63  # System time              : 0.063 s
% 7.25/1.63  # Total time               : 1.101 s
% 7.25/1.63  # Maximum resident set size: 7752 pages
% 7.25/1.63  
% 7.25/1.63  # -------------------------------------------------
% 7.25/1.63  # User time                : 1.241 s
% 7.25/1.63  # System time              : 0.146 s
% 7.25/1.63  # Total time               : 1.387 s
% 7.25/1.63  # Maximum resident set size: 2356 pages
% 7.25/1.63  % E---3.1 exiting
% 7.25/1.63  % E exiting
%------------------------------------------------------------------------------