TSTP Solution File: SEU787^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SEU787^1 : 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 03:30:14 EDT 2024

% Result   : Theorem 1.44s 0.78s
% Output   : CNFRefutation 1.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  747
% Syntax   : Number of formulae    :  827 (  25 unt; 442 typ;   0 def)
%            Number of atoms       : 4250 ( 640 equ;   0 cnn)
%            Maximal formula atoms : 1423 (  11 avg)
%            Number of connectives : 17588 (1207   ~;1308   |; 662   &;11888   @)
%                                         ( 396 <=>;2127  =>;   0  <=;   0 <~>)
%            Maximal formula depth : 1431 (  15 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  651 ( 651   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  446 ( 442 usr; 315 con; 0-6 aty)
%            Number of variables   : 3366 ( 168   ^3075   !; 123   ?;3366   :)

% 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,
    inComplementUnionImpNotIn1: $o ).

thf(decl_321,type,
    inComplementUnionImpInComplement1: $o ).

thf(decl_322,type,
    binunionTE: $o ).

thf(decl_323,type,
    binunionTEcontra: $o ).

thf(decl_324,type,
    demorgan2a1: $o ).

thf(decl_325,type,
    complementUnionInPowersetComplement: $o ).

thf(decl_326,type,
    demorgan2a2: $o ).

thf(decl_327,type,
    demorgan1a: $o ).

thf(decl_328,type,
    demorgan1b: $o ).

thf(decl_329,type,
    demorgan1: $o ).

thf(decl_330,type,
    demorgan2a: $o ).

thf(decl_331,type,
    demorgan2b2: $o ).

thf(decl_332,type,
    demorgan2b: $o ).

thf(decl_333,type,
    demorgan2: $o ).

thf(decl_334,type,
    woz13rule0: $o ).

thf(decl_335,type,
    woz13rule1: $o ).

thf(decl_336,type,
    woz13rule2: $o ).

thf(decl_337,type,
    woz13rule3: $o ).

thf(decl_338,type,
    woz13rule4: $o ).

thf(decl_339,type,
    woz1_1: $o ).

thf(decl_340,type,
    woz1_2: $o ).

thf(decl_341,type,
    woz1_3: $o ).

thf(decl_342,type,
    woz1_4: $o ).

thf(decl_343,type,
    woz1_5: $o ).

thf(decl_344,type,
    breln1: $i > $i > $o ).

thf(decl_345,type,
    breln1all2: $o ).

thf(decl_346,type,
    breln1Set: $i > $i ).

thf(decl_347,type,
    breln1SetBreln1: $o ).

thf(decl_354,type,
    choice2fnsingleton: $o ).

thf(decl_355,type,
    setOfPairsIsBReln1: $o ).

thf(decl_356,type,
    breln1all1: $o ).

thf(decl_357,type,
    subbreln1: $o ).

thf(decl_358,type,
    eqbreln1: $o ).

thf(decl_359,type,
    breln1invset: $i > $i > $i ).

thf(decl_360,type,
    breln1invprop: $o ).

thf(decl_361,type,
    breln1invI: $o ).

thf(decl_362,type,
    breln1invE: $o ).

thf(decl_363,type,
    breln1compset: $i > $i > $i > $i ).

thf(decl_364,type,
    breln1compprop: $o ).

thf(decl_365,type,
    breln1compI: $o ).

thf(decl_366,type,
    breln1compE: $o ).

thf(decl_367,type,
    breln1compEex: $o ).

thf(decl_368,type,
    breln1unionprop: $o ).

thf(decl_369,type,
    breln1unionIL: $o ).

thf(decl_370,type,
    breln1unionIR: $o ).

thf(decl_371,type,
    breln1unionI: $o ).

thf(decl_372,type,
    breln1unionE: $o ).

thf(decl_373,type,
    epred1_0: $o ).

thf(decl_374,type,
    esk1_2: $i > $i > $i ).

thf(decl_375,type,
    esk2_2: $i > $i > $i ).

thf(decl_376,type,
    esk3_2: $i > $i > $i ).

thf(decl_377,type,
    esk4_1: $i > $i ).

thf(decl_378,type,
    esk5_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_379,type,
    esk6_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_380,type,
    esk7_2: ( $i > $i > $o ) > $i > $i ).

thf(decl_381,type,
    esk8_3: ( $i > $i > $o ) > $i > $i > $i ).

thf(decl_382,type,
    esk9_1: $i > $i ).

thf(decl_383,type,
    esk10_2: ( $i > $o ) > $i > $i ).

thf(decl_384,type,
    esk11_2: ( $i > $o ) > $i > $i ).

thf(decl_385,type,
    esk12_1: ( $i > $o ) > $i ).

thf(decl_386,type,
    esk13_2: ( $i > $o ) > $i > $i ).

thf(decl_387,type,
    esk14_1: ( $i > $o ) > $i ).

thf(decl_388,type,
    esk15_2: $i > $i > $i ).

thf(decl_389,type,
    esk16_2: $i > $i > $i ).

thf(decl_390,type,
    esk17_1: $i > $i ).

thf(decl_391,type,
    esk18_1: $i > $i ).

thf(decl_392,type,
    esk19_1: $i > $i ).

thf(decl_393,type,
    esk20_2: $i > $i > $i ).

thf(decl_394,type,
    esk21_3: $i > $i > $o > $i ).

thf(decl_395,type,
    esk22_2: ( $i > $o ) > $i > $i ).

thf(decl_396,type,
    esk23_1: ( $i > $o ) > $i ).

thf(decl_397,type,
    esk24_1: $i > $i ).

thf(decl_398,type,
    esk25_2: $i > ( $i > $o ) > $i ).

thf(decl_399,type,
    esk26_2: $i > ( $i > $o ) > $i ).

thf(decl_400,type,
    esk27_2: $i > ( $i > $o ) > $i ).

thf(decl_401,type,
    esk28_2: $i > ( $i > $o ) > $i ).

thf(decl_402,type,
    esk29_2: $i > ( $i > $o ) > $i ).

thf(decl_403,type,
    esk30_2: $i > ( $i > $o ) > $i ).

thf(decl_404,type,
    esk31_2: ( $i > $o ) > $i > $i ).

thf(decl_405,type,
    esk32_1: ( $i > $o ) > $i ).

thf(decl_406,type,
    esk33_1: ( $i > $o ) > $i ).

thf(decl_407,type,
    esk34_1: ( $i > $o ) > $i ).

thf(decl_408,type,
    esk35_1: ( $i > $o ) > $i ).

thf(decl_409,type,
    esk36_2: ( $i > $o ) > $i > $i ).

thf(decl_410,type,
    esk37_1: ( $i > $o ) > $i ).

thf(decl_411,type,
    esk38_2: ( $i > $o ) > $i > $i ).

thf(decl_412,type,
    esk39_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_413,type,
    esk40_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_414,type,
    esk41_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_415,type,
    esk42_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_416,type,
    esk43_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_417,type,
    esk44_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_418,type,
    esk45_2: ( $i > $o ) > $i > $i ).

thf(decl_419,type,
    esk46_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_420,type,
    esk47_2: ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_421,type,
    esk48_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_422,type,
    esk49_3: ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(decl_423,type,
    esk50_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_424,type,
    esk51_4: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(decl_425,type,
    esk52_2: $i > $i > $i ).

thf(decl_426,type,
    esk53_2: $i > $i > $i ).

thf(decl_427,type,
    esk54_2: $i > $i > $i ).

thf(decl_428,type,
    esk55_3: $i > $i > $i > $i ).

thf(decl_429,type,
    esk56_3: $i > $i > $i > $i ).

thf(decl_430,type,
    esk57_2: $i > $i > $i ).

thf(decl_431,type,
    esk58_2: $i > ( $i > $o ) > $i ).

thf(decl_432,type,
    esk59_2: $i > ( $i > $o ) > $i ).

thf(decl_433,type,
    esk60_2: $i > ( $i > $o ) > $i ).

thf(decl_434,type,
    esk61_3: $i > ( $i > $o ) > $i > $i ).

thf(decl_435,type,
    esk62_2: $i > ( $i > $o ) > $i ).

thf(decl_436,type,
    esk63_2: $i > ( $i > $o ) > $i ).

thf(decl_437,type,
    esk64_3: $i > $i > ( $i > $i ) > $i ).

thf(decl_438,type,
    esk65_3: $i > $i > ( $i > $i ) > $i ).

thf(decl_439,type,
    esk66_3: $i > $i > ( $i > $i ) > $i ).

thf(decl_440,type,
    esk67_4: $i > $i > $i > ( $i > $o ) > $i ).

thf(decl_441,type,
    esk68_4: $i > $i > $i > ( $i > $o ) > $i ).

thf(decl_442,type,
    esk69_4: $i > $i > $i > ( $i > $o ) > $i ).

thf(decl_443,type,
    esk70_4: $i > $i > $i > ( $i > $o ) > $i ).

thf(decl_444,type,
    esk71_4: $i > $i > $i > $i > $i ).

thf(decl_445,type,
    esk72_4: $i > $i > $i > $i > $i ).

thf(decl_446,type,
    esk73_4: $i > $i > $i > $i > $i ).

thf(decl_447,type,
    esk74_4: $i > $i > $i > $i > $i ).

thf(decl_448,type,
    esk75_4: $i > $i > $i > $i > $i ).

thf(decl_449,type,
    esk76_4: $i > $i > $i > $i > $i ).

thf(decl_450,type,
    esk77_4: $i > $i > $i > $i > $i ).

thf(decl_451,type,
    esk78_4: $i > $i > $i > $i > $i ).

thf(decl_452,type,
    esk79_4: $i > $i > $i > $i > $i ).

thf(decl_453,type,
    esk80_3: $i > $i > ( $i > $i ) > $i ).

thf(decl_454,type,
    esk81_3: $i > $i > ( $i > $i ) > $i ).

thf(decl_455,type,
    esk82_3: $i > $i > ( $i > $i ) > $i ).

thf(decl_456,type,
    esk83_3: $i > $i > $i > $i ).

thf(decl_457,type,
    esk84_3: $i > $i > $i > $i ).

thf(decl_458,type,
    esk85_3: $i > $i > $i > $i ).

thf(decl_459,type,
    esk86_3: $i > $i > $i > $i ).

thf(decl_460,type,
    esk87_3: $i > $i > ( $i > $o ) > $i ).

thf(decl_461,type,
    esk88_3: $i > $i > ( $i > $o ) > $i ).

thf(decl_462,type,
    esk89_3: $i > $i > ( $i > $o ) > $i ).

thf(decl_463,type,
    esk90_3: $i > $i > ( $i > $o ) > $i ).

thf(decl_464,type,
    esk91_3: $i > $i > $i > $i ).

thf(decl_465,type,
    esk92_3: $i > $i > $i > $i ).

thf(decl_466,type,
    esk93_3: $i > $i > $i > $i ).

thf(decl_467,type,
    esk94_3: $i > $i > $i > $i ).

thf(decl_468,type,
    esk95_3: $i > $i > $i > $i ).

thf(decl_469,type,
    esk96_3: $i > $i > $i > $i ).

thf(decl_470,type,
    esk97_5: $i > $i > $i > $i > $i > $i ).

thf(decl_471,type,
    esk98_6: $i > $i > $i > $i > $i > $o > $i ).

thf(decl_472,type,
    esk99_0: $i ).

thf(decl_473,type,
    esk100_0: $i ).

thf(decl_474,type,
    esk101_0: $i ).

thf(decl_475,type,
    esk102_0: $i ).

thf(decl_476,type,
    esk103_0: $i ).

thf(decl_477,type,
    epred2_0: $o ).

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

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

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

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

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(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(setOfPairsIsBReln1,axiom,
    ( setOfPairsIsBReln1
  <=> ! [X4: $i,X53: $i > $i > $o] :
        ( breln1 @ X4
        @ ( dpsetconstr @ X4 @ X4
          @ ^ [X2: $i,X3: $i] : ( X53 @ X2 @ X3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setOfPairsIsBReln1) ).

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

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

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(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(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(breln1unionEcases,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
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( inComplementUnionImpNotIn1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( inComplementUnionImpInComplement1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( binunionTE
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( binunionTEcontra
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( demorgan2a1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( complementUnionInPowersetComplement
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( demorgan2a2
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( demorgan1a
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( demorgan1b
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( demorgan1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( demorgan2a
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( demorgan2b2
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( demorgan2b
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( demorgan2
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( woz13rule0
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( woz13rule1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( woz13rule2
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( woz13rule3
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( woz13rule4
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( woz1_1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( woz1_2
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( woz1_3
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( woz1_4
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( woz1_5
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( breln1all2
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( breln1SetBreln1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( choice2fnsingleton
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( setOfPairsIsBReln1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( breln1all1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( subbreln1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( eqbreln1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( breln1invprop
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( breln1invI
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( breln1invE
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( breln1compprop
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( breln1compI
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( breln1compE
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( breln1compEex
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( breln1unionprop
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( breln1unionIL
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( breln1unionIR
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( breln1unionI
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( breln1unionE
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X4: $i,X33: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( breln1 @ X4 @ X33 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X35: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( breln1 @ X4 @ X35 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X2 @ X4 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X3: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X4 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( in @ ( kpair @ X2 @ X3 ) @ ( binunion @ X33 @ X35 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X55: $o] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => X55 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => X55 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => X55 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionEcases) ).

thf(demorgan2b2,axiom,
    ( demorgan2b2
  <=> ! [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 @ X48 ) )
                   => ( in @ X2 @ ( setminus @ X4 @ ( binunion @ X21 @ X48 ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan2b2) ).

thf(breln1unionE,axiom,
    ( breln1unionE
  <=> ! [X4: $i,X33: $i] :
        ( ( breln1 @ X4 @ X33 )
       => ! [X35: $i] :
            ( ( breln1 @ X4 @ X35 )
           => ! [X2: $i] :
                ( ( in @ X2 @ X4 )
               => ! [X3: $i] :
                    ( ( in @ X3 @ X4 )
                   => ( ( in @ ( kpair @ X2 @ X3 ) @ ( binunion @ X33 @ X35 ) )
                     => ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
                        | ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionE) ).

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

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

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

thf(inComplementUnionImpNotIn1,axiom,
    ( inComplementUnionImpNotIn1
  <=> ! [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(inComplementUnionImpInComplement1,axiom,
    ( inComplementUnionImpInComplement1
  <=> ! [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 @ ( setminus @ X4 @ X21 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inComplementUnionImpInComplement1) ).

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(binunionTE,axiom,
    ( binunionTE
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ! [X50: $o,X2: $i] :
                ( ( in @ X2 @ X4 )
               => ( ( in @ X2 @ ( binunion @ X21 @ X48 ) )
                 => ( ( ( in @ X2 @ X21 )
                     => X50 )
                   => ( ( ( in @ X2 @ X48 )
                       => X50 )
                     => X50 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionTE) ).

thf(binunionTEcontra,axiom,
    ( binunionTEcontra
  <=> ! [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 @ X2 @ ( binunion @ X21 @ X48 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionTEcontra) ).

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(demorgan2a1,axiom,
    ( demorgan2a1
  <=> ! [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 @ ( setminus @ X4 @ X21 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan2a1) ).

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

thf(demorgan2a2,axiom,
    ( demorgan2a2
  <=> ! [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 @ ( setminus @ X4 @ X48 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan2a2) ).

thf(demorgan1a,axiom,
    ( demorgan1a
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ! [X2: $i] :
                ( ( in @ X2 @ X4 )
               => ( ( in @ X2 @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) )
                 => ( in @ X2 @ ( binunion @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ X48 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan1a) ).

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(demorgan1b,axiom,
    ( demorgan1b
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ! [X2: $i] :
                ( ( in @ X2 @ X4 )
               => ( ( in @ X2 @ ( binunion @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ X48 ) ) )
                 => ( in @ X2 @ ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan1b) ).

thf(demorgan1,axiom,
    ( demorgan1
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ( ( setminus @ X4 @ ( binintersect @ X21 @ X48 ) )
              = ( binunion @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ X48 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan1) ).

thf(demorgan2a,axiom,
    ( demorgan2a
  <=> ! [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 @ ( binintersect @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ X48 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan2a) ).

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

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(demorgan2b,axiom,
    ( demorgan2b
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ! [X2: $i] :
                ( ( in @ X2 @ X4 )
               => ( ( in @ X2 @ ( binintersect @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ X48 ) ) )
                 => ( in @ X2 @ ( setminus @ X4 @ ( binunion @ X21 @ X48 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan2b) ).

thf(demorgan2,axiom,
    ( demorgan2
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ( ( setminus @ X4 @ ( binunion @ X21 @ X48 ) )
              = ( binintersect @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ X48 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan2) ).

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(woz13rule0,axiom,
    ( woz13rule0
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ! [X2: $i] :
                ( ( in @ X2 @ ( binintersect @ X21 @ X48 ) )
               => ( in @ X2 @ X4 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule0) ).

thf(woz13rule1,axiom,
    ( woz13rule1
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ! [X49: $i] :
                ( ( in @ X49 @ ( powerset @ X4 ) )
               => ( ( subset @ X21 @ X49 )
                 => ( subset @ ( binintersect @ X21 @ X48 ) @ X49 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule1) ).

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(woz13rule2,axiom,
    ( woz13rule2
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ! [X49: $i] :
                ( ( in @ X49 @ ( powerset @ X4 ) )
               => ( ( subset @ X48 @ X49 )
                 => ( subset @ ( binintersect @ X21 @ X48 ) @ X49 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule2) ).

thf(woz13rule3,axiom,
    ( woz13rule3
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ! [X49: $i] :
                ( ( in @ X49 @ ( powerset @ X4 ) )
               => ( ( subset @ X21 @ X48 )
                 => ( ( subset @ X21 @ X49 )
                   => ( subset @ X21 @ ( binintersect @ X48 @ X49 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule3) ).

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(woz13rule4,axiom,
    ( woz13rule4
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ! [X49: $i] :
                ( ( in @ X49 @ ( powerset @ X4 ) )
               => ! [X51: $i] :
                    ( ( in @ X51 @ ( powerset @ X4 ) )
                   => ( ( subset @ X21 @ X49 )
                     => ( ( subset @ X48 @ X51 )
                       => ( subset @ ( binintersect @ X21 @ X48 ) @ ( binintersect @ X49 @ X51 ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz13rule4) ).

thf(woz1_1,axiom,
    ( woz1_1
  <=> ! [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',woz1_1) ).

thf(woz1_2,axiom,
    ( woz1_2
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ! [X49: $i] :
                ( ( in @ X49 @ ( powerset @ X4 ) )
               => ! [X51: $i] :
                    ( ( in @ X51 @ ( powerset @ X4 ) )
                   => ( ( setminus @ X4 @ ( binintersect @ ( binunion @ X21 @ X48 ) @ ( binunion @ X49 @ X51 ) ) )
                      = ( binunion @ ( binintersect @ ( setminus @ X4 @ X21 ) @ ( setminus @ X4 @ X48 ) ) @ ( binintersect @ ( setminus @ X4 @ X49 ) @ ( setminus @ X4 @ X51 ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz1_2) ).

thf(woz1_3,axiom,
    ( woz1_3
  <=> ! [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',woz1_3) ).

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(woz1_4,axiom,
    ( woz1_4
  <=> ! [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',woz1_4) ).

thf(woz1_5,axiom,
    ( woz1_5
  <=> ! [X4: $i,X21: $i] :
        ( ( in @ X21 @ ( powerset @ X4 ) )
       => ! [X48: $i] :
            ( ( in @ X48 @ ( powerset @ X4 ) )
           => ( in @ ( setminus @ X4 @ ( binunion @ X21 @ X48 ) ) @ ( powerset @ ( setminus @ X4 @ X21 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',woz1_5) ).

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

thf(breln1all2,axiom,
    ( breln1all2
  <=> ! [X4: $i,X33: $i] :
        ( ( breln1 @ X4 @ X33 )
       => ! [X1: $i > $o] :
            ( ! [X2: $i] :
                ( ( in @ X2 @ X4 )
               => ! [X3: $i] :
                    ( ( in @ X3 @ X4 )
                   => ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
                     => ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
           => ! [X2: $i] :
                ( ( in @ X2 @ X33 )
               => ( X1 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1all2) ).

thf(breln1SetBreln1,axiom,
    ( breln1SetBreln1
  <=> ! [X4: $i,X33: $i] :
        ( ( in @ X33 @ ( breln1Set @ X4 ) )
       => ( breln1 @ X4 @ X33 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1SetBreln1) ).

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

thf(breln1all1,axiom,
    ( breln1all1
  <=> ! [X4: $i,X33: $i] :
        ( ( breln1 @ X4 @ X33 )
       => ! [X1: $i > $o] :
            ( ! [X2: $i] :
                ( ( in @ X2 @ X4 )
               => ! [X3: $i] :
                    ( ( in @ X3 @ X4 )
                   => ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
                     => ( X1 @ ( kpair @ X2 @ X3 ) ) ) ) )
           => ! [X2: $i] :
                ( ( in @ X2 @ X33 )
               => ( X1 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1all1) ).

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(subbreln1,axiom,
    ( subbreln1
  <=> ! [X4: $i,X33: $i] :
        ( ( breln1 @ X4 @ X33 )
       => ! [X35: $i] :
            ( ( breln1 @ X4 @ X35 )
           => ( ! [X2: $i] :
                  ( ( in @ X2 @ X4 )
                 => ! [X3: $i] :
                      ( ( in @ X3 @ X4 )
                     => ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
                       => ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
             => ( subset @ X33 @ X35 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subbreln1) ).

thf(eqbreln1,axiom,
    ( eqbreln1
  <=> ! [X4: $i,X33: $i] :
        ( ( breln1 @ X4 @ X33 )
       => ! [X35: $i] :
            ( ( breln1 @ X4 @ X35 )
           => ( ! [X2: $i] :
                  ( ( in @ X2 @ X4 )
                 => ! [X3: $i] :
                      ( ( in @ X3 @ X4 )
                     => ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
                       => ( in @ ( kpair @ X2 @ X3 ) @ X35 ) ) ) )
             => ( ! [X2: $i] :
                    ( ( in @ X2 @ X4 )
                   => ! [X3: $i] :
                        ( ( in @ X3 @ X4 )
                       => ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
                         => ( in @ ( kpair @ X2 @ X3 ) @ X33 ) ) ) )
               => ( X33 = X35 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqbreln1) ).

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(breln1invprop,axiom,
    ( breln1invprop
  <=> ! [X4: $i,X33: $i] :
        ( ( breln1 @ X4 @ X33 )
       => ( breln1 @ X4 @ ( breln1invset @ X4 @ X33 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1invprop) ).

thf(breln1invI,axiom,
    ( breln1invI
  <=> ! [X4: $i,X33: $i] :
        ( ( breln1 @ X4 @ X33 )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ! [X3: $i] :
                ( ( in @ X3 @ X4 )
               => ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
                 => ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X4 @ X33 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1invI) ).

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(breln1invE,axiom,
    ( breln1invE
  <=> ! [X4: $i,X33: $i] :
        ( ( breln1 @ X4 @ X33 )
       => ! [X2: $i] :
            ( ( in @ X2 @ X4 )
           => ! [X3: $i] :
                ( ( in @ X3 @ X4 )
               => ( ( in @ ( kpair @ X3 @ X2 ) @ ( breln1invset @ X4 @ X33 ) )
                 => ( in @ ( kpair @ X2 @ X3 ) @ X33 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1invE) ).

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(breln1compprop,axiom,
    ( breln1compprop
  <=> ! [X4: $i,X33: $i] :
        ( ( breln1 @ X4 @ X33 )
       => ! [X35: $i] :
            ( ( breln1 @ X4 @ X35 )
           => ( breln1 @ X4 @ ( breln1compset @ X4 @ X33 @ X35 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1compprop) ).

thf(breln1compI,axiom,
    ( breln1compI
  <=> ! [X4: $i,X33: $i] :
        ( ( breln1 @ X4 @ X33 )
       => ! [X35: $i] :
            ( ( breln1 @ X4 @ X35 )
           => ! [X2: $i] :
                ( ( in @ X2 @ X4 )
               => ! [X3: $i] :
                    ( ( in @ X3 @ X4 )
                   => ! [X14: $i] :
                        ( ( in @ X14 @ X4 )
                       => ( ( in @ ( kpair @ X2 @ X14 ) @ X33 )
                         => ( ( in @ ( kpair @ X14 @ X3 ) @ X35 )
                           => ( in @ ( kpair @ X2 @ X3 ) @ ( breln1compset @ X4 @ X33 @ X35 ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1compI) ).

thf(breln1compE,axiom,
    ( breln1compE
  <=> ! [X4: $i,X33: $i] :
        ( ( breln1 @ X4 @ X33 )
       => ! [X35: $i] :
            ( ( breln1 @ X4 @ X35 )
           => ! [X2: $i] :
                ( ( in @ X2 @ X4 )
               => ! [X3: $i] :
                    ( ( in @ X3 @ X4 )
                   => ( ( in @ ( kpair @ X2 @ X3 ) @ ( breln1compset @ X4 @ X33 @ X35 ) )
                     => ? [X14: $i] :
                          ( ( in @ X14 @ X4 )
                          & ( in @ ( kpair @ X2 @ X14 ) @ X33 )
                          & ( in @ ( kpair @ X14 @ X3 ) @ X35 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1compE) ).

thf(breln1compEex,axiom,
    ( breln1compEex
  <=> ! [X4: $i,X33: $i] :
        ( ( breln1 @ X4 @ X33 )
       => ! [X35: $i] :
            ( ( breln1 @ X4 @ X35 )
           => ! [X2: $i] :
                ( ( in @ X2 @ X4 )
               => ! [X3: $i] :
                    ( ( in @ X3 @ X4 )
                   => ( ( in @ ( kpair @ X2 @ X3 ) @ ( breln1compset @ X4 @ X33 @ X35 ) )
                     => ! [X54: $o] :
                          ( ! [X14: $i] :
                              ( ( in @ X14 @ X4 )
                             => ( ( in @ ( kpair @ X2 @ X14 ) @ X33 )
                               => ( ( in @ ( kpair @ X14 @ X3 ) @ X35 )
                                 => X54 ) ) )
                         => X54 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1compEex) ).

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(breln1unionprop,axiom,
    ( breln1unionprop
  <=> ! [X4: $i,X33: $i] :
        ( ( breln1 @ X4 @ X33 )
       => ! [X35: $i] :
            ( ( breln1 @ X4 @ X35 )
           => ( breln1 @ X4 @ ( binunion @ X33 @ X35 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionprop) ).

thf(breln1unionIL,axiom,
    ( breln1unionIL
  <=> ! [X4: $i,X33: $i] :
        ( ( breln1 @ X4 @ X33 )
       => ! [X35: $i] :
            ( ( breln1 @ X4 @ X35 )
           => ! [X2: $i] :
                ( ( in @ X2 @ X4 )
               => ! [X3: $i] :
                    ( ( in @ X3 @ X4 )
                   => ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
                     => ( in @ ( kpair @ X2 @ X3 ) @ ( binunion @ X33 @ X35 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionIL) ).

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

thf(breln1unionIR,axiom,
    ( breln1unionIR
  <=> ! [X4: $i,X33: $i] :
        ( ( breln1 @ X4 @ X33 )
       => ! [X35: $i] :
            ( ( breln1 @ X4 @ X35 )
           => ! [X2: $i] :
                ( ( in @ X2 @ X4 )
               => ! [X3: $i] :
                    ( ( in @ X3 @ X4 )
                   => ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
                     => ( in @ ( kpair @ X2 @ X3 ) @ ( binunion @ X33 @ X35 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionIR) ).

thf(breln1unionI,axiom,
    ( breln1unionI
  <=> ! [X4: $i,X33: $i] :
        ( ( breln1 @ X4 @ X33 )
       => ! [X35: $i] :
            ( ( breln1 @ X4 @ X35 )
           => ! [X2: $i] :
                ( ( in @ X2 @ X4 )
               => ! [X3: $i] :
                    ( ( in @ X3 @ X4 )
                   => ( ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
                        | ( in @ ( kpair @ X2 @ X3 ) @ X35 ) )
                     => ( in @ ( kpair @ X2 @ X3 ) @ ( binunion @ X33 @ X35 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1unionI) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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(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(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_304,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_305,plain,
    ( exu
    = ( ^ [Z0: $i > $o] :
        ? [X2: $i] :
          ( ( Z0 @ X2 )
          & ! [X3: $i] :
              ( ( Z0 @ X3 )
             => ( X2 = X3 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[exu]) ).

thf(c_0_306,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_307,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_308,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_309,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_310,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_311,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_312,plain,
    ( nonempty
    = ( ^ [Z0: $i] : ( Z0 != emptyset ) ) ),
    inference(fof_simplification,[status(thm)],[nonempty]) ).

thf(c_0_313,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_314,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_315,plain,
    ( exuE3e
  <=> ! [X1: $i > $o] :
        ( ( exu
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
       => ? [X2: $i] : ( X1 @ X2 ) ) ),
    inference(fof_simplification,[status(thm)],[exuE3e]) ).

thf(c_0_316,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_317,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_318,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_319,plain,
    ( setOfPairsIsBReln1
  <=> ! [X4: $i,X53: $i > $i > $o] :
        ( breln1 @ X4
        @ ( dpsetconstr @ X4 @ X4
          @ ^ [Z0: $i,Z1: $i] : ( X53 @ Z0 @ Z1 ) ) ) ),
    inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1]) ).

thf(c_0_320,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_321,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_322,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_323,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_324,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_325,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_326,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_327,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_328,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_329,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_330,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_331,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_332,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_333,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_334,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_335,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_336,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_337,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_338,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_339,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_340,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_341,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_342,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_343,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_344,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_345,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_346,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_347,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_348,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_349,plain,
    ( sepSubset
  <=> ! [X4: $i,X1: $i > $o] :
        ( subset
        @ ( dsetconstr @ X4
          @ ^ [Z0: $i] : ( X1 @ Z0 ) )
        @ X4 ) ),
    inference(fof_simplification,[status(thm)],[sepSubset]) ).

thf(c_0_350,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_351,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_352,plain,
    ( descr__Cong
    = ( ! [X1: $i > $o,X17: $i > $o] :
          ( ! [X2: $i,X3: $i] :
              ( ( X2 = X3 )
             => ( ( X1 @ X2 )
              <=> ( X17 @ X3 ) ) )
         => ( ? [X1075: $i] :
                ( ( X1 @ X1075 )
                & ! [X1076: $i] :
                    ( ( X1 @ X1076 )
                   => ( X1075 = X1076 ) ) )
           => ( ? [X1077: $i] :
                  ( ( X17 @ X1077 )
                  & ! [X1078: $i] :
                      ( ( X17 @ X1078 )
                     => ( X1077 = X1078 ) ) )
             => ( ( descr
                  @ ^ [Z0: $i] : ( X1 @ Z0 ) )
                = ( descr
                  @ ^ [Z0: $i] : ( X17 @ Z0 ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_304,c_0_305]) ).

thf(c_0_353,plain,
    ( exuEu
    = ( ! [X1: $i > $o] :
          ( ? [X1073: $i] :
              ( ( X1 @ X1073 )
              & ! [X1074: $i] :
                  ( ( X1 @ X1074 )
                 => ( X1073 = X1074 ) ) )
         => ! [X2: $i,X3: $i] :
              ( ( X1 @ X2 )
             => ( ( X1 @ X3 )
               => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_306,c_0_305]) ).

thf(c_0_354,plain,
    ( exu__Cong
    = ( ! [X1: $i > $o,X17: $i > $o] :
          ( ! [X2: $i,X3: $i] :
              ( ( X2 = X3 )
             => ( ( X1 @ X2 )
              <=> ( X17 @ X3 ) ) )
         => ( ? [X1069: $i] :
                ( ( X1 @ X1069 )
                & ! [X1070: $i] :
                    ( ( X1 @ X1070 )
                   => ( X1069 = X1070 ) ) )
          <=> ? [X1071: $i] :
                ( ( X17 @ X1071 )
                & ! [X1072: $i] :
                    ( ( X17 @ X1072 )
                   => ( X1071 = X1072 ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_307,c_0_305]) ).

thf(c_0_355,plain,
    ( exuE3u
    = ( ! [X1: $i > $o] :
          ( ? [X1067: $i] :
              ( ( X1 @ X1067 )
              & ! [X1068: $i] :
                  ( ( X1 @ X1068 )
                 => ( X1067 = X1068 ) ) )
         => ! [X2: $i,X3: $i] :
              ( ( X1 @ X2 )
             => ( ( X1 @ X3 )
               => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_308,c_0_305]) ).

thf(c_0_356,plain,
    ( exuI2
    = ( ! [X1: $i > $o] :
          ( ? [X2: $i] :
            ! [X3: $i] :
              ( ( X1 @ X3 )
            <=> ( X3 = X2 ) )
         => ? [X1065: $i] :
              ( ( X1 @ X1065 )
              & ! [X1066: $i] :
                  ( ( X1 @ X1066 )
                 => ( X1065 = X1066 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_309,c_0_305]) ).

thf(c_0_357,plain,
    ( exuI3
    = ( ! [X1: $i > $o] :
          ( ? [X2: $i] : ( X1 @ X2 )
         => ( ! [X2: $i,X3: $i] :
                ( ( X1 @ X2 )
               => ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) )
           => ? [X1063: $i] :
                ( ( X1 @ X1063 )
                & ! [X1064: $i] :
                    ( ( X1 @ X1064 )
                   => ( X1063 = X1064 ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_310,c_0_305]) ).

thf(c_0_358,plain,
    ( exuI1
    = ( ! [X1: $i > $o] :
          ( ? [X2: $i] :
              ( ( X1 @ X2 )
              & ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) )
         => ? [X1061: $i] :
              ( ( X1 @ X1061 )
              & ! [X1062: $i] :
                  ( ( X1 @ X1062 )
                 => ( X1061 = X1062 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_311,c_0_305]) ).

thf(c_0_359,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_360,axiom,
    ( nonemptyImpWitness
    = ( ! [X4: $i] :
          ( ( X4 != emptyset )
         => ? [X2: $i] :
              ( ( in @ X2 @ X4 )
              & $true ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyImpWitness,c_0_312]) ).

thf(c_0_361,plain,
    ( exuE2
    = ( ! [X1: $i > $o] :
          ( ? [X1059: $i] :
              ( ( X1 @ X1059 )
              & ! [X1060: $i] :
                  ( ( X1 @ X1060 )
                 => ( X1059 = X1060 ) ) )
         => ? [X2: $i] :
            ! [X3: $i] :
              ( ( X1 @ X3 )
            <=> ( X3 = X2 ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_313,c_0_305]) ).

thf(c_0_362,plain,
    ( setoftrueEq
  <=> ! [X4: $i] :
        ( ( dsetconstr @ X4
          @ ^ [Z0: $i] : $true )
        = X4 ) ),
    inference(fof_simplification,[status(thm)],[setoftrueEq]) ).

thf(c_0_363,axiom,
    ( nonemptyI1
    = ( ! [X4: $i] :
          ( ? [X2: $i] : ( in @ X2 @ X4 )
         => ( X4 != emptyset ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyI1,c_0_312]) ).

thf(c_0_364,plain,
    ( nonemptyI
    = ( ! [X4: $i,X1: $i > $o,X2: $i] :
          ( ( in @ X2 @ X4 )
         => ( ( X1 @ X2 )
           => ( ( dsetconstr @ X4
                @ ^ [Z0: $i] : ( X1 @ Z0 ) )
             != emptyset ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_314,c_0_312]) ).

thf(c_0_365,axiom,
    ( nonemptyE1
    = ( ! [X4: $i] :
          ( ( X4 != emptyset )
         => ? [X2: $i] : ( in @ X2 @ X4 ) ) ) ),
    inference(apply_def,[status(thm)],[nonemptyE1,c_0_312]) ).

thf(c_0_366,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_367,plain,
    ( exuE3e
    = ( ! [X1: $i > $o] :
          ( ? [X1057: $i] :
              ( ( X1 @ X1057 )
              & ! [X1058: $i] :
                  ( ( X1 @ X1058 )
                 => ( X1057 = X1058 ) ) )
         => ? [X2: $i] : ( X1 @ X2 ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_315,c_0_305]) ).

thf(c_0_368,plain,
    ( exuE1
    = ( ! [X1: $i > $o] :
          ( ? [X1055: $i] :
              ( ( X1 @ X1055 )
              & ! [X1056: $i] :
                  ( ( X1 @ X1056 )
                 => ( X1055 = X1056 ) ) )
         => ? [X2: $i] :
              ( ( X1 @ X2 )
              & ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_316,c_0_305]) ).

thf(c_0_369,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_370,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_371,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_372,plain,
    ( descrp
    = ( ! [X1: $i > $o] :
          ( ? [X1053: $i] :
              ( ( X1 @ X1053 )
              & ! [X1054: $i] :
                  ( ( X1 @ X1054 )
                 => ( X1053 = X1054 ) ) )
         => ( X1
            @ ( descr
              @ ^ [Z0: $i] : ( X1 @ Z0 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_317,c_0_305]) ).

thf(c_0_373,plain,
    ( replAx
    = ( ! [X6: $i > $i > $o,X4: $i] :
          ( ! [X2: $i] :
              ( ( in @ X2 @ X4 )
             => ? [X1051: $i] :
                  ( ( X6 @ X2 @ X1051 )
                  & ! [X1052: $i] :
                      ( ( X6 @ X2 @ X1052 )
                     => ( X1051 = X1052 ) ) ) )
         => ? [X5: $i] :
            ! [X2: $i] :
              ( ( in @ X2 @ X5 )
            <=> ? [X3: $i] :
                  ( ( in @ X3 @ X4 )
                  & ( X6 @ X3 @ X2 ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_318,c_0_305]) ).

thf(c_0_374,plain,
    ( epred1_0
  <=> ! [X1108: $i] :
      ? [X1109: $i] :
        ( ! [X1110: $i] :
            ( ( in @ X1110 @ X1109 )
           => ! [X1111: $i] :
                ( ( in @ X1111 @ X1110 )
               => ( in @ X1111 @ X1108 ) ) )
        & ! [X1112: $i,X1113: $i] :
            ( ( ( in @ X1112 @ X1108 )
              & ( in @ X1113 @ X1108 ) )
           => ( ! [X1114: $i] :
                  ( ( in @ X1114 @ X1109 )
                 => ( ( in @ X1112 @ X1114 )
                  <=> ( in @ X1113 @ X1114 ) ) )
             => ( X1112 = X1113 ) ) )
        & ! [X1115: $i,X1116: $i] :
            ( ( ( in @ X1115 @ X1109 )
              & ( in @ X1116 @ X1109 ) )
           => ( ! [X1117: $i] :
                  ( ( in @ X1117 @ X1115 )
                 => ( in @ X1117 @ X1116 ) )
              | ! [X1118: $i] :
                  ( ( in @ X1118 @ X1116 )
                 => ( in @ X1118 @ X1115 ) ) ) )
        & ! [X1119: $i] :
            ( ( ! [X1120: $i] :
                  ( ( in @ X1120 @ X1119 )
                 => ( in @ X1120 @ X1108 ) )
              & ? [X1121: $i] : ( in @ X1121 @ X1119 ) )
           => ? [X1122: $i,X1123: $i] :
                ( ( in @ X1122 @ X1109 )
                & ( in @ X1123 @ X1119 )
                & ~ ? [X1124: $i] :
                      ( ( in @ X1124 @ X1122 )
                      & ( in @ X1124 @ X1119 ) )
                & ! [X1125: $i] :
                    ( ( in @ X1125 @ X1109 )
                   => ( ! [X1126: $i] :
                          ( ( in @ X1126 @ X1125 )
                         => ( in @ X1126 @ X1122 ) )
                      | ( in @ X1123 @ X1125 ) ) ) ) ) ) ),
    introduced(definition) ).

thf(c_0_375,negated_conjecture,
    ~ ( ! [X1079: $i,X1080: $i] :
          ( ! [X1081: $i] :
              ( ( in @ X1081 @ X1079 )
            <=> ( in @ X1081 @ X1080 ) )
         => ( X1079 = X1080 ) )
     => ( ! [X1082: $i] :
            ~ ( in @ X1082 @ emptyset )
       => ( ! [X1083: $i,X1084: $i,X1085: $i] :
              ( ( in @ X1085 @ ( setadjoin @ X1083 @ X1084 ) )
            <=> ( ( X1085 = X1083 )
                | ( in @ X1085 @ X1084 ) ) )
         => ( ! [X1086: $i,X1087: $i] :
                ( ( in @ X1087 @ ( powerset @ X1086 ) )
              <=> ! [X1088: $i] :
                    ( ( in @ X1088 @ X1087 )
                   => ( in @ X1088 @ X1086 ) ) )
           => ( ! [X1089: $i,X1090: $i] :
                  ( ( in @ X1090 @ ( setunion @ X1089 ) )
                <=> ? [X1091: $i] :
                      ( ( in @ X1090 @ X1091 )
                      & ( in @ X1091 @ X1089 ) ) )
             => ( ( in @ emptyset @ omega )
               => ( ! [X1092: $i] :
                      ( ( in @ X1092 @ omega )
                     => ( in @ ( setadjoin @ X1092 @ X1092 ) @ omega ) )
                 => ( ! [X1093: $i] :
                        ( ( ( in @ emptyset @ X1093 )
                          & ! [X1094: $i] :
                              ( ( ( in @ X1094 @ omega )
                                & ( in @ X1094 @ X1093 ) )
                             => ( in @ ( setadjoin @ X1094 @ X1094 ) @ X1093 ) ) )
                       => ! [X1095: $i] :
                            ( ( in @ X1095 @ omega )
                           => ( in @ X1095 @ X1093 ) ) )
                   => ( ! [X1096: $i > $i > $o,X1097: $i] :
                          ( ! [X1098: $i] :
                              ( ( in @ X1098 @ X1097 )
                             => ? [X1099: $i] :
                                  ( ( X1096 @ X1098 @ X1099 )
                                  & ! [X1100: $i] :
                                      ( ( X1096 @ X1098 @ X1100 )
                                     => ( X1099 = X1100 ) ) ) )
                         => ? [X1101: $i] :
                            ! [X1102: $i] :
                              ( ( in @ X1102 @ X1101 )
                            <=> ? [X1103: $i] :
                                  ( ( in @ X1103 @ X1097 )
                                  & ( X1096 @ X1103 @ X1102 ) ) ) )
                     => ( ! [X1104: $i] :
                            ( ? [X1105: $i] : ( in @ X1105 @ X1104 )
                           => ? [X1106: $i] :
                                ( ( in @ X1106 @ X1104 )
                                & ~ ? [X1107: $i] :
                                      ( ( in @ X1107 @ X1106 )
                                      & ( in @ X1107 @ X1104 ) ) ) )
                       => ( epred1_0
                         => ( ! [X1127: $i > $o] :
                                ( ? [X1128: $i] :
                                    ( ( X1127 @ X1128 )
                                    & ! [X1129: $i] :
                                        ( ( X1127 @ X1129 )
                                       => ( X1128 = X1129 ) ) )
                               => ( X1127
                                  @ ( descr
                                    @ ^ [Z0: $i] : ( X1127 @ Z0 ) ) ) )
                           => ( ! [X1130: $i,X1131: $i > $o,X1132: $i] :
                                  ( ( in @ X1132 @ X1130 )
                                 => ( ( X1131 @ X1132 )
                                   => ( in @ X1132 @ ( dsetconstr @ X1130 @ X1131 ) ) ) )
                             => ( ! [X1133: $i,X1134: $i > $o,X1135: $i] :
                                    ( ( in @ X1135 @ ( dsetconstr @ X1133 @ X1134 ) )
                                   => ( in @ X1135 @ X1133 ) )
                               => ( ! [X1136: $i,X1137: $i > $o,X1138: $i] :
                                      ( ( in @ X1138 @ ( dsetconstr @ X1136 @ X1137 ) )
                                     => ( X1137 @ X1138 ) )
                                 => ( ! [X1139: $i > $o] :
                                        ( ? [X1140: $i] :
                                            ( ( X1139 @ X1140 )
                                            & ! [X1141: $i] :
                                                ( ( X1139 @ X1141 )
                                               => ( X1140 = X1141 ) ) )
                                       => ? [X1142: $i] :
                                            ( ( X1139 @ X1142 )
                                            & ! [X1143: $i] :
                                                ( ( X1139 @ X1143 )
                                               => ( X1142 = X1143 ) ) ) )
                                   => ( ! [X1144: $o,X1145: $i] :
                                          ( ( in @ X1145 @ ( prop2set @ X1144 ) )
                                         => X1144 )
                                     => ( ! [X1146: $i] :
                                            ( ( in @ X1146 @ emptyset )
                                           => ! [X1147: $o] : X1147 )
                                       => ( ! [X1148: $i] :
                                              ( ( in @ X1148 @ emptyset )
                                             => ~ $true )
                                         => ( ! [X1149: $i] :
                                                ~ ( in @ X1149 @ emptyset )
                                           => ( ! [X1150: $i > $o] :
                                                  ( ? [X1151: $i] :
                                                      ( ( X1150 @ X1151 )
                                                      & ! [X1152: $i] :
                                                          ( ( X1150 @ X1152 )
                                                         => ( X1151 = X1152 ) ) )
                                                 => ? [X1153: $i] : ( X1150 @ X1153 ) )
                                             => ( ! [X1154: $i,X1155: $i] :
                                                    ( ! [X1156: $i] :
                                                        ( ( in @ X1156 @ X1154 )
                                                       => ( in @ X1156 @ X1155 ) )
                                                   => ( ! [X1157: $i] :
                                                          ( ( in @ X1157 @ X1155 )
                                                         => ( in @ X1157 @ X1154 ) )
                                                     => ( X1154 = X1155 ) ) )
                                               => ( ! [X1158: $i] :
                                                      ( ! [X1159: $i] :
                                                          ~ ( in @ X1159 @ X1158 )
                                                     => ( X1158 = emptyset ) )
                                                 => ( ! [X1160: $i] :
                                                        ( ! [X1161: $i] :
                                                            ~ ( in @ X1161 @ X1160 )
                                                       => ( X1160 = emptyset ) )
                                                   => ( ! [X1162: $i,X1163: $i > $o,X1164: $i] :
                                                          ( ( in @ X1164 @ X1162 )
                                                         => ( ( in @ X1164 @ ( dsetconstr @ X1162 @ X1163 ) )
                                                          <=> ( X1163 @ X1164 ) ) )
                                                     => ( ! [X1165: $i] :
                                                            ( ( X1165 != emptyset )
                                                           => ? [X1166: $i] : ( in @ X1166 @ X1165 ) )
                                                       => ( ! [X1167: $i,X1168: $i > $o,X1169: $i] :
                                                              ( ( in @ X1169 @ X1167 )
                                                             => ( ( X1168 @ X1169 )
                                                               => ( ( dsetconstr @ X1167 @ X1168 )
                                                                 != emptyset ) ) )
                                                         => ( ! [X1170: $i] :
                                                                ( ? [X1171: $i] : ( in @ X1171 @ X1170 )
                                                               => ( X1170 != emptyset ) )
                                                           => ( ! [X1172: $i,X1173: $i] : ( in @ X1172 @ ( setadjoin @ X1172 @ X1173 ) )
                                                             => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                               => ( ! [X1174: $i,X1175: $i,X1176: $i] :
                                                                      ( ( in @ X1176 @ X1175 )
                                                                     => ( in @ X1176 @ ( setadjoin @ X1174 @ X1175 ) ) )
                                                                 => ( ! [X1177: $i,X1178: $i,X1179: $i] :
                                                                        ( ( in @ X1179 @ ( setadjoin @ X1177 @ X1178 ) )
                                                                       => ! [X1180: $o] :
                                                                            ( ( ( X1179 = X1177 )
                                                                             => X1180 )
                                                                           => ( ( ( in @ X1179 @ X1178 )
                                                                               => X1180 )
                                                                             => X1180 ) ) )
                                                                   => ( ! [X1181: $i,X1182: $i,X1183: $i] :
                                                                          ( ( in @ X1183 @ ( setadjoin @ X1181 @ X1182 ) )
                                                                         => ( ( X1183 = X1181 )
                                                                            | ( in @ X1183 @ X1182 ) ) )
                                                                     => ( ! [X1184: $i] :
                                                                            ( ( dsetconstr @ X1184
                                                                              @ ^ [Z0: $i] : $true )
                                                                            = X1184 )
                                                                       => ( ! [X1185: $i,X1186: $i] :
                                                                              ( ! [X1187: $i] :
                                                                                  ( ( in @ X1187 @ X1186 )
                                                                                 => ( in @ X1187 @ X1185 ) )
                                                                             => ( in @ X1186 @ ( powerset @ X1185 ) ) )
                                                                         => ( ! [X1188: $i] : ( in @ emptyset @ ( powerset @ X1188 ) )
                                                                           => ( ! [X1189: $i] : ( in @ emptyset @ ( powerset @ X1189 ) )
                                                                             => ( ! [X1190: $i,X1191: $i,X1192: $i] :
                                                                                    ( ( in @ X1191 @ ( powerset @ X1190 ) )
                                                                                   => ( ( in @ X1192 @ X1191 )
                                                                                     => ( in @ X1192 @ X1190 ) ) )
                                                                               => ( ! [X1193: $i,X1194: $i,X1195: $i] :
                                                                                      ( ( in @ X1194 @ X1195 )
                                                                                     => ( ( in @ X1195 @ X1193 )
                                                                                       => ( in @ X1194 @ ( setunion @ X1193 ) ) ) )
                                                                                 => ( ! [X1196: $i,X1197: $i] :
                                                                                        ( ( in @ X1197 @ ( setunion @ X1196 ) )
                                                                                       => ! [X1198: $o] :
                                                                                            ( ! [X1199: $i] :
                                                                                                ( ( in @ X1197 @ X1199 )
                                                                                               => ( ( in @ X1199 @ X1196 )
                                                                                                 => X1198 ) )
                                                                                           => X1198 ) )
                                                                                   => ( ! [X1200: $i,X1201: $i] :
                                                                                          ( ( in @ X1201 @ X1200 )
                                                                                         => ( in @ X1201 @ ( powerset @ ( setunion @ X1200 ) ) ) )
                                                                                     => ( ! [X1202: $i > $o] :
                                                                                            ( ? [X1203: $i] :
                                                                                                ( ( X1202 @ X1203 )
                                                                                                & ! [X1204: $i] :
                                                                                                    ( ( X1202 @ X1204 )
                                                                                                   => ( X1203 = X1204 ) ) )
                                                                                           => ? [X1205: $i] :
                                                                                              ! [X1206: $i] :
                                                                                                ( ( X1202 @ X1206 )
                                                                                              <=> ( X1206 = X1205 ) ) )
                                                                                       => ( ! [X1207: $i] :
                                                                                              ( ( X1207 != emptyset )
                                                                                             => ? [X1208: $i] :
                                                                                                  ( ( in @ X1208 @ X1207 )
                                                                                                  & $true ) )
                                                                                         => ( ! [X1209: $i,X1210: $i] :
                                                                                                ( ( in @ X1209 @ ( setadjoin @ X1210 @ emptyset ) )
                                                                                               => ( X1209 = X1210 ) )
                                                                                           => ( ! [X1211: $i,X1212: $i] :
                                                                                                  ( ( X1211 != X1212 )
                                                                                                 => ~ ( in @ X1212 @ ( setadjoin @ X1211 @ emptyset ) ) )
                                                                                             => ( ! [X1213: $i,X1214: $i] :
                                                                                                    ( ( X1213 = X1214 )
                                                                                                   => ( in @ X1213 @ ( setadjoin @ X1214 @ emptyset ) ) )
                                                                                               => ( ! [X1215: $i,X1216: $i] :
                                                                                                      ( ( in @ X1215 @ ( setadjoin @ X1216 @ emptyset ) )
                                                                                                     => ( in @ X1216 @ ( setadjoin @ X1215 @ emptyset ) ) )
                                                                                                 => ( ! [X1217: $i,X1218: $i,X1219: $i] :
                                                                                                        ( ( in @ X1219 @ ( setadjoin @ X1217 @ ( setadjoin @ X1218 @ emptyset ) ) )
                                                                                                       => ( ( X1219 = X1217 )
                                                                                                          | ( X1219 = X1218 ) ) )
                                                                                                   => ( ! [X1220: $i,X1221: $i] : ( in @ X1220 @ ( setadjoin @ X1220 @ ( setadjoin @ X1221 @ emptyset ) ) )
                                                                                                     => ( ! [X1222: $i,X1223: $i] : ( in @ X1223 @ ( setadjoin @ X1222 @ ( setadjoin @ X1223 @ emptyset ) ) )
                                                                                                       => ( ! [X1224: $i,X1225: $i > $o] :
                                                                                                              ( ? [X1226: $i] :
                                                                                                                  ( ( in @ X1226 @ X1224 )
                                                                                                                  & ( X1225 @ X1226 ) )
                                                                                                             => ( ( ( dsetconstr @ X1224 @ X1225 )
                                                                                                                  = emptyset )
                                                                                                               => ~ $true ) )
                                                                                                         => ( ! [X1227: $i > $o,X1228: $i] :
                                                                                                                ( ( in @ X1228 @ emptyset )
                                                                                                               => ( X1227 @ X1228 ) )
                                                                                                           => ( ! [X1229: $i,X1230: $i > $o] :
                                                                                                                  ( ~ ! [X1231: $i] :
                                                                                                                        ( ( in @ X1231 @ X1229 )
                                                                                                                       => ( X1230 @ X1231 ) )
                                                                                                                 => ? [X1232: $i] :
                                                                                                                      ( ( in @ X1232 @ X1229 )
                                                                                                                      & ~ ( X1230 @ X1232 ) ) )
                                                                                                             => ( ! [X1233: $i,X1234: $i > $o] :
                                                                                                                    ( ! [X1235: $i] :
                                                                                                                        ( ( in @ X1235 @ X1233 )
                                                                                                                       => ~ ( X1234 @ X1235 ) )
                                                                                                                   => ~ ? [X1236: $i] :
                                                                                                                          ( ( in @ X1236 @ X1233 )
                                                                                                                          & ( X1234 @ X1236 ) ) )
                                                                                                               => ( ! [X1237: $i,X1238: $i > $o] :
                                                                                                                      ( ~ ? [X1239: $i] :
                                                                                                                            ( ( in @ X1239 @ X1237 )
                                                                                                                            & ( X1238 @ X1239 ) )
                                                                                                                     => ! [X1240: $i] :
                                                                                                                          ( ( in @ X1240 @ X1237 )
                                                                                                                         => ~ ( X1238 @ X1240 ) ) )
                                                                                                                 => ( ! [X1241: $i,X1242: $i > $o] :
                                                                                                                        ( ? [X1243: $i] :
                                                                                                                            ( ( in @ X1243 @ X1241 )
                                                                                                                            & ~ ( X1242 @ X1243 ) )
                                                                                                                       => ~ ! [X1244: $i] :
                                                                                                                              ( ( in @ X1244 @ X1241 )
                                                                                                                             => ( X1242 @ X1244 ) ) )
                                                                                                                   => ( ! [X1245: $o] :
                                                                                                                          ( X1245
                                                                                                                         => ( in @ emptyset @ ( prop2set @ X1245 ) ) )
                                                                                                                     => ( prop2set2propI
                                                                                                                       => ( ! [X1246: $i,X1247: $i > $o] :
                                                                                                                              ( ~ ? [X1248: $i] :
                                                                                                                                    ( ( in @ X1248 @ X1246 )
                                                                                                                                    & ( X1247 @ X1248 ) )
                                                                                                                             => ! [X1249: $i] :
                                                                                                                                  ( ( in @ X1249 @ X1246 )
                                                                                                                                 => ~ ( X1247 @ X1249 ) ) )
                                                                                                                         => ( ! [X1250: $i,X1251: $i > $o] :
                                                                                                                                ( ~ ! [X1252: $i] :
                                                                                                                                      ( ( in @ X1252 @ X1250 )
                                                                                                                                     => ( X1251 @ X1252 ) )
                                                                                                                               => ? [X1253: $i] :
                                                                                                                                    ( ( in @ X1253 @ X1250 )
                                                                                                                                    & ~ ( X1251 @ X1253 ) ) )
                                                                                                                           => ( ! [X1254: $i > $o] :
                                                                                                                                  ( ? [X1255: $i] :
                                                                                                                                      ( ( X1254 @ X1255 )
                                                                                                                                      & ! [X1256: $i] :
                                                                                                                                          ( ( X1254 @ X1256 )
                                                                                                                                         => ( X1255 = X1256 ) ) )
                                                                                                                                 => ? [X1257: $i] :
                                                                                                                                      ( ( X1254 @ X1257 )
                                                                                                                                      & ! [X1258: $i] :
                                                                                                                                          ( ( X1254 @ X1258 )
                                                                                                                                         => ( X1257 = X1258 ) ) ) )
                                                                                                                             => ( ! [X1259: $i > $o] :
                                                                                                                                    ( ? [X1260: $i] : ( X1259 @ X1260 )
                                                                                                                                   => ( ! [X1261: $i,X1262: $i] :
                                                                                                                                          ( ( X1259 @ X1261 )
                                                                                                                                         => ( ( X1259 @ X1262 )
                                                                                                                                           => ( X1261 = X1262 ) ) )
                                                                                                                                     => ? [X1263: $i] :
                                                                                                                                          ( ( X1259 @ X1263 )
                                                                                                                                          & ! [X1264: $i] :
                                                                                                                                              ( ( X1259 @ X1264 )
                                                                                                                                             => ( X1263 = X1264 ) ) ) ) )
                                                                                                                               => ( ! [X1265: $i > $o] :
                                                                                                                                      ( ? [X1266: $i] :
                                                                                                                                        ! [X1267: $i] :
                                                                                                                                          ( ( X1265 @ X1267 )
                                                                                                                                        <=> ( X1267 = X1266 ) )
                                                                                                                                     => ? [X1268: $i] :
                                                                                                                                          ( ( X1265 @ X1268 )
                                                                                                                                          & ! [X1269: $i] :
                                                                                                                                              ( ( X1265 @ X1269 )
                                                                                                                                             => ( X1268 = X1269 ) ) ) )
                                                                                                                                 => ( ! [X1270: $i,X1271: $i] :
                                                                                                                                        ( ( X1270 = X1271 )
                                                                                                                                       => ! [X1272: $i,X1273: $i] :
                                                                                                                                            ( ( X1272 = X1273 )
                                                                                                                                           => ( ( in @ X1272 @ X1270 )
                                                                                                                                             => ( in @ X1273 @ X1271 ) ) ) )
                                                                                                                                   => ( ! [X1274: $i,X1275: $i] :
                                                                                                                                          ( ( X1274 = X1275 )
                                                                                                                                         => ! [X1276: $i,X1277: $i] :
                                                                                                                                              ( ( X1276 = X1277 )
                                                                                                                                             => ( ( in @ X1276 @ X1274 )
                                                                                                                                              <=> ( in @ X1277 @ X1275 ) ) ) )
                                                                                                                                     => ( ! [X1278: $i > $o] :
                                                                                                                                            ( ? [X1279: $i] :
                                                                                                                                                ( ( X1278 @ X1279 )
                                                                                                                                                & ! [X1280: $i] :
                                                                                                                                                    ( ( X1278 @ X1280 )
                                                                                                                                                   => ( X1279 = X1280 ) ) )
                                                                                                                                           => ! [X1281: $i,X1282: $i] :
                                                                                                                                                ( ( X1278 @ X1281 )
                                                                                                                                               => ( ( X1278 @ X1282 )
                                                                                                                                                 => ( X1281 = X1282 ) ) ) )
                                                                                                                                       => ( ! [X1283: $i > $o,X1284: $i > $o] :
                                                                                                                                              ( ! [X1285: $i,X1286: $i] :
                                                                                                                                                  ( ( X1285 = X1286 )
                                                                                                                                                 => ( ( X1283 @ X1285 )
                                                                                                                                                  <=> ( X1284 @ X1286 ) ) )
                                                                                                                                             => ( ? [X1287: $i] :
                                                                                                                                                    ( ( X1283 @ X1287 )
                                                                                                                                                    & ! [X1288: $i] :
                                                                                                                                                        ( ( X1283 @ X1288 )
                                                                                                                                                       => ( X1287 = X1288 ) ) )
                                                                                                                                              <=> ? [X1289: $i] :
                                                                                                                                                    ( ( X1284 @ X1289 )
                                                                                                                                                    & ! [X1290: $i] :
                                                                                                                                                        ( ( X1284 @ X1290 )
                                                                                                                                                       => ( X1289 = X1290 ) ) ) ) )
                                                                                                                                         => ( ( emptyset = emptyset )
                                                                                                                                           => ( ! [X1291: $i,X1292: $i] :
                                                                                                                                                  ( ( X1291 = X1292 )
                                                                                                                                                 => ! [X1293: $i,X1294: $i] :
                                                                                                                                                      ( ( X1293 = X1294 )
                                                                                                                                                     => ( ( setadjoin @ X1291 @ X1293 )
                                                                                                                                                        = ( setadjoin @ X1292 @ X1294 ) ) ) )
                                                                                                                                             => ( ! [X1295: $i,X1296: $i] :
                                                                                                                                                    ( ( X1295 = X1296 )
                                                                                                                                                   => ( ( powerset @ X1295 )
                                                                                                                                                      = ( powerset @ X1296 ) ) )
                                                                                                                                               => ( ! [X1297: $i,X1298: $i] :
                                                                                                                                                      ( ( X1297 = X1298 )
                                                                                                                                                     => ( ( setunion @ X1297 )
                                                                                                                                                        = ( setunion @ X1298 ) ) )
                                                                                                                                                 => ( ( omega = omega )
                                                                                                                                                   => ( ! [X1299: $i > $o] :
                                                                                                                                                          ( ? [X1300: $i] :
                                                                                                                                                              ( ( X1299 @ X1300 )
                                                                                                                                                              & ! [X1301: $i] :
                                                                                                                                                                  ( ( X1299 @ X1301 )
                                                                                                                                                                 => ( X1300 = X1301 ) ) )
                                                                                                                                                         => ! [X1302: $i,X1303: $i] :
                                                                                                                                                              ( ( X1299 @ X1302 )
                                                                                                                                                             => ( ( X1299 @ X1303 )
                                                                                                                                                               => ( X1302 = X1303 ) ) ) )
                                                                                                                                                     => ( ! [X1304: $i > $o,X1305: $i > $o] :
                                                                                                                                                            ( ! [X1306: $i,X1307: $i] :
                                                                                                                                                                ( ( X1306 = X1307 )
                                                                                                                                                               => ( ( X1304 @ X1306 )
                                                                                                                                                                <=> ( X1305 @ X1307 ) ) )
                                                                                                                                                           => ( ? [X1308: $i] :
                                                                                                                                                                  ( ( X1304 @ X1308 )
                                                                                                                                                                  & ! [X1309: $i] :
                                                                                                                                                                      ( ( X1304 @ X1309 )
                                                                                                                                                                     => ( X1308 = X1309 ) ) )
                                                                                                                                                             => ( ? [X1310: $i] :
                                                                                                                                                                    ( ( X1305 @ X1310 )
                                                                                                                                                                    & ! [X1311: $i] :
                                                                                                                                                                        ( ( X1305 @ X1311 )
                                                                                                                                                                       => ( X1310 = X1311 ) ) )
                                                                                                                                                               => ( ( descr @ X1304 )
                                                                                                                                                                  = ( descr @ X1305 ) ) ) ) )
                                                                                                                                                       => ( ! [X1312: $i,X1313: $i] :
                                                                                                                                                              ( ( X1312 = X1313 )
                                                                                                                                                             => ! [X1314: $i > $o,X1315: $i > $o] :
                                                                                                                                                                  ( ! [X1316: $i] :
                                                                                                                                                                      ( ( in @ X1316 @ X1312 )
                                                                                                                                                                     => ! [X1317: $i] :
                                                                                                                                                                          ( ( in @ X1317 @ X1313 )
                                                                                                                                                                         => ( ( X1316 = X1317 )
                                                                                                                                                                           => ( ( X1314 @ X1316 )
                                                                                                                                                                            <=> ( X1315 @ X1317 ) ) ) ) )
                                                                                                                                                                 => ( ( dsetconstr @ X1312 @ X1314 )
                                                                                                                                                                    = ( dsetconstr @ X1313 @ X1315 ) ) ) )
                                                                                                                                                         => ( ! [X1318: $i,X1319: $i] :
                                                                                                                                                                ( ! [X1320: $i] :
                                                                                                                                                                    ( ( in @ X1320 @ X1318 )
                                                                                                                                                                   => ( in @ X1320 @ X1319 ) )
                                                                                                                                                               => ( subset @ X1318 @ X1319 ) )
                                                                                                                                                           => ( ! [X1321: $i,X1322: $i] :
                                                                                                                                                                  ( ( X1321 = X1322 )
                                                                                                                                                                 => ( subset @ X1322 @ X1321 ) )
                                                                                                                                                             => ( ! [X1323: $i,X1324: $i] :
                                                                                                                                                                    ( ( X1323 = X1324 )
                                                                                                                                                                   => ( subset @ X1323 @ X1324 ) )
                                                                                                                                                               => ( ! [X1325: $i,X1326: $i] :
                                                                                                                                                                      ( ! [X1327: $i] :
                                                                                                                                                                          ( ( in @ X1327 @ X1325 )
                                                                                                                                                                         => ( in @ X1327 @ X1326 ) )
                                                                                                                                                                     => ( subset @ X1325 @ X1326 ) )
                                                                                                                                                                 => ( ! [X1328: $i] : ( subset @ emptyset @ X1328 )
                                                                                                                                                                   => ( ! [X1329: $i,X1330: $i,X1331: $i] :
                                                                                                                                                                          ( ( subset @ X1329 @ X1330 )
                                                                                                                                                                         => ( ( in @ X1331 @ X1329 )
                                                                                                                                                                           => ( in @ X1331 @ X1330 ) ) )
                                                                                                                                                                     => ( ! [X1332: $i,X1333: $i,X1334: $i] :
                                                                                                                                                                            ( ( subset @ X1332 @ X1333 )
                                                                                                                                                                           => ( ~ ( in @ X1334 @ X1333 )
                                                                                                                                                                             => ~ ( in @ X1334 @ X1332 ) ) )
                                                                                                                                                                       => ( ! [X1335: $i,X1336: $i,X1337: $i] :
                                                                                                                                                                              ( ( in @ X1337 @ X1335 )
                                                                                                                                                                             => ( ~ ( in @ X1337 @ X1336 )
                                                                                                                                                                               => ~ ( subset @ X1335 @ X1336 ) ) )
                                                                                                                                                                         => ( ! [X1338: $i,X1339: $i] :
                                                                                                                                                                                ( ~ ( subset @ X1338 @ X1339 )
                                                                                                                                                                               => ( X1338 != X1339 ) )
                                                                                                                                                                           => ( ! [X1340: $i,X1341: $i,X1342: $i] :
                                                                                                                                                                                  ( ( in @ X1342 @ X1340 )
                                                                                                                                                                                 => ( ~ ( in @ X1342 @ X1341 )
                                                                                                                                                                                   => ( X1340 != X1341 ) ) )
                                                                                                                                                                             => ( ! [X1343: $i] : ( subset @ X1343 @ X1343 )
                                                                                                                                                                               => ( ! [X1344: $i,X1345: $i,X1346: $i] :
                                                                                                                                                                                      ( ( subset @ X1344 @ X1345 )
                                                                                                                                                                                     => ( ( subset @ X1345 @ X1346 )
                                                                                                                                                                                       => ( subset @ X1344 @ X1346 ) ) )
                                                                                                                                                                                 => ( ! [X1347: $i,X1348: $i] : ( subset @ X1348 @ ( setadjoin @ X1347 @ X1348 ) )
                                                                                                                                                                                   => ( ! [X1349: $i,X1350: $i,X1351: $i] :
                                                                                                                                                                                          ( ( subset @ X1349 @ X1351 )
                                                                                                                                                                                         => ( subset @ X1349 @ ( setadjoin @ X1350 @ X1351 ) ) )
                                                                                                                                                                                     => ( ! [X1352: $i,X1353: $i] :
                                                                                                                                                                                            ( ( subset @ X1352 @ X1353 )
                                                                                                                                                                                           => ( in @ X1352 @ ( powerset @ X1353 ) ) )
                                                                                                                                                                                       => ( ! [X1354: $i,X1355: $i] :
                                                                                                                                                                                              ( ( subset @ X1354 @ X1355 )
                                                                                                                                                                                             => ( ( subset @ X1355 @ X1354 )
                                                                                                                                                                                               => ( X1354 = X1355 ) ) )
                                                                                                                                                                                         => ( ! [X1356: $i] :
                                                                                                                                                                                                ( ( subset @ X1356 @ emptyset )
                                                                                                                                                                                               => ( X1356 = emptyset ) )
                                                                                                                                                                                           => ( ! [X1357: $i,X1358: $i] :
                                                                                                                                                                                                  ( ( subset @ X1358 @ X1357 )
                                                                                                                                                                                                 => ( in @ X1358 @ ( powerset @ X1357 ) ) )
                                                                                                                                                                                             => ( ! [X1359: $i,X1360: $i] :
                                                                                                                                                                                                    ( ( in @ X1360 @ ( powerset @ X1359 ) )
                                                                                                                                                                                                   => ( subset @ X1360 @ X1359 ) )
                                                                                                                                                                                               => ( ! [X1361: $i] : ( in @ X1361 @ ( powerset @ X1361 ) )
                                                                                                                                                                                                 => ( ! [X1362: $i,X1363: $i] :
                                                                                                                                                                                                        ( ( subset @ X1362 @ X1363 )
                                                                                                                                                                                                       => ( subset @ ( powerset @ X1362 ) @ ( powerset @ X1363 ) ) )
                                                                                                                                                                                                   => ( ! [X1364: $i,X1365: $i > $o] : ( in @ ( dsetconstr @ X1364 @ X1365 ) @ ( powerset @ X1364 ) )
                                                                                                                                                                                                     => ( ! [X1366: $i,X1367: $i > $o] : ( subset @ ( dsetconstr @ X1366 @ X1367 ) @ X1366 )
                                                                                                                                                                                                       => ( ! [X1368: $i,X1369: $i,X1370: $i] :
                                                                                                                                                                                                              ( ( in @ X1370 @ X1368 )
                                                                                                                                                                                                             => ( in @ X1370 @ ( binunion @ X1368 @ X1369 ) ) )
                                                                                                                                                                                                         => ( ! [X1371: $i,X1372: $i] : ( in @ X1372 @ ( setadjoin @ X1371 @ ( setadjoin @ X1372 @ emptyset ) ) )
                                                                                                                                                                                                           => ( ! [X1373: $i,X1374: $i,X1375: $i] :
                                                                                                                                                                                                                  ( ( in @ X1375 @ X1374 )
                                                                                                                                                                                                                 => ( in @ X1375 @ ( binunion @ X1373 @ X1374 ) ) )
                                                                                                                                                                                                             => ( ! [X1376: $i,X1377: $i,X1378: $i,X1379: $o] :
                                                                                                                                                                                                                    ( ( in @ X1378 @ ( binunion @ X1376 @ X1377 ) )
                                                                                                                                                                                                                   => ( ( ( in @ X1378 @ X1376 )
                                                                                                                                                                                                                       => X1379 )
                                                                                                                                                                                                                     => ( ( ( in @ X1378 @ X1377 )
                                                                                                                                                                                                                         => X1379 )
                                                                                                                                                                                                                       => X1379 ) ) )
                                                                                                                                                                                                               => ( ! [X1380: $i,X1381: $i,X1382: $i] :
                                                                                                                                                                                                                      ( ( in @ X1382 @ ( binunion @ X1380 @ X1381 ) )
                                                                                                                                                                                                                     => ( ( in @ X1382 @ X1380 )
                                                                                                                                                                                                                        | ( in @ X1382 @ X1381 ) ) )
                                                                                                                                                                                                                 => ( ! [X1383: $i,X1384: $i] : ( subset @ X1383 @ ( binunion @ X1383 @ X1384 ) )
                                                                                                                                                                                                                   => ( ! [X1385: $i,X1386: $i] : ( subset @ X1386 @ ( binunion @ X1385 @ X1386 ) )
                                                                                                                                                                                                                     => ( ! [X1387: $i,X1388: $i,X1389: $i] :
                                                                                                                                                                                                                            ( ( in @ X1389 @ X1387 )
                                                                                                                                                                                                                           => ( ( in @ X1389 @ X1388 )
                                                                                                                                                                                                                             => ( in @ X1389 @ ( binintersect @ X1387 @ X1388 ) ) ) )
                                                                                                                                                                                                                       => ( ! [X1390: $i,X1391: $i,X1392: $i] :
                                                                                                                                                                                                                              ( ( subset @ X1392 @ X1390 )
                                                                                                                                                                                                                             => ( ( subset @ X1392 @ X1391 )
                                                                                                                                                                                                                               => ( subset @ X1392 @ ( binintersect @ X1390 @ X1391 ) ) ) )
                                                                                                                                                                                                                         => ( ! [X1393: $i,X1394: $i,X1395: $i] :
                                                                                                                                                                                                                                ( ( in @ X1395 @ ( binintersect @ X1393 @ X1394 ) )
                                                                                                                                                                                                                               => ( in @ X1395 @ X1393 ) )
                                                                                                                                                                                                                           => ( ! [X1396: $i,X1397: $i] : ( subset @ ( binintersect @ X1396 @ X1397 ) @ X1396 )
                                                                                                                                                                                                                             => ( ! [X1398: $i,X1399: $i] :
                                                                                                                                                                                                                                    ( ( subset @ X1398 @ X1399 )
                                                                                                                                                                                                                                   => ( ( binintersect @ X1398 @ X1399 )
                                                                                                                                                                                                                                      = X1398 ) )
                                                                                                                                                                                                                               => ( ! [X1400: $i,X1401: $i] :
                                                                                                                                                                                                                                      ( ( ( binintersect @ X1400 @ X1401 )
                                                                                                                                                                                                                                        = X1401 )
                                                                                                                                                                                                                                     => ( subset @ X1401 @ X1400 ) )
                                                                                                                                                                                                                                 => ( ! [X1402: $i,X1403: $i,X1404: $i] :
                                                                                                                                                                                                                                        ( ( in @ X1404 @ ( binintersect @ X1402 @ X1403 ) )
                                                                                                                                                                                                                                       => ( in @ X1404 @ X1403 ) )
                                                                                                                                                                                                                                   => ( ! [X1405: $i,X1406: $i] :
                                                                                                                                                                                                                                          ( ~ ? [X1407: $i] :
                                                                                                                                                                                                                                                ( ( in @ X1407 @ X1405 )
                                                                                                                                                                                                                                                & ( in @ X1407 @ X1406 ) )
                                                                                                                                                                                                                                         => ( ( binintersect @ X1405 @ X1406 )
                                                                                                                                                                                                                                            = emptyset ) )
                                                                                                                                                                                                                                     => ( ! [X1408: $i,X1409: $i] : ( subset @ ( binintersect @ X1408 @ X1409 ) @ X1409 )
                                                                                                                                                                                                                                       => ( ! [X1410: $i,X1411: $i] :
                                                                                                                                                                                                                                              ( ( subset @ X1411 @ X1410 )
                                                                                                                                                                                                                                             => ( ( binintersect @ X1410 @ X1411 )
                                                                                                                                                                                                                                                = X1411 ) )
                                                                                                                                                                                                                                         => ( ! [X1412: $i,X1413: $i] :
                                                                                                                                                                                                                                                ( ( ( binintersect @ X1412 @ X1413 )
                                                                                                                                                                                                                                                  = X1412 )
                                                                                                                                                                                                                                               => ( subset @ X1412 @ X1413 ) )
                                                                                                                                                                                                                                           => ( ! [X1414: $i,X1415: $i,X1416: $i] :
                                                                                                                                                                                                                                                  ( ( binintersect @ X1414 @ ( binunion @ X1415 @ X1416 ) )
                                                                                                                                                                                                                                                  = ( binunion @ ( binintersect @ X1414 @ X1415 ) @ ( binintersect @ X1414 @ X1416 ) ) )
                                                                                                                                                                                                                                             => ( ! [X1417: $i,X1418: $i,X1419: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X1419 @ X1417 )
                                                                                                                                                                                                                                                   => ( ~ ( in @ X1419 @ X1418 )
                                                                                                                                                                                                                                                     => ( in @ X1419 @ ( setminus @ X1417 @ X1418 ) ) ) )
                                                                                                                                                                                                                                               => ( ! [X1420: $i,X1421: $i,X1422: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X1422 @ ( setminus @ X1420 @ X1421 ) )
                                                                                                                                                                                                                                                     => ( in @ X1422 @ X1420 ) )
                                                                                                                                                                                                                                                 => ( ! [X1423: $i,X1424: $i,X1425: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X1425 @ ( setminus @ X1423 @ X1424 ) )
                                                                                                                                                                                                                                                       => ~ ( in @ X1425 @ X1424 ) )
                                                                                                                                                                                                                                                   => ( ! [X1426: $i,X1427: $i] :
                                                                                                                                                                                                                                                          ( ( subset @ X1426 @ X1427 )
                                                                                                                                                                                                                                                         => ( ( setminus @ X1426 @ X1427 )
                                                                                                                                                                                                                                                            = emptyset ) )
                                                                                                                                                                                                                                                     => ( ! [X1428: $i,X1429: $i,X1430: $i] :
                                                                                                                                                                                                                                                            ( ~ ( in @ X1430 @ ( setminus @ X1428 @ X1429 ) )
                                                                                                                                                                                                                                                           => ( ( in @ X1430 @ X1428 )
                                                                                                                                                                                                                                                             => ( in @ X1430 @ X1429 ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1431: $i,X1432: $i,X1433: $i] :
                                                                                                                                                                                                                                                              ( ~ ( in @ X1433 @ ( setminus @ X1431 @ X1432 ) )
                                                                                                                                                                                                                                                             => ( ~ ( in @ X1433 @ X1432 )
                                                                                                                                                                                                                                                               => ~ ( in @ X1433 @ X1431 ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1434: $i,X1435: $i,X1436: $i] :
                                                                                                                                                                                                                                                                ( ~ ( in @ X1436 @ X1434 )
                                                                                                                                                                                                                                                               => ~ ( in @ X1436 @ ( setminus @ X1434 @ X1435 ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1437: $i,X1438: $i,X1439: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X1439 @ X1438 )
                                                                                                                                                                                                                                                                 => ~ ( in @ X1439 @ ( setminus @ X1437 @ X1438 ) ) )
                                                                                                                                                                                                                                                             => ( ! [X1440: $i,X1441: $i] : ( subset @ ( setminus @ X1440 @ X1441 ) @ X1440 )
                                                                                                                                                                                                                                                               => ( ! [X1442: $i,X1443: $i] :
                                                                                                                                                                                                                                                                      ( ( ( setminus @ X1442 @ X1443 )
                                                                                                                                                                                                                                                                        = emptyset )
                                                                                                                                                                                                                                                                     => ( subset @ X1442 @ X1443 ) )
                                                                                                                                                                                                                                                                 => ( ! [X1444: $i,X1445: $i,X1446: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X1446 @ ( symdiff @ X1444 @ X1445 ) )
                                                                                                                                                                                                                                                                       => ! [X1447: $o] :
                                                                                                                                                                                                                                                                            ( ( ( in @ X1446 @ X1444 )
                                                                                                                                                                                                                                                                             => ( ~ ( in @ X1446 @ X1445 )
                                                                                                                                                                                                                                                                               => X1447 ) )
                                                                                                                                                                                                                                                                           => ( ( ~ ( in @ X1446 @ X1444 )
                                                                                                                                                                                                                                                                               => ( ( in @ X1446 @ X1445 )
                                                                                                                                                                                                                                                                                 => X1447 ) )
                                                                                                                                                                                                                                                                             => X1447 ) ) )
                                                                                                                                                                                                                                                                   => ( ! [X1448: $i,X1449: $i,X1450: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X1450 @ X1448 )
                                                                                                                                                                                                                                                                         => ( ~ ( in @ X1450 @ X1449 )
                                                                                                                                                                                                                                                                           => ( in @ X1450 @ ( symdiff @ X1448 @ X1449 ) ) ) )
                                                                                                                                                                                                                                                                     => ( ! [X1451: $i,X1452: $i,X1453: $i] :
                                                                                                                                                                                                                                                                            ( ~ ( in @ X1453 @ X1451 )
                                                                                                                                                                                                                                                                           => ( ( in @ X1453 @ X1452 )
                                                                                                                                                                                                                                                                             => ( in @ X1453 @ ( symdiff @ X1451 @ X1452 ) ) ) )
                                                                                                                                                                                                                                                                       => ( ! [X1454: $i,X1455: $i,X1456: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X1456 @ X1454 )
                                                                                                                                                                                                                                                                             => ( ( in @ X1456 @ X1455 )
                                                                                                                                                                                                                                                                               => ~ ( in @ X1456 @ ( symdiff @ X1454 @ X1455 ) ) ) )
                                                                                                                                                                                                                                                                         => ( ! [X1457: $i,X1458: $i,X1459: $i] :
                                                                                                                                                                                                                                                                                ( ~ ( in @ X1459 @ X1457 )
                                                                                                                                                                                                                                                                               => ( ~ ( in @ X1459 @ X1458 )
                                                                                                                                                                                                                                                                                 => ~ ( in @ X1459 @ ( symdiff @ X1457 @ X1458 ) ) ) )
                                                                                                                                                                                                                                                                           => ( ! [X1460: $i,X1461: $i] : ( in @ X1461 @ ( setadjoin @ X1460 @ ( setadjoin @ X1461 @ emptyset ) ) )
                                                                                                                                                                                                                                                                             => ( ! [X1462: $i,X1463: $i] : ( in @ X1462 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1462 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1462 @ ( setadjoin @ X1463 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                               => ( ! [X1464: $i,X1465: $i] : ( in @ X1465 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1464 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1464 @ ( setadjoin @ X1465 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1466: $i,X1467: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1466 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1466 @ ( setadjoin @ X1467 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1468: $i,X1469: $i] : ( iskpair @ ( kpair @ X1468 @ X1469 ) )
                                                                                                                                                                                                                                                                                     => ( ! [X1470: $i,X1471: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X1471 @ X1470 )
                                                                                                                                                                                                                                                                                           => ( subset @ ( setadjoin @ X1471 @ emptyset ) @ X1470 ) )
                                                                                                                                                                                                                                                                                       => ( ! [X1472: $i,X1473: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X1473 @ X1472 )
                                                                                                                                                                                                                                                                                             => ( in @ ( setadjoin @ X1473 @ emptyset ) @ ( powerset @ X1472 ) ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1474: $i,X1475: $i,X1476: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X1476 @ X1474 )
                                                                                                                                                                                                                                                                                               => ( in @ ( setadjoin @ X1476 @ emptyset ) @ ( powerset @ ( binunion @ X1474 @ X1475 ) ) ) )
                                                                                                                                                                                                                                                                                           => ( ! [X1477: $i,X1478: $i,X1479: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X1479 @ ( setadjoin @ X1477 @ ( setadjoin @ X1478 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                 => ( ( X1479 = X1477 )
                                                                                                                                                                                                                                                                                                    | ( X1479 = X1478 ) ) )
                                                                                                                                                                                                                                                                                             => ( ! [X1480: $i,X1481: $i,X1482: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X1482 @ X1480 )
                                                                                                                                                                                                                                                                                                   => ! [X1483: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X1483 @ X1481 )
                                                                                                                                                                                                                                                                                                       => ( subset @ ( setadjoin @ X1482 @ ( setadjoin @ X1483 @ emptyset ) ) @ ( binunion @ X1480 @ X1481 ) ) ) )
                                                                                                                                                                                                                                                                                               => ( ! [X1484: $i,X1485: $i,X1486: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ X1486 @ X1484 )
                                                                                                                                                                                                                                                                                                     => ! [X1487: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X1487 @ X1485 )
                                                                                                                                                                                                                                                                                                         => ( in @ ( setadjoin @ X1486 @ ( setadjoin @ X1487 @ emptyset ) ) @ ( powerset @ ( binunion @ X1484 @ X1485 ) ) ) ) )
                                                                                                                                                                                                                                                                                                 => ( ! [X1488: $i,X1489: $i,X1490: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X1490 @ X1488 )
                                                                                                                                                                                                                                                                                                       => ! [X1491: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X1491 @ X1489 )
                                                                                                                                                                                                                                                                                                           => ( subset @ ( setadjoin @ ( setadjoin @ X1490 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1490 @ ( setadjoin @ X1491 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1488 @ X1489 ) ) ) ) )
                                                                                                                                                                                                                                                                                                   => ( ! [X1492: $i,X1493: $i,X1494: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X1494 @ X1492 )
                                                                                                                                                                                                                                                                                                         => ! [X1495: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X1495 @ X1493 )
                                                                                                                                                                                                                                                                                                             => ( in @ ( setadjoin @ ( setadjoin @ X1494 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1494 @ ( setadjoin @ X1495 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1492 @ X1493 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                     => ( ! [X1496: $i,X1497: $i,X1498: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X1498 @ X1496 )
                                                                                                                                                                                                                                                                                                           => ! [X1499: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X1499 @ X1497 )
                                                                                                                                                                                                                                                                                                               => ( in @ ( kpair @ X1498 @ X1499 ) @ ( powerset @ ( powerset @ ( binunion @ X1496 @ X1497 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                       => ( ! [X1500: $i,X1501: $i,X1502: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X1502 @ X1500 )
                                                                                                                                                                                                                                                                                                             => ! [X1503: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ X1503 @ X1501 )
                                                                                                                                                                                                                                                                                                                 => ( in @ ( kpair @ X1502 @ X1503 ) @ ( cartprod @ X1500 @ X1501 ) ) ) )
                                                                                                                                                                                                                                                                                                         => ( ! [X1504: $i,X1505: $i,X1506: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X1506 @ ( cartprod @ X1504 @ X1505 ) )
                                                                                                                                                                                                                                                                                                               => ? [X1507: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X1507 @ X1504 )
                                                                                                                                                                                                                                                                                                                    & ? [X1508: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( in @ X1508 @ X1505 )
                                                                                                                                                                                                                                                                                                                        & ( X1506
                                                                                                                                                                                                                                                                                                                          = ( kpair @ X1507 @ X1508 ) ) ) ) )
                                                                                                                                                                                                                                                                                                           => ( ! [X1509: $i,X1510: $i,X1511: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ X1511 @ ( cartprod @ X1509 @ X1510 ) )
                                                                                                                                                                                                                                                                                                                 => ( iskpair @ X1511 ) )
                                                                                                                                                                                                                                                                                                             => ( ! [X1512: $i,X1513: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X1513 @ ( setunion @ X1512 ) )
                                                                                                                                                                                                                                                                                                                   => ? [X1514: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( in @ X1514 @ X1512 )
                                                                                                                                                                                                                                                                                                                        & ( in @ X1513 @ X1514 ) ) )
                                                                                                                                                                                                                                                                                                               => ( ! [X1515: $i] : ( subset @ ( setunion @ ( setadjoin @ X1515 @ emptyset ) ) @ X1515 )
                                                                                                                                                                                                                                                                                                                 => ( ! [X1516: $i] : ( subset @ X1516 @ ( setunion @ ( setadjoin @ X1516 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                   => ( ! [X1517: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( setunion @ ( setadjoin @ X1517 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                          = X1517 )
                                                                                                                                                                                                                                                                                                                     => ( ! [X1518: $i,X1519: $i > $o] :
                                                                                                                                                                                                                                                                                                                            ( ! [X1520: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( in @ X1520 @ X1518 )
                                                                                                                                                                                                                                                                                                                               => ! [X1521: $i] :
                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1521 @ X1518 )
                                                                                                                                                                                                                                                                                                                                   => ( ( X1519 @ X1520 )
                                                                                                                                                                                                                                                                                                                                     => ( ( X1519 @ X1521 )
                                                                                                                                                                                                                                                                                                                                       => ( X1520 = X1521 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                           => ( ? [X1522: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1522 @ X1518 )
                                                                                                                                                                                                                                                                                                                                  & ( X1519 @ X1522 ) )
                                                                                                                                                                                                                                                                                                                             => ( singleton @ ( dsetconstr @ X1518 @ X1519 ) ) ) )
                                                                                                                                                                                                                                                                                                                       => ( ! [X1523: $i,X1524: $i > $o] :
                                                                                                                                                                                                                                                                                                                              ( ( ex1 @ X1523 @ X1524 )
                                                                                                                                                                                                                                                                                                                             => ? [X1525: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1525 @ X1523 )
                                                                                                                                                                                                                                                                                                                                  & ( X1524 @ X1525 ) ) )
                                                                                                                                                                                                                                                                                                                         => ( ! [X1526: $i,X1527: $i > $o,X1528: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( in @ X1528 @ X1526 )
                                                                                                                                                                                                                                                                                                                               => ( ( X1527 @ X1528 )
                                                                                                                                                                                                                                                                                                                                 => ( ! [X1529: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1529 @ X1526 )
                                                                                                                                                                                                                                                                                                                                       => ( ( X1527 @ X1529 )
                                                                                                                                                                                                                                                                                                                                         => ( X1529 = X1528 ) ) )
                                                                                                                                                                                                                                                                                                                                   => ( ex1 @ X1526 @ X1527 ) ) ) )
                                                                                                                                                                                                                                                                                                                           => ( ! [X1530: $i,X1531: $i > $o] :
                                                                                                                                                                                                                                                                                                                                  ( ! [X1532: $i] :
                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1532 @ X1530 )
                                                                                                                                                                                                                                                                                                                                     => ! [X1533: $i] :
                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1533 @ X1530 )
                                                                                                                                                                                                                                                                                                                                         => ( ( X1531 @ X1532 )
                                                                                                                                                                                                                                                                                                                                           => ( ( X1531 @ X1533 )
                                                                                                                                                                                                                                                                                                                                             => ( X1532 = X1533 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                 => ( ? [X1534: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1534 @ X1530 )
                                                                                                                                                                                                                                                                                                                                        & ( X1531 @ X1534 ) )
                                                                                                                                                                                                                                                                                                                                   => ( ex1 @ X1530 @ X1531 ) ) )
                                                                                                                                                                                                                                                                                                                             => ( ! [X1535: $i,X1536: $i] :
                                                                                                                                                                                                                                                                                                                                    ( ( ( setadjoin @ X1535 @ emptyset )
                                                                                                                                                                                                                                                                                                                                      = ( setadjoin @ X1536 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                   => ( X1535 = X1536 ) )
                                                                                                                                                                                                                                                                                                                               => ( ! [X1537: $i,X1538: $i,X1539: $i] :
                                                                                                                                                                                                                                                                                                                                      ( ( in @ ( setadjoin @ X1539 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1537 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1537 @ ( setadjoin @ X1538 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                     => ( X1537 = X1539 ) )
                                                                                                                                                                                                                                                                                                                                 => ( ! [X1540: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( iskpair @ X1540 )
                                                                                                                                                                                                                                                                                                                                       => ( singleton
                                                                                                                                                                                                                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1540 )
                                                                                                                                                                                                                                                                                                                                            @ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X1540 ) ) ) )
                                                                                                                                                                                                                                                                                                                                   => ( ! [X1541: $i] :
                                                                                                                                                                                                                                                                                                                                          ( ( singleton @ X1541 )
                                                                                                                                                                                                                                                                                                                                         => ( in @ ( setunion @ X1541 ) @ X1541 ) )
                                                                                                                                                                                                                                                                                                                                     => ( ! [X1542: $i,X1543: $i] :
                                                                                                                                                                                                                                                                                                                                            ( ( kfst @ ( kpair @ X1542 @ X1543 ) )
                                                                                                                                                                                                                                                                                                                                            = X1542 )
                                                                                                                                                                                                                                                                                                                                       => ( ! [X1544: $i,X1545: $i,X1546: $i] :
                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1546 @ ( cartprod @ X1544 @ X1545 ) )
                                                                                                                                                                                                                                                                                                                                             => ( in @ ( kfst @ X1546 ) @ X1544 ) )
                                                                                                                                                                                                                                                                                                                                         => ( ! [X1547: $i,X1548: $i,X1549: $i,X1550: $i] :
                                                                                                                                                                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1547 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1547 @ ( setadjoin @ X1548 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X1549 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1549 @ ( setadjoin @ X1550 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                               => ( X1547 = X1549 ) )
                                                                                                                                                                                                                                                                                                                                           => ( ! [X1551: $i,X1552: $i,X1553: $i,X1554: $i] :
                                                                                                                                                                                                                                                                                                                                                  ( ( ( kpair @ X1551 @ X1552 )
                                                                                                                                                                                                                                                                                                                                                    = ( kpair @ X1553 @ X1554 ) )
                                                                                                                                                                                                                                                                                                                                                 => ( X1551 = X1553 ) )
                                                                                                                                                                                                                                                                                                                                             => ( ! [X1555: $i,X1556: $i] :
                                                                                                                                                                                                                                                                                                                                                    ( ( X1555 = X1556 )
                                                                                                                                                                                                                                                                                                                                                   => ( ( setadjoin @ X1555 @ ( setadjoin @ X1556 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                      = ( setadjoin @ X1555 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                               => ( ! [X1557: $i,X1558: $i] :
                                                                                                                                                                                                                                                                                                                                                      ( ( X1557 = X1558 )
                                                                                                                                                                                                                                                                                                                                                     => ( ( setadjoin @ ( setadjoin @ X1557 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1557 @ ( setadjoin @ X1558 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X1557 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1559: $i,X1560: $i,X1561: $i,X1562: $i] :
                                                                                                                                                                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1559 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1559 @ ( setadjoin @ X1560 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X1561 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1561 @ ( setadjoin @ X1562 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                                       => ( ( X1561 = X1562 )
                                                                                                                                                                                                                                                                                                                                                         => ( X1560 = X1562 ) ) )
                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1563: $i,X1564: $i,X1565: $i] :
                                                                                                                                                                                                                                                                                                                                                          ( ( ( setadjoin @ X1563 @ ( setadjoin @ X1564 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                            = ( setadjoin @ X1565 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                         => ( X1563 = X1564 ) )
                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1566: $i,X1567: $i,X1568: $i,X1569: $i] :
                                                                                                                                                                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1566 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1566 @ ( setadjoin @ X1567 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X1568 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1568 @ ( setadjoin @ X1569 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                                           => ( X1567 = X1569 ) )
                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1570: $i,X1571: $i,X1572: $i,X1573: $i] :
                                                                                                                                                                                                                                                                                                                                                              ( ( ( kpair @ X1570 @ X1571 )
                                                                                                                                                                                                                                                                                                                                                                = ( kpair @ X1572 @ X1573 ) )
                                                                                                                                                                                                                                                                                                                                                             => ( X1571 = X1573 ) )
                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1574: $i] :
                                                                                                                                                                                                                                                                                                                                                                ( ( iskpair @ X1574 )
                                                                                                                                                                                                                                                                                                                                                               => ( singleton
                                                                                                                                                                                                                                                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1574 )
                                                                                                                                                                                                                                                                                                                                                                    @ ^ [Z0: $i] :
                                                                                                                                                                                                                                                                                                                                                                        ( X1574
                                                                                                                                                                                                                                                                                                                                                                        = ( kpair @ ( kfst @ X1574 ) @ Z0 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1575: $i,X1576: $i] :
                                                                                                                                                                                                                                                                                                                                                                  ( ( ksnd @ ( kpair @ X1575 @ X1576 ) )
                                                                                                                                                                                                                                                                                                                                                                  = X1576 )
                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1577: $i] :
                                                                                                                                                                                                                                                                                                                                                                    ( ( iskpair @ X1577 )
                                                                                                                                                                                                                                                                                                                                                                   => ( ( kpair @ ( kfst @ X1577 ) @ ( ksnd @ X1577 ) )
                                                                                                                                                                                                                                                                                                                                                                      = X1577 ) )
                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1578: $i,X1579: $i,X1580: $i] :
                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1580 @ ( cartprod @ X1578 @ X1579 ) )
                                                                                                                                                                                                                                                                                                                                                                     => ( in @ ( ksnd @ X1580 ) @ X1579 ) )
                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1581: $i,X1582: $i,X1583: $i,X1584: $i] :
                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ ( kpair @ X1583 @ X1584 ) @ ( cartprod @ X1581 @ X1582 ) )
                                                                                                                                                                                                                                                                                                                                                                       => ( in @ X1583 @ X1581 ) )
                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1585: $i,X1586: $i,X1587: $i,X1588: $i] :
                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ ( kpair @ X1587 @ X1588 ) @ ( cartprod @ X1585 @ X1586 ) )
                                                                                                                                                                                                                                                                                                                                                                         => ( in @ X1588 @ X1586 ) )
                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1589: $i,X1590: $i,X1591: $i] :
                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1591 @ X1589 )
                                                                                                                                                                                                                                                                                                                                                                           => ! [X1592: $i] :
                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1592 @ X1590 )
                                                                                                                                                                                                                                                                                                                                                                               => ( ( kpair @ X1591 @ X1592 )
                                                                                                                                                                                                                                                                                                                                                                                  = ( kpair @ X1591 @ X1592 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1593: $i,X1594: $i,X1595: $i] :
                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1595 @ X1593 )
                                                                                                                                                                                                                                                                                                                                                                             => ! [X1596: $i] :
                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1596 @ X1594 )
                                                                                                                                                                                                                                                                                                                                                                                 => ( ( kfst @ ( kpair @ X1595 @ X1596 ) )
                                                                                                                                                                                                                                                                                                                                                                                    = X1595 ) ) )
                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1597: $i,X1598: $i,X1599: $i] :
                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1599 @ X1597 )
                                                                                                                                                                                                                                                                                                                                                                               => ! [X1600: $i] :
                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1600 @ X1598 )
                                                                                                                                                                                                                                                                                                                                                                                   => ( ( ksnd @ ( kpair @ X1599 @ X1600 ) )
                                                                                                                                                                                                                                                                                                                                                                                      = X1600 ) ) )
                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1601: $i,X1602: $i,X1603: $i] :
                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1603 @ ( cartprod @ X1601 @ X1602 ) )
                                                                                                                                                                                                                                                                                                                                                                                 => ( ( kpair @ ( kfst @ X1603 ) @ ( ksnd @ X1603 ) )
                                                                                                                                                                                                                                                                                                                                                                                    = X1603 ) )
                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1604: $i,X1605: $i,X1606: $i > $i > $o,X1607: $i] :
                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1607 @ X1604 )
                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1608: $i] :
                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1608 @ X1605 )
                                                                                                                                                                                                                                                                                                                                                                                       => ( ( X1606 @ X1607 @ X1608 )
                                                                                                                                                                                                                                                                                                                                                                                         => ( in @ ( kpair @ X1607 @ X1608 ) @ ( dpsetconstr @ X1604 @ X1605 @ X1606 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1609: $i,X1610: $i,X1611: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1609 @ X1610 @ X1611 ) @ ( cartprod @ X1609 @ X1610 ) )
                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1612: $i,X1613: $i,X1614: $i > $i > $o] : ( breln @ X1612 @ X1613 @ ( dpsetconstr @ X1612 @ X1613 @ X1614 ) )
                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1615: $i,X1616: $i,X1617: $i > $i > $o,X1618: $i] :
                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1618 @ X1615 )
                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1619: $i] :
                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1619 @ X1616 )
                                                                                                                                                                                                                                                                                                                                                                                             => ( ( in @ ( kpair @ X1618 @ X1619 ) @ ( dpsetconstr @ X1615 @ X1616 @ X1617 ) )
                                                                                                                                                                                                                                                                                                                                                                                               => ( X1617 @ X1618 @ X1619 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1620: $i,X1621: $i,X1622: $i > $i > $o,X1623: $i,X1624: $i] :
                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ ( kpair @ X1623 @ X1624 ) @ ( dpsetconstr @ X1620 @ X1621 @ X1622 ) )
                                                                                                                                                                                                                                                                                                                                                                                           => ( in @ X1623 @ X1620 ) )
                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1625: $i,X1626: $i,X1627: $i > $i > $o,X1628: $i,X1629: $i] :
                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ ( kpair @ X1628 @ X1629 ) @ ( dpsetconstr @ X1625 @ X1626 @ X1627 ) )
                                                                                                                                                                                                                                                                                                                                                                                             => ( in @ X1629 @ X1626 ) )
                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1630: $i,X1631: $i,X1632: $i > $i > $o,X1633: $i,X1634: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ ( kpair @ X1633 @ X1634 ) @ ( dpsetconstr @ X1630 @ X1631 @ X1632 ) )
                                                                                                                                                                                                                                                                                                                                                                                               => ( X1632 @ X1633 @ X1634 ) )
                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1635: $i,X1636: $i,X1637: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                  ( ( func @ X1635 @ X1636 @ X1637 )
                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1638: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1638 @ X1635 )
                                                                                                                                                                                                                                                                                                                                                                                                     => ( singleton
                                                                                                                                                                                                                                                                                                                                                                                                        @ ( dsetconstr @ X1636
                                                                                                                                                                                                                                                                                                                                                                                                          @ ^ [Z0: $i] : ( in @ ( kpair @ X1638 @ Z0 ) @ X1637 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1639: $i,X1640: $i,X1641: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                    ( ( func @ X1639 @ X1640 @ X1641 )
                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1642: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1642 @ X1639 )
                                                                                                                                                                                                                                                                                                                                                                                                       => ( in
                                                                                                                                                                                                                                                                                                                                                                                                          @ ( setunion
                                                                                                                                                                                                                                                                                                                                                                                                            @ ( dsetconstr @ X1640
                                                                                                                                                                                                                                                                                                                                                                                                              @ ^ [Z0: $i] : ( in @ ( kpair @ X1642 @ Z0 ) @ X1641 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                          @ X1640 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1643: $i,X1644: $i,X1645: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                      ( ( func @ X1643 @ X1644 @ X1645 )
                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1646: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1646 @ X1643 )
                                                                                                                                                                                                                                                                                                                                                                                                         => ( in @ ( ap @ X1643 @ X1644 @ X1645 @ X1646 ) @ X1644 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1647: $i,X1648: $i,X1649: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1649 @ ( funcSet @ X1647 @ X1648 ) )
                                                                                                                                                                                                                                                                                                                                                                                                       => ( func @ X1647 @ X1648 @ X1649 ) )
                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1650: $i,X1651: $i,X1652: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1652 @ ( funcSet @ X1650 @ X1651 ) )
                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1653: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1653 @ X1650 )
                                                                                                                                                                                                                                                                                                                                                                                                             => ( in @ ( ap @ X1650 @ X1651 @ X1652 @ X1653 ) @ X1651 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1654: $i,X1655: $i,X1656: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                            ( ( func @ X1654 @ X1655 @ X1656 )
                                                                                                                                                                                                                                                                                                                                                                                                           => ( in @ X1656 @ ( funcSet @ X1654 @ X1655 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1657: $i,X1658: $i,X1659: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                              ( ! [X1660: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1660 @ X1657 )
                                                                                                                                                                                                                                                                                                                                                                                                                 => ( in @ ( X1659 @ X1660 ) @ X1658 ) )
                                                                                                                                                                                                                                                                                                                                                                                                             => ( func @ X1657 @ X1658
                                                                                                                                                                                                                                                                                                                                                                                                                @ ( dpsetconstr @ X1657 @ X1658
                                                                                                                                                                                                                                                                                                                                                                                                                  @ ^ [Z0: $i] : ( $eq @ ( X1659 @ Z0 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1661: $i,X1662: $i,X1663: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                ( ! [X1664: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1664 @ X1661 )
                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ ( X1663 @ X1664 ) @ X1662 ) )
                                                                                                                                                                                                                                                                                                                                                                                                               => ( func @ X1661 @ X1662 @ ( lam @ X1661 @ X1662 @ X1663 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1665: $i,X1666: $i,X1667: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                  ( ! [X1668: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1668 @ X1665 )
                                                                                                                                                                                                                                                                                                                                                                                                                     => ( in @ ( X1667 @ X1668 ) @ X1666 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                 => ( in @ ( lam @ X1665 @ X1666 @ X1667 ) @ ( funcSet @ X1665 @ X1666 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1669: $i,X1670: $i,X1671: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( breln @ X1669 @ X1670 @ X1671 )
                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1672: $i > $o] :
                                                                                                                                                                                                                                                                                                                                                                                                                        ( ! [X1673: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1673 @ X1669 )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1674: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1674 @ X1670 )
                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( in @ ( kpair @ X1673 @ X1674 ) @ X1671 )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( X1672 @ ( kpair @ X1673 @ X1674 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1675: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1675 @ X1671 )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ( X1672 @ X1675 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1676: $i,X1677: $i,X1678: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( breln @ X1676 @ X1677 @ X1678 )
                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1679: $i > $o] :
                                                                                                                                                                                                                                                                                                                                                                                                                          ( ! [X1680: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1680 @ X1676 )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1681: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1681 @ X1677 )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( in @ ( kpair @ X1680 @ X1681 ) @ X1678 )
                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( X1679 @ ( kpair @ X1680 @ X1681 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1682: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1682 @ X1678 )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ( X1679 @ X1682 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1683: $i,X1684: $i > $o] :
                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( ex1 @ X1683 @ X1684 )
                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1685: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1685 @ X1683 )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1686: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1686 @ X1683 )
                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( X1684 @ X1685 )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( X1684 @ X1686 )
                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( X1685 = X1686 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1687: $i,X1688: $i,X1689: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( func @ X1687 @ X1688 @ X1689 )
                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1690: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1690 @ X1687 )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ( in @ ( kpair @ X1690 @ ( ap @ X1687 @ X1688 @ X1689 @ X1690 ) ) @ X1689 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1691: $i,X1692: $i,X1693: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1693 @ ( funcSet @ X1691 @ X1692 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1694: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1694 @ X1691 )
                                                                                                                                                                                                                                                                                                                                                                                                                               => ( in @ ( kpair @ X1694 @ ( ap @ X1691 @ X1692 @ X1693 @ X1694 ) ) @ X1693 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1695: $i,X1696: $i,X1697: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( func @ X1695 @ X1696 @ X1697 )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1698: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1698 @ X1695 )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1699: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1699 @ X1696 )
                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( in @ ( kpair @ X1698 @ X1699 ) @ X1697 )
                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( ap @ X1695 @ X1696 @ X1697 @ X1698 )
                                                                                                                                                                                                                                                                                                                                                                                                                                          = X1699 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1700: $i,X1701: $i,X1702: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( func @ X1700 @ X1701 @ X1702 )
                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1703: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( func @ X1700 @ X1701 @ X1703 )
                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1704: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1704 @ X1700 )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( ap @ X1700 @ X1701 @ X1702 @ X1704 )
                                                                                                                                                                                                                                                                                                                                                                                                                                            = ( ap @ X1700 @ X1701 @ X1703 @ X1704 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1705: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1705 @ X1700 )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1706: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1706 @ X1701 )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ( in @ ( kpair @ X1705 @ X1706 ) @ X1703 )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( in @ ( kpair @ X1705 @ X1706 ) @ X1702 ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1707: $i,X1708: $i,X1709: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1709 @ ( funcSet @ X1707 @ X1708 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1710: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1710 @ X1707 )
                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1711: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1711 @ X1708 )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( in @ ( kpair @ X1710 @ X1711 ) @ X1709 )
                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ( ap @ X1707 @ X1708 @ X1709 @ X1710 )
                                                                                                                                                                                                                                                                                                                                                                                                                                              = X1711 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1712: $i,X1713: $i,X1714: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( breln @ X1712 @ X1713 @ X1714 )
                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1715: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( breln @ X1712 @ X1713 @ X1715 )
                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1716: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1716 @ X1712 )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1717: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1717 @ X1713 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( in @ ( kpair @ X1716 @ X1717 ) @ X1714 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ ( kpair @ X1716 @ X1717 ) @ X1715 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( subset @ X1714 @ X1715 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1718: $i,X1719: $i,X1720: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( breln @ X1718 @ X1719 @ X1720 )
                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1721: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( breln @ X1718 @ X1719 @ X1721 )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1722: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1722 @ X1718 )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1723: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1723 @ X1719 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( in @ ( kpair @ X1722 @ X1723 ) @ X1720 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( in @ ( kpair @ X1722 @ X1723 ) @ X1721 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1724: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1724 @ X1718 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1725: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1725 @ X1719 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( in @ ( kpair @ X1724 @ X1725 ) @ X1721 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ ( kpair @ X1724 @ X1725 ) @ X1720 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( X1720 = X1721 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1726: $i,X1727: $i,X1728: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( func @ X1726 @ X1727 @ X1728 )
                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1729: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( func @ X1726 @ X1727 @ X1729 )
                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1730: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1730 @ X1726 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( ap @ X1726 @ X1727 @ X1728 @ X1730 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                    = ( ap @ X1726 @ X1727 @ X1729 @ X1730 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( X1728 = X1729 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1731: $i,X1732: $i,X1733: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1733 @ ( funcSet @ X1731 @ X1732 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1734: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1734 @ ( funcSet @ X1731 @ X1732 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1735: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1735 @ X1731 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( ap @ X1731 @ X1732 @ X1733 @ X1735 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                      = ( ap @ X1731 @ X1732 @ X1734 @ X1735 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( X1733 = X1734 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1736: $i,X1737: $i,X1738: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1738 @ ( funcSet @ X1736 @ X1737 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1739: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1739 @ X1736 )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( ap @ X1736 @ X1737 @ X1738 @ X1739 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                  = ( ap @ X1736 @ X1737 @ X1738 @ X1739 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1740: $i,X1741: $i,X1742: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( func @ X1740 @ X1741 @ X1742 )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1743: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1743 @ X1740 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( ap @ X1740 @ X1741 @ X1742 @ X1743 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                    = ( ap @ X1740 @ X1741 @ X1742 @ X1743 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1744: $i,X1745: $i,X1746: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ! [X1747: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1747 @ X1744 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ ( X1746 @ X1747 ) @ X1745 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1748: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1748 @ X1744 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( ap @ X1744 @ X1745 @ ( lam @ X1744 @ X1745 @ X1746 ) @ X1748 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                      = ( X1746 @ X1748 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1749: $i,X1750: $i,X1751: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( func @ X1749 @ X1750 @ X1751 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( lam @ X1749 @ X1750 @ ( ap @ X1749 @ X1750 @ X1751 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                    = X1751 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1752: $i,X1753: $i,X1754: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ! [X1755: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1755 @ X1752 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ ( X1754 @ X1755 ) @ X1753 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( lam @ X1752 @ X1753 @ X1754 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                      = ( lam @ X1752 @ X1753 @ X1754 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1756: $i,X1757: $i,X1758: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ! [X1759: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1759 @ X1756 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( in @ ( X1758 @ X1759 ) @ X1757 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1760: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1760 @ X1756 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( ap @ X1756 @ X1757 @ ( lam @ X1756 @ X1757 @ X1758 ) @ X1760 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                            = ( X1758 @ X1760 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1761: $i,X1762: $i,X1763: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1763 @ ( funcSet @ X1761 @ X1762 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( lam @ X1761 @ X1762 @ ( ap @ X1761 @ X1762 @ X1763 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                          = X1763 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1764: $i,X1765: $o,X1766: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1766 @ X1764 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1767: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1767 @ X1764 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ~ X1765
                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( in @ X1767
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  @ ( dsetconstr @ X1764
                                                                                                                                                                                                                                                                                                                                                                                                                                                                    @ ^ [Z0: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( X1765
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          & ( Z0 = X1766 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        | ( ~ X1765
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          & ( Z0 = X1767 ) ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1768: $i,X1769: $o,X1770: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1770 @ X1768 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1771: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1771 @ X1768 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ~ X1769
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( dsetconstr @ X1768
                                                                                                                                                                                                                                                                                                                                                                                                                                                                      @ ^ [Z0: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( X1769
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            & ( Z0 = X1770 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          | ( ~ X1769
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            & ( Z0 = X1771 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                    = ( setadjoin @ X1771 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1772: $i,X1773: $o,X1774: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1774 @ X1772 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1775: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1775 @ X1772 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( X1773
                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ X1774
                                                                                                                                                                                                                                                                                                                                                                                                                                                                      @ ( dsetconstr @ X1772
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        @ ^ [Z0: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( X1773
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              & ( Z0 = X1774 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            | ( ~ X1773
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              & ( Z0 = X1775 ) ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1776: $i,X1777: $o,X1778: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1778 @ X1776 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1779: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1779 @ X1776 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( X1777
                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( dsetconstr @ X1776
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          @ ^ [Z0: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( X1777
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                & ( Z0 = X1778 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | ( ~ X1777
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                & ( Z0 = X1779 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        = ( setadjoin @ X1778 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1780: $i,X1781: $o,X1782: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1782 @ X1780 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1783: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1783 @ X1780 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( singleton
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        @ ( dsetconstr @ X1780
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          @ ^ [Z0: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( X1781
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                & ( Z0 = X1782 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | ( ~ X1781
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                & ( Z0 = X1783 ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1784: $i,X1785: $o,X1786: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1786 @ X1784 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1787: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1787 @ X1784 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ ( if @ X1784 @ X1785 @ X1786 @ X1787 ) @ X1784 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1788: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( singleton @ X1788 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1789: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1789 @ X1788 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( setunion @ X1788 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            = X1789 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1790: $i,X1791: $o,X1792: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1792 @ X1790 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1793: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1793 @ X1790 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( X1791
                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ( if @ X1790 @ X1791 @ X1792 @ X1793 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                = X1792 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1794: $i,X1795: $o,X1796: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1796 @ X1794 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1797: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1797 @ X1794 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ~ X1795
                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( if @ X1794 @ X1795 @ X1796 @ X1797 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  = X1797 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1798: $i,X1799: $o,X1800: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1800 @ X1798 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1801: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1801 @ X1798 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( in @ ( if @ X1798 @ X1799 @ X1800 @ X1801 ) @ ( setadjoin @ X1800 @ ( setadjoin @ X1801 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1802: $i,X1803: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1803 @ ( powerset @ X1802 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1804: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1804 @ ( powerset @ X1802 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( in @ ( binintersect @ X1803 @ X1804 ) @ ( powerset @ X1802 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1805: $i,X1806: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1806 @ ( powerset @ X1805 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1807: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1807 @ ( powerset @ X1805 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ ( binunion @ X1806 @ X1807 ) @ ( powerset @ X1805 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1808: $i,X1809: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1809 @ ( powerset @ X1808 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( in @ ( powerset @ X1809 ) @ ( powerset @ ( powerset @ X1808 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1810: $i,X1811: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1811 @ ( powerset @ X1810 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1812: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1812 @ ( powerset @ X1810 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ ( setminus @ X1811 @ X1812 ) @ ( powerset @ X1810 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1813: $i,X1814: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1814 @ ( powerset @ X1813 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( in @ ( setminus @ X1813 @ X1814 ) @ ( powerset @ X1813 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1815: $i,X1816: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1816 @ ( powerset @ X1815 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1817: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1817 @ ( powerset @ X1815 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1818: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1818 @ X1815 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( in @ X1818 @ X1816 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ X1818 @ X1817 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1819: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1819 @ X1815 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( in @ X1819 @ X1817 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( in @ X1819 @ X1816 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( X1816 = X1817 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1820: $i,X1821: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1821 @ ( powerset @ X1820 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1822: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1822 @ ( powerset @ X1820 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1823: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1823 @ X1820 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( in @ X1823 @ X1821 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( in @ X1823 @ X1822 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( subset @ X1821 @ X1822 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1824: $i,X1825: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1825 @ ( powerset @ X1824 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1826: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1826 @ ( powerset @ X1824 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1827: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1827 @ X1824 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( in @ X1827 @ X1825 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ X1827 @ X1826 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( in @ X1825 @ ( powerset @ X1826 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1828: $i,X1829: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1829 @ ( powerset @ X1828 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1830: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1830 @ ( powerset @ X1828 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1831: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1831 @ X1828 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( in @ X1829 @ ( powerset @ X1830 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( in @ X1831 @ X1829 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( in @ X1831 @ X1830 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1832: $i,X1833: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1833 @ ( powerset @ X1832 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1834: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1834 @ X1832 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( in @ X1834 @ X1833 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ~ ( in @ X1834 @ ( setminus @ X1832 @ X1833 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1835: $i,X1836: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1836 @ ( powerset @ X1835 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1837: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1837 @ X1835 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ~ ( in @ X1837 @ ( setminus @ X1835 @ X1836 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ X1837 @ X1836 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1838: $i,X1839: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1839 @ ( powerset @ X1838 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1840: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1840 @ ( powerset @ X1838 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1841: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1841 @ X1838 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ~ ( in @ X1841 @ X1839 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ~ ( in @ X1841 @ ( binintersect @ X1839 @ X1840 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1842: $i,X1843: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1843 @ ( powerset @ X1842 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1844: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1844 @ ( powerset @ X1842 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1845: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1845 @ X1842 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ~ ( in @ X1845 @ X1844 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ~ ( in @ X1845 @ ( binintersect @ X1843 @ X1844 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1846: $i,X1847: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1847 @ ( powerset @ X1846 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1848: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1848 @ ( powerset @ X1846 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1849: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1849 @ X1846 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( subset @ X1847 @ ( setminus @ X1846 @ X1848 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( in @ X1849 @ X1848 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ~ ( in @ X1849 @ X1847 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1850: $i,X1851: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1851 @ ( powerset @ X1850 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1852: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1852 @ ( powerset @ X1850 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1853: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1853 @ X1850 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( subset @ X1851 @ X1852 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ~ ( in @ X1853 @ X1852 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ~ ( in @ X1853 @ X1851 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1854: $i,X1855: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1855 @ ( powerset @ X1854 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1856: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1856 @ ( powerset @ X1854 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( subset @ X1855 @ X1856 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( subset @ ( setminus @ X1854 @ X1856 ) @ ( setminus @ X1854 @ X1855 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1857: $i,X1858: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1858 @ ( powerset @ X1857 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1859: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1859 @ ( powerset @ X1857 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( subset @ ( setminus @ X1857 @ X1859 ) @ ( setminus @ X1857 @ X1858 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( subset @ X1858 @ X1859 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1860: $i,X1861: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1861 @ ( powerset @ X1860 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1862: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1862 @ X1860 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( in @ X1862 @ X1861 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( in @ X1862 @ ( setminus @ X1860 @ ( setminus @ X1860 @ X1861 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1863: $i,X1864: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1864 @ ( powerset @ X1863 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1865: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1865 @ X1863 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( in @ X1865 @ ( setminus @ X1863 @ ( setminus @ X1863 @ X1864 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ X1865 @ X1864 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1866: $i,X1867: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1867 @ ( powerset @ X1866 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( subset @ X1867 @ ( setminus @ X1866 @ ( setminus @ X1866 @ X1867 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1868: $i,X1869: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1869 @ ( powerset @ X1868 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( subset @ ( setminus @ X1868 @ ( setminus @ X1868 @ X1869 ) ) @ X1869 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1870: $i,X1871: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1871 @ ( powerset @ X1870 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( X1871
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          = ( setminus @ X1870 @ ( setminus @ X1870 @ X1871 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1872: $i,X1873: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1873 @ ( powerset @ X1872 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1874: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1874 @ ( powerset @ X1872 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1875: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1875 @ X1872 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( in @ X1875 @ ( setminus @ X1872 @ X1873 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ~ ( in @ X1875 @ ( binintersect @ X1873 @ X1874 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1876: $i,X1877: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1877 @ ( powerset @ X1876 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1878: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1878 @ ( powerset @ X1876 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1879: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1879 @ X1876 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( in @ X1879 @ ( setminus @ X1876 @ X1877 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( in @ X1879 @ ( setminus @ X1876 @ ( binintersect @ X1877 @ X1878 ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1880: $i,X1881: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1881 @ ( powerset @ X1880 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1882: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1882 @ ( powerset @ X1880 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( subset @ ( setminus @ X1880 @ X1881 ) @ ( setminus @ X1880 @ ( binintersect @ X1881 @ X1882 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1883: $i,X1884: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1884 @ ( powerset @ X1883 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1885: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1885 @ ( powerset @ X1883 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ ( setminus @ X1883 @ X1884 ) @ ( powerset @ ( setminus @ X1883 @ ( binintersect @ X1884 @ X1885 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1886: $i,X1887: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1887 @ ( powerset @ X1886 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1888: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1888 @ ( powerset @ X1886 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( subset @ X1887 @ ( setminus @ X1886 @ X1888 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1889: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1889 @ X1886 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ( in @ X1889 @ X1888 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( in @ X1889 @ ( setminus @ X1886 @ X1887 ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1890: $i,X1891: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1891 @ ( powerset @ X1890 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1892: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1892 @ ( powerset @ X1890 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( subset @ X1891 @ ( setminus @ X1890 @ X1892 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( subset @ X1892 @ ( setminus @ X1890 @ X1891 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1893: $i,X1894: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1894 @ ( powerset @ X1893 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1895: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1895 @ ( powerset @ X1893 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1896: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1896 @ X1893 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ~ ( in @ X1896 @ ( binunion @ X1894 @ X1895 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ~ ( in @ X1896 @ X1894 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1897: $i,X1898: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1898 @ ( powerset @ X1897 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1899: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1899 @ ( powerset @ X1897 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1900: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1900 @ X1897 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ~ ( in @ X1900 @ ( binunion @ X1898 @ X1899 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ~ ( in @ X1900 @ X1899 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1901: $i,X1902: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1902 @ ( powerset @ X1901 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1903: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1903 @ ( powerset @ X1901 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1904: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1904 @ ( powerset @ X1901 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1905: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1905 @ X1901 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( in @ X1905 @ ( binintersect @ X1902 @ X1903 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ X1905 @ ( binunion @ X1902 @ X1904 ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1906: $i,X1907: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1907 @ ( powerset @ X1906 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1908: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1908 @ ( powerset @ X1906 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1909: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1909 @ ( powerset @ X1906 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1910: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1910 @ X1906 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( in @ X1910 @ ( binintersect @ X1907 @ X1908 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( in @ X1910 @ ( binunion @ X1908 @ X1909 ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1911: $i,X1912: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1912 @ ( powerset @ X1911 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1913: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1913 @ ( powerset @ X1911 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1914: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1914 @ ( powerset @ X1911 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1915: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1915 @ X1911 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( in @ X1915 @ ( binintersect @ X1912 @ X1913 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( in @ X1915 @ ( binintersect @ ( binunion @ X1912 @ X1914 ) @ ( binunion @ X1913 @ X1914 ) ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1916: $i,X1917: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1917 @ ( powerset @ X1916 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1918: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1918 @ ( powerset @ X1916 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1919: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1919 @ ( powerset @ X1916 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ ( binintersect @ X1917 @ X1918 ) @ ( powerset @ ( binintersect @ ( binunion @ X1917 @ X1919 ) @ ( binunion @ X1918 @ X1919 ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1920: $i,X1921: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1921 @ ( powerset @ X1920 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1922: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1922 @ ( powerset @ X1920 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1923: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1923 @ X1920 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( in @ X1923 @ ( setminus @ X1920 @ ( binunion @ X1921 @ X1922 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ~ ( in @ X1923 @ X1921 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1924: $i,X1925: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1925 @ ( powerset @ X1924 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1926: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1926 @ ( powerset @ X1924 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1927: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1927 @ X1924 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ( in @ X1927 @ ( setminus @ X1924 @ ( binunion @ X1925 @ X1926 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( in @ X1927 @ ( setminus @ X1924 @ X1925 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1928: $i,X1929: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1929 @ ( powerset @ X1928 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1930: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1930 @ ( powerset @ X1928 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1931: $o,X1932: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1932 @ X1928 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ( in @ X1932 @ ( binunion @ X1929 @ X1930 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( ( in @ X1932 @ X1929 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => X1931 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( ( in @ X1932 @ X1930 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => X1931 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => X1931 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1933: $i,X1934: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1934 @ ( powerset @ X1933 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1935: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1935 @ ( powerset @ X1933 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1936: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1936 @ X1933 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ~ ( in @ X1936 @ X1934 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ~ ( in @ X1936 @ X1935 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ~ ( in @ X1936 @ ( binunion @ X1934 @ X1935 ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1937: $i,X1938: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1938 @ ( powerset @ X1937 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1939: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1939 @ ( powerset @ X1937 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1940: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1940 @ X1937 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( in @ X1940 @ ( setminus @ X1937 @ ( binunion @ X1938 @ X1939 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ X1940 @ ( setminus @ X1937 @ X1938 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1941: $i,X1942: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1942 @ ( powerset @ X1941 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1943: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1943 @ ( powerset @ X1941 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( in @ ( setminus @ X1941 @ ( binunion @ X1942 @ X1943 ) ) @ ( powerset @ ( setminus @ X1941 @ X1942 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1944: $i,X1945: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1945 @ ( powerset @ X1944 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1946: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1946 @ ( powerset @ X1944 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1947: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1947 @ X1944 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( in @ X1947 @ ( setminus @ X1944 @ ( binunion @ X1945 @ X1946 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ X1947 @ ( setminus @ X1944 @ X1946 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1948: $i,X1949: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1949 @ ( powerset @ X1948 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1950: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1950 @ ( powerset @ X1948 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1951: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1951 @ X1948 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( in @ X1951 @ ( setminus @ X1948 @ ( binintersect @ X1949 @ X1950 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( in @ X1951 @ ( binunion @ ( setminus @ X1948 @ X1949 ) @ ( setminus @ X1948 @ X1950 ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1952: $i,X1953: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1953 @ ( powerset @ X1952 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1954: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1954 @ ( powerset @ X1952 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1955: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1955 @ X1952 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( in @ X1955 @ ( binunion @ ( setminus @ X1952 @ X1953 ) @ ( setminus @ X1952 @ X1954 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( in @ X1955 @ ( setminus @ X1952 @ ( binintersect @ X1953 @ X1954 ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1956: $i,X1957: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1957 @ ( powerset @ X1956 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1958: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1958 @ ( powerset @ X1956 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( setminus @ X1956 @ ( binintersect @ X1957 @ X1958 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          = ( binunion @ ( setminus @ X1956 @ X1957 ) @ ( setminus @ X1956 @ X1958 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1959: $i,X1960: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1960 @ ( powerset @ X1959 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1961: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1961 @ ( powerset @ X1959 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1962: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1962 @ X1959 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ( in @ X1962 @ ( setminus @ X1959 @ ( binunion @ X1960 @ X1961 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( in @ X1962 @ ( binintersect @ ( setminus @ X1959 @ X1960 ) @ ( setminus @ X1959 @ X1961 ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1963: $i,X1964: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1964 @ ( powerset @ X1963 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1965: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1965 @ ( powerset @ X1963 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1966: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1966 @ X1963 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( in @ X1966 @ ( setminus @ X1963 @ X1964 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( in @ X1966 @ ( setminus @ X1963 @ X1965 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ X1966 @ ( setminus @ X1963 @ ( binunion @ X1964 @ X1965 ) ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1967: $i,X1968: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1968 @ ( powerset @ X1967 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1969: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1969 @ ( powerset @ X1967 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1970: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1970 @ X1967 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( in @ X1970 @ ( binintersect @ ( setminus @ X1967 @ X1968 ) @ ( setminus @ X1967 @ X1969 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ X1970 @ ( setminus @ X1967 @ ( binunion @ X1968 @ X1969 ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X1971: $i,X1972: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1972 @ ( powerset @ X1971 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X1973: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1973 @ ( powerset @ X1971 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( setminus @ X1971 @ ( binunion @ X1972 @ X1973 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  = ( binintersect @ ( setminus @ X1971 @ X1972 ) @ ( setminus @ X1971 @ X1973 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X1974: $i,X1975: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1975 @ ( powerset @ X1974 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1976: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1976 @ ( powerset @ X1974 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1977: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1977 @ ( binintersect @ X1975 @ X1976 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( in @ X1977 @ X1974 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X1978: $i,X1979: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X1979 @ ( powerset @ X1978 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X1980: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1980 @ ( powerset @ X1978 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1981: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1981 @ ( powerset @ X1978 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( subset @ X1979 @ X1981 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( subset @ ( binintersect @ X1979 @ X1980 ) @ X1981 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X1982: $i,X1983: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1983 @ ( powerset @ X1982 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X1984: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1984 @ ( powerset @ X1982 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1985: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1985 @ ( powerset @ X1982 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( subset @ X1984 @ X1985 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( subset @ ( binintersect @ X1983 @ X1984 ) @ X1985 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X1986: $i,X1987: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X1987 @ ( powerset @ X1986 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X1988: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1988 @ ( powerset @ X1986 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1989: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1989 @ ( powerset @ X1986 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ( subset @ X1987 @ X1988 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ( subset @ X1987 @ X1989 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( subset @ X1987 @ ( binintersect @ X1988 @ X1989 ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X1990: $i,X1991: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X1991 @ ( powerset @ X1990 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X1992: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1992 @ ( powerset @ X1990 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X1993: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X1993 @ ( powerset @ X1990 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X1994: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X1994 @ ( powerset @ X1990 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( subset @ X1991 @ X1993 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( subset @ X1992 @ X1994 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( subset @ ( binintersect @ X1991 @ X1992 ) @ ( binintersect @ X1993 @ X1994 ) ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1995: $i,X1996: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X1996 @ ( powerset @ X1995 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X1997: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X1997 @ ( powerset @ X1995 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( in @ ( setminus @ X1995 @ X1996 ) @ ( powerset @ ( setminus @ X1995 @ ( binintersect @ X1996 @ X1997 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1998: $i,X1999: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X1999 @ ( powerset @ X1998 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X2000: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X2000 @ ( powerset @ X1998 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X2001: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X2001 @ ( powerset @ X1998 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X2002: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X2002 @ ( powerset @ X1998 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( setminus @ X1998 @ ( binintersect @ ( binunion @ X1999 @ X2000 ) @ ( binunion @ X2001 @ X2002 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        = ( binunion @ ( binintersect @ ( setminus @ X1998 @ X1999 ) @ ( setminus @ X1998 @ X2000 ) ) @ ( binintersect @ ( setminus @ X1998 @ X2001 ) @ ( setminus @ X1998 @ X2002 ) ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X2003: $i,X2004: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X2004 @ ( powerset @ X2003 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X2005: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X2005 @ ( powerset @ X2003 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X2006: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X2006 @ ( powerset @ X2003 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ ( binintersect @ X2004 @ X2005 ) @ ( powerset @ ( binintersect @ ( binunion @ X2004 @ X2006 ) @ ( binunion @ X2005 @ X2006 ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X2007: $i,X2008: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X2008 @ ( powerset @ X2007 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X2009: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X2009 @ ( powerset @ X2007 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( subset @ X2008 @ ( setminus @ X2007 @ X2009 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( subset @ X2009 @ ( setminus @ X2007 @ X2008 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X2010: $i,X2011: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X2011 @ ( powerset @ X2010 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X2012: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X2012 @ ( powerset @ X2010 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ ( setminus @ X2010 @ ( binunion @ X2011 @ X2012 ) ) @ ( powerset @ ( setminus @ X2010 @ X2011 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X2013: $i,X2014: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( breln1 @ X2013 @ X2014 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X2015: $i > $o] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ! [X2016: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X2016 @ X2013 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X2017: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X2017 @ X2013 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ( in @ ( kpair @ X2016 @ X2017 ) @ X2014 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( X2015 @ ( kpair @ X2016 @ X2017 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X2018: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X2018 @ X2014 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( X2015 @ X2018 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X2019: $i,X2020: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X2020 @ ( breln1Set @ X2019 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( breln1 @ X2019 @ X2020 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( choice2fnsingleton
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X2021: $i,X2022: $i > $i > $o] : ( breln1 @ X2021 @ ( dpsetconstr @ X2021 @ X2021 @ X2022 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X2023: $i,X2024: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( breln1 @ X2023 @ X2024 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X2025: $i > $o] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ! [X2026: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X2026 @ X2023 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X2027: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X2027 @ X2023 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( in @ ( kpair @ X2026 @ X2027 ) @ X2024 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( X2025 @ ( kpair @ X2026 @ X2027 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X2028: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X2028 @ X2024 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( X2025 @ X2028 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X2029: $i,X2030: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( breln1 @ X2029 @ X2030 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X2031: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( breln1 @ X2029 @ X2031 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X2032: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X2032 @ X2029 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X2033: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X2033 @ X2029 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( in @ ( kpair @ X2032 @ X2033 ) @ X2030 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( in @ ( kpair @ X2032 @ X2033 ) @ X2031 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( subset @ X2030 @ X2031 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X2034: $i,X2035: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( breln1 @ X2034 @ X2035 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X2036: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( breln1 @ X2034 @ X2036 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X2037: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X2037 @ X2034 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X2038: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X2038 @ X2034 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ( in @ ( kpair @ X2037 @ X2038 ) @ X2035 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( in @ ( kpair @ X2037 @ X2038 ) @ X2036 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X2039: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X2039 @ X2034 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X2040: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X2040 @ X2034 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ( in @ ( kpair @ X2039 @ X2040 ) @ X2036 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( in @ ( kpair @ X2039 @ X2040 ) @ X2035 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( X2035 = X2036 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X2041: $i,X2042: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( breln1 @ X2041 @ X2042 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( breln1 @ X2041 @ ( breln1invset @ X2041 @ X2042 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X2043: $i,X2044: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( breln1 @ X2043 @ X2044 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X2045: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X2045 @ X2043 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X2046: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X2046 @ X2043 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( in @ ( kpair @ X2045 @ X2046 ) @ X2044 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( in @ ( kpair @ X2046 @ X2045 ) @ ( breln1invset @ X2043 @ X2044 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X2047: $i,X2048: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( breln1 @ X2047 @ X2048 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X2049: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X2049 @ X2047 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X2050: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X2050 @ X2047 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ( in @ ( kpair @ X2050 @ X2049 ) @ ( breln1invset @ X2047 @ X2048 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( in @ ( kpair @ X2049 @ X2050 ) @ X2048 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X2051: $i,X2052: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( breln1 @ X2051 @ X2052 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X2053: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( breln1 @ X2051 @ X2053 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( breln1 @ X2051 @ ( breln1compset @ X2051 @ X2052 @ X2053 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X2054: $i,X2055: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( breln1 @ X2054 @ X2055 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X2056: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( breln1 @ X2054 @ X2056 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X2057: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X2057 @ X2054 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X2058: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X2058 @ X2054 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X2059: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X2059 @ X2054 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( in @ ( kpair @ X2057 @ X2059 ) @ X2055 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( in @ ( kpair @ X2059 @ X2058 ) @ X2056 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( in @ ( kpair @ X2057 @ X2058 ) @ ( breln1compset @ X2054 @ X2055 @ X2056 ) ) ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X2060: $i,X2061: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( breln1 @ X2060 @ X2061 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X2062: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( breln1 @ X2060 @ X2062 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X2063: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X2063 @ X2060 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X2064: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X2064 @ X2060 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( in @ ( kpair @ X2063 @ X2064 ) @ ( breln1compset @ X2060 @ X2061 @ X2062 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ? [X2065: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X2065 @ X2060 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            & ( in @ ( kpair @ X2063 @ X2065 ) @ X2061 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            & ( in @ ( kpair @ X2065 @ X2064 ) @ X2062 ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X2066: $i,X2067: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( breln1 @ X2066 @ X2067 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X2068: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( breln1 @ X2066 @ X2068 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X2069: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X2069 @ X2066 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X2070: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X2070 @ X2066 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( in @ ( kpair @ X2069 @ X2070 ) @ ( breln1compset @ X2066 @ X2067 @ X2068 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X2071: $o] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ! [X2072: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X2072 @ X2066 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( in @ ( kpair @ X2069 @ X2072 ) @ X2067 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( in @ ( kpair @ X2072 @ X2070 ) @ X2068 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => X2071 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => X2071 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [X2073: $i,X2074: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( breln1 @ X2073 @ X2074 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X2075: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( breln1 @ X2073 @ X2075 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( breln1 @ X2073 @ ( binunion @ X2074 @ X2075 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [X2076: $i,X2077: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( breln1 @ X2076 @ X2077 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [X2078: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( breln1 @ X2076 @ X2078 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X2079: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X2079 @ X2076 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X2080: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X2080 @ X2076 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ( in @ ( kpair @ X2079 @ X2080 ) @ X2077 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( in @ ( kpair @ X2079 @ X2080 ) @ ( binunion @ X2077 @ X2078 ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [X2081: $i,X2082: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( breln1 @ X2081 @ X2082 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X2083: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( breln1 @ X2081 @ X2083 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X2084: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X2084 @ X2081 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X2085: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X2085 @ X2081 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ( in @ ( kpair @ X2084 @ X2085 ) @ X2083 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( in @ ( kpair @ X2084 @ X2085 ) @ ( binunion @ X2082 @ X2083 ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X2086: $i,X2087: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( breln1 @ X2086 @ X2087 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X2088: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( breln1 @ X2086 @ X2088 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X2089: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X2089 @ X2086 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [X2090: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X2090 @ X2086 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( ( in @ ( kpair @ X2089 @ X2090 ) @ X2087 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    | ( in @ ( kpair @ X2089 @ X2090 ) @ X2088 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( in @ ( kpair @ X2089 @ X2090 ) @ ( binunion @ X2087 @ X2088 ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X2091: $i,X2092: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( breln1 @ X2091 @ X2092 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X2093: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( breln1 @ X2091 @ X2093 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X2094: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X2094 @ X2091 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X2095: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X2095 @ X2091 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( in @ ( kpair @ X2094 @ X2095 ) @ ( binunion @ X2092 @ X2093 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( in @ ( kpair @ X2094 @ X2095 ) @ X2092 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      | ( in @ ( kpair @ X2094 @ X2095 ) @ X2093 ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [X4: $i,X33: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( breln1 @ X4 @ X33 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X35: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( breln1 @ X4 @ X35 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X2 @ X4 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [X3: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X4 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( in @ ( kpair @ X2 @ X3 ) @ ( binunion @ X33 @ X35 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X55: $o] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( ( in @ ( kpair @ X2 @ X3 ) @ X33 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => X55 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( ( in @ ( kpair @ X2 @ X3 ) @ X35 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => X55 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => X55 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    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(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_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)],[breln1unionEcases]),demorgan2b2]),breln1unionE]),complementInPowersetComplementIntersect]),contraSubsetComplement]),complementTcontraSubset]),disjointsetsI1]),binunionTILcontra]),binunionTIRcontra]),binintersectRsub]),inIntersectImpInUnion]),inIntersectImpInUnion2]),binintersectSubset4]),inIntersectImpInIntersectUnions]),intersectInPowersetIntersectUnions]),binintersectSubset1]),inComplementUnionImpNotIn1]),inComplementUnionImpInComplement1]),bs114d]),binunionTE]),binunionTEcontra]),setminusI]),demorgan2a1]),setminusEL]),complementUnionInPowersetComplement]),demorgan2a2]),demorgan1a]),setminusER]),demorgan1b]),demorgan1]),demorgan2a]),setminusSubset2]),singletoninpowerset]),demorgan2b]),demorgan2]),setminusERneg]),woz13rule0]),woz13rule1]),setminusELneg]),woz13rule2]),woz13rule3]),setminusILneg]),woz13rule4]),woz1_1]),woz1_2]),woz1_3]),setminusIRneg]),woz1_4]),woz1_5]),setminusLsub]),breln1all2]),breln1SetBreln1]),setminusSubset1]),c_0_319]),breln1all1]),symdiffE]),subbreln1]),eqbreln1]),symdiffI1]),breln1invprop]),breln1invI]),symdiffI2]),breln1invE]),symdiffIneg1]),breln1compprop]),breln1compI]),breln1compE]),breln1compEex]),symdiffIneg2]),breln1unionprop]),breln1unionIL]),secondinupair]),breln1unionIR]),breln1unionI]),setukpairIL]),setukpairIR]),kpairiskpair]),kpairp]),singletonsubset]),cartprodsndin]),cartprodpairmemEL]),cartprodpairmemER]),singletoninpowunion]),upairset2E]),upairsubunion]),upairinpowunion]),ubforcartprodlem1]),ubforcartprodlem2]),ubforcartprodlem3]),cartprodpairin]),cartprodmempair1]),cartprodmempair]),setunionE2]),setunionsingleton1]),setunionsingleton2]),setunionsingleton]),c_0_320]),c_0_321]),c_0_322]),c_0_323]),singletonsuniq]),setukpairinjL1]),c_0_324]),theprop]),upairset2IR]),kfstpairEq]),cartprodfstin]),setukpairinjL2]),setukpairinjL]),setukpairinjR11]),setukpairinjR12]),setukpairinjR1]),upairequniteq]),setukpairinjR2]),binunionIR]),setukpairinjR]),binunionEcases]),binunionE]),c_0_325]),ksndpairEq]),kpairsurjEq]),powersetTI1]),powersetTE1]),cartprodmempaircEq]),cartprodfstpairEq]),cartprodsndpairEq]),cartprodpairsurjEq]),c_0_326]),c_0_327]),c_0_328]),c_0_329]),binunionLsub]),c_0_330]),c_0_331]),c_0_332]),c_0_333]),c_0_334]),app]),infuncsetfunc]),ap2p]),funcinfuncset]),c_0_335]),c_0_336]),c_0_337]),brelnall1]),brelnall2]),c_0_338]),funcGraphProp1]),funcGraphProp3]),funcGraphProp2]),funcextLem]),funcGraphProp4]),subbreln]),eqbreln]),funcext]),funcext2]),ap2apEq1]),ap2apEq2]),c_0_339]),c_0_340]),c_0_341]),c_0_342]),c_0_343]),c_0_344]),c_0_345]),c_0_346]),c_0_347]),c_0_348]),ifp]),theeq]),iftrue]),iffalse]),iftrueorfalse]),binintersectT_lem]),binunionT_lem]),powersetT_lem]),binunionRsub]),setminusT_lem]),complementT_lem]),setextT]),binintersectI]),binintersectSubset5]),binintersectEL]),binintersectLsub]),subsetTI]),binintersectSubset2]),binintersectSubset3]),complementTI1]),complementTE1]),binintersectTELcontra]),binintersectTERcontra]),contrasubsetT]),contrasubsetT1]),contrasubsetT2]),contrasubsetT3]),doubleComplementI1]),doubleComplementE1]),doubleComplementSub1]),doubleComplementSub2]),doubleComplementEq]),complementTnotintersectT]),complementImpComplementIntersect]),complementSubsetComplementIntersect]),binintersectER]),binunionIL]),c_0_349]),c_0_350]),powersetsubset]),inPowerset]),powersetE1]),powersetI1]),subsetemptysetimpeq]),setextsub]),subset2powerset]),setadjoinSub2]),setadjoinSub]),subsetTrans]),subsetRefl]),notequalI2]),notequalI1]),notsubsetI]),subsetE2]),subsetE]),emptysetsubset]),subsetI2]),eqimpsubset1]),eqimpsubset2]),subsetI1]),c_0_351]),c_0_352]),c_0_353]),omega__Cong]),setunion__Cong]),powerset__Cong]),setadjoin__Cong]),emptyset__Cong]),c_0_354]),c_0_355]),in__Cong]),inCongP]),c_0_356]),c_0_357]),c_0_358]),notdallE]),notdexE]),prop2setI]),quantDeMorgan4]),quantDeMorgan3]),quantDeMorgan2]),quantDeMorgan1]),vacuousDall]),c_0_359]),upairsetIR]),upairsetIL]),upairsetE]),singletonsswitch]),eqinunit]),notinsingleton]),uniqinunit]),c_0_360]),c_0_361]),subPowSU]),setunionE]),setunionI]),powersetE]),emptyInPowerset]),emptyinPowerset]),powersetI]),c_0_362]),setadjoinOr]),setadjoinE]),setadjoinIR]),emptyinunitempty]),setadjoinIL]),c_0_363]),c_0_364]),c_0_365]),c_0_366]),noeltsimpempty]),emptyI]),setext]),c_0_367]),notinemptyset]),emptysetimpfalse]),emptysetE]),prop2setE]),c_0_368]),c_0_369]),c_0_370]),c_0_371]),c_0_372]),wellorderingAx]),foundationAx]),c_0_373]),omegaIndAx]),omegaSAx]),omega0Ax]),setunionAx]),powersetAx]),setadjoinAx]),emptysetAx]),setextAx])])]),c_0_374]) ).

thf(c_0_376,negated_conjecture,
    ! 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$i,X2213: $i,X2214: $i,X2216: $i,X2217: $i,X2218: $i,X2219: $i,X2220: $i,X2221: $i,X2222: $i,X2223: $i,X2224: $i,X2225: $i,X2226: $i,X2227: $i,X2228: $i,X2229: $i,X2230: $i,X2231: $i,X2232: $i > $o,X2233: $i,X2234: $i > $o,X2235: $i,X2236: $i,X2237: $i > $o,X2238: $i,X2240: $i,X2241: $i > $o,X2243: $i,X2244: $i,X2245: $i > $o,X2247: $i,X2248: $i,X2249: $i > $o,X2250: $i,X2252: $o,X2253: $i,X2254: $i > $o,X2256: $i,X2257: $i,X2258: $i > $o,X2259: $i,X2261: $i > $o,X2262: $i,X2265: $i,X2266: $i > $o,X2267: $i,X2271: $i,X2272: $i > $o,X2273: $i,X2276: $i,X2277: $i,X2278: $i,X2279: $i,X2280: $i,X2281: $i,X2282: $i,X2283: $i,X2284: $i,X2285: $i > $o,X2286: $i,X2288: $i,X2289: $i,X2290: $i > $o,X2291: $i > $o,X2294: $i,X2297: $i,X2298: $i,X2301: $i,X2302: $i,X2303: $i,X2304: $i,X2305: $i,X2306: $i,X2307: $i,X2308: $i,X2309: $i,X2310: $i > $o,X2311: $i,X2313: $i,X2314: $i,X2315: $i > $o,X2316: $i > $o,X2319: $i,X2321: $i,X2323: $i,X2324: $i,X2325: $i > $o,X2326: $i > $o,X2329: $i,X2330: $i,X2332: $i,X2333: $i,X2334: $i,X2335: $i,X2336: $i,X2337: $i,X2339: $i,X2340: $i,X2341: $i,X2342: $i,X2343: $i,X2344: $i,X2345: $i,X2346: $i,X2347: $i,X2348: $i,X2349: $i,X2350: $i,X2351: $i,X2352: $i,X2353: $i,X2354: $i,X2355: $i,X2356: $i,X2357: $i,X2358: $i,X2359: $i,X2360: $i,X2361: $i,X2362: $i,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 > $o,X2377: $i,X2378: $i > $o,X2379: $i,X2380: $i,X2381: $i,X2382: $i,X2383: $i,X2384: $i,X2385: $i,X2386: $i,X2387: $i,X2388: $i,X2389: $i,X2390: $o,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,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: $o,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,X2483: $i,X2484: $i,X2485: $i,X2486: $i,X2487: $i,X2488: $i,X2489: $i,X2490: $i,X2491: $i,X2492: $i,X2493: $i,X2494: $i,X2495: $i,X2496: $i,X2497: $i,X2498: $i,X2499: $i,X2500: $i,X2501: $i,X2502: $i,X2503: $i,X2504: $i,X2505: $i,X2506: $i,X2507: $i,X2508: $i,X2509: $i,X2510: $i,X2511: $i,X2512: $i,X2513: $i,X2514: $i,X2515: $i,X2516: $i,X2517: $i,X2520: $i,X2521: $i,X2522: $i,X2523: $i,X2524: $i,X2526: $i,X2527: $i,X2528: $i,X2529: $i,X2530: $i > $o,X2533: $i,X2534: $i,X2535: $i > $o,X2537: $i,X2538: $i > $o,X2539: $i,X2541: $i,X2542: $i > $o,X2545: $i,X2546: $i,X2547: $i,X2548: $i,X2549: $i,X2550: $i,X2551: $i,X2552: $i,X2553: $i,X2554: $i,X2555: $i,X2556: $i,X2557: $i,X2558: $i,X2559: $i,X2560: $i,X2561: $i,X2562: $i,X2563: $i,X2564: $i,X2565: $i,X2566: $i,X2567: $i,X2568: $i,X2569: $i,X2570: $i,X2571: $i,X2572: $i,X2573: $i,X2574: $i,X2575: $i,X2576: $i,X2577: $i,X2578: $i,X2579: $i,X2580: $i,X2581: $i,X2582: $i,X2583: $i,X2584: $i,X2585: $i,X2586: $i,X2587: $i,X2588: $i,X2589: $i,X2590: $i,X2591: $i,X2592: $i,X2593: $i,X2594: $i,X2595: $i,X2596: $i,X2597: $i,X2598: $i,X2599: $i,X2600: $i,X2601: $i,X2602: $i,X2603: $i,X2604: $i,X2605: $i,X2606: $i,X2607: $i,X2608: $i,X2609: $i,X2610: $i,X2611: $i,X2612: $i,X2613: $i,X2614: $i,X2615: $i,X2616: $i,X2617: $i > $i > $o,X2618: $i,X2619: $i,X2620: $i,X2621: $i,X2622: $i > $i > $o,X2623: $i,X2624: $i,X2625: $i > $i > $o,X2626: $i,X2627: $i,X2628: $i > $i > $o,X2629: $i,X2630: $i,X2631: $i,X2632: $i,X2633: $i > $i > $o,X2634: $i,X2635: $i,X2636: $i,X2637: $i,X2638: $i > $i > $o,X2639: $i,X2640: $i,X2641: $i,X2642: $i,X2643: $i > $i > $o,X2644: $i,X2645: $i,X2646: $i,X2647: $i,X2648: $i,X2649: $i,X2650: $i,X2651: $i,X2652: $i,X2653: $i,X2654: $i,X2655: $i,X2656: $i,X2657: $i,X2658: $i,X2659: $i,X2660: $i,X2661: $i,X2662: $i,X2663: $i,X2664: $i,X2665: $i,X2666: $i,X2667: $i,X2668: $i,X2669: $i,X2670: $i > $i,X2672: $i,X2673: $i,X2674: $i > $i,X2676: $i,X2677: $i,X2678: $i > $i,X2680: $i,X2681: $i,X2682: $i,X2683: $i > $o,X2686: $i,X2687: $i,X2688: $i,X2689: $i,X2690: $i > $o,X2693: $i,X2694: $i,X2695: $i > $o,X2696: $i,X2697: $i,X2698: $i,X2699: $i,X2700: $i,X2701: $i,X2702: $i,X2703: $i,X2704: $i,X2705: $i,X2706: $i,X2707: $i,X2708: $i,X2709: $i,X2710: $i,X2711: $i,X2712: $i,X2713: $i,X2714: $i,X2716: $i,X2717: $i,X2718: $i,X2719: $i,X2720: $i,X2721: $i,X2722: $i,X2723: $i,X2724: $i,X2725: $i,X2726: $i,X2729: $i,X2730: $i,X2731: $i,X2732: $i,X2737: $i,X2738: $i,X2739: $i,X2740: $i,X2742: $i,X2743: $i,X2744: $i,X2745: $i,X2747: $i,X2748: $i,X2749: $i,X2750: $i,X2751: $i,X2752: $i,X2753: $i,X2754: $i,X2755: $i,X2756: $i,X2757: $i > $i,X2759: $i,X2760: $i,X2761: $i,X2762: $i,X2763: $i,X2764: $i,X2765: $i > $i,X2767: $i,X2768: $i,X2769: $i > $i,X2771: $i,X2772: $i,X2773: $i,X2774: $i,X2775: $i,X2776: $o,X2777: $i,X2778: $i,X2779: $i,X2780: $o,X2781: $i,X2782: $i,X2783: $i,X2784: $o,X2785: $i,X2786: $i,X2787: $i,X2788: $o,X2789: $i,X2790: $i,X2791: $i,X2792: $o,X2793: $i,X2794: $i,X2795: $i,X2796: $o,X2797: $i,X2798: $i,X2799: $i,X2800: $i,X2801: $i,X2802: $o,X2803: $i,X2804: $i,X2805: $i,X2806: $o,X2807: $i,X2808: $i,X2809: $i,X2810: $o,X2811: $i,X2812: $i,X2813: $i,X2814: $i,X2815: $i,X2816: $i,X2817: $i,X2818: $i,X2819: $i,X2820: $i,X2821: $i,X2822: $i,X2823: $i,X2824: $i,X2825: $i,X2826: $i,X2827: $i,X2828: $i,X2831: $i,X2832: $i,X2833: $i,X2835: $i,X2836: $i,X2837: $i,X2839: $i,X2840: $i,X2841: $i,X2842: $i,X2843: $i,X2844: $i,X2845: $i,X2846: $i,X2847: $i,X2848: $i,X2849: $i,X2850: $i,X2851: $i,X2852: $i,X2853: $i,X2854: $i,X2855: $i,X2856: $i,X2857: $i,X2858: $i,X2859: $i,X2860: $i,X2861: $i,X2862: $i,X2863: $i,X2864: $i,X2865: $i,X2866: $i,X2867: $i,X2868: $i,X2869: $i,X2870: $i,X2871: $i,X2872: $i,X2873: $i,X2874: $i,X2875: $i,X2876: $i,X2877: $i,X2878: $i,X2879: $i,X2880: $i,X2881: $i,X2882: $i,X2883: $i,X2884: $i,X2885: $i,X2886: $i,X2887: $i,X2888: $i,X2889: $i,X2890: $i,X2891: $i,X2892: $i,X2893: $i,X2894: $i,X2895: $i,X2896: $i,X2897: $i,X2898: $i,X2899: $i,X2900: $i,X2901: $i,X2902: $i,X2903: $i,X2904: $i,X2905: $i,X2906: $i,X2907: $i,X2908: $i,X2909: $i,X2910: $i,X2911: $i,X2912: $i,X2913: $i,X2914: $i,X2915: $i,X2916: $i,X2917: $i,X2918: $i,X2919: $i,X2920: $i,X2921: $i,X2922: $i,X2923: $i,X2924: $i,X2925: $i,X2926: $i,X2927: $i,X2928: $i,X2929: $i,X2930: $i,X2931: $i,X2932: $i,X2933: $i,X2934: $i,X2935: $i,X2936: $i,X2937: $i,X2938: $i,X2939: $i,X2940: $i,X2941: $i,X2942: $o,X2943: $i,X2944: $i,X2945: $i,X2946: $i,X2947: $i,X2948: $i,X2949: $i,X2950: $i,X2951: $i,X2952: $i,X2953: $i,X2954: $i,X2955: $i,X2956: $i,X2957: $i,X2958: $i,X2959: $i,X2960: $i,X2961: $i,X2962: $i,X2963: $i,X2964: $i,X2965: $i,X2966: $i,X2967: $i,X2968: $i,X2969: $i,X2970: $i,X2971: $i,X2972: $i,X2973: $i,X2974: $i,X2975: $i,X2976: $i,X2977: $i,X2978: $i,X2979: $i,X2980: $i,X2981: $i,X2982: $i,X2983: $i,X2984: $i,X2985: $i,X2986: $i,X2987: $i,X2988: $i,X2989: $i,X2990: $i,X2991: $i,X2992: $i,X2993: $i,X2994: $i,X2995: $i,X2996: $i,X2997: $i,X2998: $i,X2999: $i,X3000: $i,X3001: $i,X3002: $i,X3003: $i,X3004: $i,X3005: $i,X3006: $i,X3007: $i,X3008: $i,X3009: $i,X3010: $i,X3011: $i,X3012: $i,X3013: $i,X3014: $i,X3015: $i,X3016: $i,X3017: $i,X3018: $i,X3019: $i,X3020: $i,X3021: $i,X3022: $i,X3023: $i,X3024: $i,X3025: $i,X3026: $i > $o,X3029: $i,X3030: $i,X3031: $i,X3032: $i,X3033: $i > $i > $o,X3034: $i,X3035: $i,X3036: $i > $o,X3039: $i,X3040: $i,X3041: $i,X3042: $i,X3045: $i,X3046: $i,X3047: $i,X3052: $i,X3053: $i,X3054: $i,X3055: $i,X3056: $i,X3057: $i,X3058: $i,X3059: $i,X3060: $i,X3061: $i,X3062: $i,X3063: $i,X3064: $i,X3065: $i,X3066: $i,X3067: $i,X3068: $i,X3069: $i,X3070: $i,X3071: $i,X3072: $i,X3073: $i,X3074: $i,X3075: $i,X3077: $i,X3078: $i,X3079: $i,X3080: $i,X3081: $i,X3082: $o,X3084: $i,X3085: $i,X3086: $i,X3087: $i,X3088: $i,X3089: $i,X3090: $i,X3091: $i,X3092: $i,X3093: $i,X3094: $i,X3095: $i,X3096: $i,X3097: $i,X3098: $i,X3099: $i,X3100: $i,X3101: $i,X3102: $i,X3103: $i,X3104: $i,X3105: $i,X3106: $i] :
      ( ( ~ ( in @ ( esk1_2 @ X2096 @ X2097 ) @ X2096 )
        | ~ ( in @ ( esk1_2 @ X2096 @ X2097 ) @ X2097 )
        | ( X2096 = X2097 ) )
      & ( ( in @ ( esk1_2 @ X2096 @ X2097 ) @ X2096 )
        | ( in @ ( esk1_2 @ X2096 @ X2097 ) @ X2097 )
        | ( X2096 = X2097 ) )
      & ~ ( in @ X2099 @ emptyset )
      & ( ~ ( in @ X2102 @ ( setadjoin @ X2100 @ X2101 ) )
        | ( X2102 = X2100 )
        | ( in @ X2102 @ X2101 ) )
      & ( ( X2102 != X2100 )
        | ( in @ X2102 @ ( setadjoin @ X2100 @ X2101 ) ) )
      & ( ~ ( in @ X2102 @ X2101 )
        | ( in @ X2102 @ ( setadjoin @ X2100 @ X2101 ) ) )
      & ( ~ ( in @ X2104 @ ( powerset @ X2103 ) )
        | ~ ( in @ X2105 @ X2104 )
        | ( in @ X2105 @ X2103 ) )
      & ( ( in @ ( esk2_2 @ X2106 @ X2107 ) @ X2107 )
        | ( in @ X2107 @ ( powerset @ X2106 ) ) )
      & ( ~ ( in @ ( esk2_2 @ X2106 @ X2107 ) @ X2106 )
        | ( in @ X2107 @ ( powerset @ X2106 ) ) )
      & ( ( in @ X2110 @ ( esk3_2 @ X2109 @ X2110 ) )
        | ~ ( in @ X2110 @ ( setunion @ X2109 ) ) )
      & ( ( in @ ( esk3_2 @ X2109 @ X2110 ) @ X2109 )
        | ~ ( in @ X2110 @ ( setunion @ X2109 ) ) )
      & ( ~ ( in @ X2113 @ X2114 )
        | ~ ( in @ X2114 @ X2112 )
        | ( in @ X2113 @ ( setunion @ X2112 ) ) )
      & ( in @ emptyset @ omega )
      & ( ~ ( in @ X2115 @ omega )
        | ( in @ ( setadjoin @ X2115 @ X2115 ) @ omega ) )
      & ( ( in @ ( esk4_1 @ X2116 ) @ omega )
        | ~ ( in @ emptyset @ X2116 )
        | ~ ( in @ X2118 @ omega )
        | ( in @ X2118 @ X2116 ) )
      & ( ( in @ ( esk4_1 @ X2116 ) @ X2116 )
        | ~ ( in @ emptyset @ X2116 )
        | ~ ( in @ X2118 @ omega )
        | ( in @ X2118 @ X2116 ) )
      & ( ~ ( in @ ( setadjoin @ ( esk4_1 @ X2116 ) @ ( esk4_1 @ X2116 ) ) @ X2116 )
        | ~ ( in @ emptyset @ X2116 )
        | ~ ( in @ X2118 @ omega )
        | ( in @ X2118 @ X2116 ) )
      & ( ( in @ ( esk8_3 @ X2119 @ X2120 @ X2125 ) @ X2120 )
        | ~ ( in @ X2125 @ ( esk7_2 @ X2119 @ X2120 ) )
        | ( in @ ( esk5_2 @ X2119 @ X2120 ) @ X2120 ) )
      & ( ( X2119 @ ( esk8_3 @ X2119 @ X2120 @ X2125 ) @ X2125 )
        | ~ ( in @ X2125 @ ( esk7_2 @ X2119 @ X2120 ) )
        | ( in @ ( esk5_2 @ X2119 @ X2120 ) @ X2120 ) )
      & ( ~ ( in @ X2128 @ X2120 )
        | ~ ( X2119 @ X2128 @ X2127 )
        | ( in @ X2127 @ ( esk7_2 @ X2119 @ X2120 ) )
        | ( in @ ( esk5_2 @ X2119 @ X2120 ) @ X2120 ) )
      & ( ( in @ ( esk8_3 @ X2119 @ X2120 @ X2125 ) @ X2120 )
        | ~ ( in @ X2125 @ ( esk7_2 @ X2119 @ X2120 ) )
        | ( X2119 @ ( esk5_2 @ X2119 @ X2120 ) @ ( esk6_3 @ X2119 @ X2120 @ X2122 ) )
        | ~ ( X2119 @ ( esk5_2 @ X2119 @ X2120 ) @ X2122 ) )
      & ( ( X2119 @ ( esk8_3 @ X2119 @ X2120 @ X2125 ) @ X2125 )
        | ~ ( in @ X2125 @ ( esk7_2 @ X2119 @ X2120 ) )
        | ( X2119 @ ( esk5_2 @ X2119 @ X2120 ) @ ( esk6_3 @ X2119 @ X2120 @ X2122 ) )
        | ~ ( X2119 @ ( esk5_2 @ X2119 @ X2120 ) @ X2122 ) )
      & ( ~ ( in @ X2128 @ X2120 )
        | ~ ( X2119 @ X2128 @ X2127 )
        | ( in @ X2127 @ ( esk7_2 @ X2119 @ X2120 ) )
        | ( X2119 @ ( esk5_2 @ X2119 @ X2120 ) @ ( esk6_3 @ X2119 @ X2120 @ X2122 ) )
        | ~ ( X2119 @ ( esk5_2 @ X2119 @ X2120 ) @ X2122 ) )
      & ( ( in @ ( esk8_3 @ X2119 @ X2120 @ X2125 ) @ X2120 )
        | ~ ( in @ X2125 @ ( esk7_2 @ X2119 @ X2120 ) )
        | ( X2122
         != ( esk6_3 @ X2119 @ X2120 @ X2122 ) )
        | ~ ( X2119 @ ( esk5_2 @ X2119 @ X2120 ) @ X2122 ) )
      & ( ( X2119 @ ( esk8_3 @ X2119 @ X2120 @ X2125 ) @ X2125 )
        | ~ ( in @ X2125 @ ( esk7_2 @ X2119 @ X2120 ) )
        | ( X2122
         != ( esk6_3 @ X2119 @ X2120 @ X2122 ) )
        | ~ ( X2119 @ ( esk5_2 @ X2119 @ X2120 ) @ X2122 ) )
      & ( ~ ( in @ X2128 @ X2120 )
        | ~ ( X2119 @ X2128 @ X2127 )
        | ( in @ X2127 @ ( esk7_2 @ X2119 @ X2120 ) )
        | ( X2122
         != ( esk6_3 @ X2119 @ X2120 @ X2122 ) )
        | ~ ( X2119 @ ( esk5_2 @ X2119 @ X2120 ) @ X2122 ) )
      & ( ( in @ ( esk9_1 @ X2129 ) @ X2129 )
        | ~ ( in @ X2130 @ X2129 ) )
      & ( ~ ( in @ X2132 @ ( esk9_1 @ X2129 ) )
        | ~ ( in @ X2132 @ X2129 )
        | ~ ( in @ X2130 @ X2129 ) )
      & epred1_0
      & ( ( X2133 @ ( esk10_2 @ X2133 @ X2134 ) )
        | ~ ( X2133 @ X2134 )
        | ( X2133 @ ( descr @ X2133 ) ) )
      & ( ( X2134
         != ( esk10_2 @ X2133 @ X2134 ) )
        | ~ ( X2133 @ X2134 )
        | ( X2133 @ ( descr @ X2133 ) ) )
      & ( ~ ( in @ X2138 @ X2136 )
        | ~ ( X2137 @ X2138 )
        | ( in @ X2138 @ ( dsetconstr @ X2136 @ X2137 ) ) )
      & ( ~ ( in @ X2141 @ ( dsetconstr @ X2139 @ X2140 ) )
        | ( in @ X2141 @ X2139 ) )
      & ( ~ ( in @ X2144 @ ( dsetconstr @ X2142 @ X2143 ) )
        | ( X2143 @ X2144 ) )
      & ( ( X2145 @ ( esk12_1 @ X2145 ) )
        | ( X2145 @ ( esk11_2 @ X2145 @ X2146 ) )
        | ~ ( X2145 @ X2146 ) )
      & ( ~ ( X2145 @ X2149 )
        | ( ( esk12_1 @ X2145 )
          = X2149 )
        | ( X2145 @ ( esk11_2 @ X2145 @ X2146 ) )
        | ~ ( X2145 @ X2146 ) )
      & ( ( X2145 @ ( esk12_1 @ X2145 ) )
        | ( X2146
         != ( esk11_2 @ X2145 @ X2146 ) )
        | ~ ( X2145 @ X2146 ) )
      & ( ~ ( X2145 @ X2149 )
        | ( ( esk12_1 @ X2145 )
          = X2149 )
        | ( X2146
         != ( esk11_2 @ X2145 @ X2146 ) )
        | ~ ( X2145 @ X2146 ) )
      & ( ~ ( in @ X2151 @ ( prop2set @ X2150 ) )
        | X2150 )
      & ( ~ ( in @ X2152 @ emptyset )
        | X2153 )
      & ( ~ ( in @ X2154 @ emptyset )
        | ~ $true )
      & ~ ( in @ X2155 @ emptyset )
      & ( ( X2156 @ ( esk13_2 @ X2156 @ X2157 ) )
        | ~ ( X2156 @ X2157 )
        | ( X2156 @ ( esk14_1 @ X2156 ) ) )
      & ( ( X2157
         != ( esk13_2 @ X2156 @ X2157 ) )
        | ~ ( X2156 @ X2157 )
        | ( X2156 @ ( esk14_1 @ X2156 ) ) )
      & ( ( in @ ( esk16_2 @ X2160 @ X2161 ) @ X2161 )
        | ( X2160 = X2161 )
        | ( in @ ( esk15_2 @ X2160 @ X2161 ) @ X2160 ) )
      & ( ~ ( in @ ( esk16_2 @ X2160 @ X2161 ) @ X2160 )
        | ( X2160 = X2161 )
        | ( in @ ( esk15_2 @ X2160 @ X2161 ) @ X2160 ) )
      & ( ( in @ ( esk16_2 @ X2160 @ X2161 ) @ X2161 )
        | ( X2160 = X2161 )
        | ~ ( in @ ( esk15_2 @ X2160 @ X2161 ) @ X2161 ) )
      & ( ~ ( in @ ( esk16_2 @ X2160 @ X2161 ) @ X2160 )
        | ( X2160 = X2161 )
        | ~ ( in @ ( esk15_2 @ X2160 @ X2161 ) @ X2161 ) )
      & ( ( in @ ( esk17_1 @ X2164 ) @ X2164 )
        | ( X2164 = emptyset ) )
      & ( ( in @ ( esk18_1 @ X2166 ) @ X2166 )
        | ( X2166 = emptyset ) )
      & ( ~ ( in @ X2170 @ ( dsetconstr @ X2168 @ X2169 ) )
        | ( X2169 @ X2170 )
        | ~ ( in @ X2170 @ X2168 ) )
      & ( ~ ( X2169 @ X2170 )
        | ( in @ X2170 @ ( dsetconstr @ X2168 @ X2169 ) )
        | ~ ( in @ X2170 @ X2168 ) )
      & ( ( X2171 = emptyset )
        | ( in @ ( esk19_1 @ X2171 ) @ X2171 ) )
      & ( ~ ( in @ X2175 @ X2173 )
        | ~ ( X2174 @ X2175 )
        | ( ( dsetconstr @ X2173 @ X2174 )
         != emptyset ) )
      & ( ~ ( in @ X2177 @ X2176 )
        | ( X2176 != emptyset ) )
      & ( in @ X2178 @ ( setadjoin @ X2178 @ X2179 ) )
      & ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
      & ( ~ ( in @ X2182 @ X2181 )
        | ( in @ X2182 @ ( setadjoin @ X2180 @ X2181 ) ) )
      & ( ( in @ X2185 @ X2184 )
        | X2186
        | ( X2185 = X2183 )
        | ~ ( in @ X2185 @ ( setadjoin @ X2183 @ X2184 ) ) )
      & ( ~ X2186
        | X2186
        | ( X2185 = X2183 )
        | ~ ( in @ X2185 @ ( setadjoin @ X2183 @ X2184 ) ) )
      & ( ( in @ X2185 @ X2184 )
        | X2186
        | ~ X2186
        | ~ ( in @ X2185 @ ( setadjoin @ X2183 @ X2184 ) ) )
      & ( ~ X2186
        | X2186
        | ~ X2186
        | ~ ( in @ X2185 @ ( setadjoin @ X2183 @ X2184 ) ) )
      & ( ~ ( in @ X2189 @ ( setadjoin @ X2187 @ X2188 ) )
        | ( X2189 = X2187 )
        | ( in @ X2189 @ X2188 ) )
      & ( ( dsetconstr @ X2190
          @ ^ [Z0: $i] : $true )
        = X2190 )
      & ( ( in @ ( esk20_2 @ X2191 @ X2192 ) @ X2192 )
        | ( in @ X2192 @ ( powerset @ X2191 ) ) )
      & ( ~ ( in @ ( esk20_2 @ X2191 @ X2192 ) @ X2191 )
        | ( in @ X2192 @ ( powerset @ X2191 ) ) )
      & ( in @ emptyset @ ( powerset @ X2194 ) )
      & ( in @ emptyset @ ( powerset @ X2195 ) )
      & ( ~ ( in @ X2197 @ ( powerset @ X2196 ) )
        | ~ ( in @ X2198 @ X2197 )
        | ( in @ X2198 @ X2196 ) )
      & ( ~ ( in @ X2200 @ X2201 )
        | ~ ( in @ X2201 @ X2199 )
        | ( in @ X2200 @ ( setunion @ X2199 ) ) )
      & ( ( in @ X2203 @ ( esk21_3 @ X2202 @ X2203 @ X2204 ) )
        | X2204
        | ~ ( in @ X2203 @ ( setunion @ X2202 ) ) )
      & ( ( in @ ( esk21_3 @ X2202 @ X2203 @ X2204 ) @ X2202 )
        | X2204
        | ~ ( in @ X2203 @ ( setunion @ X2202 ) ) )
      & ( ~ X2204
        | X2204
        | ~ ( in @ X2203 @ ( setunion @ X2202 ) ) )
      & ( ~ ( in @ X2207 @ X2206 )
        | ( in @ X2207 @ ( powerset @ ( setunion @ X2206 ) ) ) )
      & ( ~ ( X2208 @ X2212 )
        | ( X2212
          = ( esk23_1 @ X2208 ) )
        | ( X2208 @ ( esk22_2 @ X2208 @ X2209 ) )
        | ~ ( X2208 @ X2209 ) )
      & ( ( X2213
         != ( esk23_1 @ X2208 ) )
        | ( X2208 @ X2213 )
        | ( X2208 @ ( esk22_2 @ X2208 @ X2209 ) )
        | ~ ( X2208 @ X2209 ) )
      & ( ~ ( X2208 @ X2212 )
        | ( X2212
          = ( esk23_1 @ X2208 ) )
        | ( X2209
         != ( esk22_2 @ X2208 @ X2209 ) )
        | ~ ( X2208 @ X2209 ) )
      & ( ( X2213
         != ( esk23_1 @ X2208 ) )
        | ( X2208 @ X2213 )
        | ( X2209
         != ( esk22_2 @ X2208 @ X2209 ) )
        | ~ ( X2208 @ X2209 ) )
      & ( ( in @ ( esk24_1 @ X2214 ) @ X2214 )
        | ( X2214 = emptyset ) )
      & ( $true
        | ( X2214 = emptyset ) )
      & ( ~ ( in @ X2216 @ ( setadjoin @ X2217 @ emptyset ) )
        | ( X2216 = X2217 ) )
      & ( ( X2218 = X2219 )
        | ~ ( in @ X2219 @ ( setadjoin @ X2218 @ emptyset ) ) )
      & ( ( X2220 != X2221 )
        | ( in @ X2220 @ ( setadjoin @ X2221 @ emptyset ) ) )
      & ( ~ ( in @ X2222 @ ( setadjoin @ X2223 @ emptyset ) )
        | ( in @ X2223 @ ( setadjoin @ X2222 @ emptyset ) ) )
      & ( ~ ( in @ X2226 @ ( setadjoin @ X2224 @ ( setadjoin @ X2225 @ emptyset ) ) )
        | ( X2226 = X2224 )
        | ( X2226 = X2225 ) )
      & ( in @ X2227 @ ( setadjoin @ X2227 @ ( setadjoin @ X2228 @ emptyset ) ) )
      & ( in @ X2230 @ ( setadjoin @ X2229 @ ( setadjoin @ X2230 @ emptyset ) ) )
      & ( ~ ( in @ X2233 @ X2231 )
        | ~ ( X2232 @ X2233 )
        | ( ( dsetconstr @ X2231 @ X2232 )
         != emptyset )
        | ~ $true )
      & ( ~ ( in @ X2235 @ emptyset )
        | ( X2234 @ X2235 ) )
      & ( ( in @ ( esk25_2 @ X2236 @ X2237 ) @ X2236 )
        | ~ ( in @ X2238 @ X2236 )
        | ( X2237 @ X2238 ) )
      & ( ~ ( X2237 @ ( esk25_2 @ X2236 @ X2237 ) )
        | ~ ( in @ X2238 @ X2236 )
        | ( X2237 @ X2238 ) )
      & ( ( in @ ( esk26_2 @ X2240 @ X2241 ) @ X2240 )
        | ~ ( in @ X2243 @ X2240 )
        | ~ ( X2241 @ X2243 ) )
      & ( ( X2241 @ ( esk26_2 @ X2240 @ X2241 ) )
        | ~ ( in @ X2243 @ X2240 )
        | ~ ( X2241 @ X2243 ) )
      & ( ( in @ ( esk27_2 @ X2244 @ X2245 ) @ X2244 )
        | ~ ( in @ X2247 @ X2244 )
        | ~ ( X2245 @ X2247 ) )
      & ( ( X2245 @ ( esk27_2 @ X2244 @ X2245 ) )
        | ~ ( in @ X2247 @ X2244 )
        | ~ ( X2245 @ X2247 ) )
      & ( ( in @ ( esk28_2 @ X2248 @ X2249 ) @ X2248 )
        | ~ ( in @ X2250 @ X2248 )
        | ( X2249 @ X2250 ) )
      & ( ~ ( X2249 @ ( esk28_2 @ X2248 @ X2249 ) )
        | ~ ( in @ X2250 @ X2248 )
        | ( X2249 @ X2250 ) )
      & ( ~ X2252
        | ( in @ emptyset @ ( prop2set @ X2252 ) ) )
      & prop2set2propI
      & ( ( in @ ( esk29_2 @ X2253 @ X2254 ) @ X2253 )
        | ~ ( in @ X2256 @ X2253 )
        | ~ ( X2254 @ X2256 ) )
      & ( ( X2254 @ ( esk29_2 @ X2253 @ X2254 ) )
        | ~ ( in @ X2256 @ X2253 )
        | ~ ( X2254 @ X2256 ) )
      & ( ( in @ ( esk30_2 @ X2257 @ X2258 ) @ X2257 )
        | ~ ( in @ X2259 @ X2257 )
        | ( X2258 @ X2259 ) )
      & ( ~ ( X2258 @ ( esk30_2 @ X2257 @ X2258 ) )
        | ~ ( in @ X2259 @ X2257 )
        | ( X2258 @ X2259 ) )
      & ( ( X2261 @ ( esk32_1 @ X2261 ) )
        | ( X2261 @ ( esk31_2 @ X2261 @ X2262 ) )
        | ~ ( X2261 @ X2262 ) )
      & ( ~ ( X2261 @ X2265 )
        | ( ( esk32_1 @ X2261 )
          = X2265 )
        | ( X2261 @ ( esk31_2 @ X2261 @ X2262 ) )
        | ~ ( X2261 @ X2262 ) )
      & ( ( X2261 @ ( esk32_1 @ X2261 ) )
        | ( X2262
         != ( esk31_2 @ X2261 @ X2262 ) )
        | ~ ( X2261 @ X2262 ) )
      & ( ~ ( X2261 @ X2265 )
        | ( ( esk32_1 @ X2261 )
          = X2265 )
        | ( X2262
         != ( esk31_2 @ X2261 @ X2262 ) )
        | ~ ( X2261 @ X2262 ) )
      & ( ( X2266 @ ( esk35_1 @ X2266 ) )
        | ( X2266 @ ( esk33_1 @ X2266 ) )
        | ~ ( X2266 @ X2267 ) )
      & ( ~ ( X2266 @ X2271 )
        | ( ( esk35_1 @ X2266 )
          = X2271 )
        | ( X2266 @ ( esk33_1 @ X2266 ) )
        | ~ ( X2266 @ X2267 ) )
      & ( ( X2266 @ ( esk35_1 @ X2266 ) )
        | ( X2266 @ ( esk34_1 @ X2266 ) )
        | ~ ( X2266 @ X2267 ) )
      & ( ~ ( X2266 @ X2271 )
        | ( ( esk35_1 @ X2266 )
          = X2271 )
        | ( X2266 @ ( esk34_1 @ X2266 ) )
        | ~ ( X2266 @ X2267 ) )
      & ( ( X2266 @ ( esk35_1 @ X2266 ) )
        | ( ( esk33_1 @ X2266 )
         != ( esk34_1 @ X2266 ) )
        | ~ ( X2266 @ X2267 ) )
      & ( ~ ( X2266 @ X2271 )
        | ( ( esk35_1 @ X2266 )
          = X2271 )
        | ( ( esk33_1 @ X2266 )
         != ( esk34_1 @ X2266 ) )
        | ~ ( X2266 @ X2267 ) )
      & ( ( X2272 @ ( esk37_1 @ X2272 ) )
        | ~ ( X2272 @ ( esk36_2 @ X2272 @ X2273 ) )
        | ( ( esk36_2 @ X2272 @ X2273 )
         != X2273 ) )
      & ( ~ ( X2272 @ X2276 )
        | ( ( esk37_1 @ X2272 )
          = X2276 )
        | ~ ( X2272 @ ( esk36_2 @ X2272 @ X2273 ) )
        | ( ( esk36_2 @ X2272 @ X2273 )
         != X2273 ) )
      & ( ( X2272 @ ( esk37_1 @ X2272 ) )
        | ( X2272 @ ( esk36_2 @ X2272 @ X2273 ) )
        | ( ( esk36_2 @ X2272 @ X2273 )
          = X2273 ) )
      & ( ~ ( X2272 @ X2276 )
        | ( ( esk37_1 @ X2272 )
          = X2276 )
        | ( X2272 @ ( esk36_2 @ X2272 @ X2273 ) )
        | ( ( esk36_2 @ X2272 @ X2273 )
          = X2273 ) )
      & ( ( X2277 != X2278 )
        | ( X2279 != X2280 )
        | ~ ( in @ X2279 @ X2277 )
        | ( in @ X2280 @ X2278 ) )
      & ( ~ ( in @ X2283 @ X2281 )
        | ( in @ X2284 @ X2282 )
        | ( X2283 != X2284 )
        | ( X2281 != X2282 ) )
      & ( ~ ( in @ X2284 @ X2282 )
        | ( in @ X2283 @ X2281 )
        | ( X2283 != X2284 )
        | ( X2281 != X2282 ) )
      & ( ( X2285 @ ( esk38_2 @ X2285 @ X2286 ) )
        | ~ ( X2285 @ X2286 )
        | ~ ( X2285 @ X2288 )
        | ~ ( X2285 @ X2289 )
        | ( X2288 = X2289 ) )
      & ( ( X2286
         != ( esk38_2 @ X2285 @ X2286 ) )
        | ~ ( X2285 @ X2286 )
        | ~ ( X2285 @ X2288 )
        | ~ ( X2285 @ X2289 )
        | ( X2288 = X2289 ) )
      & ( ( X2291 @ ( esk42_2 @ X2290 @ X2291 ) )
        | ( X2290 @ ( esk41_3 @ X2290 @ X2291 @ X2294 ) )
        | ~ ( X2290 @ X2294 )
        | ( ( esk39_2 @ X2290 @ X2291 )
          = ( esk40_2 @ X2290 @ X2291 ) ) )
      & ( ~ ( X2291 @ X2297 )
        | ( ( esk42_2 @ X2290 @ X2291 )
          = X2297 )
        | ( X2290 @ ( esk41_3 @ X2290 @ X2291 @ X2294 ) )
        | ~ ( X2290 @ X2294 )
        | ( ( esk39_2 @ X2290 @ X2291 )
          = ( esk40_2 @ X2290 @ X2291 ) ) )
      & ( ( X2291 @ ( esk42_2 @ X2290 @ X2291 ) )
        | ( X2294
         != ( esk41_3 @ X2290 @ X2291 @ X2294 ) )
        | ~ ( X2290 @ X2294 )
        | ( ( esk39_2 @ X2290 @ X2291 )
          = ( esk40_2 @ X2290 @ X2291 ) ) )
      & ( ~ ( X2291 @ X2297 )
        | ( ( esk42_2 @ X2290 @ X2291 )
          = X2297 )
        | ( X2294
         != ( esk41_3 @ X2290 @ X2291 @ X2294 ) )
        | ~ ( X2290 @ X2294 )
        | ( ( esk39_2 @ X2290 @ X2291 )
          = ( esk40_2 @ X2290 @ X2291 ) ) )
      & ( ( X2290 @ ( esk44_2 @ X2290 @ X2291 ) )
        | ( X2291 @ ( esk43_3 @ X2290 @ X2291 @ X2298 ) )
        | ~ ( X2291 @ X2298 )
        | ( ( esk39_2 @ X2290 @ X2291 )
          = ( esk40_2 @ X2290 @ X2291 ) ) )
      & ( ~ ( X2290 @ X2301 )
        | ( ( esk44_2 @ X2290 @ X2291 )
          = X2301 )
        | ( X2291 @ ( esk43_3 @ X2290 @ X2291 @ X2298 ) )
        | ~ ( X2291 @ X2298 )
        | ( ( esk39_2 @ X2290 @ X2291 )
          = ( esk40_2 @ X2290 @ X2291 ) ) )
      & ( ( X2290 @ ( esk44_2 @ X2290 @ X2291 ) )
        | ( X2298
         != ( esk43_3 @ X2290 @ X2291 @ X2298 ) )
        | ~ ( X2291 @ X2298 )
        | ( ( esk39_2 @ X2290 @ X2291 )
          = ( esk40_2 @ X2290 @ X2291 ) ) )
      & ( ~ ( X2290 @ X2301 )
        | ( ( esk44_2 @ X2290 @ X2291 )
          = X2301 )
        | ( X2298
         != ( esk43_3 @ X2290 @ X2291 @ X2298 ) )
        | ~ ( X2291 @ X2298 )
        | ( ( esk39_2 @ X2290 @ X2291 )
          = ( esk40_2 @ X2290 @ X2291 ) ) )
      & ( ( X2291 @ ( esk42_2 @ X2290 @ X2291 ) )
        | ( X2290 @ ( esk41_3 @ X2290 @ X2291 @ X2294 ) )
        | ~ ( X2290 @ X2294 )
        | ~ ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
        | ~ ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
      & ( ~ ( X2291 @ X2297 )
        | ( ( esk42_2 @ X2290 @ X2291 )
          = X2297 )
        | ( X2290 @ ( esk41_3 @ X2290 @ X2291 @ X2294 ) )
        | ~ ( X2290 @ X2294 )
        | ~ ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
        | ~ ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
      & ( ( X2291 @ ( esk42_2 @ X2290 @ X2291 ) )
        | ( X2294
         != ( esk41_3 @ X2290 @ X2291 @ X2294 ) )
        | ~ ( X2290 @ X2294 )
        | ~ ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
        | ~ ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
      & ( ~ ( X2291 @ X2297 )
        | ( ( esk42_2 @ X2290 @ X2291 )
          = X2297 )
        | ( X2294
         != ( esk41_3 @ X2290 @ X2291 @ X2294 ) )
        | ~ ( X2290 @ X2294 )
        | ~ ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
        | ~ ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
      & ( ( X2290 @ ( esk44_2 @ X2290 @ X2291 ) )
        | ( X2291 @ ( esk43_3 @ X2290 @ X2291 @ X2298 ) )
        | ~ ( X2291 @ X2298 )
        | ~ ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
        | ~ ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
      & ( ~ ( X2290 @ X2301 )
        | ( ( esk44_2 @ X2290 @ X2291 )
          = X2301 )
        | ( X2291 @ ( esk43_3 @ X2290 @ X2291 @ X2298 ) )
        | ~ ( X2291 @ X2298 )
        | ~ ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
        | ~ ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
      & ( ( X2290 @ ( esk44_2 @ X2290 @ X2291 ) )
        | ( X2298
         != ( esk43_3 @ X2290 @ X2291 @ X2298 ) )
        | ~ ( X2291 @ X2298 )
        | ~ ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
        | ~ ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
      & ( ~ ( X2290 @ X2301 )
        | ( ( esk44_2 @ X2290 @ X2291 )
          = X2301 )
        | ( X2298
         != ( esk43_3 @ X2290 @ X2291 @ X2298 ) )
        | ~ ( X2291 @ X2298 )
        | ~ ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
        | ~ ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
      & ( ( X2291 @ ( esk42_2 @ X2290 @ X2291 ) )
        | ( X2290 @ ( esk41_3 @ X2290 @ X2291 @ X2294 ) )
        | ~ ( X2290 @ X2294 )
        | ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
        | ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
      & ( ~ ( X2291 @ X2297 )
        | ( ( esk42_2 @ X2290 @ X2291 )
          = X2297 )
        | ( X2290 @ ( esk41_3 @ X2290 @ X2291 @ X2294 ) )
        | ~ ( X2290 @ X2294 )
        | ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
        | ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
      & ( ( X2291 @ ( esk42_2 @ X2290 @ X2291 ) )
        | ( X2294
         != ( esk41_3 @ X2290 @ X2291 @ X2294 ) )
        | ~ ( X2290 @ X2294 )
        | ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
        | ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
      & ( ~ ( X2291 @ X2297 )
        | ( ( esk42_2 @ X2290 @ X2291 )
          = X2297 )
        | ( X2294
         != ( esk41_3 @ X2290 @ X2291 @ X2294 ) )
        | ~ ( X2290 @ X2294 )
        | ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
        | ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
      & ( ( X2290 @ ( esk44_2 @ X2290 @ X2291 ) )
        | ( X2291 @ ( esk43_3 @ X2290 @ X2291 @ X2298 ) )
        | ~ ( X2291 @ X2298 )
        | ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
        | ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
      & ( ~ ( X2290 @ X2301 )
        | ( ( esk44_2 @ X2290 @ X2291 )
          = X2301 )
        | ( X2291 @ ( esk43_3 @ X2290 @ X2291 @ X2298 ) )
        | ~ ( X2291 @ X2298 )
        | ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
        | ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
      & ( ( X2290 @ ( esk44_2 @ X2290 @ X2291 ) )
        | ( X2298
         != ( esk43_3 @ X2290 @ X2291 @ X2298 ) )
        | ~ ( X2291 @ X2298 )
        | ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
        | ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
      & ( ~ ( X2290 @ X2301 )
        | ( ( esk44_2 @ X2290 @ X2291 )
          = X2301 )
        | ( X2298
         != ( esk43_3 @ X2290 @ X2291 @ X2298 ) )
        | ~ ( X2291 @ X2298 )
        | ( X2290 @ ( esk39_2 @ X2290 @ X2291 ) )
        | ( X2291 @ ( esk40_2 @ X2290 @ X2291 ) ) )
      & ( emptyset = emptyset )
      & ( ( X2302 != X2303 )
        | ( X2304 != X2305 )
        | ( ( setadjoin @ X2302 @ X2304 )
          = ( setadjoin @ X2303 @ X2305 ) ) )
      & ( ( X2306 != X2307 )
        | ( ( powerset @ X2306 )
          = ( powerset @ X2307 ) ) )
      & ( ( X2308 != X2309 )
        | ( ( setunion @ X2308 )
          = ( setunion @ X2309 ) ) )
      & ( omega = omega )
      & ( ( X2310 @ ( esk45_2 @ X2310 @ X2311 ) )
        | ~ ( X2310 @ X2311 )
        | ~ ( X2310 @ X2313 )
        | ~ ( X2310 @ X2314 )
        | ( X2313 = X2314 ) )
      & ( ( X2311
         != ( esk45_2 @ X2310 @ X2311 ) )
        | ~ ( X2310 @ X2311 )
        | ~ ( X2310 @ X2313 )
        | ~ ( X2310 @ X2314 )
        | ( X2313 = X2314 ) )
      & ( ( X2316 @ ( esk49_3 @ X2315 @ X2316 @ X2321 ) )
        | ~ ( X2316 @ X2321 )
        | ( ( descr @ X2315 )
          = ( descr @ X2316 ) )
        | ( X2315 @ ( esk48_3 @ X2315 @ X2316 @ X2319 ) )
        | ~ ( X2315 @ X2319 )
        | ( ( esk46_2 @ X2315 @ X2316 )
          = ( esk47_2 @ X2315 @ X2316 ) ) )
      & ( ( X2321
         != ( esk49_3 @ X2315 @ X2316 @ X2321 ) )
        | ~ ( X2316 @ X2321 )
        | ( ( descr @ X2315 )
          = ( descr @ X2316 ) )
        | ( X2315 @ ( esk48_3 @ X2315 @ X2316 @ X2319 ) )
        | ~ ( X2315 @ X2319 )
        | ( ( esk46_2 @ X2315 @ X2316 )
          = ( esk47_2 @ X2315 @ X2316 ) ) )
      & ( ( X2316 @ ( esk49_3 @ X2315 @ X2316 @ X2321 ) )
        | ~ ( X2316 @ X2321 )
        | ( ( descr @ X2315 )
          = ( descr @ X2316 ) )
        | ( X2319
         != ( esk48_3 @ X2315 @ X2316 @ X2319 ) )
        | ~ ( X2315 @ X2319 )
        | ( ( esk46_2 @ X2315 @ X2316 )
          = ( esk47_2 @ X2315 @ X2316 ) ) )
      & ( ( X2321
         != ( esk49_3 @ X2315 @ X2316 @ X2321 ) )
        | ~ ( X2316 @ X2321 )
        | ( ( descr @ X2315 )
          = ( descr @ X2316 ) )
        | ( X2319
         != ( esk48_3 @ X2315 @ X2316 @ X2319 ) )
        | ~ ( X2315 @ X2319 )
        | ( ( esk46_2 @ X2315 @ X2316 )
          = ( esk47_2 @ X2315 @ X2316 ) ) )
      & ( ( X2316 @ ( esk49_3 @ X2315 @ X2316 @ X2321 ) )
        | ~ ( X2316 @ X2321 )
        | ( ( descr @ X2315 )
          = ( descr @ X2316 ) )
        | ( X2315 @ ( esk48_3 @ X2315 @ X2316 @ X2319 ) )
        | ~ ( X2315 @ X2319 )
        | ~ ( X2315 @ ( esk46_2 @ X2315 @ X2316 ) )
        | ~ ( X2316 @ ( esk47_2 @ X2315 @ X2316 ) ) )
      & ( ( X2321
         != ( esk49_3 @ X2315 @ X2316 @ X2321 ) )
        | ~ ( X2316 @ X2321 )
        | ( ( descr @ X2315 )
          = ( descr @ X2316 ) )
        | ( X2315 @ ( esk48_3 @ X2315 @ X2316 @ X2319 ) )
        | ~ ( X2315 @ X2319 )
        | ~ ( X2315 @ ( esk46_2 @ X2315 @ X2316 ) )
        | ~ ( X2316 @ ( esk47_2 @ X2315 @ X2316 ) ) )
      & ( ( X2316 @ ( esk49_3 @ X2315 @ X2316 @ X2321 ) )
        | ~ ( X2316 @ X2321 )
        | ( ( descr @ X2315 )
          = ( descr @ X2316 ) )
        | ( X2319
         != ( esk48_3 @ X2315 @ X2316 @ X2319 ) )
        | ~ ( X2315 @ X2319 )
        | ~ ( X2315 @ ( esk46_2 @ X2315 @ X2316 ) )
        | ~ ( X2316 @ ( esk47_2 @ X2315 @ X2316 ) ) )
      & ( ( X2321
         != ( esk49_3 @ X2315 @ X2316 @ X2321 ) )
        | ~ ( X2316 @ X2321 )
        | ( ( descr @ X2315 )
          = ( descr @ X2316 ) )
        | ( X2319
         != ( esk48_3 @ X2315 @ X2316 @ X2319 ) )
        | ~ ( X2315 @ X2319 )
        | ~ ( X2315 @ ( esk46_2 @ X2315 @ X2316 ) )
        | ~ ( X2316 @ ( esk47_2 @ X2315 @ X2316 ) ) )
      & ( ( X2316 @ ( esk49_3 @ X2315 @ X2316 @ X2321 ) )
        | ~ ( X2316 @ X2321 )
        | ( ( descr @ X2315 )
          = ( descr @ X2316 ) )
        | ( X2315 @ ( esk48_3 @ X2315 @ X2316 @ X2319 ) )
        | ~ ( X2315 @ X2319 )
        | ( X2315 @ ( esk46_2 @ X2315 @ X2316 ) )
        | ( X2316 @ ( esk47_2 @ X2315 @ X2316 ) ) )
      & ( ( X2321
         != ( esk49_3 @ X2315 @ X2316 @ X2321 ) )
        | ~ ( X2316 @ X2321 )
        | ( ( descr @ X2315 )
          = ( descr @ X2316 ) )
        | ( X2315 @ ( esk48_3 @ X2315 @ X2316 @ X2319 ) )
        | ~ ( X2315 @ X2319 )
        | ( X2315 @ ( esk46_2 @ X2315 @ X2316 ) )
        | ( X2316 @ ( esk47_2 @ X2315 @ X2316 ) ) )
      & ( ( X2316 @ ( esk49_3 @ X2315 @ X2316 @ X2321 ) )
        | ~ ( X2316 @ X2321 )
        | ( ( descr @ X2315 )
          = ( descr @ X2316 ) )
        | ( X2319
         != ( esk48_3 @ X2315 @ X2316 @ X2319 ) )
        | ~ ( X2315 @ X2319 )
        | ( X2315 @ ( esk46_2 @ X2315 @ X2316 ) )
        | ( X2316 @ ( esk47_2 @ X2315 @ X2316 ) ) )
      & ( ( X2321
         != ( esk49_3 @ X2315 @ X2316 @ X2321 ) )
        | ~ ( X2316 @ X2321 )
        | ( ( descr @ X2315 )
          = ( descr @ X2316 ) )
        | ( X2319
         != ( esk48_3 @ X2315 @ X2316 @ X2319 ) )
        | ~ ( X2315 @ X2319 )
        | ( X2315 @ ( esk46_2 @ X2315 @ X2316 ) )
        | ( X2316 @ ( esk47_2 @ X2315 @ X2316 ) ) )
      & ( ( in @ ( esk50_4 @ X2323 @ X2324 @ X2325 @ X2326 ) @ X2323 )
        | ( ( dsetconstr @ X2323 @ X2325 )
          = ( dsetconstr @ X2324 @ X2326 ) )
        | ( X2323 != X2324 ) )
      & ( ( in @ ( esk51_4 @ X2323 @ X2324 @ X2325 @ X2326 ) @ X2324 )
        | ( ( dsetconstr @ X2323 @ X2325 )
          = ( dsetconstr @ X2324 @ X2326 ) )
        | ( X2323 != X2324 ) )
      & ( ( ( esk50_4 @ X2323 @ X2324 @ X2325 @ X2326 )
          = ( esk51_4 @ X2323 @ X2324 @ X2325 @ X2326 ) )
        | ( ( dsetconstr @ X2323 @ X2325 )
          = ( dsetconstr @ X2324 @ X2326 ) )
        | ( X2323 != X2324 ) )
      & ( ~ ( X2325 @ ( esk50_4 @ X2323 @ X2324 @ X2325 @ X2326 ) )
        | ~ ( X2326 @ ( esk51_4 @ X2323 @ X2324 @ X2325 @ X2326 ) )
        | ( ( dsetconstr @ X2323 @ X2325 )
          = ( dsetconstr @ X2324 @ X2326 ) )
        | ( X2323 != X2324 ) )
      & ( ( X2325 @ ( esk50_4 @ X2323 @ X2324 @ X2325 @ X2326 ) )
        | ( X2326 @ ( esk51_4 @ X2323 @ X2324 @ X2325 @ X2326 ) )
        | ( ( dsetconstr @ X2323 @ X2325 )
          = ( dsetconstr @ X2324 @ X2326 ) )
        | ( X2323 != X2324 ) )
      & ( ( in @ ( esk52_2 @ X2329 @ X2330 ) @ X2329 )
        | ( subset @ X2329 @ X2330 ) )
      & ( ~ ( in @ ( esk52_2 @ X2329 @ X2330 ) @ X2330 )
        | ( subset @ X2329 @ X2330 ) )
      & ( ( X2332 != X2333 )
        | ( subset @ X2333 @ X2332 ) )
      & ( ( X2334 != X2335 )
        | ( subset @ X2334 @ X2335 ) )
      & ( ( in @ ( esk53_2 @ X2336 @ X2337 ) @ X2336 )
        | ( subset @ X2336 @ X2337 ) )
      & ( ~ ( in @ ( esk53_2 @ X2336 @ X2337 ) @ X2337 )
        | ( subset @ X2336 @ X2337 ) )
      & ( subset @ emptyset @ X2339 )
      & ( ~ ( subset @ X2340 @ X2341 )
        | ~ ( in @ X2342 @ X2340 )
        | ( in @ X2342 @ X2341 ) )
      & ( ~ ( subset @ X2343 @ X2344 )
        | ( in @ X2345 @ X2344 )
        | ~ ( in @ X2345 @ X2343 ) )
      & ( ~ ( in @ X2348 @ X2346 )
        | ( in @ X2348 @ X2347 )
        | ~ ( subset @ X2346 @ X2347 ) )
      & ( ( subset @ X2349 @ X2350 )
        | ( X2349 != X2350 ) )
      & ( ~ ( in @ X2353 @ X2351 )
        | ( in @ X2353 @ X2352 )
        | ( X2351 != X2352 ) )
      & ( subset @ X2354 @ X2354 )
      & ( ~ ( subset @ X2355 @ X2356 )
        | ~ ( subset @ X2356 @ X2357 )
        | ( subset @ X2355 @ X2357 ) )
      & ( subset @ X2359 @ ( setadjoin @ X2358 @ X2359 ) )
      & ( ~ ( subset @ X2360 @ X2362 )
        | ( subset @ X2360 @ ( setadjoin @ X2361 @ X2362 ) ) )
      & ( ~ ( subset @ X2363 @ X2364 )
        | ( in @ X2363 @ ( powerset @ X2364 ) ) )
      & ( ~ ( subset @ X2365 @ X2366 )
        | ~ ( subset @ X2366 @ X2365 )
        | ( X2365 = X2366 ) )
      & ( ~ ( subset @ X2367 @ emptyset )
        | ( X2367 = emptyset ) )
      & ( ~ ( subset @ X2369 @ X2368 )
        | ( in @ X2369 @ ( powerset @ X2368 ) ) )
      & ( ~ ( in @ X2371 @ ( powerset @ X2370 ) )
        | ( subset @ X2371 @ X2370 ) )
      & ( in @ X2372 @ ( powerset @ X2372 ) )
      & ( ~ ( subset @ X2373 @ X2374 )
        | ( subset @ ( powerset @ X2373 ) @ ( powerset @ X2374 ) ) )
      & ( in @ ( dsetconstr @ X2375 @ X2376 ) @ ( powerset @ X2375 ) )
      & ( subset @ ( dsetconstr @ X2377 @ X2378 ) @ X2377 )
      & ( ~ ( in @ X2381 @ X2379 )
        | ( in @ X2381 @ ( binunion @ X2379 @ X2380 ) ) )
      & ( in @ X2383 @ ( setadjoin @ X2382 @ ( setadjoin @ X2383 @ emptyset ) ) )
      & ( ~ ( in @ X2386 @ X2385 )
        | ( in @ X2386 @ ( binunion @ X2384 @ X2385 ) ) )
      & ( ( in @ X2389 @ X2388 )
        | X2390
        | ( in @ X2389 @ X2387 )
        | ~ ( in @ X2389 @ ( binunion @ X2387 @ X2388 ) ) )
      & ( ~ X2390
        | X2390
        | ( in @ X2389 @ X2387 )
        | ~ ( in @ X2389 @ ( binunion @ X2387 @ X2388 ) ) )
      & ( ( in @ X2389 @ X2388 )
        | X2390
        | ~ X2390
        | ~ ( in @ X2389 @ ( binunion @ X2387 @ X2388 ) ) )
      & ( ~ X2390
        | X2390
        | ~ X2390
        | ~ ( in @ X2389 @ ( binunion @ X2387 @ X2388 ) ) )
      & ( ~ ( in @ X2393 @ ( binunion @ X2391 @ X2392 ) )
        | ( in @ X2393 @ X2391 )
        | ( in @ X2393 @ X2392 ) )
      & ( subset @ X2394 @ ( binunion @ X2394 @ X2395 ) )
      & ( subset @ X2397 @ ( binunion @ X2396 @ X2397 ) )
      & ( ~ ( in @ X2400 @ X2398 )
        | ~ ( in @ X2400 @ X2399 )
        | ( in @ X2400 @ ( binintersect @ X2398 @ X2399 ) ) )
      & ( ~ ( subset @ X2403 @ X2401 )
        | ~ ( subset @ X2403 @ X2402 )
        | ( subset @ X2403 @ ( binintersect @ X2401 @ X2402 ) ) )
      & ( ~ ( in @ X2406 @ ( binintersect @ X2404 @ X2405 ) )
        | ( in @ X2406 @ X2404 ) )
      & ( subset @ ( binintersect @ X2407 @ X2408 ) @ X2407 )
      & ( ~ ( subset @ X2409 @ X2410 )
        | ( ( binintersect @ X2409 @ X2410 )
          = X2409 ) )
      & ( ( ( binintersect @ X2411 @ X2412 )
         != X2412 )
        | ( subset @ X2412 @ X2411 ) )
      & ( ~ ( in @ X2415 @ ( binintersect @ X2413 @ X2414 ) )
        | ( in @ X2415 @ X2414 ) )
      & ( ( in @ ( esk54_2 @ X2416 @ X2417 ) @ X2416 )
        | ( ( binintersect @ X2416 @ X2417 )
          = emptyset ) )
      & ( ( in @ ( esk54_2 @ X2416 @ X2417 ) @ X2417 )
        | ( ( binintersect @ X2416 @ X2417 )
          = emptyset ) )
      & ( subset @ ( binintersect @ X2419 @ X2420 ) @ X2420 )
      & ( ~ ( subset @ X2422 @ X2421 )
        | ( ( binintersect @ X2421 @ X2422 )
          = X2422 ) )
      & ( ( ( binintersect @ X2423 @ X2424 )
         != X2423 )
        | ( subset @ X2423 @ X2424 ) )
      & ( ( binintersect @ X2425 @ ( binunion @ X2426 @ X2427 ) )
        = ( binunion @ ( binintersect @ X2425 @ X2426 ) @ ( binintersect @ X2425 @ X2427 ) ) )
      & ( ~ ( in @ X2430 @ X2428 )
        | ( in @ X2430 @ X2429 )
        | ( in @ X2430 @ ( setminus @ X2428 @ X2429 ) ) )
      & ( ~ ( in @ X2433 @ ( setminus @ X2431 @ X2432 ) )
        | ( in @ X2433 @ X2431 ) )
      & ( ~ ( in @ X2436 @ ( setminus @ X2434 @ X2435 ) )
        | ~ ( in @ X2436 @ X2435 ) )
      & ( ~ ( subset @ X2437 @ X2438 )
        | ( ( setminus @ X2437 @ X2438 )
          = emptyset ) )
      & ( ( in @ X2441 @ ( setminus @ X2439 @ X2440 ) )
        | ~ ( in @ X2441 @ X2439 )
        | ( in @ X2441 @ X2440 ) )
      & ( ( in @ X2444 @ ( setminus @ X2442 @ X2443 ) )
        | ( in @ X2444 @ X2443 )
        | ~ ( in @ X2444 @ X2442 ) )
      & ( ( in @ X2447 @ X2445 )
        | ~ ( in @ X2447 @ ( setminus @ X2445 @ X2446 ) ) )
      & ( ~ ( in @ X2450 @ X2449 )
        | ~ ( in @ X2450 @ ( setminus @ X2448 @ X2449 ) ) )
      & ( subset @ ( setminus @ X2451 @ X2452 ) @ X2451 )
      & ( ( ( setminus @ X2453 @ X2454 )
         != emptyset )
        | ( subset @ X2453 @ X2454 ) )
      & ( ~ ( in @ X2457 @ X2455 )
        | X2458
        | ( in @ X2457 @ X2455 )
        | ~ ( in @ X2457 @ ( symdiff @ X2455 @ X2456 ) ) )
      & ( ( in @ X2457 @ X2456 )
        | X2458
        | ( in @ X2457 @ X2455 )
        | ~ ( in @ X2457 @ ( symdiff @ X2455 @ X2456 ) ) )
      & ( ~ X2458
        | X2458
        | ( in @ X2457 @ X2455 )
        | ~ ( in @ X2457 @ ( symdiff @ X2455 @ X2456 ) ) )
      & ( ~ ( in @ X2457 @ X2455 )
        | X2458
        | ~ ( in @ X2457 @ X2456 )
        | ~ ( in @ X2457 @ ( symdiff @ X2455 @ X2456 ) ) )
      & ( ( in @ X2457 @ X2456 )
        | X2458
        | ~ ( in @ X2457 @ X2456 )
        | ~ ( in @ X2457 @ ( symdiff @ X2455 @ X2456 ) ) )
      & ( ~ X2458
        | X2458
        | ~ ( in @ X2457 @ X2456 )
        | ~ ( in @ X2457 @ ( symdiff @ X2455 @ X2456 ) ) )
      & ( ~ ( in @ X2457 @ X2455 )
        | X2458
        | ~ X2458
        | ~ ( in @ X2457 @ ( symdiff @ X2455 @ X2456 ) ) )
      & ( ( in @ X2457 @ X2456 )
        | X2458
        | ~ X2458
        | ~ ( in @ X2457 @ ( symdiff @ X2455 @ X2456 ) ) )
      & ( ~ X2458
        | X2458
        | ~ X2458
        | ~ ( in @ X2457 @ ( symdiff @ X2455 @ X2456 ) ) )
      & ( ~ ( in @ X2461 @ X2459 )
        | ( in @ X2461 @ X2460 )
        | ( in @ X2461 @ ( symdiff @ X2459 @ X2460 ) ) )
      & ( ( in @ X2464 @ X2462 )
        | ~ ( in @ X2464 @ X2463 )
        | ( in @ X2464 @ ( symdiff @ X2462 @ X2463 ) ) )
      & ( ~ ( in @ X2467 @ X2465 )
        | ~ ( in @ X2467 @ X2466 )
        | ~ ( in @ X2467 @ ( symdiff @ X2465 @ X2466 ) ) )
      & ( ( in @ X2470 @ X2468 )
        | ( in @ X2470 @ X2469 )
        | ~ ( in @ X2470 @ ( symdiff @ X2468 @ X2469 ) ) )
      & ( in @ X2472 @ ( setadjoin @ X2471 @ ( setadjoin @ X2472 @ emptyset ) ) )
      & ( in @ X2473 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2473 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2473 @ ( setadjoin @ X2474 @ emptyset ) ) @ emptyset ) ) ) )
      & ( in @ X2476 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2475 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2475 @ ( setadjoin @ X2476 @ emptyset ) ) @ emptyset ) ) ) )
      & ( iskpair @ ( setadjoin @ ( setadjoin @ X2477 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2477 @ ( setadjoin @ X2478 @ emptyset ) ) @ emptyset ) ) )
      & ( iskpair @ ( kpair @ X2479 @ X2480 ) )
      & ( ~ ( in @ X2482 @ X2481 )
        | ( subset @ ( setadjoin @ X2482 @ emptyset ) @ X2481 ) )
      & ( ~ ( in @ X2484 @ X2483 )
        | ( in @ ( setadjoin @ X2484 @ emptyset ) @ ( powerset @ X2483 ) ) )
      & ( ~ ( in @ X2487 @ X2485 )
        | ( in @ ( setadjoin @ X2487 @ emptyset ) @ ( powerset @ ( binunion @ X2485 @ X2486 ) ) ) )
      & ( ~ ( in @ X2490 @ ( setadjoin @ X2488 @ ( setadjoin @ X2489 @ emptyset ) ) )
        | ( X2490 = X2488 )
        | ( X2490 = X2489 ) )
      & ( ~ ( in @ X2493 @ X2491 )
        | ~ ( in @ X2494 @ X2492 )
        | ( subset @ ( setadjoin @ X2493 @ ( setadjoin @ X2494 @ emptyset ) ) @ ( binunion @ X2491 @ X2492 ) ) )
      & ( ~ ( in @ X2497 @ X2495 )
        | ~ ( in @ X2498 @ X2496 )
        | ( in @ ( setadjoin @ X2497 @ ( setadjoin @ X2498 @ emptyset ) ) @ ( powerset @ ( binunion @ X2495 @ X2496 ) ) ) )
      & ( ~ ( in @ X2501 @ X2499 )
        | ~ ( in @ X2502 @ X2500 )
        | ( subset @ ( setadjoin @ ( setadjoin @ X2501 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2501 @ ( setadjoin @ X2502 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X2499 @ X2500 ) ) ) )
      & ( ~ ( in @ X2505 @ X2503 )
        | ~ ( in @ X2506 @ X2504 )
        | ( in @ ( setadjoin @ ( setadjoin @ X2505 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2505 @ ( setadjoin @ X2506 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X2503 @ X2504 ) ) ) ) )
      & ( ~ ( in @ X2509 @ X2507 )
        | ~ ( in @ X2510 @ X2508 )
        | ( in @ ( kpair @ X2509 @ X2510 ) @ ( powerset @ ( powerset @ ( binunion @ X2507 @ X2508 ) ) ) ) )
      & ( ~ ( in @ X2513 @ X2511 )
        | ~ ( in @ X2514 @ X2512 )
        | ( in @ ( kpair @ X2513 @ X2514 ) @ ( cartprod @ X2511 @ X2512 ) ) )
      & ( ( in @ ( esk55_3 @ X2515 @ X2516 @ X2517 ) @ X2515 )
        | ~ ( in @ X2517 @ ( cartprod @ X2515 @ X2516 ) ) )
      & ( ( in @ ( esk56_3 @ X2515 @ X2516 @ X2517 ) @ X2516 )
        | ~ ( in @ X2517 @ ( cartprod @ X2515 @ X2516 ) ) )
      & ( ( X2517
          = ( kpair @ ( esk55_3 @ X2515 @ X2516 @ X2517 ) @ ( esk56_3 @ X2515 @ X2516 @ X2517 ) ) )
        | ~ ( in @ X2517 @ ( cartprod @ X2515 @ X2516 ) ) )
      & ( ~ ( in @ X2522 @ ( cartprod @ X2520 @ X2521 ) )
        | ( iskpair @ X2522 ) )
      & ( ( in @ ( esk57_2 @ X2523 @ X2524 ) @ X2523 )
        | ~ ( in @ X2524 @ ( setunion @ X2523 ) ) )
      & ( ( in @ X2524 @ ( esk57_2 @ X2523 @ X2524 ) )
        | ~ ( in @ X2524 @ ( setunion @ X2523 ) ) )
      & ( subset @ ( setunion @ ( setadjoin @ X2526 @ emptyset ) ) @ X2526 )
      & ( subset @ X2527 @ ( setunion @ ( setadjoin @ X2527 @ emptyset ) ) )
      & ( ( setunion @ ( setadjoin @ X2528 @ emptyset ) )
        = X2528 )
      & ( ( in @ ( esk58_2 @ X2529 @ X2530 ) @ X2529 )
        | ~ ( in @ X2533 @ X2529 )
        | ~ ( X2530 @ X2533 )
        | ( singleton @ ( dsetconstr @ X2529 @ X2530 ) ) )
      & ( ( in @ ( esk59_2 @ X2529 @ X2530 ) @ X2529 )
        | ~ ( in @ X2533 @ X2529 )
        | ~ ( X2530 @ X2533 )
        | ( singleton @ ( dsetconstr @ X2529 @ X2530 ) ) )
      & ( ( X2530 @ ( esk58_2 @ X2529 @ X2530 ) )
        | ~ ( in @ X2533 @ X2529 )
        | ~ ( X2530 @ X2533 )
        | ( singleton @ ( dsetconstr @ X2529 @ X2530 ) ) )
      & ( ( X2530 @ ( esk59_2 @ X2529 @ X2530 ) )
        | ~ ( in @ X2533 @ X2529 )
        | ~ ( X2530 @ X2533 )
        | ( singleton @ ( dsetconstr @ X2529 @ X2530 ) ) )
      & ( ( ( esk58_2 @ X2529 @ X2530 )
         != ( esk59_2 @ X2529 @ X2530 ) )
        | ~ ( in @ X2533 @ X2529 )
        | ~ ( X2530 @ X2533 )
        | ( singleton @ ( dsetconstr @ X2529 @ X2530 ) ) )
      & ( ( in @ ( esk60_2 @ X2534 @ X2535 ) @ X2534 )
        | ~ ( ex1 @ X2534 @ X2535 ) )
      & ( ( X2535 @ ( esk60_2 @ X2534 @ X2535 ) )
        | ~ ( ex1 @ X2534 @ X2535 ) )
      & ( ( in @ ( esk61_3 @ X2537 @ X2538 @ X2539 ) @ X2537 )
        | ( ex1 @ X2537 @ X2538 )
        | ~ ( X2538 @ X2539 )
        | ~ ( in @ X2539 @ X2537 ) )
      & ( ( X2538 @ ( esk61_3 @ X2537 @ X2538 @ X2539 ) )
        | ( ex1 @ X2537 @ X2538 )
        | ~ ( X2538 @ X2539 )
        | ~ ( in @ X2539 @ X2537 ) )
      & ( ( ( esk61_3 @ X2537 @ X2538 @ X2539 )
         != X2539 )
        | ( ex1 @ X2537 @ X2538 )
        | ~ ( X2538 @ X2539 )
        | ~ ( in @ X2539 @ X2537 ) )
      & ( ( in @ ( esk62_2 @ X2541 @ X2542 ) @ X2541 )
        | ~ ( in @ X2545 @ X2541 )
        | ~ ( X2542 @ X2545 )
        | ( ex1 @ X2541 @ X2542 ) )
      & ( ( in @ ( esk63_2 @ X2541 @ X2542 ) @ X2541 )
        | ~ ( in @ X2545 @ X2541 )
        | ~ ( X2542 @ X2545 )
        | ( ex1 @ X2541 @ X2542 ) )
      & ( ( X2542 @ ( esk62_2 @ X2541 @ X2542 ) )
        | ~ ( in @ X2545 @ X2541 )
        | ~ ( X2542 @ X2545 )
        | ( ex1 @ X2541 @ X2542 ) )
      & ( ( X2542 @ ( esk63_2 @ X2541 @ X2542 ) )
        | ~ ( in @ X2545 @ X2541 )
        | ~ ( X2542 @ X2545 )
        | ( ex1 @ X2541 @ X2542 ) )
      & ( ( ( esk62_2 @ X2541 @ X2542 )
         != ( esk63_2 @ X2541 @ X2542 ) )
        | ~ ( in @ X2545 @ X2541 )
        | ~ ( X2542 @ X2545 )
        | ( ex1 @ X2541 @ X2542 ) )
      & ( ( ( setadjoin @ X2546 @ emptyset )
         != ( setadjoin @ X2547 @ emptyset ) )
        | ( X2546 = X2547 ) )
      & ( ~ ( in @ ( setadjoin @ X2550 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2548 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2548 @ ( setadjoin @ X2549 @ emptyset ) ) @ emptyset ) ) )
        | ( X2548 = X2550 ) )
      & ( ~ ( iskpair @ X2551 )
        | ( singleton
          @ ( dsetconstr @ ( setunion @ X2551 )
            @ ^ [Z0: $i] : ( in @ ( setadjoin @ Z0 @ emptyset ) @ X2551 ) ) ) )
      & ( ~ ( singleton @ X2552 )
        | ( in @ ( setunion @ X2552 ) @ X2552 ) )
      & ( ( kfst @ ( kpair @ X2553 @ X2554 ) )
        = X2553 )
      & ( ~ ( in @ X2557 @ ( cartprod @ X2555 @ X2556 ) )
        | ( in @ ( kfst @ X2557 ) @ X2555 ) )
      & ( ( ( setadjoin @ ( setadjoin @ X2558 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2558 @ ( setadjoin @ X2559 @ emptyset ) ) @ emptyset ) )
         != ( setadjoin @ ( setadjoin @ X2560 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2560 @ ( setadjoin @ X2561 @ emptyset ) ) @ emptyset ) ) )
        | ( X2558 = X2560 ) )
      & ( ( ( kpair @ X2562 @ X2563 )
         != ( kpair @ X2564 @ X2565 ) )
        | ( X2562 = X2564 ) )
      & ( ( X2566 != X2567 )
        | ( ( setadjoin @ X2566 @ ( setadjoin @ X2567 @ emptyset ) )
          = ( setadjoin @ X2566 @ emptyset ) ) )
      & ( ( X2568 != X2569 )
        | ( ( setadjoin @ ( setadjoin @ X2568 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2568 @ ( setadjoin @ X2569 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ X2568 @ emptyset ) @ emptyset ) ) )
      & ( ( ( setadjoin @ ( setadjoin @ X2570 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2570 @ ( setadjoin @ X2571 @ emptyset ) ) @ emptyset ) )
         != ( setadjoin @ ( setadjoin @ X2572 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2572 @ ( setadjoin @ X2573 @ emptyset ) ) @ emptyset ) ) )
        | ( X2572 != X2573 )
        | ( X2571 = X2573 ) )
      & ( ( ( setadjoin @ X2574 @ ( setadjoin @ X2575 @ emptyset ) )
         != ( setadjoin @ X2576 @ emptyset ) )
        | ( X2574 = X2575 ) )
      & ( ( ( setadjoin @ ( setadjoin @ X2577 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2577 @ ( setadjoin @ X2578 @ emptyset ) ) @ emptyset ) )
         != ( setadjoin @ ( setadjoin @ X2579 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2579 @ ( setadjoin @ X2580 @ emptyset ) ) @ emptyset ) ) )
        | ( X2578 = X2580 ) )
      & ( ( ( kpair @ X2581 @ X2582 )
         != ( kpair @ X2583 @ X2584 ) )
        | ( X2582 = X2584 ) )
      & ( ~ ( iskpair @ X2585 )
        | ( singleton
          @ ( dsetconstr @ ( setunion @ X2585 )
            @ ^ [Z0: $i] :
                ( X2585
                = ( kpair @ ( kfst @ X2585 ) @ Z0 ) ) ) ) )
      & ( ( ksnd @ ( kpair @ X2586 @ X2587 ) )
        = X2587 )
      & ( ~ ( iskpair @ X2588 )
        | ( ( kpair @ ( kfst @ X2588 ) @ ( ksnd @ X2588 ) )
          = X2588 ) )
      & ( ~ ( in @ X2591 @ ( cartprod @ X2589 @ X2590 ) )
        | ( in @ ( ksnd @ X2591 ) @ X2590 ) )
      & ( ~ ( in @ ( kpair @ X2594 @ X2595 ) @ ( cartprod @ X2592 @ X2593 ) )
        | ( in @ X2594 @ X2592 ) )
      & ( ~ ( in @ ( kpair @ X2598 @ X2599 ) @ ( cartprod @ X2596 @ X2597 ) )
        | ( in @ X2599 @ X2597 ) )
      & ( ~ ( in @ X2602 @ X2600 )
        | ~ ( in @ X2603 @ X2601 )
        | ( ( kpair @ X2602 @ X2603 )
          = ( kpair @ X2602 @ X2603 ) ) )
      & ( ~ ( in @ X2606 @ X2604 )
        | ~ ( in @ X2607 @ X2605 )
        | ( ( kfst @ ( kpair @ X2606 @ X2607 ) )
          = X2606 ) )
      & ( ~ ( in @ X2610 @ X2608 )
        | ~ ( in @ X2611 @ X2609 )
        | ( ( ksnd @ ( kpair @ X2610 @ X2611 ) )
          = X2611 ) )
      & ( ~ ( in @ X2614 @ ( cartprod @ X2612 @ X2613 ) )
        | ( ( kpair @ ( kfst @ X2614 ) @ ( ksnd @ X2614 ) )
          = X2614 ) )
      & ( ~ ( in @ X2618 @ X2615 )
        | ~ ( in @ X2619 @ X2616 )
        | ~ ( X2617 @ X2618 @ X2619 )
        | ( in @ ( kpair @ X2618 @ X2619 ) @ ( dpsetconstr @ X2615 @ X2616 @ X2617 ) ) )
      & ( subset @ ( dpsetconstr @ X2620 @ X2621 @ X2622 ) @ ( cartprod @ X2620 @ X2621 ) )
      & ( breln @ X2623 @ X2624 @ ( dpsetconstr @ X2623 @ X2624 @ X2625 ) )
      & ( ~ ( in @ X2629 @ X2626 )
        | ~ ( in @ X2630 @ X2627 )
        | ~ ( in @ ( kpair @ X2629 @ X2630 ) @ ( dpsetconstr @ X2626 @ X2627 @ X2628 ) )
        | ( X2628 @ X2629 @ X2630 ) )
      & ( ~ ( in @ ( kpair @ X2634 @ X2635 ) @ ( dpsetconstr @ X2631 @ X2632 @ X2633 ) )
        | ( in @ X2634 @ X2631 ) )
      & ( ~ ( in @ ( kpair @ X2639 @ X2640 ) @ ( dpsetconstr @ X2636 @ X2637 @ X2638 ) )
        | ( in @ X2640 @ X2637 ) )
      & ( ~ ( in @ ( kpair @ X2644 @ X2645 ) @ ( dpsetconstr @ X2641 @ X2642 @ X2643 ) )
        | ( X2643 @ X2644 @ X2645 ) )
      & ( ~ ( func @ X2646 @ X2647 @ X2648 )
        | ~ ( in @ X2649 @ X2646 )
        | ( singleton
          @ ( dsetconstr @ X2647
            @ ^ [Z0: $i] : ( in @ ( kpair @ X2649 @ Z0 ) @ X2648 ) ) ) )
      & ( ~ ( func @ X2650 @ X2651 @ X2652 )
        | ~ ( in @ X2653 @ X2650 )
        | ( in
          @ ( setunion
            @ ( dsetconstr @ X2651
              @ ^ [Z0: $i] : ( in @ ( kpair @ X2653 @ Z0 ) @ X2652 ) ) )
          @ X2651 ) )
      & ( ~ ( func @ X2654 @ X2655 @ X2656 )
        | ~ ( in @ X2657 @ X2654 )
        | ( in @ ( ap @ X2654 @ X2655 @ X2656 @ X2657 ) @ X2655 ) )
      & ( ~ ( in @ X2660 @ ( funcSet @ X2658 @ X2659 ) )
        | ( func @ X2658 @ X2659 @ X2660 ) )
      & ( ~ ( in @ X2663 @ ( funcSet @ X2661 @ X2662 ) )
        | ~ ( in @ X2664 @ X2661 )
        | ( in @ ( ap @ X2661 @ X2662 @ X2663 @ X2664 ) @ X2662 ) )
      & ( ~ ( func @ X2665 @ X2666 @ X2667 )
        | ( in @ X2667 @ ( funcSet @ X2665 @ X2666 ) ) )
      & ( ( in @ ( esk64_3 @ X2668 @ X2669 @ X2670 ) @ X2668 )
        | ( func @ X2668 @ X2669
          @ ( dpsetconstr @ X2668 @ X2669
            @ ^ [Z0: $i] : ( $eq @ ( X2670 @ Z0 ) ) ) ) )
      & ( ~ ( in @ ( X2670 @ ( esk64_3 @ X2668 @ X2669 @ X2670 ) ) @ X2669 )
        | ( func @ X2668 @ X2669
          @ ( dpsetconstr @ X2668 @ X2669
            @ ^ [Z0: $i] : ( $eq @ ( X2670 @ Z0 ) ) ) ) )
      & ( ( in @ ( esk65_3 @ X2672 @ X2673 @ X2674 ) @ X2672 )
        | ( func @ X2672 @ X2673 @ ( lam @ X2672 @ X2673 @ X2674 ) ) )
      & ( ~ ( in @ ( X2674 @ ( esk65_3 @ X2672 @ X2673 @ X2674 ) ) @ X2673 )
        | ( func @ X2672 @ X2673 @ ( lam @ X2672 @ X2673 @ X2674 ) ) )
      & ( ( in @ ( esk66_3 @ X2676 @ X2677 @ X2678 ) @ X2676 )
        | ( in @ ( lam @ X2676 @ X2677 @ X2678 ) @ ( funcSet @ X2676 @ X2677 ) ) )
      & ( ~ ( in @ ( X2678 @ ( esk66_3 @ X2676 @ X2677 @ X2678 ) ) @ X2677 )
        | ( in @ ( lam @ X2676 @ X2677 @ X2678 ) @ ( funcSet @ X2676 @ X2677 ) ) )
      & ( ( in @ ( esk67_4 @ X2680 @ X2681 @ X2682 @ X2683 ) @ X2680 )
        | ~ ( in @ X2686 @ X2682 )
        | ( X2683 @ X2686 )
        | ~ ( breln @ X2680 @ X2681 @ X2682 ) )
      & ( ( in @ ( esk68_4 @ X2680 @ X2681 @ X2682 @ X2683 ) @ X2681 )
        | ~ ( in @ X2686 @ X2682 )
        | ( X2683 @ X2686 )
        | ~ ( breln @ X2680 @ X2681 @ X2682 ) )
      & ( ( in @ ( kpair @ ( esk67_4 @ X2680 @ X2681 @ X2682 @ X2683 ) @ ( esk68_4 @ X2680 @ X2681 @ X2682 @ X2683 ) ) @ X2682 )
        | ~ ( in @ X2686 @ X2682 )
        | ( X2683 @ X2686 )
        | ~ ( breln @ X2680 @ X2681 @ X2682 ) )
      & ( ~ ( X2683 @ ( kpair @ ( esk67_4 @ X2680 @ X2681 @ X2682 @ X2683 ) @ ( esk68_4 @ X2680 @ X2681 @ X2682 @ X2683 ) ) )
        | ~ ( in @ X2686 @ X2682 )
        | ( X2683 @ X2686 )
        | ~ ( breln @ X2680 @ X2681 @ X2682 ) )
      & ( ( in @ ( esk69_4 @ X2687 @ X2688 @ X2689 @ X2690 ) @ X2687 )
        | ~ ( in @ X2693 @ X2689 )
        | ( X2690 @ X2693 )
        | ~ ( breln @ X2687 @ X2688 @ X2689 ) )
      & ( ( in @ ( esk70_4 @ X2687 @ X2688 @ X2689 @ X2690 ) @ X2688 )
        | ~ ( in @ X2693 @ X2689 )
        | ( X2690 @ X2693 )
        | ~ ( breln @ X2687 @ X2688 @ X2689 ) )
      & ( ( in @ ( kpair @ ( esk69_4 @ X2687 @ X2688 @ X2689 @ X2690 ) @ ( esk70_4 @ X2687 @ X2688 @ X2689 @ X2690 ) ) @ X2689 )
        | ~ ( in @ X2693 @ X2689 )
        | ( X2690 @ X2693 )
        | ~ ( breln @ X2687 @ X2688 @ X2689 ) )
      & ( ~ ( X2690 @ ( kpair @ ( esk69_4 @ X2687 @ X2688 @ X2689 @ X2690 ) @ ( esk70_4 @ X2687 @ X2688 @ X2689 @ X2690 ) ) )
        | ~ ( in @ X2693 @ X2689 )
        | ( X2690 @ X2693 )
        | ~ ( breln @ X2687 @ X2688 @ X2689 ) )
      & ( ~ ( ex1 @ X2694 @ X2695 )
        | ~ ( in @ X2696 @ X2694 )
        | ~ ( in @ X2697 @ X2694 )
        | ~ ( X2695 @ X2696 )
        | ~ ( X2695 @ X2697 )
        | ( X2696 = X2697 ) )
      & ( ~ ( func @ X2698 @ X2699 @ X2700 )
        | ~ ( in @ X2701 @ X2698 )
        | ( in @ ( kpair @ X2701 @ ( ap @ X2698 @ X2699 @ X2700 @ X2701 ) ) @ X2700 ) )
      & ( ~ ( in @ X2704 @ ( funcSet @ X2702 @ X2703 ) )
        | ~ ( in @ X2705 @ X2702 )
        | ( in @ ( kpair @ X2705 @ ( ap @ X2702 @ X2703 @ X2704 @ X2705 ) ) @ X2704 ) )
      & ( ~ ( func @ X2706 @ X2707 @ X2708 )
        | ~ ( in @ X2709 @ X2706 )
        | ~ ( in @ X2710 @ X2707 )
        | ~ ( in @ ( kpair @ X2709 @ X2710 ) @ X2708 )
        | ( ( ap @ X2706 @ X2707 @ X2708 @ X2709 )
          = X2710 ) )
      & ( ( in @ ( esk71_4 @ X2711 @ X2712 @ X2713 @ X2714 ) @ X2711 )
        | ~ ( in @ X2716 @ X2711 )
        | ~ ( in @ X2717 @ X2712 )
        | ~ ( in @ ( kpair @ X2716 @ X2717 ) @ X2714 )
        | ( in @ ( kpair @ X2716 @ X2717 ) @ X2713 )
        | ~ ( func @ X2711 @ X2712 @ X2714 )
        | ~ ( func @ X2711 @ X2712 @ X2713 ) )
      & ( ( ( ap @ X2711 @ X2712 @ X2713 @ ( esk71_4 @ X2711 @ X2712 @ X2713 @ X2714 ) )
         != ( ap @ X2711 @ X2712 @ X2714 @ ( esk71_4 @ X2711 @ X2712 @ X2713 @ X2714 ) ) )
        | ~ ( in @ X2716 @ X2711 )
        | ~ ( in @ X2717 @ X2712 )
        | ~ ( in @ ( kpair @ X2716 @ X2717 ) @ X2714 )
        | ( in @ ( kpair @ X2716 @ X2717 ) @ X2713 )
        | ~ ( func @ X2711 @ X2712 @ X2714 )
        | ~ ( func @ X2711 @ X2712 @ X2713 ) )
      & ( ~ ( in @ X2720 @ ( funcSet @ X2718 @ X2719 ) )
        | ~ ( in @ X2721 @ X2718 )
        | ~ ( in @ X2722 @ X2719 )
        | ~ ( in @ ( kpair @ X2721 @ X2722 ) @ X2720 )
        | ( ( ap @ X2718 @ X2719 @ X2720 @ X2721 )
          = X2722 ) )
      & ( ( in @ ( esk72_4 @ X2723 @ X2724 @ X2725 @ X2726 ) @ X2723 )
        | ( subset @ X2725 @ X2726 )
        | ~ ( breln @ X2723 @ X2724 @ X2726 )
        | ~ ( breln @ X2723 @ X2724 @ X2725 ) )
      & ( ( in @ ( esk73_4 @ X2723 @ X2724 @ X2725 @ X2726 ) @ X2724 )
        | ( subset @ X2725 @ X2726 )
        | ~ ( breln @ X2723 @ X2724 @ X2726 )
        | ~ ( breln @ X2723 @ X2724 @ X2725 ) )
      & ( ( in @ ( kpair @ ( esk72_4 @ X2723 @ X2724 @ X2725 @ X2726 ) @ ( esk73_4 @ X2723 @ X2724 @ X2725 @ X2726 ) ) @ X2725 )
        | ( subset @ X2725 @ X2726 )
        | ~ ( breln @ X2723 @ X2724 @ X2726 )
        | ~ ( breln @ X2723 @ X2724 @ X2725 ) )
      & ( ~ ( in @ ( kpair @ ( esk72_4 @ X2723 @ X2724 @ X2725 @ X2726 ) @ ( esk73_4 @ X2723 @ X2724 @ X2725 @ X2726 ) ) @ X2726 )
        | ( subset @ X2725 @ X2726 )
        | ~ ( breln @ X2723 @ X2724 @ X2726 )
        | ~ ( breln @ X2723 @ X2724 @ X2725 ) )
      & ( ( in @ ( esk76_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2729 )
        | ( X2731 = X2732 )
        | ( in @ ( esk74_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2729 )
        | ~ ( breln @ X2729 @ X2730 @ X2732 )
        | ~ ( breln @ X2729 @ X2730 @ X2731 ) )
      & ( ( in @ ( esk77_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2730 )
        | ( X2731 = X2732 )
        | ( in @ ( esk74_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2729 )
        | ~ ( breln @ X2729 @ X2730 @ X2732 )
        | ~ ( breln @ X2729 @ X2730 @ X2731 ) )
      & ( ( in @ ( kpair @ ( esk76_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk77_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2732 )
        | ( X2731 = X2732 )
        | ( in @ ( esk74_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2729 )
        | ~ ( breln @ X2729 @ X2730 @ X2732 )
        | ~ ( breln @ X2729 @ X2730 @ X2731 ) )
      & ( ~ ( in @ ( kpair @ ( esk76_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk77_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2731 )
        | ( X2731 = X2732 )
        | ( in @ ( esk74_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2729 )
        | ~ ( breln @ X2729 @ X2730 @ X2732 )
        | ~ ( breln @ X2729 @ X2730 @ X2731 ) )
      & ( ( in @ ( esk76_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2729 )
        | ( X2731 = X2732 )
        | ( in @ ( esk75_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2730 )
        | ~ ( breln @ X2729 @ X2730 @ X2732 )
        | ~ ( breln @ X2729 @ X2730 @ X2731 ) )
      & ( ( in @ ( esk77_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2730 )
        | ( X2731 = X2732 )
        | ( in @ ( esk75_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2730 )
        | ~ ( breln @ X2729 @ X2730 @ X2732 )
        | ~ ( breln @ X2729 @ X2730 @ X2731 ) )
      & ( ( in @ ( kpair @ ( esk76_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk77_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2732 )
        | ( X2731 = X2732 )
        | ( in @ ( esk75_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2730 )
        | ~ ( breln @ X2729 @ X2730 @ X2732 )
        | ~ ( breln @ X2729 @ X2730 @ X2731 ) )
      & ( ~ ( in @ ( kpair @ ( esk76_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk77_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2731 )
        | ( X2731 = X2732 )
        | ( in @ ( esk75_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2730 )
        | ~ ( breln @ X2729 @ X2730 @ X2732 )
        | ~ ( breln @ X2729 @ X2730 @ X2731 ) )
      & ( ( in @ ( esk76_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2729 )
        | ( X2731 = X2732 )
        | ( in @ ( kpair @ ( esk74_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk75_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2731 )
        | ~ ( breln @ X2729 @ X2730 @ X2732 )
        | ~ ( breln @ X2729 @ X2730 @ X2731 ) )
      & ( ( in @ ( esk77_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2730 )
        | ( X2731 = X2732 )
        | ( in @ ( kpair @ ( esk74_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk75_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2731 )
        | ~ ( breln @ X2729 @ X2730 @ X2732 )
        | ~ ( breln @ X2729 @ X2730 @ X2731 ) )
      & ( ( in @ ( kpair @ ( esk76_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk77_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2732 )
        | ( X2731 = X2732 )
        | ( in @ ( kpair @ ( esk74_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk75_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2731 )
        | ~ ( breln @ X2729 @ X2730 @ X2732 )
        | ~ ( breln @ X2729 @ X2730 @ X2731 ) )
      & ( ~ ( in @ ( kpair @ ( esk76_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk77_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2731 )
        | ( X2731 = X2732 )
        | ( in @ ( kpair @ ( esk74_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk75_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2731 )
        | ~ ( breln @ X2729 @ X2730 @ X2732 )
        | ~ ( breln @ X2729 @ X2730 @ X2731 ) )
      & ( ( in @ ( esk76_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2729 )
        | ( X2731 = X2732 )
        | ~ ( in @ ( kpair @ ( esk74_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk75_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2732 )
        | ~ ( breln @ X2729 @ X2730 @ X2732 )
        | ~ ( breln @ X2729 @ X2730 @ X2731 ) )
      & ( ( in @ ( esk77_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ X2730 )
        | ( X2731 = X2732 )
        | ~ ( in @ ( kpair @ ( esk74_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk75_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2732 )
        | ~ ( breln @ X2729 @ X2730 @ X2732 )
        | ~ ( breln @ X2729 @ X2730 @ X2731 ) )
      & ( ( in @ ( kpair @ ( esk76_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk77_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2732 )
        | ( X2731 = X2732 )
        | ~ ( in @ ( kpair @ ( esk74_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk75_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2732 )
        | ~ ( breln @ X2729 @ X2730 @ X2732 )
        | ~ ( breln @ X2729 @ X2730 @ X2731 ) )
      & ( ~ ( in @ ( kpair @ ( esk76_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk77_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2731 )
        | ( X2731 = X2732 )
        | ~ ( in @ ( kpair @ ( esk74_4 @ X2729 @ X2730 @ X2731 @ X2732 ) @ ( esk75_4 @ X2729 @ X2730 @ X2731 @ X2732 ) ) @ X2732 )
        | ~ ( breln @ X2729 @ X2730 @ X2732 )
        | ~ ( breln @ X2729 @ X2730 @ X2731 ) )
      & ( ( in @ ( esk78_4 @ X2737 @ X2738 @ X2739 @ X2740 ) @ X2737 )
        | ( X2739 = X2740 )
        | ~ ( func @ X2737 @ X2738 @ X2740 )
        | ~ ( func @ X2737 @ X2738 @ X2739 ) )
      & ( ( ( ap @ X2737 @ X2738 @ X2739 @ ( esk78_4 @ X2737 @ X2738 @ X2739 @ X2740 ) )
         != ( ap @ X2737 @ X2738 @ X2740 @ ( esk78_4 @ X2737 @ X2738 @ X2739 @ X2740 ) ) )
        | ( X2739 = X2740 )
        | ~ ( func @ X2737 @ X2738 @ X2740 )
        | ~ ( func @ X2737 @ X2738 @ X2739 ) )
      & ( ( in @ ( esk79_4 @ X2742 @ X2743 @ X2744 @ X2745 ) @ X2742 )
        | ( X2744 = X2745 )
        | ~ ( in @ X2745 @ ( funcSet @ X2742 @ X2743 ) )
        | ~ ( in @ X2744 @ ( funcSet @ X2742 @ X2743 ) ) )
      & ( ( ( ap @ X2742 @ X2743 @ X2744 @ ( esk79_4 @ X2742 @ X2743 @ X2744 @ X2745 ) )
         != ( ap @ X2742 @ X2743 @ X2745 @ ( esk79_4 @ X2742 @ X2743 @ X2744 @ X2745 ) ) )
        | ( X2744 = X2745 )
        | ~ ( in @ X2745 @ ( funcSet @ X2742 @ X2743 ) )
        | ~ ( in @ X2744 @ ( funcSet @ X2742 @ X2743 ) ) )
      & ( ~ ( in @ X2749 @ ( funcSet @ X2747 @ X2748 ) )
        | ~ ( in @ X2750 @ X2747 )
        | ( ( ap @ X2747 @ X2748 @ X2749 @ X2750 )
          = ( ap @ X2747 @ X2748 @ X2749 @ X2750 ) ) )
      & ( ~ ( func @ X2751 @ X2752 @ X2753 )
        | ~ ( in @ X2754 @ X2751 )
        | ( ( ap @ X2751 @ X2752 @ X2753 @ X2754 )
          = ( ap @ X2751 @ X2752 @ X2753 @ X2754 ) ) )
      & ( ( in @ ( esk80_3 @ X2755 @ X2756 @ X2757 ) @ X2755 )
        | ~ ( in @ X2759 @ X2755 )
        | ( ( ap @ X2755 @ X2756 @ ( lam @ X2755 @ X2756 @ X2757 ) @ X2759 )
          = ( X2757 @ X2759 ) ) )
      & ( ~ ( in @ ( X2757 @ ( esk80_3 @ X2755 @ X2756 @ X2757 ) ) @ X2756 )
        | ~ ( in @ X2759 @ X2755 )
        | ( ( ap @ X2755 @ X2756 @ ( lam @ X2755 @ X2756 @ X2757 ) @ X2759 )
          = ( X2757 @ X2759 ) ) )
      & ( ~ ( func @ X2760 @ X2761 @ X2762 )
        | ( ( lam @ X2760 @ X2761 @ ( ap @ X2760 @ X2761 @ X2762 ) )
          = X2762 ) )
      & ( ( in @ ( esk81_3 @ X2763 @ X2764 @ X2765 ) @ X2763 )
        | ( ( lam @ X2763 @ X2764 @ X2765 )
          = ( lam @ X2763 @ X2764 @ X2765 ) ) )
      & ( ~ ( in @ ( X2765 @ ( esk81_3 @ X2763 @ X2764 @ X2765 ) ) @ X2764 )
        | ( ( lam @ X2763 @ X2764 @ X2765 )
          = ( lam @ X2763 @ X2764 @ X2765 ) ) )
      & ( ( in @ ( esk82_3 @ X2767 @ X2768 @ X2769 ) @ X2767 )
        | ~ ( in @ X2771 @ X2767 )
        | ( ( ap @ X2767 @ X2768 @ ( lam @ X2767 @ X2768 @ X2769 ) @ X2771 )
          = ( X2769 @ X2771 ) ) )
      & ( ~ ( in @ ( X2769 @ ( esk82_3 @ X2767 @ X2768 @ X2769 ) ) @ X2768 )
        | ~ ( in @ X2771 @ X2767 )
        | ( ( ap @ X2767 @ X2768 @ ( lam @ X2767 @ X2768 @ X2769 ) @ X2771 )
          = ( X2769 @ X2771 ) ) )
      & ( ~ ( in @ X2774 @ ( funcSet @ X2772 @ X2773 ) )
        | ( ( lam @ X2772 @ X2773 @ ( ap @ X2772 @ X2773 @ X2774 ) )
          = X2774 ) )
      & ( ~ ( in @ X2777 @ X2775 )
        | ~ ( in @ X2778 @ X2775 )
        | X2776
        | ( in @ X2778
          @ ( dsetconstr @ X2775
            @ ^ [Z0: $i] :
                ( ( X2776
                  & ( Z0 = X2777 ) )
                | ( ~ X2776
                  & ( Z0 = X2778 ) ) ) ) ) )
      & ( ~ ( in @ X2781 @ X2779 )
        | ~ ( in @ X2782 @ X2779 )
        | X2780
        | ( ( dsetconstr @ X2779
            @ ^ [Z0: $i] :
                ( ( X2780
                  & ( Z0 = X2781 ) )
                | ( ~ X2780
                  & ( Z0 = X2782 ) ) ) )
          = ( setadjoin @ X2782 @ emptyset ) ) )
      & ( ~ ( in @ X2785 @ X2783 )
        | ~ ( in @ X2786 @ X2783 )
        | ~ X2784
        | ( in @ X2785
          @ ( dsetconstr @ X2783
            @ ^ [Z0: $i] :
                ( ( X2784
                  & ( Z0 = X2785 ) )
                | ( ~ X2784
                  & ( Z0 = X2786 ) ) ) ) ) )
      & ( ~ ( in @ X2789 @ X2787 )
        | ~ ( in @ X2790 @ X2787 )
        | ~ X2788
        | ( ( dsetconstr @ X2787
            @ ^ [Z0: $i] :
                ( ( X2788
                  & ( Z0 = X2789 ) )
                | ( ~ X2788
                  & ( Z0 = X2790 ) ) ) )
          = ( setadjoin @ X2789 @ emptyset ) ) )
      & ( ~ ( in @ X2793 @ X2791 )
        | ~ ( in @ X2794 @ X2791 )
        | ( singleton
          @ ( dsetconstr @ X2791
            @ ^ [Z0: $i] :
                ( ( X2792
                  & ( Z0 = X2793 ) )
                | ( ~ X2792
                  & ( Z0 = X2794 ) ) ) ) ) )
      & ( ~ ( in @ X2797 @ X2795 )
        | ~ ( in @ X2798 @ X2795 )
        | ( in @ ( if @ X2795 @ X2796 @ X2797 @ X2798 ) @ X2795 ) )
      & ( ~ ( singleton @ X2799 )
        | ~ ( in @ X2800 @ X2799 )
        | ( ( setunion @ X2799 )
          = X2800 ) )
      & ( ~ ( in @ X2803 @ X2801 )
        | ~ ( in @ X2804 @ X2801 )
        | ~ X2802
        | ( ( if @ X2801 @ X2802 @ X2803 @ X2804 )
          = X2803 ) )
      & ( ~ ( in @ X2807 @ X2805 )
        | ~ ( in @ X2808 @ X2805 )
        | X2806
        | ( ( if @ X2805 @ X2806 @ X2807 @ X2808 )
          = X2808 ) )
      & ( ~ ( in @ X2811 @ X2809 )
        | ~ ( in @ X2812 @ X2809 )
        | ( in @ ( if @ X2809 @ X2810 @ X2811 @ X2812 ) @ ( setadjoin @ X2811 @ ( setadjoin @ X2812 @ emptyset ) ) ) )
      & ( ~ ( in @ X2814 @ ( powerset @ X2813 ) )
        | ~ ( in @ X2815 @ ( powerset @ X2813 ) )
        | ( in @ ( binintersect @ X2814 @ X2815 ) @ ( powerset @ X2813 ) ) )
      & ( ~ ( in @ X2817 @ ( powerset @ X2816 ) )
        | ~ ( in @ X2818 @ ( powerset @ X2816 ) )
        | ( in @ ( binunion @ X2817 @ X2818 ) @ ( powerset @ X2816 ) ) )
      & ( ~ ( in @ X2820 @ ( powerset @ X2819 ) )
        | ( in @ ( powerset @ X2820 ) @ ( powerset @ ( powerset @ X2819 ) ) ) )
      & ( ~ ( in @ X2822 @ ( powerset @ X2821 ) )
        | ~ ( in @ X2823 @ ( powerset @ X2821 ) )
        | ( in @ ( setminus @ X2822 @ X2823 ) @ ( powerset @ X2821 ) ) )
      & ( ~ ( in @ X2825 @ ( powerset @ X2824 ) )
        | ( in @ ( setminus @ X2824 @ X2825 ) @ ( powerset @ X2824 ) ) )
      & ( ( in @ ( esk84_3 @ X2826 @ X2827 @ X2828 ) @ X2826 )
        | ( X2827 = X2828 )
        | ( in @ ( esk83_3 @ X2826 @ X2827 @ X2828 ) @ X2826 )
        | ~ ( in @ X2828 @ ( powerset @ X2826 ) )
        | ~ ( in @ X2827 @ ( powerset @ X2826 ) ) )
      & ( ( in @ ( esk84_3 @ X2826 @ X2827 @ X2828 ) @ X2828 )
        | ( X2827 = X2828 )
        | ( in @ ( esk83_3 @ X2826 @ X2827 @ X2828 ) @ X2826 )
        | ~ ( in @ X2828 @ ( powerset @ X2826 ) )
        | ~ ( in @ X2827 @ ( powerset @ X2826 ) ) )
      & ( ~ ( in @ ( esk84_3 @ X2826 @ X2827 @ X2828 ) @ X2827 )
        | ( X2827 = X2828 )
        | ( in @ ( esk83_3 @ X2826 @ X2827 @ X2828 ) @ X2826 )
        | ~ ( in @ X2828 @ ( powerset @ X2826 ) )
        | ~ ( in @ X2827 @ ( powerset @ X2826 ) ) )
      & ( ( in @ ( esk84_3 @ X2826 @ X2827 @ X2828 ) @ X2826 )
        | ( X2827 = X2828 )
        | ( in @ ( esk83_3 @ X2826 @ X2827 @ X2828 ) @ X2827 )
        | ~ ( in @ X2828 @ ( powerset @ X2826 ) )
        | ~ ( in @ X2827 @ ( powerset @ X2826 ) ) )
      & ( ( in @ ( esk84_3 @ X2826 @ X2827 @ X2828 ) @ X2828 )
        | ( X2827 = X2828 )
        | ( in @ ( esk83_3 @ X2826 @ X2827 @ X2828 ) @ X2827 )
        | ~ ( in @ X2828 @ ( powerset @ X2826 ) )
        | ~ ( in @ X2827 @ ( powerset @ X2826 ) ) )
      & ( ~ ( in @ ( esk84_3 @ X2826 @ X2827 @ X2828 ) @ X2827 )
        | ( X2827 = X2828 )
        | ( in @ ( esk83_3 @ X2826 @ X2827 @ X2828 ) @ X2827 )
        | ~ ( in @ X2828 @ ( powerset @ X2826 ) )
        | ~ ( in @ X2827 @ ( powerset @ X2826 ) ) )
      & ( ( in @ ( esk84_3 @ X2826 @ X2827 @ X2828 ) @ X2826 )
        | ( X2827 = X2828 )
        | ~ ( in @ ( esk83_3 @ X2826 @ X2827 @ X2828 ) @ X2828 )
        | ~ ( in @ X2828 @ ( powerset @ X2826 ) )
        | ~ ( in @ X2827 @ ( powerset @ X2826 ) ) )
      & ( ( in @ ( esk84_3 @ X2826 @ X2827 @ X2828 ) @ X2828 )
        | ( X2827 = X2828 )
        | ~ ( in @ ( esk83_3 @ X2826 @ X2827 @ X2828 ) @ X2828 )
        | ~ ( in @ X2828 @ ( powerset @ X2826 ) )
        | ~ ( in @ X2827 @ ( powerset @ X2826 ) ) )
      & ( ~ ( in @ ( esk84_3 @ X2826 @ X2827 @ X2828 ) @ X2827 )
        | ( X2827 = X2828 )
        | ~ ( in @ ( esk83_3 @ X2826 @ X2827 @ X2828 ) @ X2828 )
        | ~ ( in @ X2828 @ ( powerset @ X2826 ) )
        | ~ ( in @ X2827 @ ( powerset @ X2826 ) ) )
      & ( ( in @ ( esk85_3 @ X2831 @ X2832 @ X2833 ) @ X2831 )
        | ( subset @ X2832 @ X2833 )
        | ~ ( in @ X2833 @ ( powerset @ X2831 ) )
        | ~ ( in @ X2832 @ ( powerset @ X2831 ) ) )
      & ( ( in @ ( esk85_3 @ X2831 @ X2832 @ X2833 ) @ X2832 )
        | ( subset @ X2832 @ X2833 )
        | ~ ( in @ X2833 @ ( powerset @ X2831 ) )
        | ~ ( in @ X2832 @ ( powerset @ X2831 ) ) )
      & ( ~ ( in @ ( esk85_3 @ X2831 @ X2832 @ X2833 ) @ X2833 )
        | ( subset @ X2832 @ X2833 )
        | ~ ( in @ X2833 @ ( powerset @ X2831 ) )
        | ~ ( in @ X2832 @ ( powerset @ X2831 ) ) )
      & ( ( in @ ( esk86_3 @ X2835 @ X2836 @ X2837 ) @ X2835 )
        | ( in @ X2836 @ ( powerset @ X2837 ) )
        | ~ ( in @ X2837 @ ( powerset @ X2835 ) )
        | ~ ( in @ X2836 @ ( powerset @ X2835 ) ) )
      & ( ( in @ ( esk86_3 @ X2835 @ X2836 @ X2837 ) @ X2836 )
        | ( in @ X2836 @ ( powerset @ X2837 ) )
        | ~ ( in @ X2837 @ ( powerset @ X2835 ) )
        | ~ ( in @ X2836 @ ( powerset @ X2835 ) ) )
      & ( ~ ( in @ ( esk86_3 @ X2835 @ X2836 @ X2837 ) @ X2837 )
        | ( in @ X2836 @ ( powerset @ X2837 ) )
        | ~ ( in @ X2837 @ ( powerset @ X2835 ) )
        | ~ ( in @ X2836 @ ( powerset @ X2835 ) ) )
      & ( ~ ( in @ X2840 @ ( powerset @ X2839 ) )
        | ~ ( in @ X2841 @ ( powerset @ X2839 ) )
        | ~ ( in @ X2842 @ X2839 )
        | ~ ( in @ X2840 @ ( powerset @ X2841 ) )
        | ~ ( in @ X2842 @ X2840 )
        | ( in @ X2842 @ X2841 ) )
      & ( ~ ( in @ X2844 @ ( powerset @ X2843 ) )
        | ~ ( in @ X2845 @ X2843 )
        | ~ ( in @ X2845 @ X2844 )
        | ~ ( in @ X2845 @ ( setminus @ X2843 @ X2844 ) ) )
      & ( ~ ( in @ X2847 @ ( powerset @ X2846 ) )
        | ~ ( in @ X2848 @ X2846 )
        | ( in @ X2848 @ ( setminus @ X2846 @ X2847 ) )
        | ( in @ X2848 @ X2847 ) )
      & ( ~ ( in @ X2850 @ ( powerset @ X2849 ) )
        | ~ ( in @ X2851 @ ( powerset @ X2849 ) )
        | ~ ( in @ X2852 @ X2849 )
        | ( in @ X2852 @ X2850 )
        | ~ ( in @ X2852 @ ( binintersect @ X2850 @ X2851 ) ) )
      & ( ~ ( in @ X2854 @ ( powerset @ X2853 ) )
        | ~ ( in @ X2855 @ ( powerset @ X2853 ) )
        | ~ ( in @ X2856 @ X2853 )
        | ( in @ X2856 @ X2855 )
        | ~ ( in @ X2856 @ ( binintersect @ X2854 @ X2855 ) ) )
      & ( ~ ( in @ X2858 @ ( powerset @ X2857 ) )
        | ~ ( in @ X2859 @ ( powerset @ X2857 ) )
        | ~ ( in @ X2860 @ X2857 )
        | ~ ( subset @ X2858 @ ( setminus @ X2857 @ X2859 ) )
        | ~ ( in @ X2860 @ X2859 )
        | ~ ( in @ X2860 @ X2858 ) )
      & ( ~ ( in @ X2862 @ ( powerset @ X2861 ) )
        | ~ ( in @ X2863 @ ( powerset @ X2861 ) )
        | ~ ( in @ X2864 @ X2861 )
        | ~ ( subset @ X2862 @ X2863 )
        | ( in @ X2864 @ X2863 )
        | ~ ( in @ X2864 @ X2862 ) )
      & ( ~ ( in @ X2866 @ ( powerset @ X2865 ) )
        | ~ ( in @ X2867 @ ( powerset @ X2865 ) )
        | ~ ( subset @ X2866 @ X2867 )
        | ( subset @ ( setminus @ X2865 @ X2867 ) @ ( setminus @ X2865 @ X2866 ) ) )
      & ( ~ ( in @ X2869 @ ( powerset @ X2868 ) )
        | ~ ( in @ X2870 @ ( powerset @ X2868 ) )
        | ~ ( subset @ ( setminus @ X2868 @ X2870 ) @ ( setminus @ X2868 @ X2869 ) )
        | ( subset @ X2869 @ X2870 ) )
      & ( ~ ( in @ X2872 @ ( powerset @ X2871 ) )
        | ~ ( in @ X2873 @ X2871 )
        | ~ ( in @ X2873 @ X2872 )
        | ( in @ X2873 @ ( setminus @ X2871 @ ( setminus @ X2871 @ X2872 ) ) ) )
      & ( ~ ( in @ X2875 @ ( powerset @ X2874 ) )
        | ~ ( in @ X2876 @ X2874 )
        | ~ ( in @ X2876 @ ( setminus @ X2874 @ ( setminus @ X2874 @ X2875 ) ) )
        | ( in @ X2876 @ X2875 ) )
      & ( ~ ( in @ X2878 @ ( powerset @ X2877 ) )
        | ( subset @ X2878 @ ( setminus @ X2877 @ ( setminus @ X2877 @ X2878 ) ) ) )
      & ( ~ ( in @ X2880 @ ( powerset @ X2879 ) )
        | ( subset @ ( setminus @ X2879 @ ( setminus @ X2879 @ X2880 ) ) @ X2880 ) )
      & ( ~ ( in @ X2882 @ ( powerset @ X2881 ) )
        | ( X2882
          = ( setminus @ X2881 @ ( setminus @ X2881 @ X2882 ) ) ) )
      & ( ~ ( in @ X2884 @ ( powerset @ X2883 ) )
        | ~ ( in @ X2885 @ ( powerset @ X2883 ) )
        | ~ ( in @ X2886 @ X2883 )
        | ~ ( in @ X2886 @ ( setminus @ X2883 @ X2884 ) )
        | ~ ( in @ X2886 @ ( binintersect @ X2884 @ X2885 ) ) )
      & ( ~ ( in @ X2888 @ ( powerset @ X2887 ) )
        | ~ ( in @ X2889 @ ( powerset @ X2887 ) )
        | ~ ( in @ X2890 @ X2887 )
        | ~ ( in @ X2890 @ ( setminus @ X2887 @ X2888 ) )
        | ( in @ X2890 @ ( setminus @ X2887 @ ( binintersect @ X2888 @ X2889 ) ) ) )
      & ( ~ ( in @ X2892 @ ( powerset @ X2891 ) )
        | ~ ( in @ X2893 @ ( powerset @ X2891 ) )
        | ( subset @ ( setminus @ X2891 @ X2892 ) @ ( setminus @ X2891 @ ( binintersect @ X2892 @ X2893 ) ) ) )
      & ( ~ ( in @ X2895 @ ( powerset @ X2894 ) )
        | ~ ( in @ X2896 @ ( powerset @ X2894 ) )
        | ( in @ ( setminus @ X2894 @ X2895 ) @ ( powerset @ ( setminus @ X2894 @ ( binintersect @ X2895 @ X2896 ) ) ) ) )
      & ( ~ ( in @ X2898 @ ( powerset @ X2897 ) )
        | ~ ( in @ X2899 @ ( powerset @ X2897 ) )
        | ~ ( subset @ X2898 @ ( setminus @ X2897 @ X2899 ) )
        | ~ ( in @ X2900 @ X2897 )
        | ~ ( in @ X2900 @ X2899 )
        | ( in @ X2900 @ ( setminus @ X2897 @ X2898 ) ) )
      & ( ~ ( in @ X2902 @ ( powerset @ X2901 ) )
        | ~ ( in @ X2903 @ ( powerset @ X2901 ) )
        | ~ ( subset @ X2902 @ ( setminus @ X2901 @ X2903 ) )
        | ( subset @ X2903 @ ( setminus @ X2901 @ X2902 ) ) )
      & ( ~ ( in @ X2905 @ ( powerset @ X2904 ) )
        | ~ ( in @ X2906 @ ( powerset @ X2904 ) )
        | ~ ( in @ X2907 @ X2904 )
        | ( in @ X2907 @ ( binunion @ X2905 @ X2906 ) )
        | ~ ( in @ X2907 @ X2905 ) )
      & ( ~ ( in @ X2909 @ ( powerset @ X2908 ) )
        | ~ ( in @ X2910 @ ( powerset @ X2908 ) )
        | ~ ( in @ X2911 @ X2908 )
        | ( in @ X2911 @ ( binunion @ X2909 @ X2910 ) )
        | ~ ( in @ X2911 @ X2910 ) )
      & ( ~ ( in @ X2913 @ ( powerset @ X2912 ) )
        | ~ ( in @ X2914 @ ( powerset @ X2912 ) )
        | ~ ( in @ X2915 @ ( powerset @ X2912 ) )
        | ~ ( in @ X2916 @ X2912 )
        | ~ ( in @ X2916 @ ( binintersect @ X2913 @ X2914 ) )
        | ( in @ X2916 @ ( binunion @ X2913 @ X2915 ) ) )
      & ( ~ ( in @ X2918 @ ( powerset @ X2917 ) )
        | ~ ( in @ X2919 @ ( powerset @ X2917 ) )
        | ~ ( in @ X2920 @ ( powerset @ X2917 ) )
        | ~ ( in @ X2921 @ X2917 )
        | ~ ( in @ X2921 @ ( binintersect @ X2918 @ X2919 ) )
        | ( in @ X2921 @ ( binunion @ X2919 @ X2920 ) ) )
      & ( ~ ( in @ X2923 @ ( powerset @ X2922 ) )
        | ~ ( in @ X2924 @ ( powerset @ X2922 ) )
        | ~ ( in @ X2925 @ ( powerset @ X2922 ) )
        | ~ ( in @ X2926 @ X2922 )
        | ~ ( in @ X2926 @ ( binintersect @ X2923 @ X2924 ) )
        | ( in @ X2926 @ ( binintersect @ ( binunion @ X2923 @ X2925 ) @ ( binunion @ X2924 @ X2925 ) ) ) )
      & ( ~ ( in @ X2928 @ ( powerset @ X2927 ) )
        | ~ ( in @ X2929 @ ( powerset @ X2927 ) )
        | ~ ( in @ X2930 @ ( powerset @ X2927 ) )
        | ( in @ ( binintersect @ X2928 @ X2929 ) @ ( powerset @ ( binintersect @ ( binunion @ X2928 @ X2930 ) @ ( binunion @ X2929 @ X2930 ) ) ) ) )
      & ( ~ ( in @ X2932 @ ( powerset @ X2931 ) )
        | ~ ( in @ X2933 @ ( powerset @ X2931 ) )
        | ~ ( in @ X2934 @ X2931 )
        | ~ ( in @ X2934 @ ( setminus @ X2931 @ ( binunion @ X2932 @ X2933 ) ) )
        | ~ ( in @ X2934 @ X2932 ) )
      & ( ~ ( in @ X2936 @ ( powerset @ X2935 ) )
        | ~ ( in @ X2937 @ ( powerset @ X2935 ) )
        | ~ ( in @ X2938 @ X2935 )
        | ~ ( in @ X2938 @ ( setminus @ X2935 @ ( binunion @ X2936 @ X2937 ) ) )
        | ( in @ X2938 @ ( setminus @ X2935 @ X2936 ) ) )
      & ( ( in @ X2943 @ X2941 )
        | X2942
        | ( in @ X2943 @ X2940 )
        | ~ ( in @ X2943 @ ( binunion @ X2940 @ X2941 ) )
        | ~ ( in @ X2943 @ X2939 )
        | ~ ( in @ X2941 @ ( powerset @ X2939 ) )
        | ~ ( in @ X2940 @ ( powerset @ X2939 ) ) )
      & ( ~ X2942
        | X2942
        | ( in @ X2943 @ X2940 )
        | ~ ( in @ X2943 @ ( binunion @ X2940 @ X2941 ) )
        | ~ ( in @ X2943 @ X2939 )
        | ~ ( in @ X2941 @ ( powerset @ X2939 ) )
        | ~ ( in @ X2940 @ ( powerset @ X2939 ) ) )
      & ( ( in @ X2943 @ X2941 )
        | X2942
        | ~ X2942
        | ~ ( in @ X2943 @ ( binunion @ X2940 @ X2941 ) )
        | ~ ( in @ X2943 @ X2939 )
        | ~ ( in @ X2941 @ ( powerset @ X2939 ) )
        | ~ ( in @ X2940 @ ( powerset @ X2939 ) ) )
      & ( ~ X2942
        | X2942
        | ~ X2942
        | ~ ( in @ X2943 @ ( binunion @ X2940 @ X2941 ) )
        | ~ ( in @ X2943 @ X2939 )
        | ~ ( in @ X2941 @ ( powerset @ X2939 ) )
        | ~ ( in @ X2940 @ ( powerset @ X2939 ) ) )
      & ( ~ ( in @ X2945 @ ( powerset @ X2944 ) )
        | ~ ( in @ X2946 @ ( powerset @ X2944 ) )
        | ~ ( in @ X2947 @ X2944 )
        | ( in @ X2947 @ X2945 )
        | ( in @ X2947 @ X2946 )
        | ~ ( in @ X2947 @ ( binunion @ X2945 @ X2946 ) ) )
      & ( ~ ( in @ X2949 @ ( powerset @ X2948 ) )
        | ~ ( in @ X2950 @ ( powerset @ X2948 ) )
        | ~ ( in @ X2951 @ X2948 )
        | ~ ( in @ X2951 @ ( setminus @ X2948 @ ( binunion @ X2949 @ X2950 ) ) )
        | ( in @ X2951 @ ( setminus @ X2948 @ X2949 ) ) )
      & ( ~ ( in @ X2953 @ ( powerset @ X2952 ) )
        | ~ ( in @ X2954 @ ( powerset @ X2952 ) )
        | ( in @ ( setminus @ X2952 @ ( binunion @ X2953 @ X2954 ) ) @ ( powerset @ ( setminus @ X2952 @ X2953 ) ) ) )
      & ( ~ ( in @ X2956 @ ( powerset @ X2955 ) )
        | ~ ( in @ X2957 @ ( powerset @ X2955 ) )
        | ~ ( in @ X2958 @ X2955 )
        | ~ ( in @ X2958 @ ( setminus @ X2955 @ ( binunion @ X2956 @ X2957 ) ) )
        | ( in @ X2958 @ ( setminus @ X2955 @ X2957 ) ) )
      & ( ~ ( in @ X2960 @ ( powerset @ X2959 ) )
        | ~ ( in @ X2961 @ ( powerset @ X2959 ) )
        | ~ ( in @ X2962 @ X2959 )
        | ~ ( in @ X2962 @ ( setminus @ X2959 @ ( binintersect @ X2960 @ X2961 ) ) )
        | ( in @ X2962 @ ( binunion @ ( setminus @ X2959 @ X2960 ) @ ( setminus @ X2959 @ X2961 ) ) ) )
      & ( ~ ( in @ X2964 @ ( powerset @ X2963 ) )
        | ~ ( in @ X2965 @ ( powerset @ X2963 ) )
        | ~ ( in @ X2966 @ X2963 )
        | ~ ( in @ X2966 @ ( binunion @ ( setminus @ X2963 @ X2964 ) @ ( setminus @ X2963 @ X2965 ) ) )
        | ( in @ X2966 @ ( setminus @ X2963 @ ( binintersect @ X2964 @ X2965 ) ) ) )
      & ( ~ ( in @ X2968 @ ( powerset @ X2967 ) )
        | ~ ( in @ X2969 @ ( powerset @ X2967 ) )
        | ( ( setminus @ X2967 @ ( binintersect @ X2968 @ X2969 ) )
          = ( binunion @ ( setminus @ X2967 @ X2968 ) @ ( setminus @ X2967 @ X2969 ) ) ) )
      & ( ~ ( in @ X2971 @ ( powerset @ X2970 ) )
        | ~ ( in @ X2972 @ ( powerset @ X2970 ) )
        | ~ ( in @ X2973 @ X2970 )
        | ~ ( in @ X2973 @ ( setminus @ X2970 @ ( binunion @ X2971 @ X2972 ) ) )
        | ( in @ X2973 @ ( binintersect @ ( setminus @ X2970 @ X2971 ) @ ( setminus @ X2970 @ X2972 ) ) ) )
      & ( ~ ( in @ X2975 @ ( powerset @ X2974 ) )
        | ~ ( in @ X2976 @ ( powerset @ X2974 ) )
        | ~ ( in @ X2977 @ X2974 )
        | ~ ( in @ X2977 @ ( setminus @ X2974 @ X2975 ) )
        | ~ ( in @ X2977 @ ( setminus @ X2974 @ X2976 ) )
        | ( in @ X2977 @ ( setminus @ X2974 @ ( binunion @ X2975 @ X2976 ) ) ) )
      & ( ~ ( in @ X2979 @ ( powerset @ X2978 ) )
        | ~ ( in @ X2980 @ ( powerset @ X2978 ) )
        | ~ ( in @ X2981 @ X2978 )
        | ~ ( in @ X2981 @ ( binintersect @ ( setminus @ X2978 @ X2979 ) @ ( setminus @ X2978 @ X2980 ) ) )
        | ( in @ X2981 @ ( setminus @ X2978 @ ( binunion @ X2979 @ X2980 ) ) ) )
      & ( ~ ( in @ X2983 @ ( powerset @ X2982 ) )
        | ~ ( in @ X2984 @ ( powerset @ X2982 ) )
        | ( ( setminus @ X2982 @ ( binunion @ X2983 @ X2984 ) )
          = ( binintersect @ ( setminus @ X2982 @ X2983 ) @ ( setminus @ X2982 @ X2984 ) ) ) )
      & ( ~ ( in @ X2986 @ ( powerset @ X2985 ) )
        | ~ ( in @ X2987 @ ( powerset @ X2985 ) )
        | ~ ( in @ X2988 @ ( binintersect @ X2986 @ X2987 ) )
        | ( in @ X2988 @ X2985 ) )
      & ( ~ ( in @ X2990 @ ( powerset @ X2989 ) )
        | ~ ( in @ X2991 @ ( powerset @ X2989 ) )
        | ~ ( in @ X2992 @ ( powerset @ X2989 ) )
        | ~ ( subset @ X2990 @ X2992 )
        | ( subset @ ( binintersect @ X2990 @ X2991 ) @ X2992 ) )
      & ( ~ ( in @ X2994 @ ( powerset @ X2993 ) )
        | ~ ( in @ X2995 @ ( powerset @ X2993 ) )
        | ~ ( in @ X2996 @ ( powerset @ X2993 ) )
        | ~ ( subset @ X2995 @ X2996 )
        | ( subset @ ( binintersect @ X2994 @ X2995 ) @ X2996 ) )
      & ( ~ ( in @ X2998 @ ( powerset @ X2997 ) )
        | ~ ( in @ X2999 @ ( powerset @ X2997 ) )
        | ~ ( in @ X3000 @ ( powerset @ X2997 ) )
        | ~ ( subset @ X2998 @ X2999 )
        | ~ ( subset @ X2998 @ X3000 )
        | ( subset @ X2998 @ ( binintersect @ X2999 @ X3000 ) ) )
      & ( ~ ( in @ X3002 @ ( powerset @ X3001 ) )
        | ~ ( in @ X3003 @ ( powerset @ X3001 ) )
        | ~ ( in @ X3004 @ ( powerset @ X3001 ) )
        | ~ ( in @ X3005 @ ( powerset @ X3001 ) )
        | ~ ( subset @ X3002 @ X3004 )
        | ~ ( subset @ X3003 @ X3005 )
        | ( subset @ ( binintersect @ X3002 @ X3003 ) @ ( binintersect @ X3004 @ X3005 ) ) )
      & ( ~ ( in @ X3007 @ ( powerset @ X3006 ) )
        | ~ ( in @ X3008 @ ( powerset @ X3006 ) )
        | ( in @ ( setminus @ X3006 @ X3007 ) @ ( powerset @ ( setminus @ X3006 @ ( binintersect @ X3007 @ X3008 ) ) ) ) )
      & ( ~ ( in @ X3010 @ ( powerset @ X3009 ) )
        | ~ ( in @ X3011 @ ( powerset @ X3009 ) )
        | ~ ( in @ X3012 @ ( powerset @ X3009 ) )
        | ~ ( in @ X3013 @ ( powerset @ X3009 ) )
        | ( ( setminus @ X3009 @ ( binintersect @ ( binunion @ X3010 @ X3011 ) @ ( binunion @ X3012 @ X3013 ) ) )
          = ( binunion @ ( binintersect @ ( setminus @ X3009 @ X3010 ) @ ( setminus @ X3009 @ X3011 ) ) @ ( binintersect @ ( setminus @ X3009 @ X3012 ) @ ( setminus @ X3009 @ X3013 ) ) ) ) )
      & ( ~ ( in @ X3015 @ ( powerset @ X3014 ) )
        | ~ ( in @ X3016 @ ( powerset @ X3014 ) )
        | ~ ( in @ X3017 @ ( powerset @ X3014 ) )
        | ( in @ ( binintersect @ X3015 @ X3016 ) @ ( powerset @ ( binintersect @ ( binunion @ X3015 @ X3017 ) @ ( binunion @ X3016 @ X3017 ) ) ) ) )
      & ( ~ ( in @ X3019 @ ( powerset @ X3018 ) )
        | ~ ( in @ X3020 @ ( powerset @ X3018 ) )
        | ~ ( subset @ X3019 @ ( setminus @ X3018 @ X3020 ) )
        | ( subset @ X3020 @ ( setminus @ X3018 @ X3019 ) ) )
      & ( ~ ( in @ X3022 @ ( powerset @ X3021 ) )
        | ~ ( in @ X3023 @ ( powerset @ X3021 ) )
        | ( in @ ( setminus @ X3021 @ ( binunion @ X3022 @ X3023 ) ) @ ( powerset @ ( setminus @ X3021 @ X3022 ) ) ) )
      & ( ( in @ ( esk87_3 @ X3024 @ X3025 @ X3026 ) @ X3024 )
        | ~ ( in @ X3029 @ X3025 )
        | ( X3026 @ X3029 )
        | ~ ( breln1 @ X3024 @ X3025 ) )
      & ( ( in @ ( esk88_3 @ X3024 @ X3025 @ X3026 ) @ X3024 )
        | ~ ( in @ X3029 @ X3025 )
        | ( X3026 @ X3029 )
        | ~ ( breln1 @ X3024 @ X3025 ) )
      & ( ( in @ ( kpair @ ( esk87_3 @ X3024 @ X3025 @ X3026 ) @ ( esk88_3 @ X3024 @ X3025 @ X3026 ) ) @ X3025 )
        | ~ ( in @ X3029 @ X3025 )
        | ( X3026 @ X3029 )
        | ~ ( breln1 @ X3024 @ X3025 ) )
      & ( ~ ( X3026 @ ( kpair @ ( esk87_3 @ X3024 @ X3025 @ X3026 ) @ ( esk88_3 @ X3024 @ X3025 @ X3026 ) ) )
        | ~ ( in @ X3029 @ X3025 )
        | ( X3026 @ X3029 )
        | ~ ( breln1 @ X3024 @ X3025 ) )
      & ( ~ ( in @ X3031 @ ( breln1Set @ X3030 ) )
        | ( breln1 @ X3030 @ X3031 ) )
      & choice2fnsingleton
      & ( breln1 @ X3032 @ ( dpsetconstr @ X3032 @ X3032 @ X3033 ) )
      & ( ( in @ ( esk89_3 @ X3034 @ X3035 @ X3036 ) @ X3034 )
        | ~ ( in @ X3039 @ X3035 )
        | ( X3036 @ X3039 )
        | ~ ( breln1 @ X3034 @ X3035 ) )
      & ( ( in @ ( esk90_3 @ X3034 @ X3035 @ X3036 ) @ X3034 )
        | ~ ( in @ X3039 @ X3035 )
        | ( X3036 @ X3039 )
        | ~ ( breln1 @ X3034 @ X3035 ) )
      & ( ( in @ ( kpair @ ( esk89_3 @ X3034 @ X3035 @ X3036 ) @ ( esk90_3 @ X3034 @ X3035 @ X3036 ) ) @ X3035 )
        | ~ ( in @ X3039 @ X3035 )
        | ( X3036 @ X3039 )
        | ~ ( breln1 @ X3034 @ X3035 ) )
      & ( ~ ( X3036 @ ( kpair @ ( esk89_3 @ X3034 @ X3035 @ X3036 ) @ ( esk90_3 @ X3034 @ X3035 @ X3036 ) ) )
        | ~ ( in @ X3039 @ X3035 )
        | ( X3036 @ X3039 )
        | ~ ( breln1 @ X3034 @ X3035 ) )
      & ( ( in @ ( esk91_3 @ X3040 @ X3041 @ X3042 ) @ X3040 )
        | ( subset @ X3041 @ X3042 )
        | ~ ( breln1 @ X3040 @ X3042 )
        | ~ ( breln1 @ X3040 @ X3041 ) )
      & ( ( in @ ( esk92_3 @ X3040 @ X3041 @ X3042 ) @ X3040 )
        | ( subset @ X3041 @ X3042 )
        | ~ ( breln1 @ X3040 @ X3042 )
        | ~ ( breln1 @ X3040 @ X3041 ) )
      & ( ( in @ ( kpair @ ( esk91_3 @ X3040 @ X3041 @ X3042 ) @ ( esk92_3 @ X3040 @ X3041 @ X3042 ) ) @ X3041 )
        | ( subset @ X3041 @ X3042 )
        | ~ ( breln1 @ X3040 @ X3042 )
        | ~ ( breln1 @ X3040 @ X3041 ) )
      & ( ~ ( in @ ( kpair @ ( esk91_3 @ X3040 @ X3041 @ X3042 ) @ ( esk92_3 @ X3040 @ X3041 @ X3042 ) ) @ X3042 )
        | ( subset @ X3041 @ X3042 )
        | ~ ( breln1 @ X3040 @ X3042 )
        | ~ ( breln1 @ X3040 @ X3041 ) )
      & ( ( in @ ( esk95_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
        | ( X3046 = X3047 )
        | ( in @ ( esk93_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
        | ~ ( breln1 @ X3045 @ X3047 )
        | ~ ( breln1 @ X3045 @ X3046 ) )
      & ( ( in @ ( esk96_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
        | ( X3046 = X3047 )
        | ( in @ ( esk93_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
        | ~ ( breln1 @ X3045 @ X3047 )
        | ~ ( breln1 @ X3045 @ X3046 ) )
      & ( ( in @ ( kpair @ ( esk95_3 @ X3045 @ X3046 @ X3047 ) @ ( esk96_3 @ X3045 @ X3046 @ X3047 ) ) @ X3047 )
        | ( X3046 = X3047 )
        | ( in @ ( esk93_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
        | ~ ( breln1 @ X3045 @ X3047 )
        | ~ ( breln1 @ X3045 @ X3046 ) )
      & ( ~ ( in @ ( kpair @ ( esk95_3 @ X3045 @ X3046 @ X3047 ) @ ( esk96_3 @ X3045 @ X3046 @ X3047 ) ) @ X3046 )
        | ( X3046 = X3047 )
        | ( in @ ( esk93_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
        | ~ ( breln1 @ X3045 @ X3047 )
        | ~ ( breln1 @ X3045 @ X3046 ) )
      & ( ( in @ ( esk95_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
        | ( X3046 = X3047 )
        | ( in @ ( esk94_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
        | ~ ( breln1 @ X3045 @ X3047 )
        | ~ ( breln1 @ X3045 @ X3046 ) )
      & ( ( in @ ( esk96_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
        | ( X3046 = X3047 )
        | ( in @ ( esk94_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
        | ~ ( breln1 @ X3045 @ X3047 )
        | ~ ( breln1 @ X3045 @ X3046 ) )
      & ( ( in @ ( kpair @ ( esk95_3 @ X3045 @ X3046 @ X3047 ) @ ( esk96_3 @ X3045 @ X3046 @ X3047 ) ) @ X3047 )
        | ( X3046 = X3047 )
        | ( in @ ( esk94_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
        | ~ ( breln1 @ X3045 @ X3047 )
        | ~ ( breln1 @ X3045 @ X3046 ) )
      & ( ~ ( in @ ( kpair @ ( esk95_3 @ X3045 @ X3046 @ X3047 ) @ ( esk96_3 @ X3045 @ X3046 @ X3047 ) ) @ X3046 )
        | ( X3046 = X3047 )
        | ( in @ ( esk94_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
        | ~ ( breln1 @ X3045 @ X3047 )
        | ~ ( breln1 @ X3045 @ X3046 ) )
      & ( ( in @ ( esk95_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
        | ( X3046 = X3047 )
        | ( in @ ( kpair @ ( esk93_3 @ X3045 @ X3046 @ X3047 ) @ ( esk94_3 @ X3045 @ X3046 @ X3047 ) ) @ X3046 )
        | ~ ( breln1 @ X3045 @ X3047 )
        | ~ ( breln1 @ X3045 @ X3046 ) )
      & ( ( in @ ( esk96_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
        | ( X3046 = X3047 )
        | ( in @ ( kpair @ ( esk93_3 @ X3045 @ X3046 @ X3047 ) @ ( esk94_3 @ X3045 @ X3046 @ X3047 ) ) @ X3046 )
        | ~ ( breln1 @ X3045 @ X3047 )
        | ~ ( breln1 @ X3045 @ X3046 ) )
      & ( ( in @ ( kpair @ ( esk95_3 @ X3045 @ X3046 @ X3047 ) @ ( esk96_3 @ X3045 @ X3046 @ X3047 ) ) @ X3047 )
        | ( X3046 = X3047 )
        | ( in @ ( kpair @ ( esk93_3 @ X3045 @ X3046 @ X3047 ) @ ( esk94_3 @ X3045 @ X3046 @ X3047 ) ) @ X3046 )
        | ~ ( breln1 @ X3045 @ X3047 )
        | ~ ( breln1 @ X3045 @ X3046 ) )
      & ( ~ ( in @ ( kpair @ ( esk95_3 @ X3045 @ X3046 @ X3047 ) @ ( esk96_3 @ X3045 @ X3046 @ X3047 ) ) @ X3046 )
        | ( X3046 = X3047 )
        | ( in @ ( kpair @ ( esk93_3 @ X3045 @ X3046 @ X3047 ) @ ( esk94_3 @ X3045 @ X3046 @ X3047 ) ) @ X3046 )
        | ~ ( breln1 @ X3045 @ X3047 )
        | ~ ( breln1 @ X3045 @ X3046 ) )
      & ( ( in @ ( esk95_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
        | ( X3046 = X3047 )
        | ~ ( in @ ( kpair @ ( esk93_3 @ X3045 @ X3046 @ X3047 ) @ ( esk94_3 @ X3045 @ X3046 @ X3047 ) ) @ X3047 )
        | ~ ( breln1 @ X3045 @ X3047 )
        | ~ ( breln1 @ X3045 @ X3046 ) )
      & ( ( in @ ( esk96_3 @ X3045 @ X3046 @ X3047 ) @ X3045 )
        | ( X3046 = X3047 )
        | ~ ( in @ ( kpair @ ( esk93_3 @ X3045 @ X3046 @ X3047 ) @ ( esk94_3 @ X3045 @ X3046 @ X3047 ) ) @ X3047 )
        | ~ ( breln1 @ X3045 @ X3047 )
        | ~ ( breln1 @ X3045 @ X3046 ) )
      & ( ( in @ ( kpair @ ( esk95_3 @ X3045 @ X3046 @ X3047 ) @ ( esk96_3 @ X3045 @ X3046 @ X3047 ) ) @ X3047 )
        | ( X3046 = X3047 )
        | ~ ( in @ ( kpair @ ( esk93_3 @ X3045 @ X3046 @ X3047 ) @ ( esk94_3 @ X3045 @ X3046 @ X3047 ) ) @ X3047 )
        | ~ ( breln1 @ X3045 @ X3047 )
        | ~ ( breln1 @ X3045 @ X3046 ) )
      & ( ~ ( in @ ( kpair @ ( esk95_3 @ X3045 @ X3046 @ X3047 ) @ ( esk96_3 @ X3045 @ X3046 @ X3047 ) ) @ X3046 )
        | ( X3046 = X3047 )
        | ~ ( in @ ( kpair @ ( esk93_3 @ X3045 @ X3046 @ X3047 ) @ ( esk94_3 @ X3045 @ X3046 @ X3047 ) ) @ X3047 )
        | ~ ( breln1 @ X3045 @ X3047 )
        | ~ ( breln1 @ X3045 @ X3046 ) )
      & ( ~ ( breln1 @ X3052 @ X3053 )
        | ( breln1 @ X3052 @ ( breln1invset @ X3052 @ X3053 ) ) )
      & ( ~ ( breln1 @ X3054 @ X3055 )
        | ~ ( in @ X3056 @ X3054 )
        | ~ ( in @ X3057 @ X3054 )
        | ~ ( in @ ( kpair @ X3056 @ X3057 ) @ X3055 )
        | ( in @ ( kpair @ X3057 @ X3056 ) @ ( breln1invset @ X3054 @ X3055 ) ) )
      & ( ~ ( breln1 @ X3058 @ X3059 )
        | ~ ( in @ X3060 @ X3058 )
        | ~ ( in @ X3061 @ X3058 )
        | ~ ( in @ ( kpair @ X3061 @ X3060 ) @ ( breln1invset @ X3058 @ X3059 ) )
        | ( in @ ( kpair @ X3060 @ X3061 ) @ X3059 ) )
      & ( ~ ( breln1 @ X3062 @ X3063 )
        | ~ ( breln1 @ X3062 @ X3064 )
        | ( breln1 @ X3062 @ ( breln1compset @ X3062 @ X3063 @ X3064 ) ) )
      & ( ~ ( breln1 @ X3065 @ X3066 )
        | ~ ( breln1 @ X3065 @ X3067 )
        | ~ ( in @ X3068 @ X3065 )
        | ~ ( in @ X3069 @ X3065 )
        | ~ ( in @ X3070 @ X3065 )
        | ~ ( in @ ( kpair @ X3068 @ X3070 ) @ X3066 )
        | ~ ( in @ ( kpair @ X3070 @ X3069 ) @ X3067 )
        | ( in @ ( kpair @ X3068 @ X3069 ) @ ( breln1compset @ X3065 @ X3066 @ X3067 ) ) )
      & ( ( in @ ( esk97_5 @ X3071 @ X3072 @ X3073 @ X3074 @ X3075 ) @ X3071 )
        | ~ ( in @ ( kpair @ X3074 @ X3075 ) @ ( breln1compset @ X3071 @ X3072 @ X3073 ) )
        | ~ ( in @ X3075 @ X3071 )
        | ~ ( in @ X3074 @ X3071 )
        | ~ ( breln1 @ X3071 @ X3073 )
        | ~ ( breln1 @ X3071 @ X3072 ) )
      & ( ( in @ ( kpair @ X3074 @ ( esk97_5 @ X3071 @ X3072 @ X3073 @ X3074 @ X3075 ) ) @ X3072 )
        | ~ ( in @ ( kpair @ X3074 @ X3075 ) @ ( breln1compset @ X3071 @ X3072 @ X3073 ) )
        | ~ ( in @ X3075 @ X3071 )
        | ~ ( in @ X3074 @ X3071 )
        | ~ ( breln1 @ X3071 @ X3073 )
        | ~ ( breln1 @ X3071 @ X3072 ) )
      & ( ( in @ ( kpair @ ( esk97_5 @ X3071 @ X3072 @ X3073 @ X3074 @ X3075 ) @ X3075 ) @ X3073 )
        | ~ ( in @ ( kpair @ X3074 @ X3075 ) @ ( breln1compset @ X3071 @ X3072 @ X3073 ) )
        | ~ ( in @ X3075 @ X3071 )
        | ~ ( in @ X3074 @ X3071 )
        | ~ ( breln1 @ X3071 @ X3073 )
        | ~ ( breln1 @ X3071 @ X3072 ) )
      & ( ( in @ ( esk98_6 @ X3077 @ X3078 @ X3079 @ X3080 @ X3081 @ X3082 ) @ X3077 )
        | X3082
        | ~ ( in @ ( kpair @ X3080 @ X3081 ) @ ( breln1compset @ X3077 @ X3078 @ X3079 ) )
        | ~ ( in @ X3081 @ X3077 )
        | ~ ( in @ X3080 @ X3077 )
        | ~ ( breln1 @ X3077 @ X3079 )
        | ~ ( breln1 @ X3077 @ X3078 ) )
      & ( ( in @ ( kpair @ X3080 @ ( esk98_6 @ X3077 @ X3078 @ X3079 @ X3080 @ X3081 @ X3082 ) ) @ X3078 )
        | X3082
        | ~ ( in @ ( kpair @ X3080 @ X3081 ) @ ( breln1compset @ X3077 @ X3078 @ X3079 ) )
        | ~ ( in @ X3081 @ X3077 )
        | ~ ( in @ X3080 @ X3077 )
        | ~ ( breln1 @ X3077 @ X3079 )
        | ~ ( breln1 @ X3077 @ X3078 ) )
      & ( ( in @ ( kpair @ ( esk98_6 @ X3077 @ X3078 @ X3079 @ X3080 @ X3081 @ X3082 ) @ X3081 ) @ X3079 )
        | X3082
        | ~ ( in @ ( kpair @ X3080 @ X3081 ) @ ( breln1compset @ X3077 @ X3078 @ X3079 ) )
        | ~ ( in @ X3081 @ X3077 )
        | ~ ( in @ X3080 @ X3077 )
        | ~ ( breln1 @ X3077 @ X3079 )
        | ~ ( breln1 @ X3077 @ X3078 ) )
      & ( ~ X3082
        | X3082
        | ~ ( in @ ( kpair @ X3080 @ X3081 ) @ ( breln1compset @ X3077 @ X3078 @ X3079 ) )
        | ~ ( in @ X3081 @ X3077 )
        | ~ ( in @ X3080 @ X3077 )
        | ~ ( breln1 @ X3077 @ X3079 )
        | ~ ( breln1 @ X3077 @ X3078 ) )
      & ( ~ ( breln1 @ X3084 @ X3085 )
        | ~ ( breln1 @ X3084 @ X3086 )
        | ( breln1 @ X3084 @ ( binunion @ X3085 @ X3086 ) ) )
      & ( ~ ( breln1 @ X3087 @ X3088 )
        | ~ ( breln1 @ X3087 @ X3089 )
        | ~ ( in @ X3090 @ X3087 )
        | ~ ( in @ X3091 @ X3087 )
        | ~ ( in @ ( kpair @ X3090 @ X3091 ) @ X3088 )
        | ( in @ ( kpair @ X3090 @ X3091 ) @ ( binunion @ X3088 @ X3089 ) ) )
      & ( ~ ( breln1 @ X3092 @ X3093 )
        | ~ ( breln1 @ X3092 @ X3094 )
        | ~ ( in @ X3095 @ X3092 )
        | ~ ( in @ X3096 @ X3092 )
        | ~ ( in @ ( kpair @ X3095 @ X3096 ) @ X3094 )
        | ( in @ ( kpair @ X3095 @ X3096 ) @ ( binunion @ X3093 @ X3094 ) ) )
      & ( ~ ( in @ ( kpair @ X3100 @ X3101 ) @ X3098 )
        | ( in @ ( kpair @ X3100 @ X3101 ) @ ( binunion @ X3098 @ X3099 ) )
        | ~ ( in @ X3101 @ X3097 )
        | ~ ( in @ X3100 @ X3097 )
        | ~ ( breln1 @ X3097 @ X3099 )
        | ~ ( breln1 @ X3097 @ X3098 ) )
      & ( ~ ( in @ ( kpair @ X3100 @ X3101 ) @ X3099 )
        | ( in @ ( kpair @ X3100 @ X3101 ) @ ( binunion @ X3098 @ X3099 ) )
        | ~ ( in @ X3101 @ X3097 )
        | ~ ( in @ X3100 @ X3097 )
        | ~ ( breln1 @ X3097 @ X3099 )
        | ~ ( breln1 @ X3097 @ X3098 ) )
      & ( ~ ( breln1 @ X3102 @ X3103 )
        | ~ ( breln1 @ X3102 @ X3104 )
        | ~ ( in @ X3105 @ X3102 )
        | ~ ( in @ X3106 @ X3102 )
        | ~ ( in @ ( kpair @ X3105 @ X3106 ) @ ( binunion @ X3103 @ X3104 ) )
        | ( in @ ( kpair @ X3105 @ X3106 ) @ X3103 )
        | ( in @ ( kpair @ X3105 @ X3106 ) @ X3104 ) )
      & ( breln1 @ esk99_0 @ esk100_0 )
      & ( breln1 @ esk99_0 @ esk101_0 )
      & ( in @ esk102_0 @ esk99_0 )
      & ( in @ esk103_0 @ esk99_0 )
      & ( in @ ( kpair @ esk102_0 @ esk103_0 ) @ ( binunion @ esk100_0 @ esk101_0 ) )
      & ( ~ ( in @ ( kpair @ esk102_0 @ esk103_0 ) @ esk100_0 )
        | epred2_0 )
      & ( ~ ( in @ ( kpair @ esk102_0 @ esk103_0 ) @ esk101_0 )
        | epred2_0 )
      & ~ epred2_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_375])])])])])])]) ).

thf(c_0_377,negated_conjecture,
    ( epred2_0
    | ~ ( in @ ( kpair @ esk102_0 @ esk103_0 ) @ esk100_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_376]) ).

thf(c_0_378,negated_conjecture,
    ~ epred2_0,
    inference(split_conjunct,[status(thm)],[c_0_376]) ).

thf(c_0_379,negated_conjecture,
    ( epred2_0
    | ~ ( in @ ( kpair @ esk102_0 @ esk103_0 ) @ esk101_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_376]) ).

thf(c_0_380,negated_conjecture,
    ! [X2: $i,X4: $i,X3: $i] :
      ( ( in @ X2 @ X3 )
      | ( in @ X2 @ X4 )
      | ~ ( in @ X2 @ ( binunion @ X4 @ X3 ) ) ),
    inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_376])])]) ).

thf(c_0_381,negated_conjecture,
    in @ ( kpair @ esk102_0 @ esk103_0 ) @ ( binunion @ esk100_0 @ esk101_0 ),
    inference(split_conjunct,[status(thm)],[c_0_376]) ).

thf(c_0_382,negated_conjecture,
    ~ ( in @ ( kpair @ esk102_0 @ esk103_0 ) @ esk100_0 ),
    inference(sr,[status(thm)],[c_0_377,c_0_378]) ).

thf(c_0_383,negated_conjecture,
    ~ ( in @ ( kpair @ esk102_0 @ esk103_0 ) @ esk101_0 ),
    inference(sr,[status(thm)],[c_0_379,c_0_378]) ).

thf(c_0_384,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_380,c_0_381]),c_0_382]),c_0_383]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU787^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.13  % 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 17:09:08 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
% 1.44/0.78  # Version: 3.1.0-ho
% 1.44/0.78  # Preprocessing class: HSLMSLSSLLLCHFA.
% 1.44/0.78  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.44/0.78  # Starting ehoh_best5 with 300s (1) cores
% 1.44/0.78  # Starting almost_fo_3_lam with 300s (1) cores
% 1.44/0.78  # Starting new_bool_5 with 300s (1) cores
% 1.44/0.78  # Starting pre_casc_3 with 300s (1) cores
% 1.44/0.78  # Starting ho_unfolding_8 with 300s (1) cores
% 1.44/0.78  # Starting new_ho_10_cnf2 with 300s (1) cores
% 1.44/0.78  # Starting new_bool_3 with 300s (1) cores
% 1.44/0.78  # Starting new_ho_5 with 300s (1) cores
% 1.44/0.78  # new_ho_5 with pid 13033 completed with status 8
% 1.44/0.78  # pre_casc_3 with pid 13029 completed with status 8
% 1.44/0.78  # new_bool_3 with pid 13032 completed with status 0
% 1.44/0.78  # Result found by new_bool_3
% 1.44/0.78  # Preprocessing class: HSLMSLSSLLLCHFA.
% 1.44/0.78  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.44/0.78  # Starting ehoh_best5 with 300s (1) cores
% 1.44/0.78  # Starting almost_fo_3_lam with 300s (1) cores
% 1.44/0.78  # Starting new_bool_5 with 300s (1) cores
% 1.44/0.78  # Starting pre_casc_3 with 300s (1) cores
% 1.44/0.78  # Starting ho_unfolding_8 with 300s (1) cores
% 1.44/0.78  # Starting new_ho_10_cnf2 with 300s (1) cores
% 1.44/0.78  # Starting new_bool_3 with 300s (1) cores
% 1.44/0.78  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.44/0.78  # Search class: HGHSM-FSLM32-MHFMMSBN
% 1.44/0.78  # Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 1.44/0.78  # Starting ho_unfolding_8 with 61s (1) cores
% 1.44/0.78  # ho_unfolding_8 with pid 13049 completed with status 0
% 1.44/0.78  # Result found by ho_unfolding_8
% 1.44/0.78  # Preprocessing class: HSLMSLSSLLLCHFA.
% 1.44/0.78  # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.44/0.78  # Starting ehoh_best5 with 300s (1) cores
% 1.44/0.78  # Starting almost_fo_3_lam with 300s (1) cores
% 1.44/0.78  # Starting new_bool_5 with 300s (1) cores
% 1.44/0.78  # Starting pre_casc_3 with 300s (1) cores
% 1.44/0.78  # Starting ho_unfolding_8 with 300s (1) cores
% 1.44/0.78  # Starting new_ho_10_cnf2 with 300s (1) cores
% 1.44/0.78  # Starting new_bool_3 with 300s (1) cores
% 1.44/0.78  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.44/0.78  # Search class: HGHSM-FSLM32-MHFMMSBN
% 1.44/0.78  # Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 1.44/0.78  # Starting ho_unfolding_8 with 61s (1) cores
% 1.44/0.78  # Preprocessing time       : 0.065 s
% 1.44/0.78  # Presaturation interreduction done
% 1.44/0.78  
% 1.44/0.78  # Proof found!
% 1.44/0.78  # SZS status Theorem
% 1.44/0.78  # SZS output start CNFRefutation
% See solution above
% 1.44/0.79  # Parsed axioms                        : 657
% 1.44/0.79  # Removed by relevancy pruning/SinE    : 353
% 1.44/0.79  # Initial clauses                      : 525
% 1.44/0.79  # Removed in clause preprocessing      : 33
% 1.44/0.79  # Initial clauses in saturation        : 492
% 1.44/0.79  # Processed clauses                    : 642
% 1.44/0.79  # ...of these trivial                  : 9
% 1.44/0.79  # ...subsumed                          : 48
% 1.44/0.79  # ...remaining for further processing  : 585
% 1.44/0.79  # Other redundant clauses eliminated   : 24
% 1.44/0.79  # Clauses deleted for lack of memory   : 0
% 1.44/0.79  # Backward-subsumed                    : 2
% 1.44/0.79  # Backward-rewritten                   : 1
% 1.44/0.79  # Generated clauses                    : 846
% 1.44/0.79  # ...of the previous two non-redundant : 767
% 1.44/0.79  # ...aggressively subsumed             : 0
% 1.44/0.79  # Contextual simplify-reflections      : 14
% 1.44/0.79  # Paramodulations                      : 814
% 1.44/0.79  # Factorizations                       : 0
% 1.44/0.79  # NegExts                              : 0
% 1.44/0.79  # Equation resolutions                 : 29
% 1.44/0.79  # Disequality decompositions           : 0
% 1.44/0.79  # Total rewrite steps                  : 92
% 1.44/0.79  # ...of those cached                   : 64
% 1.44/0.79  # Propositional unsat checks           : 0
% 1.44/0.79  #    Propositional check models        : 0
% 1.44/0.79  #    Propositional check unsatisfiable : 0
% 1.44/0.79  #    Propositional clauses             : 0
% 1.44/0.79  #    Propositional clauses after purity: 0
% 1.44/0.79  #    Propositional unsat core size     : 0
% 1.44/0.79  #    Propositional preprocessing time  : 0.000
% 1.44/0.79  #    Propositional encoding time       : 0.000
% 1.44/0.79  #    Propositional solver time         : 0.000
% 1.44/0.79  #    Success case prop preproc time    : 0.000
% 1.44/0.79  #    Success case prop encoding time   : 0.000
% 1.44/0.79  #    Success case prop solver time     : 0.000
% 1.44/0.79  # Current number of processed clauses  : 140
% 1.44/0.79  #    Positive orientable unit clauses  : 37
% 1.44/0.79  #    Positive unorientable unit clauses: 0
% 1.44/0.79  #    Negative unit clauses             : 5
% 1.44/0.79  #    Non-unit-clauses                  : 98
% 1.44/0.79  # Current number of unprocessed clauses: 1032
% 1.44/0.79  # ...number of literals in the above   : 3107
% 1.44/0.79  # Current number of archived formulas  : 0
% 1.44/0.79  # Current number of archived clauses   : 430
% 1.44/0.79  # Clause-clause subsumption calls (NU) : 43649
% 1.44/0.79  # Rec. Clause-clause subsumption calls : 12146
% 1.44/0.79  # Non-unit clause-clause subsumptions  : 59
% 1.44/0.79  # Unit Clause-clause subsumption calls : 163
% 1.44/0.79  # Rewrite failures with RHS unbound    : 0
% 1.44/0.79  # BW rewrite match attempts            : 22
% 1.44/0.79  # BW rewrite match successes           : 1
% 1.44/0.79  # Condensation attempts                : 0
% 1.44/0.79  # Condensation successes               : 0
% 1.44/0.79  # Termbank termtop insertions          : 108656
% 1.44/0.79  # Search garbage collected termcells   : 33492
% 1.44/0.79  
% 1.44/0.79  # -------------------------------------------------
% 1.44/0.79  # User time                : 0.231 s
% 1.44/0.79  # System time              : 0.025 s
% 1.44/0.79  # Total time               : 0.256 s
% 1.44/0.79  # Maximum resident set size: 10168 pages
% 1.44/0.79  
% 1.44/0.79  # -------------------------------------------------
% 1.44/0.79  # User time                : 0.471 s
% 1.44/0.79  # System time              : 0.091 s
% 1.44/0.79  # Total time               : 0.563 s
% 1.44/0.79  # Maximum resident set size: 2884 pages
% 1.44/0.79  % E---3.1 exiting
% 1.44/0.79  % E exiting
%------------------------------------------------------------------------------