TSTP Solution File: SEU744^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU744^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n018.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 03:29:46 EDT 2024

% Result   : Theorem 1.17s 0.87s
% Output   : CNFRefutation 1.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :  626
% Syntax   : Number of formulae    :  685 (   4 unt; 365 typ;   0 def)
%            Number of atoms       : 3248 ( 457 equ;   0 cnn)
%            Maximal formula atoms : 1021 (  10 avg)
%            Number of connectives : 12473 ( 795   ~; 800   |; 500   &;8411   @)
%                                         ( 347 <=>;1620  =>;   0  <=;   0 <~>)
%            Maximal formula depth : 1126 (  15 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  509 ( 509   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  369 ( 365 usr; 270 con; 0-4 aty)
%            Number of variables   : 2711 ( 156   ^2475   !;  80   ?;2711   :)

% 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,
    binintersectT_lem: $o ).

thf(decl_287,type,
    binunionT_lem: $o ).

thf(decl_288,type,
    powersetT_lem: $o ).

thf(decl_289,type,
    setminusT_lem: $o ).

thf(decl_290,type,
    complementT_lem: $o ).

thf(decl_291,type,
    setextT: $o ).

thf(decl_292,type,
    subsetTI: $o ).

thf(decl_293,type,
    powersetTI1: $o ).

thf(decl_294,type,
    powersetTE1: $o ).

thf(decl_295,type,
    complementTI1: $o ).

thf(decl_296,type,
    complementTE1: $o ).

thf(decl_297,type,
    binintersectTELcontra: $o ).

thf(decl_298,type,
    binintersectTERcontra: $o ).

thf(decl_299,type,
    contrasubsetT: $o ).

thf(decl_300,type,
    contrasubsetT1: $o ).

thf(decl_301,type,
    contrasubsetT2: $o ).

thf(decl_302,type,
    contrasubsetT3: $o ).

thf(decl_303,type,
    doubleComplementI1: $o ).

thf(decl_304,type,
    doubleComplementE1: $o ).

thf(decl_305,type,
    doubleComplementSub1: $o ).

thf(decl_306,type,
    doubleComplementSub2: $o ).

thf(decl_307,type,
    doubleComplementEq: $o ).

thf(decl_308,type,
    complementTnotintersectT: $o ).

thf(decl_309,type,
    complementImpComplementIntersect: $o ).

thf(decl_310,type,
    complementSubsetComplementIntersect: $o ).

thf(decl_311,type,
    complementInPowersetComplementIntersect: $o ).

thf(decl_312,type,
    contraSubsetComplement: $o ).

thf(decl_313,type,
    complementTcontraSubset: $o ).

thf(decl_314,type,
    binunionTILcontra: $o ).

thf(decl_315,type,
    binunionTIRcontra: $o ).

thf(decl_316,type,
    inIntersectImpInUnion: $o ).

thf(decl_317,type,
    inIntersectImpInUnion2: $o ).

thf(decl_318,type,
    inIntersectImpInIntersectUnions: $o ).

thf(decl_319,type,
    intersectInPowersetIntersectUnions: $o ).

thf(decl_320,type,
    epred1_0: $o ).

thf(decl_321,type,
    esk1_2: $i > $i > $i ).

thf(decl_322,type,
    esk2_2: $i > $i > $i ).

thf(decl_323,type,
    esk3_2: $i > $i > $i ).

thf(decl_324,type,
    esk4_1: $i > $i ).

thf(decl_325,type,
    esk5_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_326,type,
    esk6_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_327,type,
    esk7_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_328,type,
    esk8_1: $i > $i ).

thf(decl_329,type,
    esk9_1: ( $i > $o ) > $i ).

thf(decl_330,type,
    esk10_1: ( $i > $o ) > $i ).

thf(decl_331,type,
    esk11_2: $i > $i > $i ).

thf(decl_332,type,
    esk12_2: $i > $i > $i ).

thf(decl_333,type,
    esk13_1: $i > $i ).

thf(decl_334,type,
    esk14_1: $i > $i ).

thf(decl_335,type,
    esk15_1: $i > $i ).

thf(decl_336,type,
    esk16_2: $i > $i > $i ).

thf(decl_337,type,
    esk17_3: $i > $i > $o > $i ).

thf(decl_338,type,
    esk18_1: ( $i > $o ) > $i ).

thf(decl_339,type,
    esk19_1: $i > $i ).

thf(decl_340,type,
    esk20_2: $i > ( $i > $o ) > $i ).

thf(decl_341,type,
    esk21_2: $i > ( $i > $o ) > $i ).

thf(decl_342,type,
    esk22_2: $i > ( $i > $o ) > $i ).

thf(decl_343,type,
    esk23_2: $i > ( $i > $o ) > $i ).

thf(decl_344,type,
    esk24_2: $i > ( $i > $o ) > $i ).

thf(decl_345,type,
    esk25_2: $i > ( $i > $o ) > $i ).

thf(decl_346,type,
    esk26_2: ( $i > $o ) > $i > $i ).

thf(decl_347,type,
    esk27_1: ( $i > $o ) > $i ).

thf(decl_348,type,
    esk28_1: ( $i > $o ) > $i ).

thf(decl_349,type,
    esk29_2: ( $i > $o ) > $i > $i ).

thf(decl_350,type,
    esk30_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_351,type,
    esk31_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_352,type,
    esk32_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_353,type,
    esk33_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_354,type,
    esk34_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_355,type,
    esk35_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_356,type,
    esk36_2: $i > $i > $i ).

thf(decl_357,type,
    esk37_2: $i > $i > $i ).

thf(decl_358,type,
    esk38_2: $i > $i > $i ).

thf(decl_359,type,
    esk39_3: $i > $i > $i > $i ).

thf(decl_360,type,
    esk40_3: $i > $i > $i > $i ).

thf(decl_361,type,
    esk41_2: $i > $i > $i ).

thf(decl_362,type,
    esk42_2: $i > ( $i > $o ) > $i ).

thf(decl_363,type,
    esk43_2: $i > ( $i > $o ) > $i ).

thf(decl_364,type,
    esk44_2: $i > ( $i > $o ) > $i ).

thf(decl_365,type,
    esk45_3: $i > ( $i > $o ) > $i > $i ).

thf(decl_366,type,
    esk46_2: $i > ( $i > $o ) > $i ).

thf(decl_367,type,
    esk47_2: $i > ( $i > $o ) > $i ).

thf(decl_368,type,
    esk48_3: $i > $i > ( $i > $i ) > $i ).

thf(decl_369,type,
    esk49_3: $i > $i > ( $i > $i ) > $i ).

thf(decl_370,type,
    esk50_3: $i > $i > ( $i > $i ) > $i ).

thf(decl_371,type,
    esk51_4: $i > $i > $i > ( $i > $o ) > $i ).

thf(decl_372,type,
    esk52_4: $i > $i > $i > ( $i > $o ) > $i ).

thf(decl_373,type,
    esk53_4: $i > $i > $i > ( $i > $o ) > $i ).

thf(decl_374,type,
    esk54_4: $i > $i > $i > ( $i > $o ) > $i ).

thf(decl_375,type,
    esk55_4: $i > $i > $i > $i > $i ).

thf(decl_376,type,
    esk56_4: $i > $i > $i > $i > $i ).

thf(decl_377,type,
    esk57_4: $i > $i > $i > $i > $i ).

thf(decl_378,type,
    esk58_4: $i > $i > $i > $i > $i ).

thf(decl_379,type,
    esk59_4: $i > $i > $i > $i > $i ).

thf(decl_380,type,
    esk60_4: $i > $i > $i > $i > $i ).

thf(decl_381,type,
    esk61_4: $i > $i > $i > $i > $i ).

thf(decl_382,type,
    esk62_4: $i > $i > $i > $i > $i ).

thf(decl_383,type,
    esk63_4: $i > $i > $i > $i > $i ).

thf(decl_384,type,
    esk64_3: $i > $i > ( $i > $i ) > $i ).

thf(decl_385,type,
    esk65_3: $i > $i > ( $i > $i ) > $i ).

thf(decl_386,type,
    esk66_3: $i > $i > ( $i > $i ) > $i ).

thf(decl_387,type,
    esk67_3: $i > $i > $i > $i ).

thf(decl_388,type,
    esk68_3: $i > $i > $i > $i ).

thf(decl_389,type,
    esk69_3: $i > $i > $i > $i ).

thf(decl_390,type,
    esk70_3: $i > $i > $i > $i ).

thf(decl_391,type,
    esk71_0: $i ).

thf(decl_392,type,
    esk72_0: $i ).

thf(decl_393,type,
    esk73_0: $i ).

thf(decl_394,type,
    esk74_0: $i ).

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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',iftrueProp1) ).

thf(sepInPowerset,axiom,
    ( sepInPowerset
  <=> ! [X4: $i,X1: $i > $o] :
        ( in
        @ ( dsetconstr @ X4
          @ ^ [X2: $i] : ( X1 @ X2 ) )
        @ ( powerset @ X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepInPowerset) ).

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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ifSingleton) ).

thf(sepSubset,axiom,
    ( sepSubset
  <=> ! [X4: $i,X1: $i > $o] :
        ( subset
        @ ( dsetconstr @ X4
          @ ^ [X2: $i] : ( X1 @ X2 ) )
        @ X4 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepSubset) ).

thf(kfstsingleton,axiom,
    ( kfstsingleton
  <=> ! [X18: $i] :
        ( ( iskpair @ X18 )
       => ( singleton
          @ ( dsetconstr @ ( setunion @ X18 )
            @ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X18 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstsingleton) ).

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/sandbox2/benchmark/theBenchmark.p',singletonprop) ).

thf(ex1E1,axiom,
    ( ex1E1
  <=> ! [X4: $i,X1: $i > $o] :
        ( ( ex1 @ X4
          @ ^ [X2: $i] : ( X1 @ X2 ) )
       => ? [X2: $i] :
            ( ( in @ X2 @ X4 )
            & ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ex1I2) ).

thf(ksndsingleton,axiom,
    ( ksndsingleton
  <=> ! [X18: $i] :
        ( ( iskpair @ X18 )
       => ( singleton
          @ ( dsetconstr @ ( setunion @ X18 )
            @ ^ [X2: $i] :
                ( X18
                = ( kpair @ ( kfst @ X18 ) @ X2 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',dpsetconstrSub) ).

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/sandbox2/benchmark/theBenchmark.p',setOfPairsIsBReln) ).

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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',funcImageSingleton) ).

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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',lam2p) ).

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/sandbox2/benchmark/theBenchmark.p',ex1E2) ).

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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',beta2) ).

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/sandbox2/benchmark/theBenchmark.p',dsetconstr__Cong) ).

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/sandbox2/benchmark/theBenchmark.p',descr__Cong) ).

thf(exuEu,axiom,
    ( exuEu
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [X2: $i] : ( X1 @ X2 ) )
       => ! [X2: $i,X3: $i] :
            ( ( X1 @ X2 )
           => ( ( X1 @ X3 )
             => ( X2 = X3 ) ) ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',exuI1) ).

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/sandbox2/benchmark/theBenchmark.p',emptyE1) ).

thf(exuE2,axiom,
    ( exuE2
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [X2: $i] : ( X1 @ X2 ) )
       => ? [X2: $i] :
          ! [X3: $i] :
            ( ( X1 @ X3 )
          <=> ( X3 = X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE2) ).

thf(setoftrueEq,axiom,
    ( setoftrueEq
  <=> ! [X4: $i] :
        ( ( dsetconstr @ X4
          @ ^ [X2: $i] : $true )
        = X4 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setoftrueEq) ).

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/sandbox2/benchmark/theBenchmark.p',nonemptyI) ).

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/sandbox2/benchmark/theBenchmark.p',setbeta) ).

thf(exuE3e,axiom,
    ( exuE3e
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [X2: $i] : ( X1 @ X2 ) )
       => ? [X2: $i] : ( X1 @ X2 ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',exuE1) ).

thf(dsetconstrER,axiom,
    ( dsetconstrER
  <=> ! [X4: $i,X1: $i > $o,X2: $i] :
        ( ( in @ X2
          @ ( dsetconstr @ X4
            @ ^ [X3: $i] : ( X1 @ X3 ) ) )
       => ( X1 @ X2 ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).

thf(descrp,axiom,
    ( descrp
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [X2: $i] : ( X1 @ X2 ) )
       => ( X1
          @ ( descr
            @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',replAx) ).

thf(inComplementUnionImpNotIn1,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
                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( binintersectT_lem
                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( binunionT_lem
                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( powersetT_lem
                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( setminusT_lem
                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( complementT_lem
                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( setextT
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( subsetTI
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( powersetTI1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( powersetTE1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( complementTI1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( complementTE1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( binintersectTELcontra
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( binintersectTERcontra
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( contrasubsetT
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( contrasubsetT1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( contrasubsetT2
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( contrasubsetT3
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( doubleComplementI1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( doubleComplementE1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( doubleComplementSub1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( doubleComplementSub2
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( doubleComplementEq
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( complementTnotintersectT
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( complementImpComplementIntersect
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( complementSubsetComplementIntersect
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( complementInPowersetComplementIntersect
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( contraSubsetComplement
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( complementTcontraSubset
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( binunionTILcontra
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( binunionTIRcontra
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( inIntersectImpInUnion
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( inIntersectImpInUnion2
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( inIntersectImpInIntersectUnions
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( intersectInPowersetIntersectUnions
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X4: $i,X21: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X21 @ ( powerset @ X4 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X48: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X48 @ ( powerset @ X4 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X2 @ X4 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( in @ X2 @ ( setminus @ X4 @ ( binunion @ X21 @ X48 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ~ ( in @ X2 @ X21 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inComplementUnionImpNotIn1) ).

thf(complementTE1,axiom,
    ( complementTE1
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( ~ ( in @ X2 @ ( setminus @ X4 @ X21 ) )
             => ( in @ X2 @ X21 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementTE1) ).

thf(intersectInPowersetIntersectUnions,axiom,
    ( intersectInPowersetIntersectUnions
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ! [X49: $i] :
                ( ( in @ X49 @ ( powerset @ X4 ) )
               => ( in @ ( binintersect @ X21 @ X48 ) @ ( powerset @ ( binintersect @ ( binunion @ X21 @ X49 ) @ ( binunion @ X48 @ X49 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersectInPowersetIntersectUnions) ).

thf(powersetsubset,axiom,
    ( powersetsubset
  <=> ! [X4: $i,X5: $i] :
        ( ( subset @ X4 @ X5 )
       => ( subset @ ( powerset @ X4 ) @ ( powerset @ X5 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetsubset) ).

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/sandbox2/benchmark/theBenchmark.p',ifp) ).

thf(theeq,axiom,
    ( theeq
  <=> ! [X21: $i] :
        ( ( singleton @ X21 )
       => ! [X2: $i] :
            ( ( in @ X2 @ X21 )
           => ( ( setunion @ X21 )
              = X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theeq) ).

thf(binunionIL,axiom,
    ( binunionIL
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIL) ).

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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',iffalse) ).

thf(upairset2IR,axiom,
    ( upairset2IR
  <=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2IR) ).

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/sandbox2/benchmark/theBenchmark.p',iftrueorfalse) ).

thf(binintersectT_lem,axiom,
    ( binintersectT_lem
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ( in @ ( binintersect @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectT_lem) ).

thf(binunionIR,axiom,
    ( binunionIR
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X5 )
       => ( in @ X2 @ ( binunion @ X4 @ X5 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIR) ).

thf(binunionT_lem,axiom,
    ( binunionT_lem
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ( in @ ( binunion @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionT_lem) ).

thf(powersetT_lem,axiom,
    ( powersetT_lem
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ( in @ ( powerset @ X21 ) @ ( powerset @ ( powerset @ X4 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetT_lem) ).

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/sandbox2/benchmark/theBenchmark.p',binunionEcases) ).

thf(setminusT_lem,axiom,
    ( setminusT_lem
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ( in @ ( setminus @ X21 @ X48 ) @ ( powerset @ X4 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusT_lem) ).

thf(binunionE,axiom,
    ( binunionE
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ ( binunion @ X4 @ X5 ) )
       => ( ( in @ X2 @ X4 )
          | ( in @ X2 @ X5 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionE) ).

thf(complementT_lem,axiom,
    ( complementT_lem
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ( in @ ( setminus @ X4 @ X21 ) @ ( powerset @ X4 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementT_lem) ).

thf(setextT,axiom,
    ( setextT
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ( ! [X2: $i] :
                  ( ( in @ X2 @ X4 )
                 => ( ( in @ X2 @ X21 )
                   => ( in @ X2 @ X48 ) ) )
             => ( ! [X2: $i] :
                    ( ( in @ X2 @ X4 )
                   => ( ( in @ X2 @ X48 )
                     => ( in @ X2 @ X21 ) ) )
               => ( X21 = X48 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextT) ).

thf(subsetTI,axiom,
    ( subsetTI
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ( ! [X2: $i] :
                  ( ( in @ X2 @ X4 )
                 => ( ( in @ X2 @ X21 )
                   => ( in @ X2 @ X48 ) ) )
             => ( subset @ X21 @ X48 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTI) ).

thf(binunionLsub,axiom,
    ( binunionLsub
  <=> ! [X4: $i,X5: $i] : ( subset @ X4 @ ( binunion @ X4 @ X5 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionLsub) ).

thf(powersetTI1,axiom,
    ( powersetTI1
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ( ! [X2: $i] :
                  ( ( in @ X2 @ X4 )
                 => ( ( in @ X2 @ X21 )
                   => ( in @ X2 @ X48 ) ) )
             => ( in @ X21 @ ( powerset @ X48 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetTI1) ).

thf(powersetTE1,axiom,
    ( powersetTE1
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ! [X2: $i] :
                ( ( in @ X2 @ X4 )
               => ( ( in @ X21 @ ( powerset @ X48 ) )
                 => ( ( in @ X2 @ X21 )
                   => ( in @ X2 @ X48 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetTE1) ).

thf(complementTI1,axiom,
    ( complementTI1
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( ( in @ X2 @ X21 )
             => ~ ( in @ X2 @ ( setminus @ X4 @ X21 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementTI1) ).

thf(binunionRsub,axiom,
    ( binunionRsub
  <=> ! [X4: $i,X5: $i] : ( subset @ X5 @ ( binunion @ X4 @ X5 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionRsub) ).

thf(setminusILneg,axiom,
    ( setminusILneg
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ~ ( in @ X2 @ X4 )
       => ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusILneg) ).

thf(binintersectTELcontra,axiom,
    ( binintersectTELcontra
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ! [X2: $i] :
                ( ( in @ X2 @ X4 )
               => ( ~ ( in @ X2 @ X21 )
                 => ~ ( in @ X2 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectTELcontra) ).

thf(binintersectTERcontra,axiom,
    ( binintersectTERcontra
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ! [X2: $i] :
                ( ( in @ X2 @ X4 )
               => ( ~ ( in @ X2 @ X48 )
                 => ~ ( in @ X2 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectTERcontra) ).

thf(binintersectI,axiom,
    ( binintersectI
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ( in @ X2 @ X5 )
         => ( in @ X2 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectI) ).

thf(contrasubsetT,axiom,
    ( contrasubsetT
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ! [X2: $i] :
                ( ( in @ X2 @ X4 )
               => ( ( subset @ X21 @ ( setminus @ X4 @ X48 ) )
                 => ( ( in @ X2 @ X48 )
                   => ~ ( in @ X2 @ X21 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contrasubsetT) ).

thf(contrasubsetT1,axiom,
    ( contrasubsetT1
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ! [X2: $i] :
                ( ( in @ X2 @ X4 )
               => ( ( subset @ X21 @ X48 )
                 => ( ~ ( in @ X2 @ X48 )
                   => ~ ( in @ X2 @ X21 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contrasubsetT1) ).

thf(binintersectSubset5,axiom,
    ( binintersectSubset5
  <=> ! [X4: $i,X5: $i,X7: $i] :
        ( ( subset @ X7 @ X4 )
       => ( ( subset @ X7 @ X5 )
         => ( subset @ X7 @ ( binintersect @ X4 @ X5 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset5) ).

thf(contrasubsetT2,axiom,
    ( contrasubsetT2
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ( ( subset @ X21 @ X48 )
             => ( subset @ ( setminus @ X4 @ X48 ) @ ( setminus @ X4 @ X21 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contrasubsetT2) ).

thf(contrasubsetT3,axiom,
    ( contrasubsetT3
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ( ( subset @ ( setminus @ X4 @ X48 ) @ ( setminus @ X4 @ X21 ) )
             => ( subset @ X21 @ X48 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contrasubsetT3) ).

thf(binintersectEL,axiom,
    ( binintersectEL
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
       => ( in @ X2 @ X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectEL) ).

thf(doubleComplementI1,axiom,
    ( doubleComplementI1
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( ( in @ X2 @ X21 )
             => ( in @ X2 @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementI1) ).

thf(doubleComplementE1,axiom,
    ( doubleComplementE1
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( ( in @ X2 @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) )
             => ( in @ X2 @ X21 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementE1) ).

thf(doubleComplementSub1,axiom,
    ( doubleComplementSub1
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ( subset @ X21 @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementSub1) ).

thf(doubleComplementSub2,axiom,
    ( doubleComplementSub2
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ( subset @ ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) @ X21 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementSub2) ).

thf(binintersectLsub,axiom,
    ( binintersectLsub
  <=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X4 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectLsub) ).

thf(doubleComplementEq,axiom,
    ( doubleComplementEq
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ( X21
          = ( setminus @ X4 @ ( setminus @ X4 @ X21 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementEq) ).

thf(complementTnotintersectT,axiom,
    ( complementTnotintersectT
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ! [X2: $i] :
                ( ( in @ X2 @ X4 )
               => ( ( in @ X2 @ ( setminus @ X4 @ X21 ) )
                 => ~ ( in @ X2 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementTnotintersectT) ).

thf(binintersectSubset2,axiom,
    ( binintersectSubset2
  <=> ! [X4: $i,X5: $i] :
        ( ( subset @ X4 @ X5 )
       => ( ( binintersect @ X4 @ X5 )
          = X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset2) ).

thf(complementImpComplementIntersect,axiom,
    ( complementImpComplementIntersect
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ! [X2: $i] :
                ( ( in @ X2 @ X4 )
               => ( ( in @ X2 @ ( setminus @ X4 @ X21 ) )
                 => ( in @ X2 @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementImpComplementIntersect) ).

thf(complementSubsetComplementIntersect,axiom,
    ( complementSubsetComplementIntersect
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ( subset @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementSubsetComplementIntersect) ).

thf(binintersectSubset3,axiom,
    ( binintersectSubset3
  <=> ! [X4: $i,X5: $i] :
        ( ( ( binintersect @ X4 @ X5 )
          = X5 )
       => ( subset @ X5 @ X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset3) ).

thf(complementInPowersetComplementIntersect,axiom,
    ( complementInPowersetComplementIntersect
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ( in @ ( setminus @ X4 @ X21 ) @ ( powerset @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementInPowersetComplementIntersect) ).

thf(contraSubsetComplement,axiom,
    ( contraSubsetComplement
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ( ( subset @ X21 @ ( setminus @ X4 @ X48 ) )
             => ! [X2: $i] :
                  ( ( in @ X2 @ X4 )
                 => ( ( in @ X2 @ X48 )
                   => ( in @ X2 @ ( setminus @ X4 @ X21 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contraSubsetComplement) ).

thf(binintersectER,axiom,
    ( binintersectER
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ ( binintersect @ X4 @ X5 ) )
       => ( in @ X2 @ X5 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectER) ).

thf(complementTcontraSubset,axiom,
    ( complementTcontraSubset
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ( ( subset @ X21 @ ( setminus @ X4 @ X48 ) )
             => ( subset @ X48 @ ( setminus @ X4 @ X21 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementTcontraSubset) ).

thf(binunionTILcontra,axiom,
    ( binunionTILcontra
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ! [X2: $i] :
                ( ( in @ X2 @ X4 )
               => ( ~ ( in @ X2 @ ( binunion @ X21 @ X48 ) )
                 => ~ ( in @ X2 @ X21 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionTILcontra) ).

thf(disjointsetsI1,axiom,
    ( disjointsetsI1
  <=> ! [X4: $i,X5: $i] :
        ( ~ ? [X2: $i] :
              ( ( in @ X2 @ X4 )
              & ( in @ X2 @ X5 ) )
       => ( ( binintersect @ X4 @ X5 )
          = emptyset ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjointsetsI1) ).

thf(binunionTIRcontra,axiom,
    ( binunionTIRcontra
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ! [X2: $i] :
                ( ( in @ X2 @ X4 )
               => ( ~ ( in @ X2 @ ( binunion @ X21 @ X48 ) )
                 => ~ ( in @ X2 @ X48 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionTIRcontra) ).

thf(inIntersectImpInUnion,axiom,
    ( inIntersectImpInUnion
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ! [X49: $i] :
                ( ( in @ X49 @ ( powerset @ X4 ) )
               => ! [X2: $i] :
                    ( ( in @ X2 @ X4 )
                   => ( ( in @ X2 @ ( binintersect @ X21 @ X48 ) )
                     => ( in @ X2 @ ( binunion @ X21 @ X49 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inIntersectImpInUnion) ).

thf(binintersectRsub,axiom,
    ( binintersectRsub
  <=> ! [X4: $i,X5: $i] : ( subset @ ( binintersect @ X4 @ X5 ) @ X5 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectRsub) ).

thf(inIntersectImpInUnion2,axiom,
    ( inIntersectImpInUnion2
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ! [X49: $i] :
                ( ( in @ X49 @ ( powerset @ X4 ) )
               => ! [X2: $i] :
                    ( ( in @ X2 @ X4 )
                   => ( ( in @ X2 @ ( binintersect @ X21 @ X48 ) )
                     => ( in @ X2 @ ( binunion @ X48 @ X49 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inIntersectImpInUnion2) ).

thf(inIntersectImpInIntersectUnions,axiom,
    ( inIntersectImpInIntersectUnions
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ! [X49: $i] :
                ( ( in @ X49 @ ( powerset @ X4 ) )
               => ! [X2: $i] :
                    ( ( in @ X2 @ X4 )
                   => ( ( in @ X2 @ ( binintersect @ X21 @ X48 ) )
                     => ( in @ X2 @ ( binintersect @ ( binunion @ X21 @ X49 ) @ ( binunion @ X48 @ X49 ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inIntersectImpInIntersectUnions) ).

thf(binintersectSubset4,axiom,
    ( binintersectSubset4
  <=> ! [X4: $i,X5: $i] :
        ( ( subset @ X5 @ X4 )
       => ( ( binintersect @ X4 @ X5 )
          = X5 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset4) ).

thf(binintersectSubset1,axiom,
    ( binintersectSubset1
  <=> ! [X4: $i,X5: $i] :
        ( ( ( binintersect @ X4 @ X5 )
          = X4 )
       => ( subset @ X4 @ X5 ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setminusER) ).

thf(setminusSubset2,axiom,
    ( setminusSubset2
  <=> ! [X4: $i,X5: $i] :
        ( ( subset @ X4 @ X5 )
       => ( ( setminus @ X4 @ X5 )
          = emptyset ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setminusELneg) ).

thf(theprop,axiom,
    ( theprop
  <=> ! [X21: $i] :
        ( ( singleton @ X21 )
       => ( in @ ( setunion @ X21 ) @ X21 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theprop) ).

thf(setminusIRneg,axiom,
    ( setminusIRneg
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X5 )
       => ~ ( in @ X2 @ ( setminus @ X4 @ X5 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusIRneg) ).

thf(setminusLsub,axiom,
    ( setminusLsub
  <=> ! [X4: $i,X5: $i] : ( subset @ ( setminus @ X4 @ X5 ) @ X4 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusLsub) ).

thf(setminusSubset1,axiom,
    ( setminusSubset1
  <=> ! [X4: $i,X5: $i] :
        ( ( ( setminus @ X4 @ X5 )
          = emptyset )
       => ( subset @ X4 @ X5 ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',symdiffIneg2) ).

thf(secondinupair,axiom,
    ( secondinupair
  <=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',kpairiskpair) ).

thf(kpairp,axiom,
    ( kpairp
  <=> ! [X2: $i,X3: $i] : ( iskpair @ ( kpair @ X2 @ X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairp) ).

thf(singletonsubset,axiom,
    ( singletonsubset
  <=> ! [X4: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsubset) ).

thf(singletoninpowerset,axiom,
    ( singletoninpowerset
  <=> ! [X4: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X4 ) ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',singletoninpowunion) ).

thf(upairset2E,axiom,
    ( upairset2E
  <=> ! [X2: $i,X3: $i,X14: $i] :
        ( ( in @ X14 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
       => ( ( X14 = X2 )
          | ( X14 = X3 ) ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',upairinpowunion) ).

thf(ubforcartprodlem1,axiom,
    ( ubforcartprodlem1
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X5 )
           => ( subset @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem2) ).

thf(ubforcartprodlem3,axiom,
    ( ubforcartprodlem3
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ! [X3: $i] :
            ( ( in @ X3 @ X5 )
           => ( in @ ( kpair @ X2 @ X3 ) @ ( powerset @ ( powerset @ ( binunion @ X4 @ X5 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem3) ).

thf(subsetRefl,axiom,
    ( subsetRefl
  <=> ! [X4: $i] : ( subset @ X4 @ X4 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetRefl) ).

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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cartprodmempair1) ).

thf(cartprodmempair,axiom,
    ( cartprodmempair
  <=> ! [X4: $i,X5: $i,X18: $i] :
        ( ( in @ X18 @ ( cartprod @ X4 @ X5 ) )
       => ( iskpair @ X18 ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setunionE2) ).

thf(setunionsingleton1,axiom,
    ( setunionsingleton1
  <=> ! [X4: $i] : ( subset @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) @ X4 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton1) ).

thf(setunionsingleton2,axiom,
    ( setunionsingleton2
  <=> ! [X4: $i] : ( subset @ X4 @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton2) ).

thf(setunionsingleton,axiom,
    ( setunionsingleton
  <=> ! [X2: $i] :
        ( ( setunion @ ( setadjoin @ X2 @ emptyset ) )
        = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton) ).

thf(subsetTrans,axiom,
    ( subsetTrans
  <=> ! [X4: $i,X5: $i,X7: $i] :
        ( ( subset @ X4 @ X5 )
       => ( ( subset @ X5 @ X7 )
         => ( subset @ X4 @ X7 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTrans) ).

thf(setadjoinSub,axiom,
    ( setadjoinSub
  <=> ! [X2: $i,X4: $i] : ( subset @ X4 @ ( setadjoin @ X2 @ X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub) ).

thf(setadjoinSub2,axiom,
    ( setadjoinSub2
  <=> ! [X4: $i,X2: $i,X5: $i] :
        ( ( subset @ X4 @ X5 )
       => ( subset @ X4 @ ( setadjoin @ X2 @ X5 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub2) ).

thf(singletonsuniq,axiom,
    ( singletonsuniq
  <=> ! [X2: $i,X3: $i] :
        ( ( ( setadjoin @ X2 @ emptyset )
          = ( setadjoin @ X3 @ emptyset ) )
       => ( X2 = X3 ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setukpairinjL1) ).

thf(kfstpairEq,axiom,
    ( kfstpairEq
  <=> ! [X2: $i,X3: $i] :
        ( ( kfst @ ( kpair @ X2 @ X3 ) )
        = X2 ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',upairequniteq) ).

thf(subset2powerset,axiom,
    ( subset2powerset
  <=> ! [X4: $i,X5: $i] :
        ( ( subset @ X4 @ X5 )
       => ( in @ X4 @ ( powerset @ X5 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset2powerset) ).

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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setukpairinjR) ).

thf(ksndpairEq,axiom,
    ( ksndpairEq
  <=> ! [X2: $i,X3: $i] :
        ( ( ksnd @ ( kpair @ X2 @ X3 ) )
        = X3 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ksndpairEq) ).

thf(kpairsurjEq,axiom,
    ( kpairsurjEq
  <=> ! [X18: $i] :
        ( ( iskpair @ X18 )
       => ( ( kpair @ ( kfst @ X18 ) @ ( ksnd @ X18 ) )
          = X18 ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cartprodpairsurjEq) ).

thf(app,axiom,
    ( app
  <=> ! [X4: $i,X5: $i,X29: $i] :
        ( ( func @ X4 @ X5 @ X29 )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( in @ ( ap @ X4 @ X5 @ X29 @ X2 ) @ X5 ) ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ap2p) ).

thf(funcinfuncset,axiom,
    ( funcinfuncset
  <=> ! [X4: $i,X5: $i,X29: $i] :
        ( ( func @ X4 @ X5 @ X29 )
       => ( in @ X29 @ ( funcSet @ X4 @ X5 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcinfuncset) ).

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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',brelnall2) ).

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/sandbox2/benchmark/theBenchmark.p',funcGraphProp1) ).

thf(funcGraphProp3,axiom,
    ( funcGraphProp3
  <=> ! [X4: $i,X5: $i,X29: $i] :
        ( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( in @ ( kpair @ X2 @ ( ap @ X4 @ X5 @ X29 @ X2 ) ) @ X29 ) ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',funcGraphProp2) ).

thf(funcextLem,axiom,
    ( funcextLem
  <=> ! [X4: $i,X5: $i,X29: $i] :
        ( ( func @ X4 @ X5 @ X29 )
       => ! [X34: $i] :
            ( ( func @ X4 @ X5 @ X34 )
           => ( ! [X2: $i] :
                  ( ( in @ X2 @ X4 )
                 => ( ( ap @ X4 @ X5 @ X29 @ X2 )
                    = ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
             => ! [X2: $i] :
                  ( ( in @ X2 @ X4 )
                 => ! [X3: $i] :
                      ( ( in @ X3 @ X5 )
                     => ( ( in @ ( kpair @ X2 @ X3 ) @ X34 )
                       => ( in @ ( kpair @ X2 @ X3 ) @ X29 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',funcGraphProp4) ).

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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',eqbreln) ).

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/sandbox2/benchmark/theBenchmark.p',funcext) ).

thf(funcext2,axiom,
    ( funcext2
  <=> ! [X4: $i,X5: $i,X29: $i] :
        ( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
       => ! [X34: $i] :
            ( ( in @ X34 @ ( funcSet @ X4 @ X5 ) )
           => ( ! [X2: $i] :
                  ( ( in @ X2 @ X4 )
                 => ( ( ap @ X4 @ X5 @ X29 @ X2 )
                    = ( ap @ X4 @ X5 @ X34 @ X2 ) ) )
             => ( X29 = X34 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcext2) ).

thf(ap2apEq1,axiom,
    ( ap2apEq1
  <=> ! [X4: $i,X5: $i,X29: $i] :
        ( ( in @ X29 @ ( funcSet @ X4 @ X5 ) )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( ( ap @ X4 @ X5 @ X29 @ X2 )
              = ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap2apEq1) ).

thf(ap2apEq2,axiom,
    ( ap2apEq2
  <=> ! [X4: $i,X5: $i,X29: $i] :
        ( ( func @ X4 @ X5 @ X29 )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( ( ap @ X4 @ X5 @ X29 @ X2 )
              = ( ap @ X4 @ X5 @ X29 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap2apEq2) ).

thf(setextsub,axiom,
    ( setextsub
  <=> ! [X4: $i,X5: $i] :
        ( ( subset @ X4 @ X5 )
       => ( ( subset @ X5 @ X4 )
         => ( X4 = X5 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextsub) ).

thf(subsetemptysetimpeq,axiom,
    ( subsetemptysetimpeq
  <=> ! [X4: $i] :
        ( ( subset @ X4 @ emptyset )
       => ( X4 = emptyset ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetemptysetimpeq) ).

thf(powersetI1,axiom,
    ( powersetI1
  <=> ! [X4: $i,X5: $i] :
        ( ( subset @ X5 @ X4 )
       => ( in @ X5 @ ( powerset @ X4 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI1) ).

thf(powersetE1,axiom,
    ( powersetE1
  <=> ! [X4: $i,X5: $i] :
        ( ( in @ X5 @ ( powerset @ X4 ) )
       => ( subset @ X5 @ X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE1) ).

thf(inPowerset,axiom,
    ( inPowerset
  <=> ! [X4: $i] : ( in @ X4 @ ( powerset @ X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inPowerset) ).

thf(notequalI2,axiom,
    ( notequalI2
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ~ ( in @ X2 @ X5 )
         => ( X4 != X5 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI2) ).

thf(notequalI1,axiom,
    ( notequalI1
  <=> ! [X4: $i,X5: $i] :
        ( ~ ( subset @ X4 @ X5 )
       => ( X4 != X5 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI1) ).

thf(notsubsetI,axiom,
    ( notsubsetI
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( ~ ( in @ X2 @ X5 )
         => ~ ( subset @ X4 @ X5 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notsubsetI) ).

thf(subsetE2,axiom,
    ( subsetE2
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( subset @ X4 @ X5 )
       => ( ~ ( in @ X2 @ X5 )
         => ~ ( in @ X2 @ X4 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE2) ).

thf(subsetE,axiom,
    ( subsetE
  <=> ! [X4: $i,X5: $i,X2: $i] :
        ( ( subset @ X4 @ X5 )
       => ( ( in @ X2 @ X4 )
         => ( in @ X2 @ X5 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE) ).

thf(emptysetsubset,axiom,
    ( emptysetsubset
  <=> ! [X4: $i] : ( subset @ emptyset @ X4 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetsubset) ).

thf(subsetI2,axiom,
    ( subsetI2
  <=> ! [X4: $i,X5: $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ( in @ X2 @ X5 ) )
       => ( subset @ X4 @ X5 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2) ).

thf(eqimpsubset1,axiom,
    ( eqimpsubset1
  <=> ! [X4: $i,X5: $i] :
        ( ( X4 = X5 )
       => ( subset @ X4 @ X5 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset1) ).

thf(eqimpsubset2,axiom,
    ( eqimpsubset2
  <=> ! [X4: $i,X5: $i] :
        ( ( X4 = X5 )
       => ( subset @ X5 @ X4 ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',subsetI1) ).

thf(omega__Cong,axiom,
    ( omega__Cong
  <=> ( omega = omega ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega__Cong) ).

thf(setunion__Cong,axiom,
    ( setunion__Cong
  <=> ! [X4: $i,X5: $i] :
        ( ( X4 = X5 )
       => ( ( setunion @ X4 )
          = ( setunion @ X5 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunion__Cong) ).

thf(powerset__Cong,axiom,
    ( powerset__Cong
  <=> ! [X4: $i,X5: $i] :
        ( ( X4 = X5 )
       => ( ( powerset @ X4 )
          = ( powerset @ X5 ) ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setadjoin__Cong) ).

thf(emptyset__Cong,axiom,
    ( emptyset__Cong
  <=> ( emptyset = emptyset ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',notdexE) ).

thf(prop2setI,axiom,
    ( prop2setI
  <=> ! [X15: $o] :
        ( X15
       => ( in @ emptyset @ ( prop2set @ X15 ) ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',quantDeMorgan1) ).

thf(vacuousDall,axiom,
    ( vacuousDall
  <=> ! [X1: $i > $o,X2: $i] :
        ( ( in @ X2 @ emptyset )
       => ( X1 @ X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vacuousDall) ).

thf(upairsetIR,axiom,
    ( upairsetIR
  <=> ! [X2: $i,X3: $i] : ( in @ X3 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR) ).

thf(upairsetIL,axiom,
    ( upairsetIL
  <=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',singletonsswitch) ).

thf(eqinunit,axiom,
    ( eqinunit
  <=> ! [X2: $i,X3: $i] :
        ( ( X2 = X3 )
       => ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit) ).

thf(notinsingleton,axiom,
    ( notinsingleton
  <=> ! [X2: $i,X3: $i] :
        ( ( X2 != X3 )
       => ~ ( in @ X3 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton) ).

thf(uniqinunit,axiom,
    ( uniqinunit
  <=> ! [X2: $i,X3: $i] :
        ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
       => ( X2 = X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).

thf(nonemptyImpWitness,axiom,
    ( nonemptyImpWitness
  <=> ! [X4: $i] :
        ( ( nonempty @ X4 )
       => ? [X2: $i] :
            ( ( in @ X2 @ X4 )
            & $true ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyImpWitness) ).

thf(subPowSU,axiom,
    ( subPowSU
  <=> ! [X4: $i,X2: $i] :
        ( ( in @ X2 @ X4 )
       => ( in @ X2 @ ( powerset @ ( setunion @ X4 ) ) ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',powersetE) ).

thf(emptyInPowerset,axiom,
    ( emptyInPowerset
  <=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyInPowerset) ).

thf(emptyinPowerset,axiom,
    ( emptyinPowerset
  <=> ! [X4: $i] : ( in @ emptyset @ ( powerset @ X4 ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setadjoinIR) ).

thf(emptyinunitempty,axiom,
    ( emptyinunitempty
  <=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinunitempty) ).

thf(setadjoinIL,axiom,
    ( setadjoinIL
  <=> ! [X2: $i,X3: $i] : ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).

thf(nonemptyI1,axiom,
    ( nonemptyI1
  <=> ! [X4: $i] :
        ( ? [X2: $i] : ( in @ X2 @ X4 )
       => ( nonempty @ X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1) ).

thf(nonemptyE1,axiom,
    ( nonemptyE1
  <=> ! [X4: $i] :
        ( ( nonempty @ X4 )
       => ? [X2: $i] : ( in @ X2 @ X4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyE1) ).

thf(noeltsimpempty,axiom,
    ( noeltsimpempty
  <=> ! [X4: $i] :
        ( ! [X2: $i] :
            ~ ( in @ X2 @ X4 )
       => ( X4 = emptyset ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty) ).

thf(emptyI,axiom,
    ( emptyI
  <=> ! [X4: $i] :
        ( ! [X2: $i] :
            ~ ( in @ X2 @ X4 )
       => ( X4 = emptyset ) ) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setext) ).

thf(notinemptyset,axiom,
    ( notinemptyset
  <=> ! [X2: $i] :
        ~ ( in @ X2 @ emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).

thf(emptysetimpfalse,axiom,
    ( emptysetimpfalse
  <=> ! [X2: $i] :
        ( ( in @ X2 @ emptyset )
       => ~ $true ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse) ).

thf(emptysetE,axiom,
    ( emptysetE
  <=> ! [X2: $i] :
        ( ( in @ X2 @ emptyset )
       => ! [X11: $o] : X11 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).

thf(prop2setE,axiom,
    ( prop2setE
  <=> ! [X10: $o,X2: $i] :
        ( ( in @ X2 @ ( prop2set @ X10 ) )
       => X10 ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',omegaIndAx) ).

thf(omegaSAx,axiom,
    ( omegaSAx
  <=> ! [X2: $i] :
        ( ( in @ X2 @ omega )
       => ( in @ ( setadjoin @ X2 @ X2 ) @ omega ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx) ).

thf(omega0Ax,axiom,
    ( omega0Ax
  <=> ( in @ emptyset @ omega ) ),
    file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setadjoinAx) ).

thf(emptysetAx,axiom,
    ( emptysetAx
  <=> ! [X2: $i] :
        ~ ( in @ X2 @ emptyset ) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',setextAx) ).

thf(c_0_260,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_261,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_262,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_263,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_264,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_265,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_266,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_267,plain,
    ( sepSubset
  <=> ! [X4: $i,X1: $i > $o] :
        ( subset
        @ ( dsetconstr @ X4
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
        @ X4 ) ),
    inference(fof_simplification,[status(thm)],[sepSubset]) ).

thf(c_0_268,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_269,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_270,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_271,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_272,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_273,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_274,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_275,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_276,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_277,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_278,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_279,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_280,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_281,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_282,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_283,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_284,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_285,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_286,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_287,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_288,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_289,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_290,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_291,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_292,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_293,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_294,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_295,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_296,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_297,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_298,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_299,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_300,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_301,plain,
    ( setoftrueEq
  <=> ! [X4: $i] :
        ( ( dsetconstr @ X4
          @ ^ [Z0: $i] : $true )
        = X4 ) ),
    inference(fof_simplification,[status(thm)],[setoftrueEq]) ).

thf(c_0_302,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_303,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_304,plain,
    ( exuE3e
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ? [X2: $i] : ( X1 @ X2 ) ) ),
    inference(fof_simplification,[status(thm)],[exuE3e]) ).

thf(c_0_305,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_306,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_307,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_308,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_309,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_310,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_311,plain,
    ( epred1_0
  <=> ! [X894: $i] :
      ? [X895: $i] :
        ( ! [X896: $i] :
            ( ( in @ X896 @ X895 )
           => ! [X897: $i] :
                ( ( in @ X897 @ X896 )
               => ( in @ X897 @ X894 ) ) )
        & ! [X898: $i,X899: $i] :
            ( ( ( in @ X898 @ X894 )
              & ( in @ X899 @ X894 ) )
           => ( ! [X900: $i] :
                  ( ( in @ X900 @ X895 )
                 => ( ( in @ X898 @ X900 )
                  <=> ( in @ X899 @ X900 ) ) )
             => ( X898 = X899 ) ) )
        & ! [X901: $i,X902: $i] :
            ( ( ( in @ X901 @ X895 )
              & ( in @ X902 @ X895 ) )
           => ( ! [X903: $i] :
                  ( ( in @ X903 @ X901 )
                 => ( in @ X903 @ X902 ) )
              | ! [X904: $i] :
                  ( ( in @ X904 @ X902 )
                 => ( in @ X904 @ X901 ) ) ) )
        & ! [X905: $i] :
            ( ( ! [X906: $i] :
                  ( ( in @ X906 @ X905 )
                 => ( in @ X906 @ X894 ) )
              & ? [X907: $i] : ( in @ X907 @ X905 ) )
           => ? [X908: $i,X909: $i] :
                ( ( in @ X908 @ X895 )
                & ( in @ X909 @ X905 )
                & ~ ? [X910: $i] :
                      ( ( in @ X910 @ X908 )
                      & ( in @ X910 @ X905 ) )
                & ! [X911: $i] :
                    ( ( in @ X911 @ X895 )
                   => ( ! [X912: $i] :
                          ( ( in @ X912 @ X911 )
                         => ( in @ X912 @ X908 ) )
                      | ( in @ X909 @ X911 ) ) ) ) ) ) ),
    introduced(definition) ).

thf(c_0_312,negated_conjecture,
    ~ ( ! [X867: $i,X868: $i] :
          ( ! [X869: $i] :
              ( ( in @ X869 @ X867 )
            <=> ( in @ X869 @ X868 ) )
         => ( X867 = X868 ) )
     => ( ! [X870: $i] :
            ~ ( in @ X870 @ emptyset )
       => ( ! [X871: $i,X872: $i,X873: $i] :
              ( ( in @ X873 @ ( setadjoin @ X871 @ X872 ) )
            <=> ( ( X873 = X871 )
                | ( in @ X873 @ X872 ) ) )
         => ( ! [X874: $i,X875: $i] :
                ( ( in @ X875 @ ( powerset @ X874 ) )
              <=> ! [X876: $i] :
                    ( ( in @ X876 @ X875 )
                   => ( in @ X876 @ X874 ) ) )
           => ( ! [X877: $i,X878: $i] :
                  ( ( in @ X878 @ ( setunion @ X877 ) )
                <=> ? [X879: $i] :
                      ( ( in @ X878 @ X879 )
                      & ( in @ X879 @ X877 ) ) )
             => ( ( in @ emptyset @ omega )
               => ( ! [X880: $i] :
                      ( ( in @ X880 @ omega )
                     => ( in @ ( setadjoin @ X880 @ X880 ) @ omega ) )
                 => ( ! [X881: $i] :
                        ( ( ( in @ emptyset @ X881 )
                          & ! [X882: $i] :
                              ( ( ( in @ X882 @ omega )
                                & ( in @ X882 @ X881 ) )
                             => ( in @ ( setadjoin @ X882 @ X882 ) @ X881 ) ) )
                       => ! [X883: $i] :
                            ( ( in @ X883 @ omega )
                           => ( in @ X883 @ X881 ) ) )
                   => ( ! [X884: $i > $i > $o,X885: $i] :
                          ( ! [X886: $i] :
                              ( ( in @ X886 @ X885 )
                             => ( exu @ ( X884 @ X886 ) ) )
                         => ? [X887: $i] :
                            ! [X888: $i] :
                              ( ( in @ X888 @ X887 )
                            <=> ? [X889: $i] :
                                  ( ( in @ X889 @ X885 )
                                  & ( X884 @ X889 @ X888 ) ) ) )
                     => ( ! [X890: $i] :
                            ( ? [X891: $i] : ( in @ X891 @ X890 )
                           => ? [X892: $i] :
                                ( ( in @ X892 @ X890 )
                                & ~ ? [X893: $i] :
                                      ( ( in @ X893 @ X892 )
                                      & ( in @ X893 @ X890 ) ) ) )
                       => ( epred1_0
                         => ( ! [X913: $i > $o] :
                                ( ( exu @ X913 )
                               => ( X913
                                  @ ( descr
                                    @ ^ [Z0: $i] : ( X913 @ Z0 ) ) ) )
                           => ( ! [X914: $i,X915: $i > $o,X916: $i] :
                                  ( ( in @ X916 @ X914 )
                                 => ( ( X915 @ X916 )
                                   => ( in @ X916 @ ( dsetconstr @ X914 @ X915 ) ) ) )
                             => ( ! [X917: $i,X918: $i > $o,X919: $i] :
                                    ( ( in @ X919 @ ( dsetconstr @ X917 @ X918 ) )
                                   => ( in @ X919 @ X917 ) )
                               => ( ! [X920: $i,X921: $i > $o,X922: $i] :
                                      ( ( in @ X922 @ ( dsetconstr @ X920 @ X921 ) )
                                     => ( X921 @ X922 ) )
                                 => ( ! [X923: $i > $o] :
                                        ( ( exu @ X923 )
                                       => ? [X924: $i] :
                                            ( ( X923 @ X924 )
                                            & ! [X925: $i] :
                                                ( ( X923 @ X925 )
                                               => ( X924 = X925 ) ) ) )
                                   => ( ! [X926: $o,X927: $i] :
                                          ( ( in @ X927 @ ( prop2set @ X926 ) )
                                         => X926 )
                                     => ( ! [X928: $i] :
                                            ( ( in @ X928 @ emptyset )
                                           => ! [X929: $o] : X929 )
                                       => ( ! [X930: $i] :
                                              ( ( in @ X930 @ emptyset )
                                             => ~ $true )
                                         => ( ! [X931: $i] :
                                                ~ ( in @ X931 @ emptyset )
                                           => ( ! [X932: $i > $o] :
                                                  ( ( exu @ X932 )
                                                 => ? [X933: $i] : ( X932 @ X933 ) )
                                             => ( ! [X934: $i,X935: $i] :
                                                    ( ! [X936: $i] :
                                                        ( ( in @ X936 @ X934 )
                                                       => ( in @ X936 @ X935 ) )
                                                   => ( ! [X937: $i] :
                                                          ( ( in @ X937 @ X935 )
                                                         => ( in @ X937 @ X934 ) )
                                                     => ( X934 = X935 ) ) )
                                               => ( ! [X938: $i] :
                                                      ( ! [X939: $i] :
                                                          ~ ( in @ X939 @ X938 )
                                                     => ( X938 = emptyset ) )
                                                 => ( ! [X940: $i] :
                                                        ( ! [X941: $i] :
                                                            ~ ( in @ X941 @ X940 )
                                                       => ( X940 = emptyset ) )
                                                   => ( ! [X942: $i,X943: $i > $o,X944: $i] :
                                                          ( ( in @ X944 @ X942 )
                                                         => ( ( in @ X944 @ ( dsetconstr @ X942 @ X943 ) )
                                                          <=> ( X943 @ X944 ) ) )
                                                     => ( ! [X945: $i] :
                                                            ( ( nonempty @ X945 )
                                                           => ? [X946: $i] : ( in @ X946 @ X945 ) )
                                                       => ( ! [X947: $i,X948: $i > $o,X949: $i] :
                                                              ( ( in @ X949 @ X947 )
                                                             => ( ( X948 @ X949 )
                                                               => ( nonempty @ ( dsetconstr @ X947 @ X948 ) ) ) )
                                                         => ( ! [X950: $i] :
                                                                ( ? [X951: $i] : ( in @ X951 @ X950 )
                                                               => ( nonempty @ X950 ) )
                                                           => ( ! [X952: $i,X953: $i] : ( in @ X952 @ ( setadjoin @ X952 @ X953 ) )
                                                             => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                               => ( ! [X954: $i,X955: $i,X956: $i] :
                                                                      ( ( in @ X956 @ X955 )
                                                                     => ( in @ X956 @ ( setadjoin @ X954 @ X955 ) ) )
                                                                 => ( ! [X957: $i,X958: $i,X959: $i] :
                                                                        ( ( in @ X959 @ ( setadjoin @ X957 @ X958 ) )
                                                                       => ! [X960: $o] :
                                                                            ( ( ( X959 = X957 )
                                                                             => X960 )
                                                                           => ( ( ( in @ X959 @ X958 )
                                                                               => X960 )
                                                                             => X960 ) ) )
                                                                   => ( ! [X961: $i,X962: $i,X963: $i] :
                                                                          ( ( in @ X963 @ ( setadjoin @ X961 @ X962 ) )
                                                                         => ( ( X963 = X961 )
                                                                            | ( in @ X963 @ X962 ) ) )
                                                                     => ( ! [X964: $i] :
                                                                            ( ( dsetconstr @ X964
                                                                              @ ^ [Z0: $i] : $true )
                                                                            = X964 )
                                                                       => ( ! [X965: $i,X966: $i] :
                                                                              ( ! [X967: $i] :
                                                                                  ( ( in @ X967 @ X966 )
                                                                                 => ( in @ X967 @ X965 ) )
                                                                             => ( in @ X966 @ ( powerset @ X965 ) ) )
                                                                         => ( ! [X968: $i] : ( in @ emptyset @ ( powerset @ X968 ) )
                                                                           => ( ! [X969: $i] : ( in @ emptyset @ ( powerset @ X969 ) )
                                                                             => ( ! [X970: $i,X971: $i,X972: $i] :
                                                                                    ( ( in @ X971 @ ( powerset @ X970 ) )
                                                                                   => ( ( in @ X972 @ X971 )
                                                                                     => ( in @ X972 @ X970 ) ) )
                                                                               => ( ! [X973: $i,X974: $i,X975: $i] :
                                                                                      ( ( in @ X974 @ X975 )
                                                                                     => ( ( in @ X975 @ X973 )
                                                                                       => ( in @ X974 @ ( setunion @ X973 ) ) ) )
                                                                                 => ( ! [X976: $i,X977: $i] :
                                                                                        ( ( in @ X977 @ ( setunion @ X976 ) )
                                                                                       => ! [X978: $o] :
                                                                                            ( ! [X979: $i] :
                                                                                                ( ( in @ X977 @ X979 )
                                                                                               => ( ( in @ X979 @ X976 )
                                                                                                 => X978 ) )
                                                                                           => X978 ) )
                                                                                   => ( ! [X980: $i,X981: $i] :
                                                                                          ( ( in @ X981 @ X980 )
                                                                                         => ( in @ X981 @ ( powerset @ ( setunion @ X980 ) ) ) )
                                                                                     => ( ! [X982: $i > $o] :
                                                                                            ( ( exu @ X982 )
                                                                                           => ? [X983: $i] :
                                                                                              ! [X984: $i] :
                                                                                                ( ( X982 @ X984 )
                                                                                              <=> ( X984 = X983 ) ) )
                                                                                       => ( ! [X985: $i] :
                                                                                              ( ( nonempty @ X985 )
                                                                                             => ? [X986: $i] :
                                                                                                  ( ( in @ X986 @ X985 )
                                                                                                  & $true ) )
                                                                                         => ( ! [X987: $i,X988: $i] :
                                                                                                ( ( in @ X987 @ ( setadjoin @ X988 @ emptyset ) )
                                                                                               => ( X987 = X988 ) )
                                                                                           => ( ! [X989: $i,X990: $i] :
                                                                                                  ( ( X989 != X990 )
                                                                                                 => ~ ( in @ X990 @ ( setadjoin @ X989 @ emptyset ) ) )
                                                                                             => ( ! [X991: $i,X992: $i] :
                                                                                                    ( ( X991 = X992 )
                                                                                                   => ( in @ X991 @ ( setadjoin @ X992 @ emptyset ) ) )
                                                                                               => ( ! [X993: $i,X994: $i] :
                                                                                                      ( ( in @ X993 @ ( setadjoin @ X994 @ emptyset ) )
                                                                                                     => ( in @ X994 @ ( setadjoin @ X993 @ emptyset ) ) )
                                                                                                 => ( ! [X995: $i,X996: $i,X997: $i] :
                                                                                                        ( ( in @ X997 @ ( setadjoin @ X995 @ ( setadjoin @ X996 @ emptyset ) ) )
                                                                                                       => ( ( X997 = X995 )
                                                                                                          | ( X997 = X996 ) ) )
                                                                                                   => ( ! [X998: $i,X999: $i] : ( in @ X998 @ ( setadjoin @ X998 @ ( setadjoin @ X999 @ emptyset ) ) )
                                                                                                     => ( ! [X1000: $i,X1001: $i] : ( in @ X1001 @ ( setadjoin @ X1000 @ ( setadjoin @ X1001 @ emptyset ) ) )
                                                                                                       => ( ! [X1002: $i,X1003: $i > $o] :
                                                                                                              ( ? [X1004: $i] :
                                                                                                                  ( ( in @ X1004 @ X1002 )
                                                                                                                  & ( X1003 @ X1004 ) )
                                                                                                             => ( ( ( dsetconstr @ X1002 @ X1003 )
                                                                                                                  = emptyset )
                                                                                                               => ~ $true ) )
                                                                                                         => ( ! [X1005: $i > $o,X1006: $i] :
                                                                                                                ( ( in @ X1006 @ emptyset )
                                                                                                               => ( X1005 @ X1006 ) )
                                                                                                           => ( ! [X1007: $i,X1008: $i > $o] :
                                                                                                                  ( ~ ! [X1009: $i] :
                                                                                                                        ( ( in @ X1009 @ X1007 )
                                                                                                                       => ( X1008 @ X1009 ) )
                                                                                                                 => ? [X1010: $i] :
                                                                                                                      ( ( in @ X1010 @ X1007 )
                                                                                                                      & ~ ( X1008 @ X1010 ) ) )
                                                                                                             => ( ! [X1011: $i,X1012: $i > $o] :
                                                                                                                    ( ! [X1013: $i] :
                                                                                                                        ( ( in @ X1013 @ X1011 )
                                                                                                                       => ~ ( X1012 @ X1013 ) )
                                                                                                                   => ~ ? [X1014: $i] :
                                                                                                                          ( ( in @ X1014 @ X1011 )
                                                                                                                          & ( X1012 @ X1014 ) ) )
                                                                                                               => ( ! [X1015: $i,X1016: $i > $o] :
                                                                                                                      ( ~ ? [X1017: $i] :
                                                                                                                            ( ( in @ X1017 @ X1015 )
                                                                                                                            & ( X1016 @ X1017 ) )
                                                                                                                     => ! [X1018: $i] :
                                                                                                                          ( ( in @ X1018 @ X1015 )
                                                                                                                         => ~ ( X1016 @ X1018 ) ) )
                                                                                                                 => ( ! [X1019: $i,X1020: $i > $o] :
                                                                                                                        ( ? [X1021: $i] :
                                                                                                                            ( ( in @ X1021 @ X1019 )
                                                                                                                            & ~ ( X1020 @ X1021 ) )
                                                                                                                       => ~ ! [X1022: $i] :
                                                                                                                              ( ( in @ X1022 @ X1019 )
                                                                                                                             => ( X1020 @ X1022 ) ) )
                                                                                                                   => ( ! [X1023: $o] :
                                                                                                                          ( X1023
                                                                                                                         => ( in @ emptyset @ ( prop2set @ X1023 ) ) )
                                                                                                                     => ( prop2set2propI
                                                                                                                       => ( ! [X1024: $i,X1025: $i > $o] :
                                                                                                                              ( ~ ? [X1026: $i] :
                                                                                                                                    ( ( in @ X1026 @ X1024 )
                                                                                                                                    & ( X1025 @ X1026 ) )
                                                                                                                             => ! [X1027: $i] :
                                                                                                                                  ( ( in @ X1027 @ X1024 )
                                                                                                                                 => ~ ( X1025 @ X1027 ) ) )
                                                                                                                         => ( ! [X1028: $i,X1029: $i > $o] :
                                                                                                                                ( ~ ! [X1030: $i] :
                                                                                                                                      ( ( in @ X1030 @ X1028 )
                                                                                                                                     => ( X1029 @ X1030 ) )
                                                                                                                               => ? [X1031: $i] :
                                                                                                                                    ( ( in @ X1031 @ X1028 )
                                                                                                                                    & ~ ( X1029 @ X1031 ) ) )
                                                                                                                           => ( ! [X1032: $i > $o] :
                                                                                                                                  ( ? [X1033: $i] :
                                                                                                                                      ( ( X1032 @ X1033 )
                                                                                                                                      & ! [X1034: $i] :
                                                                                                                                          ( ( X1032 @ X1034 )
                                                                                                                                         => ( X1033 = X1034 ) ) )
                                                                                                                                 => ( exu @ X1032 ) )
                                                                                                                             => ( ! [X1035: $i > $o] :
                                                                                                                                    ( ? [X1036: $i] : ( X1035 @ X1036 )
                                                                                                                                   => ( ! [X1037: $i,X1038: $i] :
                                                                                                                                          ( ( X1035 @ X1037 )
                                                                                                                                         => ( ( X1035 @ X1038 )
                                                                                                                                           => ( X1037 = X1038 ) ) )
                                                                                                                                     => ( exu @ X1035 ) ) )
                                                                                                                               => ( ! [X1039: $i > $o] :
                                                                                                                                      ( ? [X1040: $i] :
                                                                                                                                        ! [X1041: $i] :
                                                                                                                                          ( ( X1039 @ X1041 )
                                                                                                                                        <=> ( X1041 = X1040 ) )
                                                                                                                                     => ( exu @ X1039 ) )
                                                                                                                                 => ( ! [X1042: $i,X1043: $i] :
                                                                                                                                        ( ( X1042 = X1043 )
                                                                                                                                       => ! [X1044: $i,X1045: $i] :
                                                                                                                                            ( ( X1044 = X1045 )
                                                                                                                                           => ( ( in @ X1044 @ X1042 )
                                                                                                                                             => ( in @ X1045 @ X1043 ) ) ) )
                                                                                                                                   => ( ! [X1046: $i,X1047: $i] :
                                                                                                                                          ( ( X1046 = X1047 )
                                                                                                                                         => ! [X1048: $i,X1049: $i] :
                                                                                                                                              ( ( X1048 = X1049 )
                                                                                                                                             => ( ( in @ X1048 @ X1046 )
                                                                                                                                              <=> ( in @ X1049 @ X1047 ) ) ) )
                                                                                                                                     => ( ! [X1050: $i > $o] :
                                                                                                                                            ( ( exu @ X1050 )
                                                                                                                                           => ! [X1051: $i,X1052: $i] :
                                                                                                                                                ( ( X1050 @ X1051 )
                                                                                                                                               => ( ( X1050 @ X1052 )
                                                                                                                                                 => ( X1051 = X1052 ) ) ) )
                                                                                                                                       => ( ! [X1053: $i > $o,X1054: $i > $o] :
                                                                                                                                              ( ! [X1055: $i,X1056: $i] :
                                                                                                                                                  ( ( X1055 = X1056 )
                                                                                                                                                 => ( ( X1053 @ X1055 )
                                                                                                                                                  <=> ( X1054 @ X1056 ) ) )
                                                                                                                                             => ( ( exu @ X1053 )
                                                                                                                                              <=> ( exu @ X1054 ) ) )
                                                                                                                                         => ( ( emptyset = emptyset )
                                                                                                                                           => ( ! [X1057: $i,X1058: $i] :
                                                                                                                                                  ( ( X1057 = X1058 )
                                                                                                                                                 => ! [X1059: $i,X1060: $i] :
                                                                                                                                                      ( ( X1059 = X1060 )
                                                                                                                                                     => ( ( setadjoin @ X1057 @ X1059 )
                                                                                                                                                        = ( setadjoin @ X1058 @ X1060 ) ) ) )
                                                                                                                                             => ( ! [X1061: $i,X1062: $i] :
                                                                                                                                                    ( ( X1061 = X1062 )
                                                                                                                                                   => ( ( powerset @ X1061 )
                                                                                                                                                      = ( powerset @ X1062 ) ) )
                                                                                                                                               => ( ! [X1063: $i,X1064: $i] :
                                                                                                                                                      ( ( X1063 = X1064 )
                                                                                                                                                     => ( ( setunion @ X1063 )
                                                                                                                                                        = ( setunion @ X1064 ) ) )
                                                                                                                                                 => ( ( omega = omega )
                                                                                                                                                   => ( ! [X1065: $i > $o] :
                                                                                                                                                          ( ( exu @ X1065 )
                                                                                                                                                         => ! [X1066: $i,X1067: $i] :
                                                                                                                                                              ( ( X1065 @ X1066 )
                                                                                                                                                             => ( ( X1065 @ X1067 )
                                                                                                                                                               => ( X1066 = X1067 ) ) ) )
                                                                                                                                                     => ( ! [X1068: $i > $o,X1069: $i > $o] :
                                                                                                                                                            ( ! [X1070: $i,X1071: $i] :
                                                                                                                                                                ( ( X1070 = X1071 )
                                                                                                                                                               => ( ( X1068 @ X1070 )
                                                                                                                                                                <=> ( X1069 @ X1071 ) ) )
                                                                                                                                                           => ( ( exu @ X1068 )
                                                                                                                                                             => ( ( exu @ X1069 )
                                                                                                                                                               => ( ( descr @ X1068 )
                                                                                                                                                                  = ( descr @ X1069 ) ) ) ) )
                                                                                                                                                       => ( ! [X1072: $i,X1073: $i] :
                                                                                                                                                              ( ( X1072 = X1073 )
                                                                                                                                                             => ! [X1074: $i > $o,X1075: $i > $o] :
                                                                                                                                                                  ( ! [X1076: $i] :
                                                                                                                                                                      ( ( in @ X1076 @ X1072 )
                                                                                                                                                                     => ! [X1077: $i] :
                                                                                                                                                                          ( ( in @ X1077 @ X1073 )
                                                                                                                                                                         => ( ( X1076 = X1077 )
                                                                                                                                                                           => ( ( X1074 @ X1076 )
                                                                                                                                                                            <=> ( X1075 @ X1077 ) ) ) ) )
                                                                                                                                                                 => ( ( dsetconstr @ X1072 @ X1074 )
                                                                                                                                                                    = ( dsetconstr @ X1073 @ X1075 ) ) ) )
                                                                                                                                                         => ( ! [X1078: $i,X1079: $i] :
                                                                                                                                                                ( ! [X1080: $i] :
                                                                                                                                                                    ( ( in @ X1080 @ X1078 )
                                                                                                                                                                   => ( in @ X1080 @ X1079 ) )
                                                                                                                                                               => ( subset @ X1078 @ X1079 ) )
                                                                                                                                                           => ( ! [X1081: $i,X1082: $i] :
                                                                                                                                                                  ( ( X1081 = X1082 )
                                                                                                                                                                 => ( subset @ X1082 @ X1081 ) )
                                                                                                                                                             => ( ! [X1083: $i,X1084: $i] :
                                                                                                                                                                    ( ( X1083 = X1084 )
                                                                                                                                                                   => ( subset @ X1083 @ X1084 ) )
                                                                                                                                                               => ( ! [X1085: $i,X1086: $i] :
                                                                                                                                                                      ( ! [X1087: $i] :
                                                                                                                                                                          ( ( in @ X1087 @ X1085 )
                                                                                                                                                                         => ( in @ X1087 @ X1086 ) )
                                                                                                                                                                     => ( subset @ X1085 @ X1086 ) )
                                                                                                                                                                 => ( ! [X1088: $i] : ( subset @ emptyset @ X1088 )
                                                                                                                                                                   => ( ! [X1089: $i,X1090: $i,X1091: $i] :
                                                                                                                                                                          ( ( subset @ X1089 @ X1090 )
                                                                                                                                                                         => ( ( in @ X1091 @ X1089 )
                                                                                                                                                                           => ( in @ X1091 @ X1090 ) ) )
                                                                                                                                                                     => ( ! [X1092: $i,X1093: $i,X1094: $i] :
                                                                                                                                                                            ( ( subset @ X1092 @ X1093 )
                                                                                                                                                                           => ( ~ ( in @ X1094 @ X1093 )
                                                                                                                                                                             => ~ ( in @ X1094 @ X1092 ) ) )
                                                                                                                                                                       => ( ! [X1095: $i,X1096: $i,X1097: $i] :
                                                                                                                                                                              ( ( in @ X1097 @ X1095 )
                                                                                                                                                                             => ( ~ ( in @ X1097 @ X1096 )
                                                                                                                                                                               => ~ ( subset @ X1095 @ X1096 ) ) )
                                                                                                                                                                         => ( ! [X1098: $i,X1099: $i] :
                                                                                                                                                                                ( ~ ( subset @ X1098 @ X1099 )
                                                                                                                                                                               => ( X1098 != X1099 ) )
                                                                                                                                                                           => ( ! [X1100: $i,X1101: $i,X1102: $i] :
                                                                                                                                                                                  ( ( in @ X1102 @ X1100 )
                                                                                                                                                                                 => ( ~ ( in @ X1102 @ X1101 )
                                                                                                                                                                                   => ( X1100 != X1101 ) ) )
                                                                                                                                                                             => ( ! [X1103: $i] : ( subset @ X1103 @ X1103 )
                                                                                                                                                                               => ( ! [X1104: $i,X1105: $i,X1106: $i] :
                                                                                                                                                                                      ( ( subset @ X1104 @ X1105 )
                                                                                                                                                                                     => ( ( subset @ X1105 @ X1106 )
                                                                                                                                                                                       => ( subset @ X1104 @ X1106 ) ) )
                                                                                                                                                                                 => ( ! [X1107: $i,X1108: $i] : ( subset @ X1108 @ ( setadjoin @ X1107 @ X1108 ) )
                                                                                                                                                                                   => ( ! [X1109: $i,X1110: $i,X1111: $i] :
                                                                                                                                                                                          ( ( subset @ X1109 @ X1111 )
                                                                                                                                                                                         => ( subset @ X1109 @ ( setadjoin @ X1110 @ X1111 ) ) )
                                                                                                                                                                                     => ( ! [X1112: $i,X1113: $i] :
                                                                                                                                                                                            ( ( subset @ X1112 @ X1113 )
                                                                                                                                                                                           => ( in @ X1112 @ ( powerset @ X1113 ) ) )
                                                                                                                                                                                       => ( ! [X1114: $i,X1115: $i] :
                                                                                                                                                                                              ( ( subset @ X1114 @ X1115 )
                                                                                                                                                                                             => ( ( subset @ X1115 @ X1114 )
                                                                                                                                                                                               => ( X1114 = X1115 ) ) )
                                                                                                                                                                                         => ( ! [X1116: $i] :
                                                                                                                                                                                                ( ( subset @ X1116 @ emptyset )
                                                                                                                                                                                               => ( X1116 = emptyset ) )
                                                                                                                                                                                           => ( ! [X1117: $i,X1118: $i] :
                                                                                                                                                                                                  ( ( subset @ X1118 @ X1117 )
                                                                                                                                                                                                 => ( in @ X1118 @ ( powerset @ X1117 ) ) )
                                                                                                                                                                                             => ( ! [X1119: $i,X1120: $i] :
                                                                                                                                                                                                    ( ( in @ X1120 @ ( powerset @ X1119 ) )
                                                                                                                                                                                                   => ( subset @ X1120 @ X1119 ) )
                                                                                                                                                                                               => ( ! [X1121: $i] : ( in @ X1121 @ ( powerset @ X1121 ) )
                                                                                                                                                                                                 => ( ! [X1122: $i,X1123: $i] :
                                                                                                                                                                                                        ( ( subset @ X1122 @ X1123 )
                                                                                                                                                                                                       => ( subset @ ( powerset @ X1122 ) @ ( powerset @ X1123 ) ) )
                                                                                                                                                                                                   => ( ! [X1124: $i,X1125: $i > $o] : ( in @ ( dsetconstr @ X1124 @ X1125 ) @ ( powerset @ X1124 ) )
                                                                                                                                                                                                     => ( ! [X1126: $i,X1127: $i > $o] : ( subset @ ( dsetconstr @ X1126 @ X1127 ) @ X1126 )
                                                                                                                                                                                                       => ( ! [X1128: $i,X1129: $i,X1130: $i] :
                                                                                                                                                                                                              ( ( in @ X1130 @ X1128 )
                                                                                                                                                                                                             => ( in @ X1130 @ ( binunion @ X1128 @ X1129 ) ) )
                                                                                                                                                                                                         => ( ! [X1131: $i,X1132: $i] : ( in @ X1132 @ ( setadjoin @ X1131 @ ( setadjoin @ X1132 @ emptyset ) ) )
                                                                                                                                                                                                           => ( ! [X1133: $i,X1134: $i,X1135: $i] :
                                                                                                                                                                                                                  ( ( in @ X1135 @ X1134 )
                                                                                                                                                                                                                 => ( in @ X1135 @ ( binunion @ X1133 @ X1134 ) ) )
                                                                                                                                                                                                             => ( ! [X1136: $i,X1137: $i,X1138: $i,X1139: $o] :
                                                                                                                                                                                                                    ( ( in @ X1138 @ ( binunion @ X1136 @ X1137 ) )
                                                                                                                                                                                                                   => ( ( ( in @ X1138 @ X1136 )
                                                                                                                                                                                                                       => X1139 )
                                                                                                                                                                                                                     => ( ( ( in @ X1138 @ X1137 )
                                                                                                                                                                                                                         => X1139 )
                                                                                                                                                                                                                       => X1139 ) ) )
                                                                                                                                                                                                               => ( ! [X1140: $i,X1141: $i,X1142: $i] :
                                                                                                                                                                                                                      ( ( in @ X1142 @ ( binunion @ X1140 @ X1141 ) )
                                                                                                                                                                                                                     => ( ( in @ X1142 @ X1140 )
                                                                                                                                                                                                                        | ( in @ X1142 @ X1141 ) ) )
                                                                                                                                                                                                                 => ( ! [X1143: $i,X1144: $i] : ( subset @ X1143 @ ( binunion @ X1143 @ X1144 ) )
                                                                                                                                                                                                                   => ( ! [X1145: $i,X1146: $i] : ( subset @ X1146 @ ( binunion @ X1145 @ X1146 ) )
                                                                                                                                                                                                                     => ( ! [X1147: $i,X1148: $i,X1149: $i] :
                                                                                                                                                                                                                            ( ( in @ X1149 @ X1147 )
                                                                                                                                                                                                                           => ( ( in @ X1149 @ X1148 )
                                                                                                                                                                                                                             => ( in @ X1149 @ ( binintersect @ X1147 @ X1148 ) ) ) )
                                                                                                                                                                                                                       => ( ! [X1150: $i,X1151: $i,X1152: $i] :
                                                                                                                                                                                                                              ( ( subset @ X1152 @ X1150 )
                                                                                                                                                                                                                             => ( ( subset @ X1152 @ X1151 )
                                                                                                                                                                                                                               => ( subset @ X1152 @ ( binintersect @ X1150 @ X1151 ) ) ) )
                                                                                                                                                                                                                         => ( ! [X1153: $i,X1154: $i,X1155: $i] :
                                                                                                                                                                                                                                ( ( in @ X1155 @ ( binintersect @ X1153 @ X1154 ) )
                                                                                                                                                                                                                               => ( in @ X1155 @ X1153 ) )
                                                                                                                                                                                                                           => ( ! [X1156: $i,X1157: $i] : ( subset @ ( binintersect @ X1156 @ X1157 ) @ X1156 )
                                                                                                                                                                                                                             => ( ! [X1158: $i,X1159: $i] :
                                                                                                                                                                                                                                    ( ( subset @ X1158 @ X1159 )
                                                                                                                                                                                                                                   => ( ( binintersect @ X1158 @ X1159 )
                                                                                                                                                                                                                                      = X1158 ) )
                                                                                                                                                                                                                               => ( ! [X1160: $i,X1161: $i] :
                                                                                                                                                                                                                                      ( ( ( binintersect @ X1160 @ X1161 )
                                                                                                                                                                                                                                        = X1161 )
                                                                                                                                                                                                                                     => ( subset @ X1161 @ X1160 ) )
                                                                                                                                                                                                                                 => ( ! [X1162: $i,X1163: $i,X1164: $i] :
                                                                                                                                                                                                                                        ( ( in @ X1164 @ ( binintersect @ X1162 @ X1163 ) )
                                                                                                                                                                                                                                       => ( in @ X1164 @ X1163 ) )
                                                                                                                                                                                                                                   => ( ! [X1165: $i,X1166: $i] :
                                                                                                                                                                                                                                          ( ~ ? [X1167: $i] :
                                                                                                                                                                                                                                                ( ( in @ X1167 @ X1165 )
                                                                                                                                                                                                                                                & ( in @ X1167 @ X1166 ) )
                                                                                                                                                                                                                                         => ( ( binintersect @ X1165 @ X1166 )
                                                                                                                                                                                                                                            = emptyset ) )
                                                                                                                                                                                                                                     => ( ! [X1168: $i,X1169: $i] : ( subset @ ( binintersect @ X1168 @ X1169 ) @ X1169 )
                                                                                                                                                                                                                                       => ( ! [X1170: $i,X1171: $i] :
                                                                                                                                                                                                                                              ( ( subset @ X1171 @ X1170 )
                                                                                                                                                                                                                                             => ( ( binintersect @ X1170 @ X1171 )
                                                                                                                                                                                                                                                = X1171 ) )
                                                                                                                                                                                                                                         => ( ! [X1172: $i,X1173: $i] :
                                                                                                                                                                                                                                                ( ( ( binintersect @ X1172 @ X1173 )
                                                                                                                                                                                                                                                  = X1172 )
                                                                                                                                                                                                                                               => ( subset @ X1172 @ X1173 ) )
                                                                                                                                                                                                                                           => ( ! [X1174: $i,X1175: $i,X1176: $i] :
                                                                                                                                                                                                                                                  ( ( binintersect @ X1174 @ ( binunion @ X1175 @ X1176 ) )
                                                                                                                                                                                                                                                  = ( binunion @ ( binintersect @ X1174 @ X1175 ) @ ( binintersect @ X1174 @ X1176 ) ) )
                                                                                                                                                                                                                                             => ( ! [X1177: $i,X1178: $i,X1179: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X1179 @ X1177 )
                                                                                                                                                                                                                                                   => ( ~ ( in @ X1179 @ X1178 )
                                                                                                                                                                                                                                                     => ( in @ X1179 @ ( setminus @ X1177 @ X1178 ) ) ) )
                                                                                                                                                                                                                                               => ( ! [X1180: $i,X1181: $i,X1182: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X1182 @ ( setminus @ X1180 @ X1181 ) )
                                                                                                                                                                                                                                                     => ( in @ X1182 @ X1180 ) )
                                                                                                                                                                                                                                                 => ( ! [X1183: $i,X1184: $i,X1185: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X1185 @ ( setminus @ X1183 @ X1184 ) )
                                                                                                                                                                                                                                                       => ~ ( in @ X1185 @ X1184 ) )
                                                                                                                                                                                                                                                   => ( ! [X1186: $i,X1187: $i] :
                                                                                                                                                                                                                                                          ( ( subset @ X1186 @ X1187 )
                                                                                                                                                                                                                                                         => ( ( setminus @ X1186 @ X1187 )
                                                                                                                                                                                                                                                            = emptyset ) )
                                                                                                                                                                                                                                                     => ( ! [X1188: $i,X1189: $i,X1190: $i] :
                                                                                                                                                                                                                                                            ( ~ ( in @ X1190 @ ( setminus @ X1188 @ X1189 ) )
                                                                                                                                                                                                                                                           => ( ( in @ X1190 @ X1188 )
                                                                                                                                                                                                                                                             => ( in @ X1190 @ X1189 ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1191: $i,X1192: $i,X1193: $i] :
                                                                                                                                                                                                                                                              ( ~ ( in @ X1193 @ ( setminus @ X1191 @ X1192 ) )
                                                                                                                                                                                                                                                             => ( ~ ( in @ X1193 @ X1192 )
                                                                                                                                                                                                                                                               => ~ ( in @ X1193 @ X1191 ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1194: $i,X1195: $i,X1196: $i] :
                                                                                                                                                                                                                                                                ( ~ ( in @ X1196 @ X1194 )
                                                                                                                                                                                                                                                               => ~ ( in @ X1196 @ ( setminus @ X1194 @ X1195 ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1197: $i,X1198: $i,X1199: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X1199 @ X1198 )
                                                                                                                                                                                                                                                                 => ~ ( in @ X1199 @ ( setminus @ X1197 @ X1198 ) ) )
                                                                                                                                                                                                                                                             => ( ! [X1200: $i,X1201: $i] : ( subset @ ( setminus @ X1200 @ X1201 ) @ X1200 )
                                                                                                                                                                                                                                                               => ( ! [X1202: $i,X1203: $i] :
                                                                                                                                                                                                                                                                      ( ( ( setminus @ X1202 @ X1203 )
                                                                                                                                                                                                                                                                        = emptyset )
                                                                                                                                                                                                                                                                     => ( subset @ X1202 @ X1203 ) )
                                                                                                                                                                                                                                                                 => ( ! [X1204: $i,X1205: $i,X1206: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X1206 @ ( symdiff @ X1204 @ X1205 ) )
                                                                                                                                                                                                                                                                       => ! [X1207: $o] :
                                                                                                                                                                                                                                                                            ( ( ( in @ X1206 @ X1204 )
                                                                                                                                                                                                                                                                             => ( ~ ( in @ X1206 @ X1205 )
                                                                                                                                                                                                                                                                               => X1207 ) )
                                                                                                                                                                                                                                                                           => ( ( ~ ( in @ X1206 @ X1204 )
                                                                                                                                                                                                                                                                               => ( ( in @ X1206 @ X1205 )
                                                                                                                                                                                                                                                                                 => X1207 ) )
                                                                                                                                                                                                                                                                             => X1207 ) ) )
                                                                                                                                                                                                                                                                   => ( ! [X1208: $i,X1209: $i,X1210: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X1210 @ X1208 )
                                                                                                                                                                                                                                                                         => ( ~ ( in @ X1210 @ X1209 )
                                                                                                                                                                                                                                                                           => ( in @ X1210 @ ( symdiff @ X1208 @ X1209 ) ) ) )
                                                                                                                                                                                                                                                                     => ( ! [X1211: $i,X1212: $i,X1213: $i] :
                                                                                                                                                                                                                                                                            ( ~ ( in @ X1213 @ X1211 )
                                                                                                                                                                                                                                                                           => ( ( in @ X1213 @ X1212 )
                                                                                                                                                                                                                                                                             => ( in @ X1213 @ ( symdiff @ X1211 @ X1212 ) ) ) )
                                                                                                                                                                                                                                                                       => ( ! [X1214: $i,X1215: $i,X1216: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X1216 @ X1214 )
                                                                                                                                                                                                                                                                             => ( ( in @ X1216 @ X1215 )
                                                                                                                                                                                                                                                                               => ~ ( in @ X1216 @ ( symdiff @ X1214 @ X1215 ) ) ) )
                                                                                                                                                                                                                                                                         => ( ! [X1217: $i,X1218: $i,X1219: $i] :
                                                                                                                                                                                                                                                                                ( ~ ( in @ X1219 @ X1217 )
                                                                                                                                                                                                                                                                               => ( ~ ( in @ X1219 @ X1218 )
                                                                                                                                                                                                                                                                                 => ~ ( in @ X1219 @ ( symdiff @ X1217 @ X1218 ) ) ) )
                                                                                                                                                                                                                                                                           => ( ! [X1220: $i,X1221: $i] : ( in @ X1221 @ ( setadjoin @ X1220 @ ( setadjoin @ X1221 @ emptyset ) ) )
                                                                                                                                                                                                                                                                             => ( ! [X1222: $i,X1223: $i] : ( in @ X1222 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1222 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1222 @ ( setadjoin @ X1223 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                               => ( ! [X1224: $i,X1225: $i] : ( in @ X1225 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1224 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1224 @ ( setadjoin @ X1225 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1226: $i,X1227: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1226 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1226 @ ( setadjoin @ X1227 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1228: $i,X1229: $i] : ( iskpair @ ( kpair @ X1228 @ X1229 ) )
                                                                                                                                                                                                                                                                                     => ( ! [X1230: $i,X1231: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X1231 @ X1230 )
                                                                                                                                                                                                                                                                                           => ( subset @ ( setadjoin @ X1231 @ emptyset ) @ X1230 ) )
                                                                                                                                                                                                                                                                                       => ( ! [X1232: $i,X1233: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X1233 @ X1232 )
                                                                                                                                                                                                                                                                                             => ( in @ ( setadjoin @ X1233 @ emptyset ) @ ( powerset @ X1232 ) ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1234: $i,X1235: $i,X1236: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X1236 @ X1234 )
                                                                                                                                                                                                                                                                                               => ( in @ ( setadjoin @ X1236 @ emptyset ) @ ( powerset @ ( binunion @ X1234 @ X1235 ) ) ) )
                                                                                                                                                                                                                                                                                           => ( ! [X1237: $i,X1238: $i,X1239: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X1239 @ ( setadjoin @ X1237 @ ( setadjoin @ X1238 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                 => ( ( X1239 = X1237 )
                                                                                                                                                                                                                                                                                                    | ( X1239 = X1238 ) ) )
                                                                                                                                                                                                                                                                                             => ( ! [X1240: $i,X1241: $i,X1242: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X1242 @ X1240 )
                                                                                                                                                                                                                                                                                                   => ! [X1243: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X1243 @ X1241 )
                                                                                                                                                                                                                                                                                                       => ( subset @ ( setadjoin @ X1242 @ ( setadjoin @ X1243 @ emptyset ) ) @ ( binunion @ X1240 @ X1241 ) ) ) )
                                                                                                                                                                                                                                                                                               => ( ! [X1244: $i,X1245: $i,X1246: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ X1246 @ X1244 )
                                                                                                                                                                                                                                                                                                     => ! [X1247: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X1247 @ X1245 )
                                                                                                                                                                                                                                                                                                         => ( in @ ( setadjoin @ X1246 @ ( setadjoin @ X1247 @ emptyset ) ) @ ( powerset @ ( binunion @ X1244 @ X1245 ) ) ) ) )
                                                                                                                                                                                                                                                                                                 => ( ! [X1248: $i,X1249: $i,X1250: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X1250 @ X1248 )
                                                                                                                                                                                                                                                                                                       => ! [X1251: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X1251 @ X1249 )
                                                                                                                                                                                                                                                                                                           => ( subset @ ( setadjoin @ ( setadjoin @ X1250 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1250 @ ( setadjoin @ X1251 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1248 @ X1249 ) ) ) ) )
                                                                                                                                                                                                                                                                                                   => ( ! [X1252: $i,X1253: $i,X1254: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X1254 @ X1252 )
                                                                                                                                                                                                                                                                                                         => ! [X1255: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X1255 @ X1253 )
                                                                                                                                                                                                                                                                                                             => ( in @ ( setadjoin @ ( setadjoin @ X1254 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1254 @ ( setadjoin @ X1255 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1252 @ X1253 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                     => ( ! [X1256: $i,X1257: $i,X1258: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X1258 @ X1256 )
                                                                                                                                                                                                                                                                                                           => ! [X1259: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X1259 @ X1257 )
                                                                                                                                                                                                                                                                                                               => ( in @ ( kpair @ X1258 @ X1259 ) @ ( powerset @ ( powerset @ ( binunion @ X1256 @ X1257 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                       => ( ! [X1260: $i,X1261: $i,X1262: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X1262 @ X1260 )
                                                                                                                                                                                                                                                                                                             => ! [X1263: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ X1263 @ X1261 )
                                                                                                                                                                                                                                                                                                                 => ( in @ ( kpair @ X1262 @ X1263 ) @ ( cartprod @ X1260 @ X1261 ) ) ) )
                                                                                                                                                                                                                                                                                                         => ( ! [X1264: $i,X1265: $i,X1266: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X1266 @ ( cartprod @ X1264 @ X1265 ) )
                                                                                                                                                                                                                                                                                                               => ? [X1267: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X1267 @ X1264 )
                                                                                                                                                                                                                                                                                                                    & ? [X1268: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( in @ X1268 @ X1265 )
                                                                                                                                                                                                                                                                                                                        & ( X1266
                                                                                                                                                                                                                                                                                                                          = ( kpair @ X1267 @ X1268 ) ) ) ) )
                                                                                                                                                                                                                                                                                                           => ( ! [X1269: $i,X1270: $i,X1271: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ X1271 @ ( cartprod @ X1269 @ X1270 ) )
                                                                                                                                                                                                                                                                                                                 => ( iskpair @ X1271 ) )
                                                                                                                                                                                                                                                                                                             => ( ! [X1272: $i,X1273: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X1273 @ ( setunion @ X1272 ) )
                                                                                                                                                                                                                                                                                                                   => ? [X1274: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( in @ X1274 @ X1272 )
                                                                                                                                                                                                                                                                                                                        & ( in @ X1273 @ X1274 ) ) )
                                                                                                                                                                                                                                                                                                               => ( ! [X1275: $i] : ( subset @ ( setunion @ ( setadjoin @ X1275 @ emptyset ) ) @ X1275 )
                                                                                                                                                                                                                                                                                                                 => ( ! [X1276: $i] : ( subset @ X1276 @ ( setunion @ ( setadjoin @ X1276 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                   => ( ! [X1277: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( setunion @ ( setadjoin @ X1277 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                          = X1277 )
                                                                                                                                                                                                                                                                                                                     => ( ! [X1278: $i,X1279: $i > $o] :
                                                                                                                                                                                                                                                                                                                            ( ! [X1280: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( in @ X1280 @ X1278 )
                                                                                                                                                                                                                                                                                                                               => ! [X1281: $i] :
                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1281 @ X1278 )
                                                                                                                                                                                                                                                                                                                                   => ( ( X1279 @ X1280 )
                                                                                                                                                                                                                                                                                                                                     => ( ( X1279 @ X1281 )
                                                                                                                                                                                                                                                                                                                                       => ( X1280 = X1281 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                           => ( ? [X1282: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1282 @ X1278 )
                                                                                                                                                                                                                                                                                                                                  & ( X1279 @ X1282 ) )
                                                                                                                                                                                                                                                                                                                             => ( singleton @ ( dsetconstr @ X1278 @ X1279 ) ) ) )
                                                                                                                                                                                                                                                                                                                       => ( ! [X1283: $i,X1284: $i > $o] :
                                                                                                                                                                                                                                                                                                                              ( ( ex1 @ X1283 @ X1284 )
                                                                                                                                                                                                                                                                                                                             => ? [X1285: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1285 @ X1283 )
                                                                                                                                                                                                                                                                                                                                  & ( X1284 @ X1285 ) ) )
                                                                                                                                                                                                                                                                                                                         => ( ! [X1286: $i,X1287: $i > $o,X1288: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( in @ X1288 @ X1286 )
                                                                                                                                                                                                                                                                                                                               => ( ( X1287 @ X1288 )
                                                                                                                                                                                                                                                                                                                                 => ( ! [X1289: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1289 @ X1286 )
                                                                                                                                                                                                                                                                                                                                       => ( ( X1287 @ X1289 )
                                                                                                                                                                                                                                                                                                                                         => ( X1289 = X1288 ) ) )
                                                                                                                                                                                                                                                                                                                                   => ( ex1 @ X1286 @ X1287 ) ) ) )
                                                                                                                                                                                                                                                                                                                           => ( ! [X1290: $i,X1291: $i > $o] :
                                                                                                                                                                                                                                                                                                                                  ( ! [X1292: $i] :
                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1292 @ X1290 )
                                                                                                                                                                                                                                                                                                                                     => ! [X1293: $i] :
                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1293 @ X1290 )
                                                                                                                                                                                                                                                                                                                                         => ( ( X1291 @ X1292 )
                                                                                                                                                                                                                                                                                                                                           => ( ( X1291 @ X1293 )
                                                                                                                                                                                                                                                                                                                                             => ( X1292 = X1293 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                 => ( ? [X1294: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1294 @ X1290 )
                                                                                                                                                                                                                                                                                                                                        & ( X1291 @ X1294 ) )
                                                                                                                                                                                                                                                                                                                                   => ( ex1 @ X1290 @ X1291 ) ) )
                                                                                                                                                                                                                                                                                                                             => ( ! [X1295: $i,X1296: $i] :
                                                                                                                                                                                                                                                                                                                                    ( ( ( setadjoin @ X1295 @ emptyset )
                                                                                                                                                                                                                                                                                                                                      = ( setadjoin @ X1296 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                   => ( X1295 = X1296 ) )
                                                                                                                                                                                                                                                                                                                               => ( ! [X1297: $i,X1298: $i,X1299: $i] :
                                                                                                                                                                                                                                                                                                                                      ( ( in @ ( setadjoin @ X1299 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1297 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1297 @ ( setadjoin @ X1298 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                     => ( X1297 = X1299 ) )
                                                                                                                                                                                                                                                                                                                                 => ( ! [X1300: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( iskpair @ X1300 )
                                                                                                                                                                                                                                                                                                                                       => ( singleton
                                                                                                                                                                                                                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1300 )
                                                                                                                                                                                                                                                                                                                                            @ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1300 ) ) ) )
                                                                                                                                                                                                                                                                                                                                   => ( ! [X1301: $i] :
                                                                                                                                                                                                                                                                                                                                          ( ( singleton @ X1301 )
                                                                                                                                                                                                                                                                                                                                         => ( in @ ( setunion @ X1301 ) @ X1301 ) )
                                                                                                                                                                                                                                                                                                                                     => ( ! [X1302: $i,X1303: $i] :
                                                                                                                                                                                                                                                                                                                                            ( ( kfst @ ( kpair @ X1302 @ X1303 ) )
                                                                                                                                                                                                                                                                                                                                            = X1302 )
                                                                                                                                                                                                                                                                                                                                       => ( ! [X1304: $i,X1305: $i,X1306: $i] :
                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1306 @ ( cartprod @ X1304 @ X1305 ) )
                                                                                                                                                                                                                                                                                                                                             => ( in @ ( kfst @ X1306 ) @ X1304 ) )
                                                                                                                                                                                                                                                                                                                                         => ( ! [X1307: $i,X1308: $i,X1309: $i,X1310: $i] :
                                                                                                                                                                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1307 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1307 @ ( setadjoin @ X1308 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X1309 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1309 @ ( setadjoin @ X1310 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                               => ( X1307 = X1309 ) )
                                                                                                                                                                                                                                                                                                                                           => ( ! [X1311: $i,X1312: $i,X1313: $i,X1314: $i] :
                                                                                                                                                                                                                                                                                                                                                  ( ( ( kpair @ X1311 @ X1312 )
                                                                                                                                                                                                                                                                                                                                                    = ( kpair @ X1313 @ X1314 ) )
                                                                                                                                                                                                                                                                                                                                                 => ( X1311 = X1313 ) )
                                                                                                                                                                                                                                                                                                                                             => ( ! [X1315: $i,X1316: $i] :
                                                                                                                                                                                                                                                                                                                                                    ( ( X1315 = X1316 )
                                                                                                                                                                                                                                                                                                                                                   => ( ( setadjoin @ X1315 @ ( setadjoin @ X1316 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                      = ( setadjoin @ X1315 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                               => ( ! [X1317: $i,X1318: $i] :
                                                                                                                                                                                                                                                                                                                                                      ( ( X1317 = X1318 )
                                                                                                                                                                                                                                                                                                                                                     => ( ( setadjoin @ ( setadjoin @ X1317 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1317 @ ( setadjoin @ X1318 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X1317 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1319: $i,X1320: $i,X1321: $i,X1322: $i] :
                                                                                                                                                                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1319 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1319 @ ( setadjoin @ X1320 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X1321 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1321 @ ( setadjoin @ X1322 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                                       => ( ( X1321 = X1322 )
                                                                                                                                                                                                                                                                                                                                                         => ( X1320 = X1322 ) ) )
                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1323: $i,X1324: $i,X1325: $i] :
                                                                                                                                                                                                                                                                                                                                                          ( ( ( setadjoin @ X1323 @ ( setadjoin @ X1324 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                            = ( setadjoin @ X1325 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                         => ( X1323 = X1324 ) )
                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1326: $i,X1327: $i,X1328: $i,X1329: $i] :
                                                                                                                                                                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1326 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1326 @ ( setadjoin @ X1327 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X1328 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1328 @ ( setadjoin @ X1329 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                                           => ( X1327 = X1329 ) )
                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1330: $i,X1331: $i,X1332: $i,X1333: $i] :
                                                                                                                                                                                                                                                                                                                                                              ( ( ( kpair @ X1330 @ X1331 )
                                                                                                                                                                                                                                                                                                                                                                = ( kpair @ X1332 @ X1333 ) )
                                                                                                                                                                                                                                                                                                                                                             => ( X1331 = X1333 ) )
                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1334: $i] :
                                                                                                                                                                                                                                                                                                                                                                ( ( iskpair @ X1334 )
                                                                                                                                                                                                                                                                                                                                                               => ( singleton
                                                                                                                                                                                                                                                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1334 )
                                                                                                                                                                                                                                                                                                                                                                    @ ^ [Z0: $i] :
                                                                                                                                                                                                                                                                                                                                                                        ( X1334
                                                                                                                                                                                                                                                                                                                                                                        = ( kpair @ ( kfst @ X1334 ) @ Z0 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1335: $i,X1336: $i] :
                                                                                                                                                                                                                                                                                                                                                                  ( ( ksnd @ ( kpair @ X1335 @ X1336 ) )
                                                                                                                                                                                                                                                                                                                                                                  = X1336 )
                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1337: $i] :
                                                                                                                                                                                                                                                                                                                                                                    ( ( iskpair @ X1337 )
                                                                                                                                                                                                                                                                                                                                                                   => ( ( kpair @ ( kfst @ X1337 ) @ ( ksnd @ X1337 ) )
                                                                                                                                                                                                                                                                                                                                                                      = X1337 ) )
                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1338: $i,X1339: $i,X1340: $i] :
                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1340 @ ( cartprod @ X1338 @ X1339 ) )
                                                                                                                                                                                                                                                                                                                                                                     => ( in @ ( ksnd @ X1340 ) @ X1339 ) )
                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1341: $i,X1342: $i,X1343: $i,X1344: $i] :
                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ ( kpair @ X1343 @ X1344 ) @ ( cartprod @ X1341 @ X1342 ) )
                                                                                                                                                                                                                                                                                                                                                                       => ( in @ X1343 @ X1341 ) )
                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1345: $i,X1346: $i,X1347: $i,X1348: $i] :
                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ ( kpair @ X1347 @ X1348 ) @ ( cartprod @ X1345 @ X1346 ) )
                                                                                                                                                                                                                                                                                                                                                                         => ( in @ X1348 @ X1346 ) )
                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1349: $i,X1350: $i,X1351: $i] :
                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1351 @ X1349 )
                                                                                                                                                                                                                                                                                                                                                                           => ! [X1352: $i] :
                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1352 @ X1350 )
                                                                                                                                                                                                                                                                                                                                                                               => ( ( kpair @ X1351 @ X1352 )
                                                                                                                                                                                                                                                                                                                                                                                  = ( kpair @ X1351 @ X1352 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1353: $i,X1354: $i,X1355: $i] :
                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1355 @ X1353 )
                                                                                                                                                                                                                                                                                                                                                                             => ! [X1356: $i] :
                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1356 @ X1354 )
                                                                                                                                                                                                                                                                                                                                                                                 => ( ( kfst @ ( kpair @ X1355 @ X1356 ) )
                                                                                                                                                                                                                                                                                                                                                                                    = X1355 ) ) )
                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1357: $i,X1358: $i,X1359: $i] :
                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1359 @ X1357 )
                                                                                                                                                                                                                                                                                                                                                                               => ! [X1360: $i] :
                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1360 @ X1358 )
                                                                                                                                                                                                                                                                                                                                                                                   => ( ( ksnd @ ( kpair @ X1359 @ X1360 ) )
                                                                                                                                                                                                                                                                                                                                                                                      = X1360 ) ) )
                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1361: $i,X1362: $i,X1363: $i] :
                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1363 @ ( cartprod @ X1361 @ X1362 ) )
                                                                                                                                                                                                                                                                                                                                                                                 => ( ( kpair @ ( kfst @ X1363 ) @ ( ksnd @ X1363 ) )
                                                                                                                                                                                                                                                                                                                                                                                    = X1363 ) )
                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1364: $i,X1365: $i,X1366: $i > $i > $o,X1367: $i] :
                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1367 @ X1364 )
                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1368: $i] :
                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1368 @ X1365 )
                                                                                                                                                                                                                                                                                                                                                                                       => ( ( X1366 @ X1367 @ X1368 )
                                                                                                                                                                                                                                                                                                                                                                                         => ( in @ ( kpair @ X1367 @ X1368 ) @ ( dpsetconstr @ X1364 @ X1365 @ X1366 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1369: $i,X1370: $i,X1371: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1369 @ X1370 @ X1371 ) @ ( cartprod @ X1369 @ X1370 ) )
                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1372: $i,X1373: $i,X1374: $i > $i > $o] : ( breln @ X1372 @ X1373 @ ( dpsetconstr @ X1372 @ X1373 @ X1374 ) )
                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1375: $i,X1376: $i,X1377: $i > $i > $o,X1378: $i] :
                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1378 @ X1375 )
                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1379: $i] :
                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1379 @ X1376 )
                                                                                                                                                                                                                                                                                                                                                                                             => ( ( in @ ( kpair @ X1378 @ X1379 ) @ ( dpsetconstr @ X1375 @ X1376 @ X1377 ) )
                                                                                                                                                                                                                                                                                                                                                                                               => ( X1377 @ X1378 @ X1379 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1380: $i,X1381: $i,X1382: $i > $i > $o,X1383: $i,X1384: $i] :
                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ ( kpair @ X1383 @ X1384 ) @ ( dpsetconstr @ X1380 @ X1381 @ X1382 ) )
                                                                                                                                                                                                                                                                                                                                                                                           => ( in @ X1383 @ X1380 ) )
                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1385: $i,X1386: $i,X1387: $i > $i > $o,X1388: $i,X1389: $i] :
                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ ( kpair @ X1388 @ X1389 ) @ ( dpsetconstr @ X1385 @ X1386 @ X1387 ) )
                                                                                                                                                                                                                                                                                                                                                                                             => ( in @ X1389 @ X1386 ) )
                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1390: $i,X1391: $i,X1392: $i > $i > $o,X1393: $i,X1394: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ ( kpair @ X1393 @ X1394 ) @ ( dpsetconstr @ X1390 @ X1391 @ X1392 ) )
                                                                                                                                                                                                                                                                                                                                                                                               => ( X1392 @ X1393 @ X1394 ) )
                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1395: $i,X1396: $i,X1397: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                  ( ( func @ X1395 @ X1396 @ X1397 )
                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1398: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1398 @ X1395 )
                                                                                                                                                                                                                                                                                                                                                                                                     => ( singleton
                                                                                                                                                                                                                                                                                                                                                                                                        @ ( dsetconstr @ X1396
                                                                                                                                                                                                                                                                                                                                                                                                          @ ^ [Z0: $i] : ( in @ ( kpair @ X1398 @ Z0 ) @ X1397 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1399: $i,X1400: $i,X1401: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                    ( ( func @ X1399 @ X1400 @ X1401 )
                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1402: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1402 @ X1399 )
                                                                                                                                                                                                                                                                                                                                                                                                       => ( in
                                                                                                                                                                                                                                                                                                                                                                                                          @ ( setunion
                                                                                                                                                                                                                                                                                                                                                                                                            @ ( dsetconstr @ X1400
                                                                                                                                                                                                                                                                                                                                                                                                              @ ^ [Z0: $i] : ( in @ ( kpair @ X1402 @ Z0 ) @ X1401 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                          @ X1400 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1403: $i,X1404: $i,X1405: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                      ( ( func @ X1403 @ X1404 @ X1405 )
                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1406: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1406 @ X1403 )
                                                                                                                                                                                                                                                                                                                                                                                                         => ( in @ ( ap @ X1403 @ X1404 @ X1405 @ X1406 ) @ X1404 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1407: $i,X1408: $i,X1409: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1409 @ ( funcSet @ X1407 @ X1408 ) )
                                                                                                                                                                                                                                                                                                                                                                                                       => ( func @ X1407 @ X1408 @ X1409 ) )
                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1410: $i,X1411: $i,X1412: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1412 @ ( funcSet @ X1410 @ X1411 ) )
                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1413: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1413 @ X1410 )
                                                                                                                                                                                                                                                                                                                                                                                                             => ( in @ ( ap @ X1410 @ X1411 @ X1412 @ X1413 ) @ X1411 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1414: $i,X1415: $i,X1416: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                            ( ( func @ X1414 @ X1415 @ X1416 )
                                                                                                                                                                                                                                                                                                                                                                                                           => ( in @ X1416 @ ( funcSet @ X1414 @ X1415 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1417: $i,X1418: $i,X1419: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                              ( ! [X1420: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1420 @ X1417 )
                                                                                                                                                                                                                                                                                                                                                                                                                 => ( in @ ( X1419 @ X1420 ) @ X1418 ) )
                                                                                                                                                                                                                                                                                                                                                                                                             => ( func @ X1417 @ X1418
                                                                                                                                                                                                                                                                                                                                                                                                                @ ( dpsetconstr @ X1417 @ X1418
                                                                                                                                                                                                                                                                                                                                                                                                                  @ ^ [Z0: $i] : ( $eq @ ( X1419 @ Z0 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1421: $i,X1422: $i,X1423: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                ( ! [X1424: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1424 @ X1421 )
                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ ( X1423 @ X1424 ) @ X1422 ) )
                                                                                                                                                                                                                                                                                                                                                                                                               => ( func @ X1421 @ X1422 @ ( lam @ X1421 @ X1422 @ X1423 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1425: $i,X1426: $i,X1427: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                  ( ! [X1428: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1428 @ X1425 )
                                                                                                                                                                                                                                                                                                                                                                                                                     => ( in @ ( X1427 @ X1428 ) @ X1426 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                 => ( in @ ( lam @ X1425 @ X1426 @ X1427 ) @ ( funcSet @ X1425 @ X1426 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1429: $i,X1430: $i,X1431: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( breln @ X1429 @ X1430 @ X1431 )
                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1432: $i > $o] :
                                                                                                                                                                                                                                                                                                                                                                                                                        ( ! [X1433: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1433 @ X1429 )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1434: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1434 @ X1430 )
                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( in @ ( kpair @ X1433 @ X1434 ) @ X1431 )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( X1432 @ ( kpair @ X1433 @ X1434 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1435: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1435 @ X1431 )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ( X1432 @ X1435 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1436: $i,X1437: $i,X1438: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( breln @ X1436 @ X1437 @ X1438 )
                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1439: $i > $o] :
                                                                                                                                                                                                                                                                                                                                                                                                                          ( ! [X1440: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1440 @ X1436 )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1441: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1441 @ X1437 )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( in @ ( kpair @ X1440 @ X1441 ) @ X1438 )
                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( X1439 @ ( kpair @ X1440 @ X1441 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1442: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1442 @ X1438 )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ( X1439 @ X1442 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1443: $i,X1444: $i > $o] :
                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( ex1 @ X1443 @ X1444 )
                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1445: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1445 @ X1443 )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1446: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1446 @ X1443 )
                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( X1444 @ X1445 )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( X1444 @ X1446 )
                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( X1445 = X1446 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1447: $i,X1448: $i,X1449: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( func @ X1447 @ X1448 @ X1449 )
                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1450: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1450 @ X1447 )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ( in @ ( kpair @ X1450 @ ( ap @ X1447 @ X1448 @ X1449 @ X1450 ) ) @ X1449 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1451: $i,X1452: $i,X1453: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1453 @ ( funcSet @ X1451 @ X1452 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1454: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1454 @ X1451 )
                                                                                                                                                                                                                                                                                                                                                                                                                               => ( in @ ( kpair @ X1454 @ ( ap @ X1451 @ X1452 @ X1453 @ X1454 ) ) @ X1453 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1455: $i,X1456: $i,X1457: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( func @ X1455 @ X1456 @ X1457 )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1458: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1458 @ X1455 )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1459: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1459 @ X1456 )
                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( in @ ( kpair @ X1458 @ X1459 ) @ X1457 )
                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( ap @ X1455 @ X1456 @ X1457 @ X1458 )
                                                                                                                                                                                                                                                                                                                                                                                                                                          = X1459 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1460: $i,X1461: $i,X1462: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( func @ X1460 @ X1461 @ X1462 )
                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1463: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( func @ X1460 @ X1461 @ X1463 )
                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1464: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1464 @ X1460 )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( ap @ X1460 @ X1461 @ X1462 @ X1464 )
                                                                                                                                                                                                                                                                                                                                                                                                                                            = ( ap @ X1460 @ X1461 @ X1463 @ X1464 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1465: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1465 @ X1460 )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1466: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1466 @ X1461 )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ( in @ ( kpair @ X1465 @ X1466 ) @ X1463 )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( in @ ( kpair @ X1465 @ X1466 ) @ X1462 ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1467: $i,X1468: $i,X1469: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1469 @ ( funcSet @ X1467 @ X1468 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1470: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1470 @ X1467 )
                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1471: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1471 @ X1468 )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( in @ ( kpair @ X1470 @ X1471 ) @ X1469 )
                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ( ap @ X1467 @ X1468 @ X1469 @ X1470 )
                                                                                                                                                                                                                                                                                                                                                                                                                                              = X1471 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1472: $i,X1473: $i,X1474: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( breln @ X1472 @ X1473 @ X1474 )
                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1475: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( breln @ X1472 @ X1473 @ X1475 )
                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1476: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1476 @ X1472 )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1477: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1477 @ X1473 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( in @ ( kpair @ X1476 @ X1477 ) @ X1474 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ ( kpair @ X1476 @ X1477 ) @ X1475 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( subset @ X1474 @ X1475 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1478: $i,X1479: $i,X1480: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( breln @ X1478 @ X1479 @ X1480 )
                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1481: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( breln @ X1478 @ X1479 @ X1481 )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1482: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1482 @ X1478 )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1483: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1483 @ X1479 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( in @ ( kpair @ X1482 @ X1483 ) @ X1480 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( in @ ( kpair @ X1482 @ X1483 ) @ X1481 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1484: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1484 @ X1478 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1485: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1485 @ X1479 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( in @ ( kpair @ X1484 @ X1485 ) @ X1481 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ ( kpair @ X1484 @ X1485 ) @ X1480 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( X1480 = X1481 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1486: $i,X1487: $i,X1488: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( func @ X1486 @ X1487 @ X1488 )
                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1489: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( func @ X1486 @ X1487 @ X1489 )
                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1490: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1490 @ X1486 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( ap @ X1486 @ X1487 @ X1488 @ X1490 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                    = ( ap @ X1486 @ X1487 @ X1489 @ X1490 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( X1488 = X1489 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1491: $i,X1492: $i,X1493: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1493 @ ( funcSet @ X1491 @ X1492 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1494: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1494 @ ( funcSet @ X1491 @ X1492 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1495: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1495 @ X1491 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( ap @ X1491 @ X1492 @ X1493 @ X1495 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                      = ( ap @ X1491 @ X1492 @ X1494 @ X1495 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( X1493 = X1494 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1496: $i,X1497: $i,X1498: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1498 @ ( funcSet @ X1496 @ X1497 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1499: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1499 @ X1496 )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( ap @ X1496 @ X1497 @ X1498 @ X1499 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                  = ( ap @ X1496 @ X1497 @ X1498 @ X1499 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1500: $i,X1501: $i,X1502: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( func @ X1500 @ X1501 @ X1502 )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1503: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1503 @ X1500 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( ap @ X1500 @ X1501 @ X1502 @ X1503 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                    = ( ap @ X1500 @ X1501 @ X1502 @ X1503 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1504: $i,X1505: $i,X1506: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ! [X1507: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1507 @ X1504 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ ( X1506 @ X1507 ) @ X1505 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1508: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1508 @ X1504 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( ap @ X1504 @ X1505 @ ( lam @ X1504 @ X1505 @ X1506 ) @ X1508 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                      = ( X1506 @ X1508 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1509: $i,X1510: $i,X1511: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( func @ X1509 @ X1510 @ X1511 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( lam @ X1509 @ X1510 @ ( ap @ X1509 @ X1510 @ X1511 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                    = X1511 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1512: $i,X1513: $i,X1514: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ! [X1515: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1515 @ X1512 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ ( X1514 @ X1515 ) @ X1513 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( lam @ X1512 @ X1513 @ X1514 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                      = ( lam @ X1512 @ X1513 @ X1514 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1516: $i,X1517: $i,X1518: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ! [X1519: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1519 @ X1516 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( in @ ( X1518 @ X1519 ) @ X1517 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1520: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1520 @ X1516 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( ap @ X1516 @ X1517 @ ( lam @ X1516 @ X1517 @ X1518 ) @ X1520 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                            = ( X1518 @ X1520 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1521: $i,X1522: $i,X1523: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1523 @ ( funcSet @ X1521 @ X1522 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( lam @ X1521 @ X1522 @ ( ap @ X1521 @ X1522 @ X1523 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                          = X1523 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1524: $i,X1525: $o,X1526: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1526 @ X1524 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1527: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1527 @ X1524 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ~ X1525
                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( in @ X1527
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  @ ( dsetconstr @ X1524
                                                                                                                                                                                                                                                                                                                                                                                                                                                                    @ ^ [Z0: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( X1525
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          & ( Z0 = X1526 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        | ( ~ X1525
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          & ( Z0 = X1527 ) ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1528: $i,X1529: $o,X1530: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1530 @ X1528 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1531: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1531 @ X1528 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ~ X1529
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( dsetconstr @ X1528
                                                                                                                                                                                                                                                                                                                                                                                                                                                                      @ ^ [Z0: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( X1529
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            & ( Z0 = X1530 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          | ( ~ X1529
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            & ( Z0 = X1531 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                    = ( setadjoin @ X1531 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1532: $i,X1533: $o,X1534: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1534 @ X1532 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1535: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1535 @ X1532 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( X1533
                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ X1534
                                                                                                                                                                                                                                                                                                                                                                                                                                                                      @ ( dsetconstr @ X1532
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        @ ^ [Z0: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( X1533
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              & ( Z0 = X1534 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            | ( ~ X1533
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              & ( Z0 = X1535 ) ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1536: $i,X1537: $o,X1538: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1538 @ X1536 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1539: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1539 @ X1536 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( X1537
                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( dsetconstr @ X1536
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          @ ^ [Z0: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( X1537
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                & ( Z0 = X1538 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | ( ~ X1537
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                & ( Z0 = X1539 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        = ( setadjoin @ X1538 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1540: $i,X1541: $o,X1542: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1542 @ X1540 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1543: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1543 @ X1540 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( singleton
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        @ ( dsetconstr @ X1540
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          @ ^ [Z0: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( X1541
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                & ( Z0 = X1542 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | ( ~ X1541
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                & ( Z0 = X1543 ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1544: $i,X1545: $o,X1546: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1546 @ X1544 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1547: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1547 @ X1544 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ ( if @ X1544 @ X1545 @ X1546 @ X1547 ) @ X1544 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1548: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( singleton @ X1548 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1549: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1549 @ X1548 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( setunion @ X1548 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            = X1549 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1550: $i,X1551: $o,X1552: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1552 @ X1550 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1553: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1553 @ X1550 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( X1551
                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ( if @ X1550 @ X1551 @ X1552 @ X1553 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                = X1552 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1554: $i,X1555: $o,X1556: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1556 @ X1554 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1557: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1557 @ X1554 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ~ X1555
                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( if @ X1554 @ X1555 @ X1556 @ X1557 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  = X1557 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1558: $i,X1559: $o,X1560: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1560 @ X1558 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1561: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1561 @ X1558 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( in @ ( if @ X1558 @ X1559 @ X1560 @ X1561 ) @ ( setadjoin @ X1560 @ ( setadjoin @ X1561 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1562: $i,X1563: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1563 @ ( powerset @ X1562 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1564: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1564 @ ( powerset @ X1562 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( in @ ( binintersect @ X1563 @ X1564 ) @ ( powerset @ X1562 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1565: $i,X1566: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1566 @ ( powerset @ X1565 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1567: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1567 @ ( powerset @ X1565 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ ( binunion @ X1566 @ X1567 ) @ ( powerset @ X1565 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1568: $i,X1569: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1569 @ ( powerset @ X1568 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( in @ ( powerset @ X1569 ) @ ( powerset @ ( powerset @ X1568 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1570: $i,X1571: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1571 @ ( powerset @ X1570 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1572: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1572 @ ( powerset @ X1570 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ ( setminus @ X1571 @ X1572 ) @ ( powerset @ X1570 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1573: $i,X1574: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1574 @ ( powerset @ X1573 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( in @ ( setminus @ X1573 @ X1574 ) @ ( powerset @ X1573 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1575: $i,X1576: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1576 @ ( powerset @ X1575 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1577: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1577 @ ( powerset @ X1575 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1578: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1578 @ X1575 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( in @ X1578 @ X1576 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ X1578 @ X1577 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1579: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1579 @ X1575 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( in @ X1579 @ X1577 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( in @ X1579 @ X1576 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( X1576 = X1577 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1580: $i,X1581: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1581 @ ( powerset @ X1580 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1582: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1582 @ ( powerset @ X1580 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1583: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1583 @ X1580 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( in @ X1583 @ X1581 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( in @ X1583 @ X1582 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( subset @ X1581 @ X1582 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1584: $i,X1585: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1585 @ ( powerset @ X1584 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1586: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1586 @ ( powerset @ X1584 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1587: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1587 @ X1584 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( in @ X1587 @ X1585 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ X1587 @ X1586 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( in @ X1585 @ ( powerset @ X1586 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1588: $i,X1589: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1589 @ ( powerset @ X1588 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1590: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1590 @ ( powerset @ X1588 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1591: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1591 @ X1588 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( in @ X1589 @ ( powerset @ X1590 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( in @ X1591 @ X1589 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( in @ X1591 @ X1590 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1592: $i,X1593: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1593 @ ( powerset @ X1592 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1594: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1594 @ X1592 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( in @ X1594 @ X1593 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ~ ( in @ X1594 @ ( setminus @ X1592 @ X1593 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1595: $i,X1596: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1596 @ ( powerset @ X1595 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1597: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1597 @ X1595 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ~ ( in @ X1597 @ ( setminus @ X1595 @ X1596 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ X1597 @ X1596 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1598: $i,X1599: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1599 @ ( powerset @ X1598 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1600: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1600 @ ( powerset @ X1598 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1601: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1601 @ X1598 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ~ ( in @ X1601 @ X1599 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ~ ( in @ X1601 @ ( binintersect @ X1599 @ X1600 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1602: $i,X1603: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1603 @ ( powerset @ X1602 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1604: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1604 @ ( powerset @ X1602 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1605: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1605 @ X1602 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ~ ( in @ X1605 @ X1604 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ~ ( in @ X1605 @ ( binintersect @ X1603 @ X1604 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1606: $i,X1607: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1607 @ ( powerset @ X1606 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1608: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1608 @ ( powerset @ X1606 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1609: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1609 @ X1606 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( subset @ X1607 @ ( setminus @ X1606 @ X1608 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( in @ X1609 @ X1608 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ~ ( in @ X1609 @ X1607 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1610: $i,X1611: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1611 @ ( powerset @ X1610 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1612: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1612 @ ( powerset @ X1610 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1613: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1613 @ X1610 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( subset @ X1611 @ X1612 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ~ ( in @ X1613 @ X1612 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ~ ( in @ X1613 @ X1611 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1614: $i,X1615: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1615 @ ( powerset @ X1614 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1616: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1616 @ ( powerset @ X1614 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( subset @ X1615 @ X1616 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( subset @ ( setminus @ X1614 @ X1616 ) @ ( setminus @ X1614 @ X1615 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1617: $i,X1618: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1618 @ ( powerset @ X1617 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1619: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1619 @ ( powerset @ X1617 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( subset @ ( setminus @ X1617 @ X1619 ) @ ( setminus @ X1617 @ X1618 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( subset @ X1618 @ X1619 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1620: $i,X1621: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1621 @ ( powerset @ X1620 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1622: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1622 @ X1620 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( in @ X1622 @ X1621 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( in @ X1622 @ ( setminus @ X1620 @ ( setminus @ X1620 @ X1621 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1623: $i,X1624: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1624 @ ( powerset @ X1623 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1625: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1625 @ X1623 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( in @ X1625 @ ( setminus @ X1623 @ ( setminus @ X1623 @ X1624 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ X1625 @ X1624 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1626: $i,X1627: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1627 @ ( powerset @ X1626 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( subset @ X1627 @ ( setminus @ X1626 @ ( setminus @ X1626 @ X1627 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1628: $i,X1629: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1629 @ ( powerset @ X1628 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( subset @ ( setminus @ X1628 @ ( setminus @ X1628 @ X1629 ) ) @ X1629 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1630: $i,X1631: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1631 @ ( powerset @ X1630 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( X1631
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          = ( setminus @ X1630 @ ( setminus @ X1630 @ X1631 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1632: $i,X1633: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1633 @ ( powerset @ X1632 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1634: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1634 @ ( powerset @ X1632 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1635: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1635 @ X1632 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( in @ X1635 @ ( setminus @ X1632 @ X1633 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ~ ( in @ X1635 @ ( binintersect @ X1633 @ X1634 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1636: $i,X1637: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1637 @ ( powerset @ X1636 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1638: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1638 @ ( powerset @ X1636 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1639: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1639 @ X1636 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( in @ X1639 @ ( setminus @ X1636 @ X1637 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( in @ X1639 @ ( setminus @ X1636 @ ( binintersect @ X1637 @ X1638 ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1640: $i,X1641: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1641 @ ( powerset @ X1640 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1642: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1642 @ ( powerset @ X1640 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( subset @ ( setminus @ X1640 @ X1641 ) @ ( setminus @ X1640 @ ( binintersect @ X1641 @ X1642 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1643: $i,X1644: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1644 @ ( powerset @ X1643 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1645: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1645 @ ( powerset @ X1643 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ ( setminus @ X1643 @ X1644 ) @ ( powerset @ ( setminus @ X1643 @ ( binintersect @ X1644 @ X1645 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1646: $i,X1647: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1647 @ ( powerset @ X1646 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1648: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1648 @ ( powerset @ X1646 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( subset @ X1647 @ ( setminus @ X1646 @ X1648 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1649: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1649 @ X1646 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ( in @ X1649 @ X1648 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( in @ X1649 @ ( setminus @ X1646 @ X1647 ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1650: $i,X1651: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1651 @ ( powerset @ X1650 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1652: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1652 @ ( powerset @ X1650 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( subset @ X1651 @ ( setminus @ X1650 @ X1652 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( subset @ X1652 @ ( setminus @ X1650 @ X1651 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1653: $i,X1654: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1654 @ ( powerset @ X1653 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1655: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1655 @ ( powerset @ X1653 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1656: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1656 @ X1653 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ~ ( in @ X1656 @ ( binunion @ X1654 @ X1655 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ~ ( in @ X1656 @ X1654 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1657: $i,X1658: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1658 @ ( powerset @ X1657 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1659: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1659 @ ( powerset @ X1657 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1660: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1660 @ X1657 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ~ ( in @ X1660 @ ( binunion @ X1658 @ X1659 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ~ ( in @ X1660 @ X1659 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1661: $i,X1662: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1662 @ ( powerset @ X1661 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1663: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1663 @ ( powerset @ X1661 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1664: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1664 @ ( powerset @ X1661 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1665: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1665 @ X1661 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( in @ X1665 @ ( binintersect @ X1662 @ X1663 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ X1665 @ ( binunion @ X1662 @ X1664 ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1666: $i,X1667: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1667 @ ( powerset @ X1666 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1668: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1668 @ ( powerset @ X1666 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1669: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1669 @ ( powerset @ X1666 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1670: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1670 @ X1666 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( in @ X1670 @ ( binintersect @ X1667 @ X1668 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( in @ X1670 @ ( binunion @ X1668 @ X1669 ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1671: $i,X1672: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1672 @ ( powerset @ X1671 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1673: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1673 @ ( powerset @ X1671 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1674: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1674 @ ( powerset @ X1671 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1675: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1675 @ X1671 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( in @ X1675 @ ( binintersect @ X1672 @ X1673 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( in @ X1675 @ ( binintersect @ ( binunion @ X1672 @ X1674 ) @ ( binunion @ X1673 @ X1674 ) ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1676: $i,X1677: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1677 @ ( powerset @ X1676 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1678: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1678 @ ( powerset @ X1676 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1679: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1679 @ ( powerset @ X1676 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ ( binintersect @ X1677 @ X1678 ) @ ( powerset @ ( binintersect @ ( binunion @ X1677 @ X1679 ) @ ( binunion @ X1678 @ X1679 ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X4: $i,X21: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X21 @ ( powerset @ X4 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X48: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X48 @ ( powerset @ X4 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X2 @ X4 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( in @ X2 @ ( setminus @ X4 @ ( binunion @ X21 @ X48 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ~ ( in @ X2 @ X21 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    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(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_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)],[inComplementUnionImpNotIn1]),complementTE1]),intersectInPowersetIntersectUnions]),c_0_260]),powersetsubset]),c_0_261]),c_0_262]),c_0_263]),c_0_264]),c_0_265]),c_0_266]),c_0_267]),ifp]),theeq]),binunionIL]),iftrue]),iffalse]),upairset2IR]),iftrueorfalse]),binintersectT_lem]),binunionIR]),binunionT_lem]),powersetT_lem]),binunionEcases]),setminusT_lem]),binunionE]),complementT_lem]),setextT]),subsetTI]),binunionLsub]),powersetTI1]),powersetTE1]),complementTI1]),binunionRsub]),setminusILneg]),binintersectTELcontra]),binintersectTERcontra]),binintersectI]),contrasubsetT]),contrasubsetT1]),binintersectSubset5]),contrasubsetT2]),contrasubsetT3]),binintersectEL]),doubleComplementI1]),doubleComplementE1]),doubleComplementSub1]),doubleComplementSub2]),binintersectLsub]),doubleComplementEq]),complementTnotintersectT]),binintersectSubset2]),complementImpComplementIntersect]),complementSubsetComplementIntersect]),binintersectSubset3]),complementInPowersetComplementIntersect]),contraSubsetComplement]),binintersectER]),complementTcontraSubset]),binunionTILcontra]),disjointsetsI1]),binunionTIRcontra]),inIntersectImpInUnion]),binintersectRsub]),inIntersectImpInUnion2]),inIntersectImpInIntersectUnions]),binintersectSubset4]),binintersectSubset1]),bs114d]),setminusI]),setminusEL]),setminusER]),setminusSubset2]),setminusERneg]),setminusELneg]),c_0_268]),theprop]),setminusIRneg]),setminusLsub]),setminusSubset1]),symdiffE]),symdiffI1]),symdiffI2]),symdiffIneg1]),symdiffIneg2]),secondinupair]),setukpairIL]),setukpairIR]),kpairiskpair]),kpairp]),singletonsubset]),singletoninpowerset]),singletoninpowunion]),upairset2E]),upairsubunion]),upairinpowunion]),ubforcartprodlem1]),ubforcartprodlem2]),ubforcartprodlem3]),subsetRefl]),cartprodpairin]),cartprodmempair1]),cartprodmempair]),setunionE2]),setunionsingleton1]),setunionsingleton2]),setunionsingleton]),c_0_269]),subsetTrans]),c_0_270]),c_0_271]),setadjoinSub]),setadjoinSub2]),c_0_272]),singletonsuniq]),setukpairinjL1]),kfstpairEq]),cartprodfstin]),setukpairinjL2]),setukpairinjL]),setukpairinjR11]),setukpairinjR12]),setukpairinjR1]),upairequniteq]),subset2powerset]),setukpairinjR2]),setukpairinjR]),c_0_273]),ksndpairEq]),kpairsurjEq]),cartprodsndin]),cartprodpairmemEL]),cartprodpairmemER]),cartprodmempaircEq]),cartprodfstpairEq]),cartprodsndpairEq]),cartprodpairsurjEq]),c_0_274]),c_0_275]),c_0_276]),c_0_277]),c_0_278]),c_0_279]),c_0_280]),c_0_281]),c_0_282]),app]),infuncsetfunc]),ap2p]),funcinfuncset]),c_0_283]),c_0_284]),c_0_285]),brelnall1]),brelnall2]),c_0_286]),funcGraphProp1]),funcGraphProp3]),funcGraphProp2]),funcextLem]),funcGraphProp4]),subbreln]),eqbreln]),funcext]),funcext2]),ap2apEq1]),ap2apEq2]),c_0_287]),c_0_288]),c_0_289]),setextsub]),c_0_290]),subsetemptysetimpeq]),powersetI1]),powersetE1]),inPowerset]),notequalI2]),notequalI1]),notsubsetI]),subsetE2]),subsetE]),emptysetsubset]),subsetI2]),eqimpsubset1]),eqimpsubset2]),subsetI1]),c_0_291]),c_0_292]),c_0_293]),omega__Cong]),setunion__Cong]),powerset__Cong]),setadjoin__Cong]),emptyset__Cong]),c_0_294]),c_0_295]),in__Cong]),inCongP]),c_0_296]),c_0_297]),c_0_298]),notdallE]),notdexE]),prop2setI]),quantDeMorgan4]),quantDeMorgan3]),quantDeMorgan2]),quantDeMorgan1]),vacuousDall]),c_0_299]),upairsetIR]),upairsetIL]),upairsetE]),singletonsswitch]),eqinunit]),notinsingleton]),uniqinunit]),nonemptyImpWitness]),c_0_300]),subPowSU]),setunionE]),setunionI]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_301]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),nonemptyI1]),c_0_302]),nonemptyE1]),c_0_303]),noeltsimpempty]),emptyI]),setext]),c_0_304]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_305]),c_0_306]),c_0_307]),c_0_308]),c_0_309]),wellorderingAx]),foundationAx]),c_0_310]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_311]) ).

thf(c_0_313,negated_conjecture,
    ! [X1680: $i,X1681: $i,X1683: $i,X1684: $i,X1685: $i,X1686: $i,X1687: $i,X1688: $i,X1689: $i,X1690: $i,X1691: $i,X1693: $i,X1694: $i,X1696: $i,X1697: $i,X1698: $i,X1699: $i,X1700: $i,X1702: $i,X1703: $i > $i > $o,X1704: $i,X1707: $i,X1709: $i,X1710: $i,X1711: $i,X1712: $i,X1714: $i,X1715: $i > $o,X1716: $i,X1717: $i > $o,X1718: $i,X1719: $i,X1720: $i > $o,X1721: $i,X1722: $i,X1723: $i > $o,X1724: $i,X1725: $i > $o,X1727: $i,X1728: $o,X1729: $i,X1730: $i,X1731: $o,X1732: $i,X1733: $i,X1734: $i > $o,X1736: $i,X1737: $i,X1740: $i,X1742: $i,X1744: $i,X1745: $i > $o,X1746: $i,X1747: $i,X1749: $i,X1750: $i > $o,X1751: $i,X1752: $i,X1753: $i,X1754: $i,X1755: $i,X1756: $i,X1757: $i,X1758: $i,X1759: $i,X1760: $i,X1761: $i,X1762: $o,X1763: $i,X1764: $i,X1765: $i,X1766: $i,X1767: $i,X1768: $i,X1770: $i,X1771: $i,X1772: $i,X1773: $i,X1774: $i,X1775: $i,X1776: $i,X1777: $i,X1778: $i,X1779: $i,X1780: $o,X1782: $i,X1783: $i,X1784: $i > $o,X1786: $i,X1787: $i,X1788: $i,X1790: $i,X1791: $i,X1792: $i,X1793: $i,X1794: $i,X1795: $i,X1796: $i,X1797: $i,X1798: $i,X1799: $i,X1800: $i,X1801: $i,X1802: $i,X1803: $i,X1804: $i,X1805: $i,X1806: $i > $o,X1807: $i,X1808: $i > $o,X1809: $i,X1810: $i,X1811: $i > $o,X1812: $i,X1814: $i,X1815: $i > $o,X1817: $i,X1818: $i,X1819: $i > $o,X1821: $i,X1822: $i,X1823: $i > $o,X1824: $i,X1826: $o,X1827: $i,X1828: $i > $o,X1830: $i,X1831: $i,X1832: $i > $o,X1833: $i,X1835: $i > $o,X1836: $i,X1838: $i > $o,X1839: $i,X1842: $i > $o,X1843: $i,X1845: $i,X1846: $i,X1847: $i,X1848: $i,X1849: $i,X1850: $i,X1851: $i,X1852: $i,X1853: $i > $o,X1854: $i,X1855: $i,X1856: $i > $o,X1857: $i > $o,X1860: $i,X1861: $i,X1862: $i,X1863: $i,X1864: $i,X1865: $i,X1866: $i,X1867: $i,X1868: $i > $o,X1869: $i,X1870: $i,X1871: $i > $o,X1872: $i > $o,X1875: $i,X1876: $i,X1877: $i > $o,X1878: $i > $o,X1881: $i,X1882: $i,X1884: $i,X1885: $i,X1886: $i,X1887: $i,X1888: $i,X1889: $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,X1920: $i,X1921: $i,X1922: $i,X1923: $i,X1924: $i,X1925: $i,X1926: $i,X1927: $i,X1928: $i > $o,X1929: $i,X1930: $i > $o,X1931: $i,X1932: $i,X1933: $i,X1934: $i,X1935: $i,X1936: $i,X1937: $i,X1938: $i,X1939: $i,X1940: $i,X1941: $i,X1942: $o,X1943: $i,X1944: $i,X1945: $i,X1946: $i,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,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: $o,X2011: $i,X2012: $i,X2013: $i,X2014: $i,X2015: $i,X2016: $i,X2017: $i,X2018: $i,X2019: $i,X2020: $i,X2021: $i,X2022: $i,X2023: $i,X2024: $i,X2025: $i,X2026: $i,X2027: $i,X2028: $i,X2029: $i,X2030: $i,X2031: $i,X2032: $i,X2033: $i,X2034: $i,X2035: $i,X2036: $i,X2037: $i,X2038: $i,X2039: $i,X2040: $i,X2041: $i,X2042: $i,X2043: $i,X2044: $i,X2045: $i,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,X2072: $i,X2073: $i,X2074: $i,X2075: $i,X2076: $i,X2078: $i,X2079: $i,X2080: $i,X2081: $i,X2082: $i > $o,X2085: $i,X2086: $i,X2087: $i > $o,X2089: $i,X2090: $i > $o,X2091: $i,X2093: $i,X2094: $i > $o,X2097: $i,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,X2117: $i,X2118: $i,X2119: $i,X2120: $i,X2121: $i,X2122: $i,X2123: $i,X2124: $i,X2125: $i,X2126: $i,X2127: $i,X2128: $i,X2129: $i,X2130: $i,X2131: $i,X2132: $i,X2133: $i,X2134: $i,X2135: $i,X2136: $i,X2137: $i,X2138: $i,X2139: $i,X2140: $i,X2141: $i,X2142: $i,X2143: $i,X2144: $i,X2145: $i,X2146: $i,X2147: $i,X2148: $i,X2149: $i,X2150: $i,X2151: $i,X2152: $i,X2153: $i,X2154: $i,X2155: $i,X2156: $i,X2157: $i,X2158: $i,X2159: $i,X2160: $i,X2161: $i,X2162: $i,X2163: $i,X2164: $i,X2165: $i,X2166: $i,X2167: $i,X2168: $i,X2169: $i > $i > $o,X2170: $i,X2171: $i,X2172: $i,X2173: $i,X2174: $i > $i > $o,X2175: $i,X2176: $i,X2177: $i > $i > $o,X2178: $i,X2179: $i,X2180: $i > $i > $o,X2181: $i,X2182: $i,X2183: $i,X2184: $i,X2185: $i > $i > $o,X2186: $i,X2187: $i,X2188: $i,X2189: $i,X2190: $i > $i > $o,X2191: $i,X2192: $i,X2193: $i,X2194: $i,X2195: $i > $i > $o,X2196: $i,X2197: $i,X2198: $i,X2199: $i,X2200: $i,X2201: $i,X2202: $i,X2203: $i,X2204: $i,X2205: $i,X2206: $i,X2207: $i,X2208: $i,X2209: $i,X2210: $i,X2211: $i,X2212: $i,X2213: $i,X2214: $i,X2215: $i,X2216: $i,X2217: $i,X2218: $i,X2219: $i,X2220: $i,X2221: $i,X2222: $i > $i,X2224: $i,X2225: $i,X2226: $i > $i,X2228: $i,X2229: $i,X2230: $i > $i,X2232: $i,X2233: $i,X2234: $i,X2235: $i > $o,X2238: $i,X2239: $i,X2240: $i,X2241: $i,X2242: $i > $o,X2245: $i,X2246: $i,X2247: $i > $o,X2248: $i,X2249: $i,X2250: $i,X2251: $i,X2252: $i,X2253: $i,X2254: $i,X2255: $i,X2256: $i,X2257: $i,X2258: $i,X2259: $i,X2260: $i,X2261: $i,X2262: $i,X2263: $i,X2264: $i,X2265: $i,X2266: $i,X2268: $i,X2269: $i,X2270: $i,X2271: $i,X2272: $i,X2273: $i,X2274: $i,X2275: $i,X2276: $i,X2277: $i,X2278: $i,X2281: $i,X2282: $i,X2283: $i,X2284: $i,X2289: $i,X2290: $i,X2291: $i,X2292: $i,X2294: $i,X2295: $i,X2296: $i,X2297: $i,X2299: $i,X2300: $i,X2301: $i,X2302: $i,X2303: $i,X2304: $i,X2305: $i,X2306: $i,X2307: $i,X2308: $i,X2309: $i > $i,X2311: $i,X2312: $i,X2313: $i,X2314: $i,X2315: $i,X2316: $i,X2317: $i > $i,X2319: $i,X2320: $i,X2321: $i > $i,X2323: $i,X2324: $i,X2325: $i,X2326: $i,X2327: $i,X2328: $o,X2329: $i,X2330: $i,X2331: $i,X2332: $o,X2333: $i,X2334: $i,X2335: $i,X2336: $o,X2337: $i,X2338: $i,X2339: $i,X2340: $o,X2341: $i,X2342: $i,X2343: $i,X2344: $o,X2345: $i,X2346: $i,X2347: $i,X2348: $o,X2349: $i,X2350: $i,X2351: $i,X2352: $i,X2353: $i,X2354: $o,X2355: $i,X2356: $i,X2357: $i,X2358: $o,X2359: $i,X2360: $i,X2361: $i,X2362: $o,X2363: $i,X2364: $i,X2365: $i,X2366: $i,X2367: $i,X2368: $i,X2369: $i,X2370: $i,X2371: $i,X2372: $i,X2373: $i,X2374: $i,X2375: $i,X2376: $i,X2377: $i,X2378: $i,X2379: $i,X2380: $i,X2383: $i,X2384: $i,X2385: $i,X2387: $i,X2388: $i,X2389: $i,X2391: $i,X2392: $i,X2393: $i,X2394: $i,X2395: $i,X2396: $i,X2397: $i,X2398: $i,X2399: $i,X2400: $i,X2401: $i,X2402: $i,X2403: $i,X2404: $i,X2405: $i,X2406: $i,X2407: $i,X2408: $i,X2409: $i,X2410: $i,X2411: $i,X2412: $i,X2413: $i,X2414: $i,X2415: $i,X2416: $i,X2417: $i,X2418: $i,X2419: $i,X2420: $i,X2421: $i,X2422: $i,X2423: $i,X2424: $i,X2425: $i,X2426: $i,X2427: $i,X2428: $i,X2429: $i,X2430: $i,X2431: $i,X2432: $i,X2433: $i,X2434: $i,X2435: $i,X2436: $i,X2437: $i,X2438: $i,X2439: $i,X2440: $i,X2441: $i,X2442: $i,X2443: $i,X2444: $i,X2445: $i,X2446: $i,X2447: $i,X2448: $i,X2449: $i,X2450: $i,X2451: $i,X2452: $i,X2453: $i,X2454: $i,X2455: $i,X2456: $i,X2457: $i,X2458: $i,X2459: $i,X2460: $i,X2461: $i,X2462: $i,X2463: $i,X2464: $i,X2465: $i,X2466: $i,X2467: $i,X2468: $i,X2469: $i,X2470: $i,X2471: $i,X2472: $i,X2473: $i,X2474: $i,X2475: $i,X2476: $i,X2477: $i,X2478: $i,X2479: $i,X2480: $i,X2481: $i,X2482: $i] :
      ( ( ~ ( in @ ( esk1_2 @ X1680 @ X1681 ) @ X1680 )
        | ~ ( in @ ( esk1_2 @ X1680 @ X1681 ) @ X1681 )
        | ( X1680 = X1681 ) )
      & ( ( in @ ( esk1_2 @ X1680 @ X1681 ) @ X1680 )
        | ( in @ ( esk1_2 @ X1680 @ X1681 ) @ X1681 )
        | ( X1680 = X1681 ) )
      & ~ ( in @ X1683 @ emptyset )
      & ( ~ ( in @ X1686 @ ( setadjoin @ X1684 @ X1685 ) )
        | ( X1686 = X1684 )
        | ( in @ X1686 @ X1685 ) )
      & ( ( X1686 != X1684 )
        | ( in @ X1686 @ ( setadjoin @ X1684 @ X1685 ) ) )
      & ( ~ ( in @ X1686 @ X1685 )
        | ( in @ X1686 @ ( setadjoin @ X1684 @ X1685 ) ) )
      & ( ~ ( in @ X1688 @ ( powerset @ X1687 ) )
        | ~ ( in @ X1689 @ X1688 )
        | ( in @ X1689 @ X1687 ) )
      & ( ( in @ ( esk2_2 @ X1690 @ X1691 ) @ X1691 )
        | ( in @ X1691 @ ( powerset @ X1690 ) ) )
      & ( ~ ( in @ ( esk2_2 @ X1690 @ X1691 ) @ X1690 )
        | ( in @ X1691 @ ( powerset @ X1690 ) ) )
      & ( ( in @ X1694 @ ( esk3_2 @ X1693 @ X1694 ) )
        | ~ ( in @ X1694 @ ( setunion @ X1693 ) ) )
      & ( ( in @ ( esk3_2 @ X1693 @ X1694 ) @ X1693 )
        | ~ ( in @ X1694 @ ( setunion @ X1693 ) ) )
      & ( ~ ( in @ X1697 @ X1698 )
        | ~ ( in @ X1698 @ X1696 )
        | ( in @ X1697 @ ( setunion @ X1696 ) ) )
      & ( in @ emptyset @ omega )
      & ( ~ ( in @ X1699 @ omega )
        | ( in @ ( setadjoin @ X1699 @ X1699 ) @ omega ) )
      & ( ( in @ ( esk4_1 @ X1700 ) @ omega )
        | ~ ( in @ emptyset @ X1700 )
        | ~ ( in @ X1702 @ omega )
        | ( in @ X1702 @ X1700 ) )
      & ( ( in @ ( esk4_1 @ X1700 ) @ X1700 )
        | ~ ( in @ emptyset @ X1700 )
        | ~ ( in @ X1702 @ omega )
        | ( in @ X1702 @ X1700 ) )
      & ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X1700 ) @ ( esk4_1 @ X1700 ) ) @ X1700 )
        | ~ ( in @ emptyset @ X1700 )
        | ~ ( in @ X1702 @ omega )
        | ( in @ X1702 @ X1700 ) )
      & ( ( in @ ( esk7_3 @ X1703 @ X1704 @ X1707 ) @ X1704 )
        | ~ ( in @ X1707 @ ( esk6_2 @ X1703 @ X1704 ) )
        | ( in @ ( esk5_2 @ X1703 @ X1704 ) @ X1704 ) )
      & ( ( X1703 @ ( esk7_3 @ X1703 @ X1704 @ X1707 ) @ X1707 )
        | ~ ( in @ X1707 @ ( esk6_2 @ X1703 @ X1704 ) )
        | ( in @ ( esk5_2 @ X1703 @ X1704 ) @ X1704 ) )
      & ( ~ ( in @ X1710 @ X1704 )
        | ~ ( X1703 @ X1710 @ X1709 )
        | ( in @ X1709 @ ( esk6_2 @ X1703 @ X1704 ) )
        | ( in @ ( esk5_2 @ X1703 @ X1704 ) @ X1704 ) )
      & ( ( in @ ( esk7_3 @ X1703 @ X1704 @ X1707 ) @ X1704 )
        | ~ ( in @ X1707 @ ( esk6_2 @ X1703 @ X1704 ) )
        | ~ ( exu @ ( X1703 @ ( esk5_2 @ X1703 @ X1704 ) ) ) )
      & ( ( X1703 @ ( esk7_3 @ X1703 @ X1704 @ X1707 ) @ X1707 )
        | ~ ( in @ X1707 @ ( esk6_2 @ X1703 @ X1704 ) )
        | ~ ( exu @ ( X1703 @ ( esk5_2 @ X1703 @ X1704 ) ) ) )
      & ( ~ ( in @ X1710 @ X1704 )
        | ~ ( X1703 @ X1710 @ X1709 )
        | ( in @ X1709 @ ( esk6_2 @ X1703 @ X1704 ) )
        | ~ ( exu @ ( X1703 @ ( esk5_2 @ X1703 @ X1704 ) ) ) )
      & ( ( in @ ( esk8_1 @ X1711 ) @ X1711 )
        | ~ ( in @ X1712 @ X1711 ) )
      & ( ~ ( in @ X1714 @ ( esk8_1 @ X1711 ) )
        | ~ ( in @ X1714 @ X1711 )
        | ~ ( in @ X1712 @ X1711 ) )
      & epred1_0
      & ( ~ ( exu @ X1715 )
        | ( X1715 @ ( descr @ X1715 ) ) )
      & ( ~ ( in @ X1718 @ X1716 )
        | ~ ( X1717 @ X1718 )
        | ( in @ X1718 @ ( dsetconstr @ X1716 @ X1717 ) ) )
      & ( ~ ( in @ X1721 @ ( dsetconstr @ X1719 @ X1720 ) )
        | ( in @ X1721 @ X1719 ) )
      & ( ~ ( in @ X1724 @ ( dsetconstr @ X1722 @ X1723 ) )
        | ( X1723 @ X1724 ) )
      & ( ( X1725 @ ( esk9_1 @ X1725 ) )
        | ~ ( exu @ X1725 ) )
      & ( ~ ( X1725 @ X1727 )
        | ( ( esk9_1 @ X1725 )
          = X1727 )
        | ~ ( exu @ X1725 ) )
      & ( ~ ( in @ X1729 @ ( prop2set @ X1728 ) )
        | X1728 )
      & ( ~ ( in @ X1730 @ emptyset )
        | X1731 )
      & ( ~ ( in @ X1732 @ emptyset )
        | ~ $true )
      & ~ ( in @ X1733 @ emptyset )
      & ( ~ ( exu @ X1734 )
        | ( X1734 @ ( esk10_1 @ X1734 ) ) )
      & ( ( in @ ( esk12_2 @ X1736 @ X1737 ) @ X1737 )
        | ( X1736 = X1737 )
        | ( in @ ( esk11_2 @ X1736 @ X1737 ) @ X1736 ) )
      & ( ~ ( in @ ( esk12_2 @ X1736 @ X1737 ) @ X1736 )
        | ( X1736 = X1737 )
        | ( in @ ( esk11_2 @ X1736 @ X1737 ) @ X1736 ) )
      & ( ( in @ ( esk12_2 @ X1736 @ X1737 ) @ X1737 )
        | ( X1736 = X1737 )
        | ~ ( in @ ( esk11_2 @ X1736 @ X1737 ) @ X1737 ) )
      & ( ~ ( in @ ( esk12_2 @ X1736 @ X1737 ) @ X1736 )
        | ( X1736 = X1737 )
        | ~ ( in @ ( esk11_2 @ X1736 @ X1737 ) @ X1737 ) )
      & ( ( in @ ( esk13_1 @ X1740 ) @ X1740 )
        | ( X1740 = emptyset ) )
      & ( ( in @ ( esk14_1 @ X1742 ) @ X1742 )
        | ( X1742 = emptyset ) )
      & ( ~ ( in @ X1746 @ ( dsetconstr @ X1744 @ X1745 ) )
        | ( X1745 @ X1746 )
        | ~ ( in @ X1746 @ X1744 ) )
      & ( ~ ( X1745 @ X1746 )
        | ( in @ X1746 @ ( dsetconstr @ X1744 @ X1745 ) )
        | ~ ( in @ X1746 @ X1744 ) )
      & ( ~ ( nonempty @ X1747 )
        | ( in @ ( esk15_1 @ X1747 ) @ X1747 ) )
      & ( ~ ( in @ X1751 @ X1749 )
        | ~ ( X1750 @ X1751 )
        | ( nonempty @ ( dsetconstr @ X1749 @ X1750 ) ) )
      & ( ~ ( in @ X1753 @ X1752 )
        | ( nonempty @ X1752 ) )
      & ( in @ X1754 @ ( setadjoin @ X1754 @ X1755 ) )
      & ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
      & ( ~ ( in @ X1758 @ X1757 )
        | ( in @ X1758 @ ( setadjoin @ X1756 @ X1757 ) ) )
      & ( ( in @ X1761 @ X1760 )
        | X1762
        | ( X1761 = X1759 )
        | ~ ( in @ X1761 @ ( setadjoin @ X1759 @ X1760 ) ) )
      & ( ~ X1762
        | X1762
        | ( X1761 = X1759 )
        | ~ ( in @ X1761 @ ( setadjoin @ X1759 @ X1760 ) ) )
      & ( ( in @ X1761 @ X1760 )
        | X1762
        | ~ X1762
        | ~ ( in @ X1761 @ ( setadjoin @ X1759 @ X1760 ) ) )
      & ( ~ X1762
        | X1762
        | ~ X1762
        | ~ ( in @ X1761 @ ( setadjoin @ X1759 @ X1760 ) ) )
      & ( ~ ( in @ X1765 @ ( setadjoin @ X1763 @ X1764 ) )
        | ( X1765 = X1763 )
        | ( in @ X1765 @ X1764 ) )
      & ( ( dsetconstr @ X1766
          @ ^ [Z0: $i] : $true )
        = X1766 )
      & ( ( in @ ( esk16_2 @ X1767 @ X1768 ) @ X1768 )
        | ( in @ X1768 @ ( powerset @ X1767 ) ) )
      & ( ~ ( in @ ( esk16_2 @ X1767 @ X1768 ) @ X1767 )
        | ( in @ X1768 @ ( powerset @ X1767 ) ) )
      & ( in @ emptyset @ ( powerset @ X1770 ) )
      & ( in @ emptyset @ ( powerset @ X1771 ) )
      & ( ~ ( in @ X1773 @ ( powerset @ X1772 ) )
        | ~ ( in @ X1774 @ X1773 )
        | ( in @ X1774 @ X1772 ) )
      & ( ~ ( in @ X1776 @ X1777 )
        | ~ ( in @ X1777 @ X1775 )
        | ( in @ X1776 @ ( setunion @ X1775 ) ) )
      & ( ( in @ X1779 @ ( esk17_3 @ X1778 @ X1779 @ X1780 ) )
        | X1780
        | ~ ( in @ X1779 @ ( setunion @ X1778 ) ) )
      & ( ( in @ ( esk17_3 @ X1778 @ X1779 @ X1780 ) @ X1778 )
        | X1780
        | ~ ( in @ X1779 @ ( setunion @ X1778 ) ) )
      & ( ~ X1780
        | X1780
        | ~ ( in @ X1779 @ ( setunion @ X1778 ) ) )
      & ( ~ ( in @ X1783 @ X1782 )
        | ( in @ X1783 @ ( powerset @ ( setunion @ X1782 ) ) ) )
      & ( ~ ( X1784 @ X1786 )
        | ( X1786
          = ( esk18_1 @ X1784 ) )
        | ~ ( exu @ X1784 ) )
      & ( ( X1787
         != ( esk18_1 @ X1784 ) )
        | ( X1784 @ X1787 )
        | ~ ( exu @ X1784 ) )
      & ( ( in @ ( esk19_1 @ X1788 ) @ X1788 )
        | ~ ( nonempty @ X1788 ) )
      & ( $true
        | ~ ( nonempty @ X1788 ) )
      & ( ~ ( in @ X1790 @ ( setadjoin @ X1791 @ emptyset ) )
        | ( X1790 = X1791 ) )
      & ( ( X1792 = X1793 )
        | ~ ( in @ X1793 @ ( setadjoin @ X1792 @ emptyset ) ) )
      & ( ( X1794 != X1795 )
        | ( in @ X1794 @ ( setadjoin @ X1795 @ emptyset ) ) )
      & ( ~ ( in @ X1796 @ ( setadjoin @ X1797 @ emptyset ) )
        | ( in @ X1797 @ ( setadjoin @ X1796 @ emptyset ) ) )
      & ( ~ ( in @ X1800 @ ( setadjoin @ X1798 @ ( setadjoin @ X1799 @ emptyset ) ) )
        | ( X1800 = X1798 )
        | ( X1800 = X1799 ) )
      & ( in @ X1801 @ ( setadjoin @ X1801 @ ( setadjoin @ X1802 @ emptyset ) ) )
      & ( in @ X1804 @ ( setadjoin @ X1803 @ ( setadjoin @ X1804 @ emptyset ) ) )
      & ( ~ ( in @ X1807 @ X1805 )
        | ~ ( X1806 @ X1807 )
        | ( ( dsetconstr @ X1805 @ X1806 )
         != emptyset )
        | ~ $true )
      & ( ~ ( in @ X1809 @ emptyset )
        | ( X1808 @ X1809 ) )
      & ( ( in @ ( esk20_2 @ X1810 @ X1811 ) @ X1810 )
        | ~ ( in @ X1812 @ X1810 )
        | ( X1811 @ X1812 ) )
      & ( ~ ( X1811 @ ( esk20_2 @ X1810 @ X1811 ) )
        | ~ ( in @ X1812 @ X1810 )
        | ( X1811 @ X1812 ) )
      & ( ( in @ ( esk21_2 @ X1814 @ X1815 ) @ X1814 )
        | ~ ( in @ X1817 @ X1814 )
        | ~ ( X1815 @ X1817 ) )
      & ( ( X1815 @ ( esk21_2 @ X1814 @ X1815 ) )
        | ~ ( in @ X1817 @ X1814 )
        | ~ ( X1815 @ X1817 ) )
      & ( ( in @ ( esk22_2 @ X1818 @ X1819 ) @ X1818 )
        | ~ ( in @ X1821 @ X1818 )
        | ~ ( X1819 @ X1821 ) )
      & ( ( X1819 @ ( esk22_2 @ X1818 @ X1819 ) )
        | ~ ( in @ X1821 @ X1818 )
        | ~ ( X1819 @ X1821 ) )
      & ( ( in @ ( esk23_2 @ X1822 @ X1823 ) @ X1822 )
        | ~ ( in @ X1824 @ X1822 )
        | ( X1823 @ X1824 ) )
      & ( ~ ( X1823 @ ( esk23_2 @ X1822 @ X1823 ) )
        | ~ ( in @ X1824 @ X1822 )
        | ( X1823 @ X1824 ) )
      & ( ~ X1826
        | ( in @ emptyset @ ( prop2set @ X1826 ) ) )
      & prop2set2propI
      & ( ( in @ ( esk24_2 @ X1827 @ X1828 ) @ X1827 )
        | ~ ( in @ X1830 @ X1827 )
        | ~ ( X1828 @ X1830 ) )
      & ( ( X1828 @ ( esk24_2 @ X1827 @ X1828 ) )
        | ~ ( in @ X1830 @ X1827 )
        | ~ ( X1828 @ X1830 ) )
      & ( ( in @ ( esk25_2 @ X1831 @ X1832 ) @ X1831 )
        | ~ ( in @ X1833 @ X1831 )
        | ( X1832 @ X1833 ) )
      & ( ~ ( X1832 @ ( esk25_2 @ X1831 @ X1832 ) )
        | ~ ( in @ X1833 @ X1831 )
        | ( X1832 @ X1833 ) )
      & ( ( X1835 @ ( esk26_2 @ X1835 @ X1836 ) )
        | ~ ( X1835 @ X1836 )
        | ( exu @ X1835 ) )
      & ( ( X1836
         != ( esk26_2 @ X1835 @ X1836 ) )
        | ~ ( X1835 @ X1836 )
        | ( exu @ X1835 ) )
      & ( ( X1838 @ ( esk27_1 @ X1838 ) )
        | ( exu @ X1838 )
        | ~ ( X1838 @ X1839 ) )
      & ( ( X1838 @ ( esk28_1 @ X1838 ) )
        | ( exu @ X1838 )
        | ~ ( X1838 @ X1839 ) )
      & ( ( ( esk27_1 @ X1838 )
         != ( esk28_1 @ X1838 ) )
        | ( exu @ X1838 )
        | ~ ( X1838 @ X1839 ) )
      & ( ~ ( X1842 @ ( esk29_2 @ X1842 @ X1843 ) )
        | ( ( esk29_2 @ X1842 @ X1843 )
         != X1843 )
        | ( exu @ X1842 ) )
      & ( ( X1842 @ ( esk29_2 @ X1842 @ X1843 ) )
        | ( ( esk29_2 @ X1842 @ X1843 )
          = X1843 )
        | ( exu @ X1842 ) )
      & ( ( X1845 != X1846 )
        | ( X1847 != X1848 )
        | ~ ( in @ X1847 @ X1845 )
        | ( in @ X1848 @ X1846 ) )
      & ( ~ ( in @ X1851 @ X1849 )
        | ( in @ X1852 @ X1850 )
        | ( X1851 != X1852 )
        | ( X1849 != X1850 ) )
      & ( ~ ( in @ X1852 @ X1850 )
        | ( in @ X1851 @ X1849 )
        | ( X1851 != X1852 )
        | ( X1849 != X1850 ) )
      & ( ~ ( exu @ X1853 )
        | ~ ( X1853 @ X1854 )
        | ~ ( X1853 @ X1855 )
        | ( X1854 = X1855 ) )
      & ( ~ ( exu @ X1856 )
        | ( exu @ X1857 )
        | ( ( esk30_2 @ X1856 @ X1857 )
          = ( esk31_2 @ X1856 @ X1857 ) ) )
      & ( ~ ( exu @ X1857 )
        | ( exu @ X1856 )
        | ( ( esk30_2 @ X1856 @ X1857 )
          = ( esk31_2 @ X1856 @ X1857 ) ) )
      & ( ~ ( exu @ X1856 )
        | ( exu @ X1857 )
        | ~ ( X1856 @ ( esk30_2 @ X1856 @ X1857 ) )
        | ~ ( X1857 @ ( esk31_2 @ X1856 @ X1857 ) ) )
      & ( ~ ( exu @ X1857 )
        | ( exu @ X1856 )
        | ~ ( X1856 @ ( esk30_2 @ X1856 @ X1857 ) )
        | ~ ( X1857 @ ( esk31_2 @ X1856 @ X1857 ) ) )
      & ( ~ ( exu @ X1856 )
        | ( exu @ X1857 )
        | ( X1856 @ ( esk30_2 @ X1856 @ X1857 ) )
        | ( X1857 @ ( esk31_2 @ X1856 @ X1857 ) ) )
      & ( ~ ( exu @ X1857 )
        | ( exu @ X1856 )
        | ( X1856 @ ( esk30_2 @ X1856 @ X1857 ) )
        | ( X1857 @ ( esk31_2 @ X1856 @ X1857 ) ) )
      & ( emptyset = emptyset )
      & ( ( X1860 != X1861 )
        | ( X1862 != X1863 )
        | ( ( setadjoin @ X1860 @ X1862 )
          = ( setadjoin @ X1861 @ X1863 ) ) )
      & ( ( X1864 != X1865 )
        | ( ( powerset @ X1864 )
          = ( powerset @ X1865 ) ) )
      & ( ( X1866 != X1867 )
        | ( ( setunion @ X1866 )
          = ( setunion @ X1867 ) ) )
      & ( omega = omega )
      & ( ~ ( exu @ X1868 )
        | ~ ( X1868 @ X1869 )
        | ~ ( X1868 @ X1870 )
        | ( X1869 = X1870 ) )
      & ( ( ( esk32_2 @ X1871 @ X1872 )
          = ( esk33_2 @ X1871 @ X1872 ) )
        | ~ ( exu @ X1871 )
        | ~ ( exu @ X1872 )
        | ( ( descr @ X1871 )
          = ( descr @ X1872 ) ) )
      & ( ~ ( X1871 @ ( esk32_2 @ X1871 @ X1872 ) )
        | ~ ( X1872 @ ( esk33_2 @ X1871 @ X1872 ) )
        | ~ ( exu @ X1871 )
        | ~ ( exu @ X1872 )
        | ( ( descr @ X1871 )
          = ( descr @ X1872 ) ) )
      & ( ( X1871 @ ( esk32_2 @ X1871 @ X1872 ) )
        | ( X1872 @ ( esk33_2 @ X1871 @ X1872 ) )
        | ~ ( exu @ X1871 )
        | ~ ( exu @ X1872 )
        | ( ( descr @ X1871 )
          = ( descr @ X1872 ) ) )
      & ( ( in @ ( esk34_4 @ X1875 @ X1876 @ X1877 @ X1878 ) @ X1875 )
        | ( ( dsetconstr @ X1875 @ X1877 )
          = ( dsetconstr @ X1876 @ X1878 ) )
        | ( X1875 != X1876 ) )
      & ( ( in @ ( esk35_4 @ X1875 @ X1876 @ X1877 @ X1878 ) @ X1876 )
        | ( ( dsetconstr @ X1875 @ X1877 )
          = ( dsetconstr @ X1876 @ X1878 ) )
        | ( X1875 != X1876 ) )
      & ( ( ( esk34_4 @ X1875 @ X1876 @ X1877 @ X1878 )
          = ( esk35_4 @ X1875 @ X1876 @ X1877 @ X1878 ) )
        | ( ( dsetconstr @ X1875 @ X1877 )
          = ( dsetconstr @ X1876 @ X1878 ) )
        | ( X1875 != X1876 ) )
      & ( ~ ( X1877 @ ( esk34_4 @ X1875 @ X1876 @ X1877 @ X1878 ) )
        | ~ ( X1878 @ ( esk35_4 @ X1875 @ X1876 @ X1877 @ X1878 ) )
        | ( ( dsetconstr @ X1875 @ X1877 )
          = ( dsetconstr @ X1876 @ X1878 ) )
        | ( X1875 != X1876 ) )
      & ( ( X1877 @ ( esk34_4 @ X1875 @ X1876 @ X1877 @ X1878 ) )
        | ( X1878 @ ( esk35_4 @ X1875 @ X1876 @ X1877 @ X1878 ) )
        | ( ( dsetconstr @ X1875 @ X1877 )
          = ( dsetconstr @ X1876 @ X1878 ) )
        | ( X1875 != X1876 ) )
      & ( ( in @ ( esk36_2 @ X1881 @ X1882 ) @ X1881 )
        | ( subset @ X1881 @ X1882 ) )
      & ( ~ ( in @ ( esk36_2 @ X1881 @ X1882 ) @ X1882 )
        | ( subset @ X1881 @ X1882 ) )
      & ( ( X1884 != X1885 )
        | ( subset @ X1885 @ X1884 ) )
      & ( ( X1886 != X1887 )
        | ( subset @ X1886 @ X1887 ) )
      & ( ( in @ ( esk37_2 @ X1888 @ X1889 ) @ X1888 )
        | ( subset @ X1888 @ X1889 ) )
      & ( ~ ( in @ ( esk37_2 @ X1888 @ X1889 ) @ X1889 )
        | ( subset @ X1888 @ X1889 ) )
      & ( subset @ emptyset @ X1891 )
      & ( ~ ( subset @ X1892 @ X1893 )
        | ~ ( in @ X1894 @ X1892 )
        | ( in @ X1894 @ X1893 ) )
      & ( ~ ( subset @ X1895 @ X1896 )
        | ( in @ X1897 @ X1896 )
        | ~ ( in @ X1897 @ X1895 ) )
      & ( ~ ( in @ X1900 @ X1898 )
        | ( in @ X1900 @ X1899 )
        | ~ ( subset @ X1898 @ X1899 ) )
      & ( ( subset @ X1901 @ X1902 )
        | ( X1901 != X1902 ) )
      & ( ~ ( in @ X1905 @ X1903 )
        | ( in @ X1905 @ X1904 )
        | ( X1903 != X1904 ) )
      & ( subset @ X1906 @ X1906 )
      & ( ~ ( subset @ X1907 @ X1908 )
        | ~ ( subset @ X1908 @ X1909 )
        | ( subset @ X1907 @ X1909 ) )
      & ( subset @ X1911 @ ( setadjoin @ X1910 @ X1911 ) )
      & ( ~ ( subset @ X1912 @ X1914 )
        | ( subset @ X1912 @ ( setadjoin @ X1913 @ X1914 ) ) )
      & ( ~ ( subset @ X1915 @ X1916 )
        | ( in @ X1915 @ ( powerset @ X1916 ) ) )
      & ( ~ ( subset @ X1917 @ X1918 )
        | ~ ( subset @ X1918 @ X1917 )
        | ( X1917 = X1918 ) )
      & ( ~ ( subset @ X1919 @ emptyset )
        | ( X1919 = emptyset ) )
      & ( ~ ( subset @ X1921 @ X1920 )
        | ( in @ X1921 @ ( powerset @ X1920 ) ) )
      & ( ~ ( in @ X1923 @ ( powerset @ X1922 ) )
        | ( subset @ X1923 @ X1922 ) )
      & ( in @ X1924 @ ( powerset @ X1924 ) )
      & ( ~ ( subset @ X1925 @ X1926 )
        | ( subset @ ( powerset @ X1925 ) @ ( powerset @ X1926 ) ) )
      & ( in @ ( dsetconstr @ X1927 @ X1928 ) @ ( powerset @ X1927 ) )
      & ( subset @ ( dsetconstr @ X1929 @ X1930 ) @ X1929 )
      & ( ~ ( in @ X1933 @ X1931 )
        | ( in @ X1933 @ ( binunion @ X1931 @ X1932 ) ) )
      & ( in @ X1935 @ ( setadjoin @ X1934 @ ( setadjoin @ X1935 @ emptyset ) ) )
      & ( ~ ( in @ X1938 @ X1937 )
        | ( in @ X1938 @ ( binunion @ X1936 @ X1937 ) ) )
      & ( ( in @ X1941 @ X1940 )
        | X1942
        | ( in @ X1941 @ X1939 )
        | ~ ( in @ X1941 @ ( binunion @ X1939 @ X1940 ) ) )
      & ( ~ X1942
        | X1942
        | ( in @ X1941 @ X1939 )
        | ~ ( in @ X1941 @ ( binunion @ X1939 @ X1940 ) ) )
      & ( ( in @ X1941 @ X1940 )
        | X1942
        | ~ X1942
        | ~ ( in @ X1941 @ ( binunion @ X1939 @ X1940 ) ) )
      & ( ~ X1942
        | X1942
        | ~ X1942
        | ~ ( in @ X1941 @ ( binunion @ X1939 @ X1940 ) ) )
      & ( ~ ( in @ X1945 @ ( binunion @ X1943 @ X1944 ) )
        | ( in @ X1945 @ X1943 )
        | ( in @ X1945 @ X1944 ) )
      & ( subset @ X1946 @ ( binunion @ X1946 @ X1947 ) )
      & ( subset @ X1949 @ ( binunion @ X1948 @ X1949 ) )
      & ( ~ ( in @ X1952 @ X1950 )
        | ~ ( in @ X1952 @ X1951 )
        | ( in @ X1952 @ ( binintersect @ X1950 @ X1951 ) ) )
      & ( ~ ( subset @ X1955 @ X1953 )
        | ~ ( subset @ X1955 @ X1954 )
        | ( subset @ X1955 @ ( binintersect @ X1953 @ X1954 ) ) )
      & ( ~ ( in @ X1958 @ ( binintersect @ X1956 @ X1957 ) )
        | ( in @ X1958 @ X1956 ) )
      & ( subset @ ( binintersect @ X1959 @ X1960 ) @ X1959 )
      & ( ~ ( subset @ X1961 @ X1962 )
        | ( ( binintersect @ X1961 @ X1962 )
          = X1961 ) )
      & ( ( ( binintersect @ X1963 @ X1964 )
         != X1964 )
        | ( subset @ X1964 @ X1963 ) )
      & ( ~ ( in @ X1967 @ ( binintersect @ X1965 @ X1966 ) )
        | ( in @ X1967 @ X1966 ) )
      & ( ( in @ ( esk38_2 @ X1968 @ X1969 ) @ X1968 )
        | ( ( binintersect @ X1968 @ X1969 )
          = emptyset ) )
      & ( ( in @ ( esk38_2 @ X1968 @ X1969 ) @ X1969 )
        | ( ( binintersect @ X1968 @ X1969 )
          = emptyset ) )
      & ( subset @ ( binintersect @ X1971 @ X1972 ) @ X1972 )
      & ( ~ ( subset @ X1974 @ X1973 )
        | ( ( binintersect @ X1973 @ X1974 )
          = X1974 ) )
      & ( ( ( binintersect @ X1975 @ X1976 )
         != X1975 )
        | ( subset @ X1975 @ X1976 ) )
      & ( ( binintersect @ X1977 @ ( binunion @ X1978 @ X1979 ) )
        = ( binunion @ ( binintersect @ X1977 @ X1978 ) @ ( binintersect @ X1977 @ X1979 ) ) )
      & ( ~ ( in @ X1982 @ X1980 )
        | ( in @ X1982 @ X1981 )
        | ( in @ X1982 @ ( setminus @ X1980 @ X1981 ) ) )
      & ( ~ ( in @ X1985 @ ( setminus @ X1983 @ X1984 ) )
        | ( in @ X1985 @ X1983 ) )
      & ( ~ ( in @ X1988 @ ( setminus @ X1986 @ X1987 ) )
        | ~ ( in @ X1988 @ X1987 ) )
      & ( ~ ( subset @ X1989 @ X1990 )
        | ( ( setminus @ X1989 @ X1990 )
          = emptyset ) )
      & ( ( in @ X1993 @ ( setminus @ X1991 @ X1992 ) )
        | ~ ( in @ X1993 @ X1991 )
        | ( in @ X1993 @ X1992 ) )
      & ( ( in @ X1996 @ ( setminus @ X1994 @ X1995 ) )
        | ( in @ X1996 @ X1995 )
        | ~ ( in @ X1996 @ X1994 ) )
      & ( ( in @ X1999 @ X1997 )
        | ~ ( in @ X1999 @ ( setminus @ X1997 @ X1998 ) ) )
      & ( ~ ( in @ X2002 @ X2001 )
        | ~ ( in @ X2002 @ ( setminus @ X2000 @ X2001 ) ) )
      & ( subset @ ( setminus @ X2003 @ X2004 ) @ X2003 )
      & ( ( ( setminus @ X2005 @ X2006 )
         != emptyset )
        | ( subset @ X2005 @ X2006 ) )
      & ( ~ ( in @ X2009 @ X2007 )
        | X2010
        | ( in @ X2009 @ X2007 )
        | ~ ( in @ X2009 @ ( symdiff @ X2007 @ X2008 ) ) )
      & ( ( in @ X2009 @ X2008 )
        | X2010
        | ( in @ X2009 @ X2007 )
        | ~ ( in @ X2009 @ ( symdiff @ X2007 @ X2008 ) ) )
      & ( ~ X2010
        | X2010
        | ( in @ X2009 @ X2007 )
        | ~ ( in @ X2009 @ ( symdiff @ X2007 @ X2008 ) ) )
      & ( ~ ( in @ X2009 @ X2007 )
        | X2010
        | ~ ( in @ X2009 @ X2008 )
        | ~ ( in @ X2009 @ ( symdiff @ X2007 @ X2008 ) ) )
      & ( ( in @ X2009 @ X2008 )
        | X2010
        | ~ ( in @ X2009 @ X2008 )
        | ~ ( in @ X2009 @ ( symdiff @ X2007 @ X2008 ) ) )
      & ( ~ X2010
        | X2010
        | ~ ( in @ X2009 @ X2008 )
        | ~ ( in @ X2009 @ ( symdiff @ X2007 @ X2008 ) ) )
      & ( ~ ( in @ X2009 @ X2007 )
        | X2010
        | ~ X2010
        | ~ ( in @ X2009 @ ( symdiff @ X2007 @ X2008 ) ) )
      & ( ( in @ X2009 @ X2008 )
        | X2010
        | ~ X2010
        | ~ ( in @ X2009 @ ( symdiff @ X2007 @ X2008 ) ) )
      & ( ~ X2010
        | X2010
        | ~ X2010
        | ~ ( in @ X2009 @ ( symdiff @ X2007 @ X2008 ) ) )
      & ( ~ ( in @ X2013 @ X2011 )
        | ( in @ X2013 @ X2012 )
        | ( in @ X2013 @ ( symdiff @ X2011 @ X2012 ) ) )
      & ( ( in @ X2016 @ X2014 )
        | ~ ( in @ X2016 @ X2015 )
        | ( in @ X2016 @ ( symdiff @ X2014 @ X2015 ) ) )
      & ( ~ ( in @ X2019 @ X2017 )
        | ~ ( in @ X2019 @ X2018 )
        | ~ ( in @ X2019 @ ( symdiff @ X2017 @ X2018 ) ) )
      & ( ( in @ X2022 @ X2020 )
        | ( in @ X2022 @ X2021 )
        | ~ ( in @ X2022 @ ( symdiff @ X2020 @ X2021 ) ) )
      & ( in @ X2024 @ ( setadjoin @ X2023 @ ( setadjoin @ X2024 @ emptyset ) ) )
      & ( in @ X2025 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2025 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2025 @ ( setadjoin @ X2026 @ emptyset ) ) @ emptyset ) ) ) )
      & ( in @ X2028 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2027 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2027 @ ( setadjoin @ X2028 @ emptyset ) ) @ emptyset ) ) ) )
      & ( iskpair @ ( setadjoin @ ( setadjoin @ X2029 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2029 @ ( setadjoin @ X2030 @ emptyset ) ) @ emptyset ) ) )
      & ( iskpair @ ( kpair @ X2031 @ X2032 ) )
      & ( ~ ( in @ X2034 @ X2033 )
        | ( subset @ ( setadjoin @ X2034 @ emptyset ) @ X2033 ) )
      & ( ~ ( in @ X2036 @ X2035 )
        | ( in @ ( setadjoin @ X2036 @ emptyset ) @ ( powerset @ X2035 ) ) )
      & ( ~ ( in @ X2039 @ X2037 )
        | ( in @ ( setadjoin @ X2039 @ emptyset ) @ ( powerset @ ( binunion @ X2037 @ X2038 ) ) ) )
      & ( ~ ( in @ X2042 @ ( setadjoin @ X2040 @ ( setadjoin @ X2041 @ emptyset ) ) )
        | ( X2042 = X2040 )
        | ( X2042 = X2041 ) )
      & ( ~ ( in @ X2045 @ X2043 )
        | ~ ( in @ X2046 @ X2044 )
        | ( subset @ ( setadjoin @ X2045 @ ( setadjoin @ X2046 @ emptyset ) ) @ ( binunion @ X2043 @ X2044 ) ) )
      & ( ~ ( in @ X2049 @ X2047 )
        | ~ ( in @ X2050 @ X2048 )
        | ( in @ ( setadjoin @ X2049 @ ( setadjoin @ X2050 @ emptyset ) ) @ ( powerset @ ( binunion @ X2047 @ X2048 ) ) ) )
      & ( ~ ( in @ X2053 @ X2051 )
        | ~ ( in @ X2054 @ X2052 )
        | ( subset @ ( setadjoin @ ( setadjoin @ X2053 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2053 @ ( setadjoin @ X2054 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X2051 @ X2052 ) ) ) )
      & ( ~ ( in @ X2057 @ X2055 )
        | ~ ( in @ X2058 @ X2056 )
        | ( in @ ( setadjoin @ ( setadjoin @ X2057 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2057 @ ( setadjoin @ X2058 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X2055 @ X2056 ) ) ) ) )
      & ( ~ ( in @ X2061 @ X2059 )
        | ~ ( in @ X2062 @ X2060 )
        | ( in @ ( kpair @ X2061 @ X2062 ) @ ( powerset @ ( powerset @ ( binunion @ X2059 @ X2060 ) ) ) ) )
      & ( ~ ( in @ X2065 @ X2063 )
        | ~ ( in @ X2066 @ X2064 )
        | ( in @ ( kpair @ X2065 @ X2066 ) @ ( cartprod @ X2063 @ X2064 ) ) )
      & ( ( in @ ( esk39_3 @ X2067 @ X2068 @ X2069 ) @ X2067 )
        | ~ ( in @ X2069 @ ( cartprod @ X2067 @ X2068 ) ) )
      & ( ( in @ ( esk40_3 @ X2067 @ X2068 @ X2069 ) @ X2068 )
        | ~ ( in @ X2069 @ ( cartprod @ X2067 @ X2068 ) ) )
      & ( ( X2069
          = ( kpair @ ( esk39_3 @ X2067 @ X2068 @ X2069 ) @ ( esk40_3 @ X2067 @ X2068 @ X2069 ) ) )
        | ~ ( in @ X2069 @ ( cartprod @ X2067 @ X2068 ) ) )
      & ( ~ ( in @ X2074 @ ( cartprod @ X2072 @ X2073 ) )
        | ( iskpair @ X2074 ) )
      & ( ( in @ ( esk41_2 @ X2075 @ X2076 ) @ X2075 )
        | ~ ( in @ X2076 @ ( setunion @ X2075 ) ) )
      & ( ( in @ X2076 @ ( esk41_2 @ X2075 @ X2076 ) )
        | ~ ( in @ X2076 @ ( setunion @ X2075 ) ) )
      & ( subset @ ( setunion @ ( setadjoin @ X2078 @ emptyset ) ) @ X2078 )
      & ( subset @ X2079 @ ( setunion @ ( setadjoin @ X2079 @ emptyset ) ) )
      & ( ( setunion @ ( setadjoin @ X2080 @ emptyset ) )
        = X2080 )
      & ( ( in @ ( esk42_2 @ X2081 @ X2082 ) @ X2081 )
        | ~ ( in @ X2085 @ X2081 )
        | ~ ( X2082 @ X2085 )
        | ( singleton @ ( dsetconstr @ X2081 @ X2082 ) ) )
      & ( ( in @ ( esk43_2 @ X2081 @ X2082 ) @ X2081 )
        | ~ ( in @ X2085 @ X2081 )
        | ~ ( X2082 @ X2085 )
        | ( singleton @ ( dsetconstr @ X2081 @ X2082 ) ) )
      & ( ( X2082 @ ( esk42_2 @ X2081 @ X2082 ) )
        | ~ ( in @ X2085 @ X2081 )
        | ~ ( X2082 @ X2085 )
        | ( singleton @ ( dsetconstr @ X2081 @ X2082 ) ) )
      & ( ( X2082 @ ( esk43_2 @ X2081 @ X2082 ) )
        | ~ ( in @ X2085 @ X2081 )
        | ~ ( X2082 @ X2085 )
        | ( singleton @ ( dsetconstr @ X2081 @ X2082 ) ) )
      & ( ( ( esk42_2 @ X2081 @ X2082 )
         != ( esk43_2 @ X2081 @ X2082 ) )
        | ~ ( in @ X2085 @ X2081 )
        | ~ ( X2082 @ X2085 )
        | ( singleton @ ( dsetconstr @ X2081 @ X2082 ) ) )
      & ( ( in @ ( esk44_2 @ X2086 @ X2087 ) @ X2086 )
        | ~ ( ex1 @ X2086 @ X2087 ) )
      & ( ( X2087 @ ( esk44_2 @ X2086 @ X2087 ) )
        | ~ ( ex1 @ X2086 @ X2087 ) )
      & ( ( in @ ( esk45_3 @ X2089 @ X2090 @ X2091 ) @ X2089 )
        | ( ex1 @ X2089 @ X2090 )
        | ~ ( X2090 @ X2091 )
        | ~ ( in @ X2091 @ X2089 ) )
      & ( ( X2090 @ ( esk45_3 @ X2089 @ X2090 @ X2091 ) )
        | ( ex1 @ X2089 @ X2090 )
        | ~ ( X2090 @ X2091 )
        | ~ ( in @ X2091 @ X2089 ) )
      & ( ( ( esk45_3 @ X2089 @ X2090 @ X2091 )
         != X2091 )
        | ( ex1 @ X2089 @ X2090 )
        | ~ ( X2090 @ X2091 )
        | ~ ( in @ X2091 @ X2089 ) )
      & ( ( in @ ( esk46_2 @ X2093 @ X2094 ) @ X2093 )
        | ~ ( in @ X2097 @ X2093 )
        | ~ ( X2094 @ X2097 )
        | ( ex1 @ X2093 @ X2094 ) )
      & ( ( in @ ( esk47_2 @ X2093 @ X2094 ) @ X2093 )
        | ~ ( in @ X2097 @ X2093 )
        | ~ ( X2094 @ X2097 )
        | ( ex1 @ X2093 @ X2094 ) )
      & ( ( X2094 @ ( esk46_2 @ X2093 @ X2094 ) )
        | ~ ( in @ X2097 @ X2093 )
        | ~ ( X2094 @ X2097 )
        | ( ex1 @ X2093 @ X2094 ) )
      & ( ( X2094 @ ( esk47_2 @ X2093 @ X2094 ) )
        | ~ ( in @ X2097 @ X2093 )
        | ~ ( X2094 @ X2097 )
        | ( ex1 @ X2093 @ X2094 ) )
      & ( ( ( esk46_2 @ X2093 @ X2094 )
         != ( esk47_2 @ X2093 @ X2094 ) )
        | ~ ( in @ X2097 @ X2093 )
        | ~ ( X2094 @ X2097 )
        | ( ex1 @ X2093 @ X2094 ) )
      & ( ( ( setadjoin @ X2098 @ emptyset )
         != ( setadjoin @ X2099 @ emptyset ) )
        | ( X2098 = X2099 ) )
      & ( ~ ( in @ ( setadjoin @ X2102 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2100 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2100 @ ( setadjoin @ X2101 @ emptyset ) ) @ emptyset ) ) )
        | ( X2100 = X2102 ) )
      & ( ~ ( iskpair @ X2103 )
        | ( singleton
          @ ( dsetconstr @ ( setunion @ X2103 )
            @ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X2103 ) ) ) )
      & ( ~ ( singleton @ X2104 )
        | ( in @ ( setunion @ X2104 ) @ X2104 ) )
      & ( ( kfst @ ( kpair @ X2105 @ X2106 ) )
        = X2105 )
      & ( ~ ( in @ X2109 @ ( cartprod @ X2107 @ X2108 ) )
        | ( in @ ( kfst @ X2109 ) @ X2107 ) )
      & ( ( ( setadjoin @ ( setadjoin @ X2110 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2110 @ ( setadjoin @ X2111 @ emptyset ) ) @ emptyset ) )
         != ( setadjoin @ ( setadjoin @ X2112 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2112 @ ( setadjoin @ X2113 @ emptyset ) ) @ emptyset ) ) )
        | ( X2110 = X2112 ) )
      & ( ( ( kpair @ X2114 @ X2115 )
         != ( kpair @ X2116 @ X2117 ) )
        | ( X2114 = X2116 ) )
      & ( ( X2118 != X2119 )
        | ( ( setadjoin @ X2118 @ ( setadjoin @ X2119 @ emptyset ) )
          = ( setadjoin @ X2118 @ emptyset ) ) )
      & ( ( X2120 != X2121 )
        | ( ( setadjoin @ ( setadjoin @ X2120 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2120 @ ( setadjoin @ X2121 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ X2120 @ emptyset ) @ emptyset ) ) )
      & ( ( ( setadjoin @ ( setadjoin @ X2122 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2122 @ ( setadjoin @ X2123 @ emptyset ) ) @ emptyset ) )
         != ( setadjoin @ ( setadjoin @ X2124 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2124 @ ( setadjoin @ X2125 @ emptyset ) ) @ emptyset ) ) )
        | ( X2124 != X2125 )
        | ( X2123 = X2125 ) )
      & ( ( ( setadjoin @ X2126 @ ( setadjoin @ X2127 @ emptyset ) )
         != ( setadjoin @ X2128 @ emptyset ) )
        | ( X2126 = X2127 ) )
      & ( ( ( setadjoin @ ( setadjoin @ X2129 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2129 @ ( setadjoin @ X2130 @ emptyset ) ) @ emptyset ) )
         != ( setadjoin @ ( setadjoin @ X2131 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2131 @ ( setadjoin @ X2132 @ emptyset ) ) @ emptyset ) ) )
        | ( X2130 = X2132 ) )
      & ( ( ( kpair @ X2133 @ X2134 )
         != ( kpair @ X2135 @ X2136 ) )
        | ( X2134 = X2136 ) )
      & ( ~ ( iskpair @ X2137 )
        | ( singleton
          @ ( dsetconstr @ ( setunion @ X2137 )
            @ ^ [Z0: $i] :
                ( X2137
                = ( kpair @ ( kfst @ X2137 ) @ Z0 ) ) ) ) )
      & ( ( ksnd @ ( kpair @ X2138 @ X2139 ) )
        = X2139 )
      & ( ~ ( iskpair @ X2140 )
        | ( ( kpair @ ( kfst @ X2140 ) @ ( ksnd @ X2140 ) )
          = X2140 ) )
      & ( ~ ( in @ X2143 @ ( cartprod @ X2141 @ X2142 ) )
        | ( in @ ( ksnd @ X2143 ) @ X2142 ) )
      & ( ~ ( in @ ( kpair @ X2146 @ X2147 ) @ ( cartprod @ X2144 @ X2145 ) )
        | ( in @ X2146 @ X2144 ) )
      & ( ~ ( in @ ( kpair @ X2150 @ X2151 ) @ ( cartprod @ X2148 @ X2149 ) )
        | ( in @ X2151 @ X2149 ) )
      & ( ~ ( in @ X2154 @ X2152 )
        | ~ ( in @ X2155 @ X2153 )
        | ( ( kpair @ X2154 @ X2155 )
          = ( kpair @ X2154 @ X2155 ) ) )
      & ( ~ ( in @ X2158 @ X2156 )
        | ~ ( in @ X2159 @ X2157 )
        | ( ( kfst @ ( kpair @ X2158 @ X2159 ) )
          = X2158 ) )
      & ( ~ ( in @ X2162 @ X2160 )
        | ~ ( in @ X2163 @ X2161 )
        | ( ( ksnd @ ( kpair @ X2162 @ X2163 ) )
          = X2163 ) )
      & ( ~ ( in @ X2166 @ ( cartprod @ X2164 @ X2165 ) )
        | ( ( kpair @ ( kfst @ X2166 ) @ ( ksnd @ X2166 ) )
          = X2166 ) )
      & ( ~ ( in @ X2170 @ X2167 )
        | ~ ( in @ X2171 @ X2168 )
        | ~ ( X2169 @ X2170 @ X2171 )
        | ( in @ ( kpair @ X2170 @ X2171 ) @ ( dpsetconstr @ X2167 @ X2168 @ X2169 ) ) )
      & ( subset @ ( dpsetconstr @ X2172 @ X2173 @ X2174 ) @ ( cartprod @ X2172 @ X2173 ) )
      & ( breln @ X2175 @ X2176 @ ( dpsetconstr @ X2175 @ X2176 @ X2177 ) )
      & ( ~ ( in @ X2181 @ X2178 )
        | ~ ( in @ X2182 @ X2179 )
        | ~ ( in @ ( kpair @ X2181 @ X2182 ) @ ( dpsetconstr @ X2178 @ X2179 @ X2180 ) )
        | ( X2180 @ X2181 @ X2182 ) )
      & ( ~ ( in @ ( kpair @ X2186 @ X2187 ) @ ( dpsetconstr @ X2183 @ X2184 @ X2185 ) )
        | ( in @ X2186 @ X2183 ) )
      & ( ~ ( in @ ( kpair @ X2191 @ X2192 ) @ ( dpsetconstr @ X2188 @ X2189 @ X2190 ) )
        | ( in @ X2192 @ X2189 ) )
      & ( ~ ( in @ ( kpair @ X2196 @ X2197 ) @ ( dpsetconstr @ X2193 @ X2194 @ X2195 ) )
        | ( X2195 @ X2196 @ X2197 ) )
      & ( ~ ( func @ X2198 @ X2199 @ X2200 )
        | ~ ( in @ X2201 @ X2198 )
        | ( singleton
          @ ( dsetconstr @ X2199
            @ ^ [Z0: $i] : ( in @ ( kpair @ X2201 @ Z0 ) @ X2200 ) ) ) )
      & ( ~ ( func @ X2202 @ X2203 @ X2204 )
        | ~ ( in @ X2205 @ X2202 )
        | ( in
          @ ( setunion
            @ ( dsetconstr @ X2203
              @ ^ [Z0: $i] : ( in @ ( kpair @ X2205 @ Z0 ) @ X2204 ) ) )
          @ X2203 ) )
      & ( ~ ( func @ X2206 @ X2207 @ X2208 )
        | ~ ( in @ X2209 @ X2206 )
        | ( in @ ( ap @ X2206 @ X2207 @ X2208 @ X2209 ) @ X2207 ) )
      & ( ~ ( in @ X2212 @ ( funcSet @ X2210 @ X2211 ) )
        | ( func @ X2210 @ X2211 @ X2212 ) )
      & ( ~ ( in @ X2215 @ ( funcSet @ X2213 @ X2214 ) )
        | ~ ( in @ X2216 @ X2213 )
        | ( in @ ( ap @ X2213 @ X2214 @ X2215 @ X2216 ) @ X2214 ) )
      & ( ~ ( func @ X2217 @ X2218 @ X2219 )
        | ( in @ X2219 @ ( funcSet @ X2217 @ X2218 ) ) )
      & ( ( in @ ( esk48_3 @ X2220 @ X2221 @ X2222 ) @ X2220 )
        | ( func @ X2220 @ X2221
          @ ( dpsetconstr @ X2220 @ X2221
            @ ^ [Z0: $i] : ( $eq @ ( X2222 @ Z0 ) ) ) ) )
      & ( ~ ( in @ ( X2222 @ ( esk48_3 @ X2220 @ X2221 @ X2222 ) ) @ X2221 )
        | ( func @ X2220 @ X2221
          @ ( dpsetconstr @ X2220 @ X2221
            @ ^ [Z0: $i] : ( $eq @ ( X2222 @ Z0 ) ) ) ) )
      & ( ( in @ ( esk49_3 @ X2224 @ X2225 @ X2226 ) @ X2224 )
        | ( func @ X2224 @ X2225 @ ( lam @ X2224 @ X2225 @ X2226 ) ) )
      & ( ~ ( in @ ( X2226 @ ( esk49_3 @ X2224 @ X2225 @ X2226 ) ) @ X2225 )
        | ( func @ X2224 @ X2225 @ ( lam @ X2224 @ X2225 @ X2226 ) ) )
      & ( ( in @ ( esk50_3 @ X2228 @ X2229 @ X2230 ) @ X2228 )
        | ( in @ ( lam @ X2228 @ X2229 @ X2230 ) @ ( funcSet @ X2228 @ X2229 ) ) )
      & ( ~ ( in @ ( X2230 @ ( esk50_3 @ X2228 @ X2229 @ X2230 ) ) @ X2229 )
        | ( in @ ( lam @ X2228 @ X2229 @ X2230 ) @ ( funcSet @ X2228 @ X2229 ) ) )
      & ( ( in @ ( esk51_4 @ X2232 @ X2233 @ X2234 @ X2235 ) @ X2232 )
        | ~ ( in @ X2238 @ X2234 )
        | ( X2235 @ X2238 )
        | ~ ( breln @ X2232 @ X2233 @ X2234 ) )
      & ( ( in @ ( esk52_4 @ X2232 @ X2233 @ X2234 @ X2235 ) @ X2233 )
        | ~ ( in @ X2238 @ X2234 )
        | ( X2235 @ X2238 )
        | ~ ( breln @ X2232 @ X2233 @ X2234 ) )
      & ( ( in @ ( kpair @ ( esk51_4 @ X2232 @ X2233 @ X2234 @ X2235 ) @ ( esk52_4 @ X2232 @ X2233 @ X2234 @ X2235 ) ) @ X2234 )
        | ~ ( in @ X2238 @ X2234 )
        | ( X2235 @ X2238 )
        | ~ ( breln @ X2232 @ X2233 @ X2234 ) )
      & ( ~ ( X2235 @ ( kpair @ ( esk51_4 @ X2232 @ X2233 @ X2234 @ X2235 ) @ ( esk52_4 @ X2232 @ X2233 @ X2234 @ X2235 ) ) )
        | ~ ( in @ X2238 @ X2234 )
        | ( X2235 @ X2238 )
        | ~ ( breln @ X2232 @ X2233 @ X2234 ) )
      & ( ( in @ ( esk53_4 @ X2239 @ X2240 @ X2241 @ X2242 ) @ X2239 )
        | ~ ( in @ X2245 @ X2241 )
        | ( X2242 @ X2245 )
        | ~ ( breln @ X2239 @ X2240 @ X2241 ) )
      & ( ( in @ ( esk54_4 @ X2239 @ X2240 @ X2241 @ X2242 ) @ X2240 )
        | ~ ( in @ X2245 @ X2241 )
        | ( X2242 @ X2245 )
        | ~ ( breln @ X2239 @ X2240 @ X2241 ) )
      & ( ( in @ ( kpair @ ( esk53_4 @ X2239 @ X2240 @ X2241 @ X2242 ) @ ( esk54_4 @ X2239 @ X2240 @ X2241 @ X2242 ) ) @ X2241 )
        | ~ ( in @ X2245 @ X2241 )
        | ( X2242 @ X2245 )
        | ~ ( breln @ X2239 @ X2240 @ X2241 ) )
      & ( ~ ( X2242 @ ( kpair @ ( esk53_4 @ X2239 @ X2240 @ X2241 @ X2242 ) @ ( esk54_4 @ X2239 @ X2240 @ X2241 @ X2242 ) ) )
        | ~ ( in @ X2245 @ X2241 )
        | ( X2242 @ X2245 )
        | ~ ( breln @ X2239 @ X2240 @ X2241 ) )
      & ( ~ ( ex1 @ X2246 @ X2247 )
        | ~ ( in @ X2248 @ X2246 )
        | ~ ( in @ X2249 @ X2246 )
        | ~ ( X2247 @ X2248 )
        | ~ ( X2247 @ X2249 )
        | ( X2248 = X2249 ) )
      & ( ~ ( func @ X2250 @ X2251 @ X2252 )
        | ~ ( in @ X2253 @ X2250 )
        | ( in @ ( kpair @ X2253 @ ( ap @ X2250 @ X2251 @ X2252 @ X2253 ) ) @ X2252 ) )
      & ( ~ ( in @ X2256 @ ( funcSet @ X2254 @ X2255 ) )
        | ~ ( in @ X2257 @ X2254 )
        | ( in @ ( kpair @ X2257 @ ( ap @ X2254 @ X2255 @ X2256 @ X2257 ) ) @ X2256 ) )
      & ( ~ ( func @ X2258 @ X2259 @ X2260 )
        | ~ ( in @ X2261 @ X2258 )
        | ~ ( in @ X2262 @ X2259 )
        | ~ ( in @ ( kpair @ X2261 @ X2262 ) @ X2260 )
        | ( ( ap @ X2258 @ X2259 @ X2260 @ X2261 )
          = X2262 ) )
      & ( ( in @ ( esk55_4 @ X2263 @ X2264 @ X2265 @ X2266 ) @ X2263 )
        | ~ ( in @ X2268 @ X2263 )
        | ~ ( in @ X2269 @ X2264 )
        | ~ ( in @ ( kpair @ X2268 @ X2269 ) @ X2266 )
        | ( in @ ( kpair @ X2268 @ X2269 ) @ X2265 )
        | ~ ( func @ X2263 @ X2264 @ X2266 )
        | ~ ( func @ X2263 @ X2264 @ X2265 ) )
      & ( ( ( ap @ X2263 @ X2264 @ X2265 @ ( esk55_4 @ X2263 @ X2264 @ X2265 @ X2266 ) )
         != ( ap @ X2263 @ X2264 @ X2266 @ ( esk55_4 @ X2263 @ X2264 @ X2265 @ X2266 ) ) )
        | ~ ( in @ X2268 @ X2263 )
        | ~ ( in @ X2269 @ X2264 )
        | ~ ( in @ ( kpair @ X2268 @ X2269 ) @ X2266 )
        | ( in @ ( kpair @ X2268 @ X2269 ) @ X2265 )
        | ~ ( func @ X2263 @ X2264 @ X2266 )
        | ~ ( func @ X2263 @ X2264 @ X2265 ) )
      & ( ~ ( in @ X2272 @ ( funcSet @ X2270 @ X2271 ) )
        | ~ ( in @ X2273 @ X2270 )
        | ~ ( in @ X2274 @ X2271 )
        | ~ ( in @ ( kpair @ X2273 @ X2274 ) @ X2272 )
        | ( ( ap @ X2270 @ X2271 @ X2272 @ X2273 )
          = X2274 ) )
      & ( ( in @ ( esk56_4 @ X2275 @ X2276 @ X2277 @ X2278 ) @ X2275 )
        | ( subset @ X2277 @ X2278 )
        | ~ ( breln @ X2275 @ X2276 @ X2278 )
        | ~ ( breln @ X2275 @ X2276 @ X2277 ) )
      & ( ( in @ ( esk57_4 @ X2275 @ X2276 @ X2277 @ X2278 ) @ X2276 )
        | ( subset @ X2277 @ X2278 )
        | ~ ( breln @ X2275 @ X2276 @ X2278 )
        | ~ ( breln @ X2275 @ X2276 @ X2277 ) )
      & ( ( in @ ( kpair @ ( esk56_4 @ X2275 @ X2276 @ X2277 @ X2278 ) @ ( esk57_4 @ X2275 @ X2276 @ X2277 @ X2278 ) ) @ X2277 )
        | ( subset @ X2277 @ X2278 )
        | ~ ( breln @ X2275 @ X2276 @ X2278 )
        | ~ ( breln @ X2275 @ X2276 @ X2277 ) )
      & ( ~ ( in @ ( kpair @ ( esk56_4 @ X2275 @ X2276 @ X2277 @ X2278 ) @ ( esk57_4 @ X2275 @ X2276 @ X2277 @ X2278 ) ) @ X2278 )
        | ( subset @ X2277 @ X2278 )
        | ~ ( breln @ X2275 @ X2276 @ X2278 )
        | ~ ( breln @ X2275 @ X2276 @ X2277 ) )
      & ( ( in @ ( esk60_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ X2281 )
        | ( X2283 = X2284 )
        | ( in @ ( esk58_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ X2281 )
        | ~ ( breln @ X2281 @ X2282 @ X2284 )
        | ~ ( breln @ X2281 @ X2282 @ X2283 ) )
      & ( ( in @ ( esk61_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ X2282 )
        | ( X2283 = X2284 )
        | ( in @ ( esk58_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ X2281 )
        | ~ ( breln @ X2281 @ X2282 @ X2284 )
        | ~ ( breln @ X2281 @ X2282 @ X2283 ) )
      & ( ( in @ ( kpair @ ( esk60_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ ( esk61_4 @ X2281 @ X2282 @ X2283 @ X2284 ) ) @ X2284 )
        | ( X2283 = X2284 )
        | ( in @ ( esk58_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ X2281 )
        | ~ ( breln @ X2281 @ X2282 @ X2284 )
        | ~ ( breln @ X2281 @ X2282 @ X2283 ) )
      & ( ~ ( in @ ( kpair @ ( esk60_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ ( esk61_4 @ X2281 @ X2282 @ X2283 @ X2284 ) ) @ X2283 )
        | ( X2283 = X2284 )
        | ( in @ ( esk58_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ X2281 )
        | ~ ( breln @ X2281 @ X2282 @ X2284 )
        | ~ ( breln @ X2281 @ X2282 @ X2283 ) )
      & ( ( in @ ( esk60_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ X2281 )
        | ( X2283 = X2284 )
        | ( in @ ( esk59_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ X2282 )
        | ~ ( breln @ X2281 @ X2282 @ X2284 )
        | ~ ( breln @ X2281 @ X2282 @ X2283 ) )
      & ( ( in @ ( esk61_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ X2282 )
        | ( X2283 = X2284 )
        | ( in @ ( esk59_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ X2282 )
        | ~ ( breln @ X2281 @ X2282 @ X2284 )
        | ~ ( breln @ X2281 @ X2282 @ X2283 ) )
      & ( ( in @ ( kpair @ ( esk60_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ ( esk61_4 @ X2281 @ X2282 @ X2283 @ X2284 ) ) @ X2284 )
        | ( X2283 = X2284 )
        | ( in @ ( esk59_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ X2282 )
        | ~ ( breln @ X2281 @ X2282 @ X2284 )
        | ~ ( breln @ X2281 @ X2282 @ X2283 ) )
      & ( ~ ( in @ ( kpair @ ( esk60_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ ( esk61_4 @ X2281 @ X2282 @ X2283 @ X2284 ) ) @ X2283 )
        | ( X2283 = X2284 )
        | ( in @ ( esk59_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ X2282 )
        | ~ ( breln @ X2281 @ X2282 @ X2284 )
        | ~ ( breln @ X2281 @ X2282 @ X2283 ) )
      & ( ( in @ ( esk60_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ X2281 )
        | ( X2283 = X2284 )
        | ( in @ ( kpair @ ( esk58_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ ( esk59_4 @ X2281 @ X2282 @ X2283 @ X2284 ) ) @ X2283 )
        | ~ ( breln @ X2281 @ X2282 @ X2284 )
        | ~ ( breln @ X2281 @ X2282 @ X2283 ) )
      & ( ( in @ ( esk61_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ X2282 )
        | ( X2283 = X2284 )
        | ( in @ ( kpair @ ( esk58_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ ( esk59_4 @ X2281 @ X2282 @ X2283 @ X2284 ) ) @ X2283 )
        | ~ ( breln @ X2281 @ X2282 @ X2284 )
        | ~ ( breln @ X2281 @ X2282 @ X2283 ) )
      & ( ( in @ ( kpair @ ( esk60_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ ( esk61_4 @ X2281 @ X2282 @ X2283 @ X2284 ) ) @ X2284 )
        | ( X2283 = X2284 )
        | ( in @ ( kpair @ ( esk58_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ ( esk59_4 @ X2281 @ X2282 @ X2283 @ X2284 ) ) @ X2283 )
        | ~ ( breln @ X2281 @ X2282 @ X2284 )
        | ~ ( breln @ X2281 @ X2282 @ X2283 ) )
      & ( ~ ( in @ ( kpair @ ( esk60_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ ( esk61_4 @ X2281 @ X2282 @ X2283 @ X2284 ) ) @ X2283 )
        | ( X2283 = X2284 )
        | ( in @ ( kpair @ ( esk58_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ ( esk59_4 @ X2281 @ X2282 @ X2283 @ X2284 ) ) @ X2283 )
        | ~ ( breln @ X2281 @ X2282 @ X2284 )
        | ~ ( breln @ X2281 @ X2282 @ X2283 ) )
      & ( ( in @ ( esk60_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ X2281 )
        | ( X2283 = X2284 )
        | ~ ( in @ ( kpair @ ( esk58_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ ( esk59_4 @ X2281 @ X2282 @ X2283 @ X2284 ) ) @ X2284 )
        | ~ ( breln @ X2281 @ X2282 @ X2284 )
        | ~ ( breln @ X2281 @ X2282 @ X2283 ) )
      & ( ( in @ ( esk61_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ X2282 )
        | ( X2283 = X2284 )
        | ~ ( in @ ( kpair @ ( esk58_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ ( esk59_4 @ X2281 @ X2282 @ X2283 @ X2284 ) ) @ X2284 )
        | ~ ( breln @ X2281 @ X2282 @ X2284 )
        | ~ ( breln @ X2281 @ X2282 @ X2283 ) )
      & ( ( in @ ( kpair @ ( esk60_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ ( esk61_4 @ X2281 @ X2282 @ X2283 @ X2284 ) ) @ X2284 )
        | ( X2283 = X2284 )
        | ~ ( in @ ( kpair @ ( esk58_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ ( esk59_4 @ X2281 @ X2282 @ X2283 @ X2284 ) ) @ X2284 )
        | ~ ( breln @ X2281 @ X2282 @ X2284 )
        | ~ ( breln @ X2281 @ X2282 @ X2283 ) )
      & ( ~ ( in @ ( kpair @ ( esk60_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ ( esk61_4 @ X2281 @ X2282 @ X2283 @ X2284 ) ) @ X2283 )
        | ( X2283 = X2284 )
        | ~ ( in @ ( kpair @ ( esk58_4 @ X2281 @ X2282 @ X2283 @ X2284 ) @ ( esk59_4 @ X2281 @ X2282 @ X2283 @ X2284 ) ) @ X2284 )
        | ~ ( breln @ X2281 @ X2282 @ X2284 )
        | ~ ( breln @ X2281 @ X2282 @ X2283 ) )
      & ( ( in @ ( esk62_4 @ X2289 @ X2290 @ X2291 @ X2292 ) @ X2289 )
        | ( X2291 = X2292 )
        | ~ ( func @ X2289 @ X2290 @ X2292 )
        | ~ ( func @ X2289 @ X2290 @ X2291 ) )
      & ( ( ( ap @ X2289 @ X2290 @ X2291 @ ( esk62_4 @ X2289 @ X2290 @ X2291 @ X2292 ) )
         != ( ap @ X2289 @ X2290 @ X2292 @ ( esk62_4 @ X2289 @ X2290 @ X2291 @ X2292 ) ) )
        | ( X2291 = X2292 )
        | ~ ( func @ X2289 @ X2290 @ X2292 )
        | ~ ( func @ X2289 @ X2290 @ X2291 ) )
      & ( ( in @ ( esk63_4 @ X2294 @ X2295 @ X2296 @ X2297 ) @ X2294 )
        | ( X2296 = X2297 )
        | ~ ( in @ X2297 @ ( funcSet @ X2294 @ X2295 ) )
        | ~ ( in @ X2296 @ ( funcSet @ X2294 @ X2295 ) ) )
      & ( ( ( ap @ X2294 @ X2295 @ X2296 @ ( esk63_4 @ X2294 @ X2295 @ X2296 @ X2297 ) )
         != ( ap @ X2294 @ X2295 @ X2297 @ ( esk63_4 @ X2294 @ X2295 @ X2296 @ X2297 ) ) )
        | ( X2296 = X2297 )
        | ~ ( in @ X2297 @ ( funcSet @ X2294 @ X2295 ) )
        | ~ ( in @ X2296 @ ( funcSet @ X2294 @ X2295 ) ) )
      & ( ~ ( in @ X2301 @ ( funcSet @ X2299 @ X2300 ) )
        | ~ ( in @ X2302 @ X2299 )
        | ( ( ap @ X2299 @ X2300 @ X2301 @ X2302 )
          = ( ap @ X2299 @ X2300 @ X2301 @ X2302 ) ) )
      & ( ~ ( func @ X2303 @ X2304 @ X2305 )
        | ~ ( in @ X2306 @ X2303 )
        | ( ( ap @ X2303 @ X2304 @ X2305 @ X2306 )
          = ( ap @ X2303 @ X2304 @ X2305 @ X2306 ) ) )
      & ( ( in @ ( esk64_3 @ X2307 @ X2308 @ X2309 ) @ X2307 )
        | ~ ( in @ X2311 @ X2307 )
        | ( ( ap @ X2307 @ X2308 @ ( lam @ X2307 @ X2308 @ X2309 ) @ X2311 )
          = ( X2309 @ X2311 ) ) )
      & ( ~ ( in @ ( X2309 @ ( esk64_3 @ X2307 @ X2308 @ X2309 ) ) @ X2308 )
        | ~ ( in @ X2311 @ X2307 )
        | ( ( ap @ X2307 @ X2308 @ ( lam @ X2307 @ X2308 @ X2309 ) @ X2311 )
          = ( X2309 @ X2311 ) ) )
      & ( ~ ( func @ X2312 @ X2313 @ X2314 )
        | ( ( lam @ X2312 @ X2313 @ ( ap @ X2312 @ X2313 @ X2314 ) )
          = X2314 ) )
      & ( ( in @ ( esk65_3 @ X2315 @ X2316 @ X2317 ) @ X2315 )
        | ( ( lam @ X2315 @ X2316 @ X2317 )
          = ( lam @ X2315 @ X2316 @ X2317 ) ) )
      & ( ~ ( in @ ( X2317 @ ( esk65_3 @ X2315 @ X2316 @ X2317 ) ) @ X2316 )
        | ( ( lam @ X2315 @ X2316 @ X2317 )
          = ( lam @ X2315 @ X2316 @ X2317 ) ) )
      & ( ( in @ ( esk66_3 @ X2319 @ X2320 @ X2321 ) @ X2319 )
        | ~ ( in @ X2323 @ X2319 )
        | ( ( ap @ X2319 @ X2320 @ ( lam @ X2319 @ X2320 @ X2321 ) @ X2323 )
          = ( X2321 @ X2323 ) ) )
      & ( ~ ( in @ ( X2321 @ ( esk66_3 @ X2319 @ X2320 @ X2321 ) ) @ X2320 )
        | ~ ( in @ X2323 @ X2319 )
        | ( ( ap @ X2319 @ X2320 @ ( lam @ X2319 @ X2320 @ X2321 ) @ X2323 )
          = ( X2321 @ X2323 ) ) )
      & ( ~ ( in @ X2326 @ ( funcSet @ X2324 @ X2325 ) )
        | ( ( lam @ X2324 @ X2325 @ ( ap @ X2324 @ X2325 @ X2326 ) )
          = X2326 ) )
      & ( ~ ( in @ X2329 @ X2327 )
        | ~ ( in @ X2330 @ X2327 )
        | X2328
        | ( in @ X2330
          @ ( dsetconstr @ X2327
            @ ^ [Z0: $i] :
                ( ( X2328
                  & ( Z0 = X2329 ) )
                | ( ~ X2328
                  & ( Z0 = X2330 ) ) ) ) ) )
      & ( ~ ( in @ X2333 @ X2331 )
        | ~ ( in @ X2334 @ X2331 )
        | X2332
        | ( ( dsetconstr @ X2331
            @ ^ [Z0: $i] :
                ( ( X2332
                  & ( Z0 = X2333 ) )
                | ( ~ X2332
                  & ( Z0 = X2334 ) ) ) )
          = ( setadjoin @ X2334 @ emptyset ) ) )
      & ( ~ ( in @ X2337 @ X2335 )
        | ~ ( in @ X2338 @ X2335 )
        | ~ X2336
        | ( in @ X2337
          @ ( dsetconstr @ X2335
            @ ^ [Z0: $i] :
                ( ( X2336
                  & ( Z0 = X2337 ) )
                | ( ~ X2336
                  & ( Z0 = X2338 ) ) ) ) ) )
      & ( ~ ( in @ X2341 @ X2339 )
        | ~ ( in @ X2342 @ X2339 )
        | ~ X2340
        | ( ( dsetconstr @ X2339
            @ ^ [Z0: $i] :
                ( ( X2340
                  & ( Z0 = X2341 ) )
                | ( ~ X2340
                  & ( Z0 = X2342 ) ) ) )
          = ( setadjoin @ X2341 @ emptyset ) ) )
      & ( ~ ( in @ X2345 @ X2343 )
        | ~ ( in @ X2346 @ X2343 )
        | ( singleton
          @ ( dsetconstr @ X2343
            @ ^ [Z0: $i] :
                ( ( X2344
                  & ( Z0 = X2345 ) )
                | ( ~ X2344
                  & ( Z0 = X2346 ) ) ) ) ) )
      & ( ~ ( in @ X2349 @ X2347 )
        | ~ ( in @ X2350 @ X2347 )
        | ( in @ ( if @ X2347 @ X2348 @ X2349 @ X2350 ) @ X2347 ) )
      & ( ~ ( singleton @ X2351 )
        | ~ ( in @ X2352 @ X2351 )
        | ( ( setunion @ X2351 )
          = X2352 ) )
      & ( ~ ( in @ X2355 @ X2353 )
        | ~ ( in @ X2356 @ X2353 )
        | ~ X2354
        | ( ( if @ X2353 @ X2354 @ X2355 @ X2356 )
          = X2355 ) )
      & ( ~ ( in @ X2359 @ X2357 )
        | ~ ( in @ X2360 @ X2357 )
        | X2358
        | ( ( if @ X2357 @ X2358 @ X2359 @ X2360 )
          = X2360 ) )
      & ( ~ ( in @ X2363 @ X2361 )
        | ~ ( in @ X2364 @ X2361 )
        | ( in @ ( if @ X2361 @ X2362 @ X2363 @ X2364 ) @ ( setadjoin @ X2363 @ ( setadjoin @ X2364 @ emptyset ) ) ) )
      & ( ~ ( in @ X2366 @ ( powerset @ X2365 ) )
        | ~ ( in @ X2367 @ ( powerset @ X2365 ) )
        | ( in @ ( binintersect @ X2366 @ X2367 ) @ ( powerset @ X2365 ) ) )
      & ( ~ ( in @ X2369 @ ( powerset @ X2368 ) )
        | ~ ( in @ X2370 @ ( powerset @ X2368 ) )
        | ( in @ ( binunion @ X2369 @ X2370 ) @ ( powerset @ X2368 ) ) )
      & ( ~ ( in @ X2372 @ ( powerset @ X2371 ) )
        | ( in @ ( powerset @ X2372 ) @ ( powerset @ ( powerset @ X2371 ) ) ) )
      & ( ~ ( in @ X2374 @ ( powerset @ X2373 ) )
        | ~ ( in @ X2375 @ ( powerset @ X2373 ) )
        | ( in @ ( setminus @ X2374 @ X2375 ) @ ( powerset @ X2373 ) ) )
      & ( ~ ( in @ X2377 @ ( powerset @ X2376 ) )
        | ( in @ ( setminus @ X2376 @ X2377 ) @ ( powerset @ X2376 ) ) )
      & ( ( in @ ( esk68_3 @ X2378 @ X2379 @ X2380 ) @ X2378 )
        | ( X2379 = X2380 )
        | ( in @ ( esk67_3 @ X2378 @ X2379 @ X2380 ) @ X2378 )
        | ~ ( in @ X2380 @ ( powerset @ X2378 ) )
        | ~ ( in @ X2379 @ ( powerset @ X2378 ) ) )
      & ( ( in @ ( esk68_3 @ X2378 @ X2379 @ X2380 ) @ X2380 )
        | ( X2379 = X2380 )
        | ( in @ ( esk67_3 @ X2378 @ X2379 @ X2380 ) @ X2378 )
        | ~ ( in @ X2380 @ ( powerset @ X2378 ) )
        | ~ ( in @ X2379 @ ( powerset @ X2378 ) ) )
      & ( ~ ( in @ ( esk68_3 @ X2378 @ X2379 @ X2380 ) @ X2379 )
        | ( X2379 = X2380 )
        | ( in @ ( esk67_3 @ X2378 @ X2379 @ X2380 ) @ X2378 )
        | ~ ( in @ X2380 @ ( powerset @ X2378 ) )
        | ~ ( in @ X2379 @ ( powerset @ X2378 ) ) )
      & ( ( in @ ( esk68_3 @ X2378 @ X2379 @ X2380 ) @ X2378 )
        | ( X2379 = X2380 )
        | ( in @ ( esk67_3 @ X2378 @ X2379 @ X2380 ) @ X2379 )
        | ~ ( in @ X2380 @ ( powerset @ X2378 ) )
        | ~ ( in @ X2379 @ ( powerset @ X2378 ) ) )
      & ( ( in @ ( esk68_3 @ X2378 @ X2379 @ X2380 ) @ X2380 )
        | ( X2379 = X2380 )
        | ( in @ ( esk67_3 @ X2378 @ X2379 @ X2380 ) @ X2379 )
        | ~ ( in @ X2380 @ ( powerset @ X2378 ) )
        | ~ ( in @ X2379 @ ( powerset @ X2378 ) ) )
      & ( ~ ( in @ ( esk68_3 @ X2378 @ X2379 @ X2380 ) @ X2379 )
        | ( X2379 = X2380 )
        | ( in @ ( esk67_3 @ X2378 @ X2379 @ X2380 ) @ X2379 )
        | ~ ( in @ X2380 @ ( powerset @ X2378 ) )
        | ~ ( in @ X2379 @ ( powerset @ X2378 ) ) )
      & ( ( in @ ( esk68_3 @ X2378 @ X2379 @ X2380 ) @ X2378 )
        | ( X2379 = X2380 )
        | ~ ( in @ ( esk67_3 @ X2378 @ X2379 @ X2380 ) @ X2380 )
        | ~ ( in @ X2380 @ ( powerset @ X2378 ) )
        | ~ ( in @ X2379 @ ( powerset @ X2378 ) ) )
      & ( ( in @ ( esk68_3 @ X2378 @ X2379 @ X2380 ) @ X2380 )
        | ( X2379 = X2380 )
        | ~ ( in @ ( esk67_3 @ X2378 @ X2379 @ X2380 ) @ X2380 )
        | ~ ( in @ X2380 @ ( powerset @ X2378 ) )
        | ~ ( in @ X2379 @ ( powerset @ X2378 ) ) )
      & ( ~ ( in @ ( esk68_3 @ X2378 @ X2379 @ X2380 ) @ X2379 )
        | ( X2379 = X2380 )
        | ~ ( in @ ( esk67_3 @ X2378 @ X2379 @ X2380 ) @ X2380 )
        | ~ ( in @ X2380 @ ( powerset @ X2378 ) )
        | ~ ( in @ X2379 @ ( powerset @ X2378 ) ) )
      & ( ( in @ ( esk69_3 @ X2383 @ X2384 @ X2385 ) @ X2383 )
        | ( subset @ X2384 @ X2385 )
        | ~ ( in @ X2385 @ ( powerset @ X2383 ) )
        | ~ ( in @ X2384 @ ( powerset @ X2383 ) ) )
      & ( ( in @ ( esk69_3 @ X2383 @ X2384 @ X2385 ) @ X2384 )
        | ( subset @ X2384 @ X2385 )
        | ~ ( in @ X2385 @ ( powerset @ X2383 ) )
        | ~ ( in @ X2384 @ ( powerset @ X2383 ) ) )
      & ( ~ ( in @ ( esk69_3 @ X2383 @ X2384 @ X2385 ) @ X2385 )
        | ( subset @ X2384 @ X2385 )
        | ~ ( in @ X2385 @ ( powerset @ X2383 ) )
        | ~ ( in @ X2384 @ ( powerset @ X2383 ) ) )
      & ( ( in @ ( esk70_3 @ X2387 @ X2388 @ X2389 ) @ X2387 )
        | ( in @ X2388 @ ( powerset @ X2389 ) )
        | ~ ( in @ X2389 @ ( powerset @ X2387 ) )
        | ~ ( in @ X2388 @ ( powerset @ X2387 ) ) )
      & ( ( in @ ( esk70_3 @ X2387 @ X2388 @ X2389 ) @ X2388 )
        | ( in @ X2388 @ ( powerset @ X2389 ) )
        | ~ ( in @ X2389 @ ( powerset @ X2387 ) )
        | ~ ( in @ X2388 @ ( powerset @ X2387 ) ) )
      & ( ~ ( in @ ( esk70_3 @ X2387 @ X2388 @ X2389 ) @ X2389 )
        | ( in @ X2388 @ ( powerset @ X2389 ) )
        | ~ ( in @ X2389 @ ( powerset @ X2387 ) )
        | ~ ( in @ X2388 @ ( powerset @ X2387 ) ) )
      & ( ~ ( in @ X2392 @ ( powerset @ X2391 ) )
        | ~ ( in @ X2393 @ ( powerset @ X2391 ) )
        | ~ ( in @ X2394 @ X2391 )
        | ~ ( in @ X2392 @ ( powerset @ X2393 ) )
        | ~ ( in @ X2394 @ X2392 )
        | ( in @ X2394 @ X2393 ) )
      & ( ~ ( in @ X2396 @ ( powerset @ X2395 ) )
        | ~ ( in @ X2397 @ X2395 )
        | ~ ( in @ X2397 @ X2396 )
        | ~ ( in @ X2397 @ ( setminus @ X2395 @ X2396 ) ) )
      & ( ~ ( in @ X2399 @ ( powerset @ X2398 ) )
        | ~ ( in @ X2400 @ X2398 )
        | ( in @ X2400 @ ( setminus @ X2398 @ X2399 ) )
        | ( in @ X2400 @ X2399 ) )
      & ( ~ ( in @ X2402 @ ( powerset @ X2401 ) )
        | ~ ( in @ X2403 @ ( powerset @ X2401 ) )
        | ~ ( in @ X2404 @ X2401 )
        | ( in @ X2404 @ X2402 )
        | ~ ( in @ X2404 @ ( binintersect @ X2402 @ X2403 ) ) )
      & ( ~ ( in @ X2406 @ ( powerset @ X2405 ) )
        | ~ ( in @ X2407 @ ( powerset @ X2405 ) )
        | ~ ( in @ X2408 @ X2405 )
        | ( in @ X2408 @ X2407 )
        | ~ ( in @ X2408 @ ( binintersect @ X2406 @ X2407 ) ) )
      & ( ~ ( in @ X2410 @ ( powerset @ X2409 ) )
        | ~ ( in @ X2411 @ ( powerset @ X2409 ) )
        | ~ ( in @ X2412 @ X2409 )
        | ~ ( subset @ X2410 @ ( setminus @ X2409 @ X2411 ) )
        | ~ ( in @ X2412 @ X2411 )
        | ~ ( in @ X2412 @ X2410 ) )
      & ( ~ ( in @ X2414 @ ( powerset @ X2413 ) )
        | ~ ( in @ X2415 @ ( powerset @ X2413 ) )
        | ~ ( in @ X2416 @ X2413 )
        | ~ ( subset @ X2414 @ X2415 )
        | ( in @ X2416 @ X2415 )
        | ~ ( in @ X2416 @ X2414 ) )
      & ( ~ ( in @ X2418 @ ( powerset @ X2417 ) )
        | ~ ( in @ X2419 @ ( powerset @ X2417 ) )
        | ~ ( subset @ X2418 @ X2419 )
        | ( subset @ ( setminus @ X2417 @ X2419 ) @ ( setminus @ X2417 @ X2418 ) ) )
      & ( ~ ( in @ X2421 @ ( powerset @ X2420 ) )
        | ~ ( in @ X2422 @ ( powerset @ X2420 ) )
        | ~ ( subset @ ( setminus @ X2420 @ X2422 ) @ ( setminus @ X2420 @ X2421 ) )
        | ( subset @ X2421 @ X2422 ) )
      & ( ~ ( in @ X2424 @ ( powerset @ X2423 ) )
        | ~ ( in @ X2425 @ X2423 )
        | ~ ( in @ X2425 @ X2424 )
        | ( in @ X2425 @ ( setminus @ X2423 @ ( setminus @ X2423 @ X2424 ) ) ) )
      & ( ~ ( in @ X2427 @ ( powerset @ X2426 ) )
        | ~ ( in @ X2428 @ X2426 )
        | ~ ( in @ X2428 @ ( setminus @ X2426 @ ( setminus @ X2426 @ X2427 ) ) )
        | ( in @ X2428 @ X2427 ) )
      & ( ~ ( in @ X2430 @ ( powerset @ X2429 ) )
        | ( subset @ X2430 @ ( setminus @ X2429 @ ( setminus @ X2429 @ X2430 ) ) ) )
      & ( ~ ( in @ X2432 @ ( powerset @ X2431 ) )
        | ( subset @ ( setminus @ X2431 @ ( setminus @ X2431 @ X2432 ) ) @ X2432 ) )
      & ( ~ ( in @ X2434 @ ( powerset @ X2433 ) )
        | ( X2434
          = ( setminus @ X2433 @ ( setminus @ X2433 @ X2434 ) ) ) )
      & ( ~ ( in @ X2436 @ ( powerset @ X2435 ) )
        | ~ ( in @ X2437 @ ( powerset @ X2435 ) )
        | ~ ( in @ X2438 @ X2435 )
        | ~ ( in @ X2438 @ ( setminus @ X2435 @ X2436 ) )
        | ~ ( in @ X2438 @ ( binintersect @ X2436 @ X2437 ) ) )
      & ( ~ ( in @ X2440 @ ( powerset @ X2439 ) )
        | ~ ( in @ X2441 @ ( powerset @ X2439 ) )
        | ~ ( in @ X2442 @ X2439 )
        | ~ ( in @ X2442 @ ( setminus @ X2439 @ X2440 ) )
        | ( in @ X2442 @ ( setminus @ X2439 @ ( binintersect @ X2440 @ X2441 ) ) ) )
      & ( ~ ( in @ X2444 @ ( powerset @ X2443 ) )
        | ~ ( in @ X2445 @ ( powerset @ X2443 ) )
        | ( subset @ ( setminus @ X2443 @ X2444 ) @ ( setminus @ X2443 @ ( binintersect @ X2444 @ X2445 ) ) ) )
      & ( ~ ( in @ X2447 @ ( powerset @ X2446 ) )
        | ~ ( in @ X2448 @ ( powerset @ X2446 ) )
        | ( in @ ( setminus @ X2446 @ X2447 ) @ ( powerset @ ( setminus @ X2446 @ ( binintersect @ X2447 @ X2448 ) ) ) ) )
      & ( ~ ( in @ X2450 @ ( powerset @ X2449 ) )
        | ~ ( in @ X2451 @ ( powerset @ X2449 ) )
        | ~ ( subset @ X2450 @ ( setminus @ X2449 @ X2451 ) )
        | ~ ( in @ X2452 @ X2449 )
        | ~ ( in @ X2452 @ X2451 )
        | ( in @ X2452 @ ( setminus @ X2449 @ X2450 ) ) )
      & ( ~ ( in @ X2454 @ ( powerset @ X2453 ) )
        | ~ ( in @ X2455 @ ( powerset @ X2453 ) )
        | ~ ( subset @ X2454 @ ( setminus @ X2453 @ X2455 ) )
        | ( subset @ X2455 @ ( setminus @ X2453 @ X2454 ) ) )
      & ( ~ ( in @ X2457 @ ( powerset @ X2456 ) )
        | ~ ( in @ X2458 @ ( powerset @ X2456 ) )
        | ~ ( in @ X2459 @ X2456 )
        | ( in @ X2459 @ ( binunion @ X2457 @ X2458 ) )
        | ~ ( in @ X2459 @ X2457 ) )
      & ( ~ ( in @ X2461 @ ( powerset @ X2460 ) )
        | ~ ( in @ X2462 @ ( powerset @ X2460 ) )
        | ~ ( in @ X2463 @ X2460 )
        | ( in @ X2463 @ ( binunion @ X2461 @ X2462 ) )
        | ~ ( in @ X2463 @ X2462 ) )
      & ( ~ ( in @ X2465 @ ( powerset @ X2464 ) )
        | ~ ( in @ X2466 @ ( powerset @ X2464 ) )
        | ~ ( in @ X2467 @ ( powerset @ X2464 ) )
        | ~ ( in @ X2468 @ X2464 )
        | ~ ( in @ X2468 @ ( binintersect @ X2465 @ X2466 ) )
        | ( in @ X2468 @ ( binunion @ X2465 @ X2467 ) ) )
      & ( ~ ( in @ X2470 @ ( powerset @ X2469 ) )
        | ~ ( in @ X2471 @ ( powerset @ X2469 ) )
        | ~ ( in @ X2472 @ ( powerset @ X2469 ) )
        | ~ ( in @ X2473 @ X2469 )
        | ~ ( in @ X2473 @ ( binintersect @ X2470 @ X2471 ) )
        | ( in @ X2473 @ ( binunion @ X2471 @ X2472 ) ) )
      & ( ~ ( in @ X2475 @ ( powerset @ X2474 ) )
        | ~ ( in @ X2476 @ ( powerset @ X2474 ) )
        | ~ ( in @ X2477 @ ( powerset @ X2474 ) )
        | ~ ( in @ X2478 @ X2474 )
        | ~ ( in @ X2478 @ ( binintersect @ X2475 @ X2476 ) )
        | ( in @ X2478 @ ( binintersect @ ( binunion @ X2475 @ X2477 ) @ ( binunion @ X2476 @ X2477 ) ) ) )
      & ( ~ ( in @ X2480 @ ( powerset @ X2479 ) )
        | ~ ( in @ X2481 @ ( powerset @ X2479 ) )
        | ~ ( in @ X2482 @ ( powerset @ X2479 ) )
        | ( in @ ( binintersect @ X2480 @ X2481 ) @ ( powerset @ ( binintersect @ ( binunion @ X2480 @ X2482 ) @ ( binunion @ X2481 @ X2482 ) ) ) ) )
      & ( in @ esk72_0 @ ( powerset @ esk71_0 ) )
      & ( in @ esk73_0 @ ( powerset @ esk71_0 ) )
      & ( in @ esk74_0 @ esk71_0 )
      & ( in @ esk74_0 @ ( setminus @ esk71_0 @ ( binunion @ esk72_0 @ esk73_0 ) ) )
      & ( in @ esk74_0 @ esk72_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_312])])])])])])]) ).

thf(c_0_314,negated_conjecture,
    ! [X2: $i,X3: $i,X4: $i] :
      ( ~ ( in @ X2 @ ( setminus @ X3 @ X4 ) )
      | ~ ( in @ X2 @ X4 ) ),
    inference(split_conjunct,[status(thm)],[c_0_313]) ).

thf(c_0_315,negated_conjecture,
    in @ esk74_0 @ ( setminus @ esk71_0 @ ( binunion @ esk72_0 @ esk73_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_313]) ).

thf(c_0_316,negated_conjecture,
    ~ ( in @ esk74_0 @ ( binunion @ esk72_0 @ esk73_0 ) ),
    inference(spm,[status(thm)],[c_0_314,c_0_315]) ).

thf(c_0_317,negated_conjecture,
    ! [X2: $i,X4: $i,X3: $i] :
      ( ( in @ X2 @ ( binunion @ X3 @ X4 ) )
      | ~ ( in @ X2 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_313]) ).

thf(c_0_318,negated_conjecture,
    in @ esk74_0 @ esk72_0,
    inference(split_conjunct,[status(thm)],[c_0_313]) ).

thf(c_0_319,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_316,c_0_317]),c_0_318])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SEU744^1 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n018.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 16:25:53 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.20/0.47  Running higher-order theorem proving
% 0.20/0.47  Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 1.17/0.87  # Version: 3.1.0-ho
% 1.17/0.87  # Preprocessing class: HSLMSLSSLLLCHFA.
% 1.17/0.87  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.17/0.87  # Starting ehoh_best5 with 300s (1) cores
% 1.17/0.87  # Starting almost_fo_3_lam with 300s (1) cores
% 1.17/0.87  # Starting new_bool_5 with 300s (1) cores
% 1.17/0.87  # Starting pre_casc_3 with 300s (1) cores
% 1.17/0.87  # Starting ho_unfolding_8 with 300s (1) cores
% 1.17/0.87  # Starting new_ho_10_cnf2 with 300s (1) cores
% 1.17/0.87  # Starting new_bool_3 with 300s (1) cores
% 1.17/0.87  # Starting new_ho_5 with 300s (1) cores
% 1.17/0.87  # new_ho_5 with pid 30785 completed with status 8
% 1.17/0.87  # pre_casc_3 with pid 30781 completed with status 8
% 1.17/0.87  # new_bool_5 with pid 30780 completed with status 0
% 1.17/0.87  # Result found by new_bool_5
% 1.17/0.87  # Preprocessing class: HSLMSLSSLLLCHFA.
% 1.17/0.87  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.17/0.87  # Starting ehoh_best5 with 300s (1) cores
% 1.17/0.87  # Starting almost_fo_3_lam with 300s (1) cores
% 1.17/0.87  # Starting new_bool_5 with 300s (1) cores
% 1.17/0.87  # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 1.17/0.87  # Search class: HGHSM-FSLM32-MHFMMSBN
% 1.17/0.87  # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 1.17/0.87  # Starting ho_unfolding_8 with 55s (1) cores
% 1.17/0.87  # ho_unfolding_8 with pid 30801 completed with status 0
% 1.17/0.87  # Result found by ho_unfolding_8
% 1.17/0.87  # Preprocessing class: HSLMSLSSLLLCHFA.
% 1.17/0.87  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.17/0.87  # Starting ehoh_best5 with 300s (1) cores
% 1.17/0.87  # Starting almost_fo_3_lam with 300s (1) cores
% 1.17/0.87  # Starting new_bool_5 with 300s (1) cores
% 1.17/0.87  # SinE strategy is GSinE(CountFormulas,hypos,1.0,,1,20000,1.0)
% 1.17/0.87  # Search class: HGHSM-FSLM32-MHFMMSBN
% 1.17/0.87  # Scheduled 10 strats onto 1 cores with 300 seconds (300 total)
% 1.17/0.87  # Starting ho_unfolding_8 with 55s (1) cores
% 1.17/0.87  # Preprocessing time       : 0.046 s
% 1.17/0.87  # Presaturation interreduction done
% 1.17/0.87  
% 1.17/0.87  # Proof found!
% 1.17/0.87  # SZS status Theorem
% 1.17/0.87  # SZS output start CNFRefutation
% See solution above
% 1.17/0.87  # Parsed axioms                        : 563
% 1.17/0.87  # Removed by relevancy pruning/SinE    : 303
% 1.17/0.87  # Initial clauses                      : 422
% 1.17/0.87  # Removed in clause preprocessing      : 34
% 1.17/0.87  # Initial clauses in saturation        : 388
% 1.17/0.87  # Processed clauses                    : 751
% 1.17/0.87  # ...of these trivial                  : 9
% 1.17/0.87  # ...subsumed                          : 39
% 1.17/0.87  # ...remaining for further processing  : 703
% 1.17/0.87  # Other redundant clauses eliminated   : 54
% 1.17/0.87  # Clauses deleted for lack of memory   : 0
% 1.17/0.87  # Backward-subsumed                    : 0
% 1.17/0.87  # Backward-rewritten                   : 3
% 1.17/0.87  # Generated clauses                    : 7852
% 1.17/0.87  # ...of the previous two non-redundant : 7614
% 1.17/0.87  # ...aggressively subsumed             : 0
% 1.17/0.87  # Contextual simplify-reflections      : 6
% 1.17/0.87  # Paramodulations                      : 7763
% 1.17/0.87  # Factorizations                       : 2
% 1.17/0.87  # NegExts                              : 0
% 1.17/0.87  # Equation resolutions                 : 61
% 1.17/0.87  # Disequality decompositions           : 0
% 1.17/0.87  # Total rewrite steps                  : 201
% 1.17/0.87  # ...of those cached                   : 134
% 1.17/0.87  # Propositional unsat checks           : 0
% 1.17/0.87  #    Propositional check models        : 0
% 1.17/0.87  #    Propositional check unsatisfiable : 0
% 1.17/0.87  #    Propositional clauses             : 0
% 1.17/0.87  #    Propositional clauses after purity: 0
% 1.17/0.87  #    Propositional unsat core size     : 0
% 1.17/0.87  #    Propositional preprocessing time  : 0.000
% 1.17/0.87  #    Propositional encoding time       : 0.000
% 1.17/0.87  #    Propositional solver time         : 0.000
% 1.17/0.87  #    Success case prop preproc time    : 0.000
% 1.17/0.87  #    Success case prop encoding time   : 0.000
% 1.17/0.87  #    Success case prop solver time     : 0.000
% 1.17/0.87  # Current number of processed clauses  : 345
% 1.17/0.87  #    Positive orientable unit clauses  : 44
% 1.17/0.87  #    Positive unorientable unit clauses: 0
% 1.17/0.87  #    Negative unit clauses             : 3
% 1.17/0.87  #    Non-unit-clauses                  : 298
% 1.17/0.87  # Current number of unprocessed clauses: 7587
% 1.17/0.87  # ...number of literals in the above   : 32152
% 1.17/0.87  # Current number of archived formulas  : 0
% 1.17/0.87  # Current number of archived clauses   : 342
% 1.17/0.87  # Clause-clause subsumption calls (NU) : 53344
% 1.17/0.87  # Rec. Clause-clause subsumption calls : 22645
% 1.17/0.87  # Non-unit clause-clause subsumptions  : 38
% 1.17/0.87  # Unit Clause-clause subsumption calls : 1063
% 1.17/0.87  # Rewrite failures with RHS unbound    : 0
% 1.17/0.87  # BW rewrite match attempts            : 33
% 1.17/0.87  # BW rewrite match successes           : 2
% 1.17/0.87  # Condensation attempts                : 0
% 1.17/0.87  # Condensation successes               : 0
% 1.17/0.87  # Termbank termtop insertions          : 204560
% 1.17/0.87  # Search garbage collected termcells   : 26022
% 1.17/0.87  
% 1.17/0.87  # -------------------------------------------------
% 1.17/0.87  # User time                : 0.320 s
% 1.17/0.87  # System time              : 0.026 s
% 1.17/0.87  # Total time               : 0.346 s
% 1.17/0.87  # Maximum resident set size: 8292 pages
% 1.17/0.87  
% 1.17/0.87  # -------------------------------------------------
% 1.17/0.87  # User time                : 0.551 s
% 1.17/0.87  # System time              : 0.095 s
% 1.17/0.87  # Total time               : 0.645 s
% 1.17/0.87  # Maximum resident set size: 2492 pages
% 1.17/0.87  % E---3.1 exiting
% 1.17/0.87  % E exiting
%------------------------------------------------------------------------------