LEO-II---2.3.1.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : LEO-II---2.3.1
% Problem  : SEU745^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Oct  7 10:47:22 AM UTC 2026

% Result   : Theorem 87.51s 14.83s
% Output   : CNFRefutation 87.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   47
%            Number of leaves      :  266
% Syntax   : Number of formulae    : 4817 (1722 unt;   0 typ; 265 def)
%            Number of atoms       : 41611 (16155 equ;   0 cnn)
%            Maximal formula atoms :  266 (   8 avg)
%            Number of connectives : 90673 (16326   ~;15378   |; 215   &;55860   @)
%                                         (  56 <=>;2838  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  274 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  : 2679 (2679   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  462 ( 459 usr; 269 con; 0-4 aty)
%            Number of variables   : 20108 (1377   ^;18552   !; 179   ?;20108   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_ap,type,
    ap: $i > $i > $i > $i > $i ).

thf(tp_ap2apEq1,type,
    ap2apEq1: $o ).

thf(tp_ap2apEq2,type,
    ap2apEq2: $o ).

thf(tp_ap2p,type,
    ap2p: $o ).

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

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

thf(tp_atleast2p,type,
    atleast2p: $i > $o ).

thf(tp_atmost1p,type,
    atmost1p: $i > $o ).

thf(tp_atmost2p,type,
    atmost2p: $i > $o ).

thf(tp_beta1,type,
    beta1: $o ).

thf(tp_beta2,type,
    beta2: $o ).

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

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

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

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

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

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

thf(tp_binintersectSubset1,type,
    binintersectSubset1: $o ).

thf(tp_binintersectSubset2,type,
    binintersectSubset2: $o ).

thf(tp_binintersectSubset3,type,
    binintersectSubset3: $o ).

thf(tp_binintersectSubset4,type,
    binintersectSubset4: $o ).

thf(tp_binintersectSubset5,type,
    binintersectSubset5: $o ).

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

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

thf(tp_binintersectT_lem,type,
    binintersectT_lem: $o ).

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

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

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

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

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

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

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

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

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

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

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

thf(tp_brelnall1,type,
    brelnall1: $o ).

thf(tp_brelnall2,type,
    brelnall2: $o ).

thf(tp_bs114d,type,
    bs114d: $o ).

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

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

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

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

thf(tp_cartprodmempair1,type,
    cartprodmempair1: $o ).

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

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

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

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

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

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

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

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

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

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

thf(tp_complementTE1,type,
    complementTE1: $o ).

thf(tp_complementTI1,type,
    complementTI1: $o ).

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

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

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

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

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

thf(tp_contrasubsetT1,type,
    contrasubsetT1: $o ).

thf(tp_contrasubsetT2,type,
    contrasubsetT2: $o ).

thf(tp_contrasubsetT3,type,
    contrasubsetT3: $o ).

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

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

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

thf(tp_disjoint,type,
    disjoint: $i > $i > $o ).

thf(tp_disjointsetsI1,type,
    disjointsetsI1: $o ).

thf(tp_doubleComplementE1,type,
    doubleComplementE1: $o ).

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

thf(tp_doubleComplementI1,type,
    doubleComplementI1: $o ).

thf(tp_doubleComplementSub1,type,
    doubleComplementSub1: $o ).

thf(tp_doubleComplementSub2,type,
    doubleComplementSub2: $o ).

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

thf(tp_dpsetconstrEL1,type,
    dpsetconstrEL1: $o ).

thf(tp_dpsetconstrEL2,type,
    dpsetconstrEL2: $o ).

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

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

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

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

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

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

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

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

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

thf(tp_emptyE1,type,
    emptyE1: $o ).

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

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

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

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

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

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

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

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

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

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

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

thf(tp_eqimpsubset1,type,
    eqimpsubset1: $o ).

thf(tp_eqimpsubset2,type,
    eqimpsubset2: $o ).

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

thf(tp_eta1,type,
    eta1: $o ).

thf(tp_eta2,type,
    eta2: $o ).

thf(tp_ex1,type,
    ex1: $i > ( $i > $o ) > $o ).

thf(tp_ex1E1,type,
    ex1E1: $o ).

thf(tp_ex1E2,type,
    ex1E2: $o ).

thf(tp_ex1I,type,
    ex1I: $o ).

thf(tp_ex1I2,type,
    ex1I2: $o ).

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

thf(tp_exuE1,type,
    exuE1: $o ).

thf(tp_exuE2,type,
    exuE2: $o ).

thf(tp_exuE3e,type,
    exuE3e: $o ).

thf(tp_exuE3u,type,
    exuE3u: $o ).

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

thf(tp_exuI1,type,
    exuI1: $o ).

thf(tp_exuI2,type,
    exuI2: $o ).

thf(tp_exuI3,type,
    exuI3: $o ).

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

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

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

thf(tp_funcGraphProp1,type,
    funcGraphProp1: $o ).

thf(tp_funcGraphProp2,type,
    funcGraphProp2: $o ).

thf(tp_funcGraphProp3,type,
    funcGraphProp3: $o ).

thf(tp_funcGraphProp4,type,
    funcGraphProp4: $o ).

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

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

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

thf(tp_funcext2,type,
    funcext2: $o ).

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

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

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

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

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

thf(tp_iffalseProp1,type,
    iffalseProp1: $o ).

thf(tp_iffalseProp2,type,
    iffalseProp2: $o ).

thf(tp_ifp,type,
    ifp: $o ).

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

thf(tp_iftrueProp1,type,
    iftrueProp1: $o ).

thf(tp_iftrueProp2,type,
    iftrueProp2: $o ).

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

thf(tp_in,type,
    in: $i > $i > $o ).

thf(tp_inComplementUnionImpNotIn1,type,
    inComplementUnionImpNotIn1: $o ).

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

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

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

thf(tp_inIntersectImpInUnion2,type,
    inIntersectImpInUnion2: $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(tp_lam2lamEq,type,
    lam2lamEq: $o ).

thf(tp_lam2p,type,
    lam2p: $o ).

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

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

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

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

thf(tp_nonemptyE1,type,
    nonemptyE1: $o ).

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

thf(tp_nonemptyI1,type,
    nonemptyI1: $o ).

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

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

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

thf(tp_notequalI1,type,
    notequalI1: $o ).

thf(tp_notequalI2,type,
    notequalI2: $o ).

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

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

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

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

thf(tp_omega0Ax,type,
    omega0Ax: $o ).

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

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

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

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

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

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

thf(tp_powersetE1,type,
    powersetE1: $o ).

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

thf(tp_powersetI1,type,
    powersetI1: $o ).

thf(tp_powersetTE1,type,
    powersetTE1: $o ).

thf(tp_powersetTI1,type,
    powersetTI1: $o ).

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

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

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

thf(tp_prop2set,type,
    prop2set: $o > $i ).

thf(tp_prop2set2propI,type,
    prop2set2propI: $o ).

thf(tp_prop2setE,type,
    prop2setE: $o ).

thf(tp_prop2setI,type,
    prop2setI: $o ).

thf(tp_quantDeMorgan1,type,
    quantDeMorgan1: $o ).

thf(tp_quantDeMorgan2,type,
    quantDeMorgan2: $o ).

thf(tp_quantDeMorgan3,type,
    quantDeMorgan3: $o ).

thf(tp_quantDeMorgan4,type,
    quantDeMorgan4: $o ).

thf(tp_regular,type,
    regular: $i > $o ).

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

thf(tp_sK100_SY3183,type,
    sK100_SY3183: ( $i > $o ) > $i > ( $i > $o ) > $i ).

thf(tp_sK101_SY3179,type,
    sK101_SY3179: $i > ( $i > $i > $o ) > $i > $i ).

thf(tp_sK102_SY2690,type,
    sK102_SY2690: $i > ( $i > $i > $o ) > $i > $i ).

thf(tp_sK103_SY3208,type,
    sK103_SY3208: $i > $i > $i > $i > $i ).

thf(tp_sK104_SY3142,type,
    sK104_SY3142: $i > $i > $i > $i > $i ).

thf(tp_sK105_SY3142,type,
    sK105_SY3142: $i > $i > $i > $i > $i ).

thf(tp_sK106_SY3142,type,
    sK106_SY3142: $i > $i > $i > $i > $i ).

thf(tp_sK107_SY3221,type,
    sK107_SY3221: $i > $i > $i > $i > $i ).

thf(tp_sK108_SY3222,type,
    sK108_SY3222: $i > $i > $i > $i > $i ).

thf(tp_sK109_SY3156,type,
    sK109_SY3156: $i > $i > $i > $i ).

thf(tp_sK10_SY2604,type,
    sK10_SY2604: $i > $i > $i ).

thf(tp_sK110_SY3205,type,
    sK110_SY3205: ( $i > $o ) > $i > ( $i > $o ) > $i ).

thf(tp_sK111_SY3206,type,
    sK111_SY3206: ( $i > $o ) > $i > ( $i > $o ) > $i ).

thf(tp_sK112_SY3226,type,
    sK112_SY3226: $i > $i > $i > $i > $i ).

thf(tp_sK113_SY3156,type,
    sK113_SY3156: $i > $i > $i > $i ).

thf(tp_sK114_SY3211,type,
    sK114_SY3211: ( $i > $o ) > $i > ( $i > $o ) > $i ).

thf(tp_sK115_SY3216,type,
    sK115_SY3216: ( $i > $o ) > $i > ( $i > $o ) > $i ).

thf(tp_sK116_SY3217,type,
    sK116_SY3217: ( $i > $o ) > $i > ( $i > $o ) > $i ).

thf(tp_sK117_SY3202,type,
    sK117_SY3202: $i > $i > $i > $i ).

thf(tp_sK118_SY3231,type,
    sK118_SY3231: $i > $i > $i > $i ).

thf(tp_sK119_SY2801,type,
    sK119_SY2801: $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK11_SY2627,type,
    sK11_SY2627: ( $i > $o ) > $i > $i ).

thf(tp_sK120_SY2394,type,
    sK120_SY2394: $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK121_SY3223,type,
    sK121_SY3223: ( $i > $o ) > $i > ( $i > $o ) > $i ).

thf(tp_sK122_SY3239,type,
    sK122_SY3239: $i > $i > $i > $i ).

thf(tp_sK123_SY2801,type,
    sK123_SY2801: $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK124_SY2394,type,
    sK124_SY2394: $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK125_SY3224,type,
    sK125_SY3224: $i > $i > ( $i > $i > $o ) > $i > $i ).

thf(tp_sK126_SY3229,type,
    sK126_SY3229: ( $i > $o ) > $i > ( $i > $o ) > $i ).

thf(tp_sK127_SY3230,type,
    sK127_SY3230: ( $i > $o ) > $i > ( $i > $o ) > $i ).

thf(tp_sK128_SY3227,type,
    sK128_SY3227: $i > $i > ( $i > $i > $o ) > $i > $i ).

thf(tp_sK129_SY3235,type,
    sK129_SY3235: ( $i > $o ) > $i > ( $i > $o ) > $i ).

thf(tp_sK12_SY2657,type,
    sK12_SY2657: ( $i > $o ) > $i > $i ).

thf(tp_sK130_SY3236,type,
    sK130_SY3236: ( $i > $o ) > $i > ( $i > $o ) > $i ).

thf(tp_sK131_SY3237,type,
    sK131_SY3237: ( $i > $o ) > $i > ( $i > $o ) > $i ).

thf(tp_sK132_SY3238,type,
    sK132_SY3238: ( $i > $o ) > $i > ( $i > $o ) > $i ).

thf(tp_sK133_SY3243,type,
    sK133_SY3243: ( $i > $o ) > $i > ( $i > $o ) > $i ).

thf(tp_sK134_SY3244,type,
    sK134_SY3244: ( $i > $o ) > $i > ( $i > $o ) > $i ).

thf(tp_sK135_SY3245,type,
    sK135_SY3245: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).

thf(tp_sK136_SY2801,type,
    sK136_SY2801: $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK137_SY2394,type,
    sK137_SY2394: $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK138_SY3246,type,
    sK138_SY3246: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).

thf(tp_sK139_SY2801,type,
    sK139_SY2801: $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK13_SY2687,type,
    sK13_SY2687: ( $i > $i > $o ) > $i > $i ).

thf(tp_sK140_SY2394,type,
    sK140_SY2394: $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK141_SY2801,type,
    sK141_SY2801: $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK142_SY2394,type,
    sK142_SY2394: $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK143_SY2801,type,
    sK143_SY2801: $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK144_SY2394,type,
    sK144_SY2394: $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK145_SY2801,type,
    sK145_SY2801: $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK146_SY2394,type,
    sK146_SY2394: $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK147_SY2801,type,
    sK147_SY2801: $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK148_SY2394,type,
    sK148_SY2394: $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK149_SY2801,type,
    sK149_SY2801: $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK14_SY2694,type,
    sK14_SY2694: $i > $i > $i ).

thf(tp_sK150_SY2394,type,
    sK150_SY2394: $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK151_SY2801,type,
    sK151_SY2801: $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK152_SY2394,type,
    sK152_SY2394: $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK153_SY3257,type,
    sK153_SY3257: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).

thf(tp_sK154_SY3258,type,
    sK154_SY3258: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).

thf(tp_sK155_SY3259,type,
    sK155_SY3259: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).

thf(tp_sK156_SY3260,type,
    sK156_SY3260: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).

thf(tp_sK157_SY3264,type,
    sK157_SY3264: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).

thf(tp_sK158_SY3265,type,
    sK158_SY3265: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).

thf(tp_sK159_SY3266,type,
    sK159_SY3266: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).

thf(tp_sK15_SY2740,type,
    sK15_SY2740: $i > $i > $i ).

thf(tp_sK160_SY3274,type,
    sK160_SY3274: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).

thf(tp_sK16_SY2777,type,
    sK16_SY2777: ( $i > $o ) > $i > $i ).

thf(tp_sK17_SY2797,type,
    sK17_SY2797: ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK18_SY3065,type,
    sK18_SY3065: ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK19_SY2927,type,
    sK19_SY2927: $i > ( $i > $i ) > $i > $i ).

thf(tp_sK1_SX0,type,
    sK1_SX0: $i ).

thf(tp_sK20_SY2930,type,
    sK20_SY2930: $i > ( $i > $i ) > $i > $i ).

thf(tp_sK21_SY2952,type,
    sK21_SY2952: $i > ( $i > $i ) > $i > $i ).

thf(tp_sK22_SY2969,type,
    sK22_SY2969: $i > ( $i > $i ) > $i > $i ).

thf(tp_sK23_SY3000,type,
    sK23_SY3000: $i > ( $i > $i ) > $i > $i ).

thf(tp_sK24_SY2355,type,
    sK24_SY2355: $i > $i ).

thf(tp_sK25_SY2785,type,
    sK25_SY2785: $i > $i > $i ).

thf(tp_sK26_SY3100,type,
    sK26_SY3100: ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK27_SY2808,type,
    sK27_SY2808: ( $i > $o ) > $i > $i ).

thf(tp_sK28_SY2426,type,
    sK28_SY2426: $i > $i ).

thf(tp_sK29_SY3031,type,
    sK29_SY3031: $i > ( $i > $i ) > $i > $i ).

thf(tp_sK2_SY2597,type,
    sK2_SY2597: $i ).

thf(tp_sK30_SY2514,type,
    sK30_SY2514: ( $i > $o ) > $i > $i ).

thf(tp_sK31_SY2534,type,
    sK31_SY2534: ( $i > $o ) > $i > $i ).

thf(tp_sK32_SY3068,type,
    sK32_SY3068: $i ).

thf(tp_sK33_SY2921,type,
    sK33_SY2921: $i > $i > $i > $i ).

thf(tp_sK34_SY3074,type,
    sK34_SY3074: ( $i > $o ) > $i > $i ).

thf(tp_sK35_SY2645,type,
    sK35_SY2645: $i > $i > $i ).

thf(tp_sK36_SY3079,type,
    sK36_SY3079: ( $i > $o ) > $i > $i ).

thf(tp_sK37_SY3106,type,
    sK37_SY3106: $i > ( $i > $o ) > $i ).

thf(tp_sK38_SY2524,type,
    sK38_SY2524: $i > $i > $i ).

thf(tp_sK39_SY2033,type,
    sK39_SY2033: $i > $i ).

thf(tp_sK3_SY2100,type,
    sK3_SY2100: $i > $i ).

thf(tp_sK40_SY2119,type,
    sK40_SY2119: $i > $i > $i ).

thf(tp_sK41_SY3107,type,
    sK41_SY3107: $o > $i > $i > $i ).

thf(tp_sK42_SX0,type,
    sK42_SX0: $i > $i > $i ).

thf(tp_sK43_SX0,type,
    sK43_SX0: $i > $i > $i ).

thf(tp_sK44_SY3111,type,
    sK44_SY3111: ( $i > $o ) > $i > $i > $i > $i ).

thf(tp_sK45_SY2586,type,
    sK45_SY2586: $i > $i > $i ).

thf(tp_sK46_SY3122,type,
    sK46_SY3122: ( $i > $o ) > $i > $i > $i > $i ).

thf(tp_sK47_SY2690,type,
    sK47_SY2690: ( $i > $i > $o ) > $i > $i ).

thf(tp_sK48_SY2242,type,
    sK48_SY2242: $i > ( $i > $o ) > $i ).

thf(tp_sK49_SY2781,type,
    sK49_SY2781: $i > $i > $i ).

thf(tp_sK4_SY2024,type,
    sK4_SY2024: $i > $i ).

thf(tp_sK50_SY3133,type,
    sK50_SY3133: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).

thf(tp_sK51_SY3066,type,
    sK51_SY3066: $i > $i > $i > $i ).

thf(tp_sK52_SY2586,type,
    sK52_SY2586: $i > $i > $i ).

thf(tp_sK53_SY2593,type,
    sK53_SY2593: $i > ( $i > $o ) > $i > $i ).

thf(tp_sK54_SY2705,type,
    sK54_SY2705: $i > ( $i > $o ) > $i > $i ).

thf(tp_sK55_SY3172,type,
    sK55_SY3172: $i > ( $i > $o ) > $i ).

thf(tp_sK56_SY3006,type,
    sK56_SY3006: $i > ( $i > $o ) > $i > $i ).

thf(tp_sK57_SY3103,type,
    sK57_SY3103: $i > $i > $i > $i ).

thf(tp_sK58_SY3104,type,
    sK58_SY3104: $i > $i > $i > $i ).

thf(tp_sK59_SY3056,type,
    sK59_SY3056: $i > ( $i > $o ) > $i ).

thf(tp_sK5_SY2073,type,
    sK5_SY2073: $i > $i ).

thf(tp_sK60_SY3057,type,
    sK60_SY3057: $i > ( $i > $o ) > $i ).

thf(tp_sK61_SY3058,type,
    sK61_SY3058: $i > ( $i > $o ) > $i ).

thf(tp_sK62_SY3060,type,
    sK62_SY3060: $i > ( $i > $o ) > $i ).

thf(tp_sK63_SY3167,type,
    sK63_SY3167: $i > $i > ( $i > $o ) > $i > $i ).

thf(tp_sK64_SY3118,type,
    sK64_SY3118: $i > $i > $i > $i > $i ).

thf(tp_sK65_SY3119,type,
    sK65_SY3119: $i > $i > $i > $i > $i ).

thf(tp_sK66_SY3077,type,
    sK66_SY3077: $i > ( $i > $o ) > $i ).

thf(tp_sK67_SY3168,type,
    sK67_SY3168: $i > $i > ( $i > $o ) > $i > $i ).

thf(tp_sK68_SY3087,type,
    sK68_SY3087: $i > ( $i > $o ) > $i ).

thf(tp_sK69_SY3125,type,
    sK69_SY3125: $i > $i > $i > $i > $i ).

thf(tp_sK6_SY2533,type,
    sK6_SY2533: $i > $i > $i ).

thf(tp_sK70_SY3128,type,
    sK70_SY3128: $i > $i > $i > $i > $i ).

thf(tp_sK71_SY3174,type,
    sK71_SY3174: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).

thf(tp_sK72_SY3099,type,
    sK72_SY3099: $i > ( $i > $o ) > $i ).

thf(tp_sK73_SY3140,type,
    sK73_SY3140: $i > $i > $i > $i > $i ).

thf(tp_sK74_SY3150,type,
    sK74_SY3150: $i > $i > $i > $i ).

thf(tp_sK75_SY3181,type,
    sK75_SY3181: $i > $i > $i > $i > $i ).

thf(tp_sK76_SY3182,type,
    sK76_SY3182: $i > $i > $i > $i > $i ).

thf(tp_sK77_SY1897,type,
    sK77_SY1897: $i > ( $i > $o ) > $i ).

thf(tp_sK78_SY2528,type,
    sK78_SY2528: $i > ( $i > $o ) > $i > $i ).

thf(tp_sK79_SY1928,type,
    sK79_SY1928: $i > ( $i > $o ) > $i ).

thf(tp_sK7_SY2572,type,
    sK7_SY2572: ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK80_SY3154,type,
    sK80_SY3154: $i > $i > $i ).

thf(tp_sK81_SY2125,type,
    sK81_SY2125: $i > ( $i > $o ) > $i ).

thf(tp_sK82_SY3162,type,
    sK82_SY3162: $i > $i > ( $i > $i > $o ) > $i ).

thf(tp_sK83_SY2244,type,
    sK83_SY2244: $i > ( $i > $o ) > $i ).

thf(tp_sK84_SY2244,type,
    sK84_SY2244: $i > ( $i > $o ) > $i ).

thf(tp_sK85_SY2378,type,
    sK85_SY2378: $i > ( $i > $o ) > $i ).

thf(tp_sK86_SY1897,type,
    sK86_SY1897: $i > ( $i > $o ) > $i ).

thf(tp_sK87_SY1928,type,
    sK87_SY1928: $i > ( $i > $o ) > $i ).

thf(tp_sK88_SY3067,type,
    sK88_SY3067: $i > $i > $i > $i ).

thf(tp_sK89_SY3067,type,
    sK89_SY3067: $i > $i > $i > $i ).

thf(tp_sK8_SY2585,type,
    sK8_SY2585: $i > $i > $i ).

thf(tp_sK90_SY2125,type,
    sK90_SY2125: $i > ( $i > $o ) > $i ).

thf(tp_sK91_SY2244,type,
    sK91_SY2244: $i > ( $i > $o ) > $i ).

thf(tp_sK92_SY2378,type,
    sK92_SY2378: $i > ( $i > $o ) > $i ).

thf(tp_sK93_SY2491,type,
    sK93_SY2491: $i > ( $i > $o ) > $i ).

thf(tp_sK94_SY3067,type,
    sK94_SY3067: $i > $i > $i > $i ).

thf(tp_sK95_SY3142,type,
    sK95_SY3142: $i > $i > $i > $i > $i ).

thf(tp_sK96_SY2491,type,
    sK96_SY2491: $i > ( $i > $o ) > $i ).

thf(tp_sK97_SY2491,type,
    sK97_SY2491: $i > ( $i > $o ) > $i ).

thf(tp_sK98_SY2690,type,
    sK98_SY2690: $i > ( $i > $i > $o ) > $i > $i ).

thf(tp_sK99_SY2491,type,
    sK99_SY2491: $i > ( $i > $o ) > $i ).

thf(tp_sK9_SY2910,type,
    sK9_SY2910: $i ).

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

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

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

thf(tp_set2prop,type,
    set2prop: $i > $o ).

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

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

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

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

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

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

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

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

thf(tp_setadjoinSub2,type,
    setadjoinSub2: $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(tp_setminusSubset1,type,
    setminusSubset1: $o ).

thf(tp_setminusSubset2,type,
    setminusSubset2: $o ).

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

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

thf(tp_setsmeet,type,
    setsmeet: $i > $i > $o ).

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

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

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

thf(tp_setukpairinjL1,type,
    setukpairinjL1: $o ).

thf(tp_setukpairinjL2,type,
    setukpairinjL2: $o ).

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

thf(tp_setukpairinjR1,type,
    setukpairinjR1: $o ).

thf(tp_setukpairinjR11,type,
    setukpairinjR11: $o ).

thf(tp_setukpairinjR12,type,
    setukpairinjR12: $o ).

thf(tp_setukpairinjR2,type,
    setukpairinjR2: $o ).

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

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

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

thf(tp_setunionE2,type,
    setunionE2: $o ).

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

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

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

thf(tp_setunionsingleton1,type,
    setunionsingleton1: $o ).

thf(tp_setunionsingleton2,type,
    setunionsingleton2: $o ).

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

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

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

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

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

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

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

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

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

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

thf(tp_subset2powerset,type,
    subset2powerset: $o ).

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

thf(tp_subsetE2,type,
    subsetE2: $o ).

thf(tp_subsetI1,type,
    subsetI1: $o ).

thf(tp_subsetI2,type,
    subsetI2: $o ).

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

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

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

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

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

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

thf(tp_symdiffI1,type,
    symdiffI1: $o ).

thf(tp_symdiffI2,type,
    symdiffI2: $o ).

thf(tp_symdiffIneg1,type,
    symdiffIneg1: $o ).

thf(tp_symdiffIneg2,type,
    symdiffIneg2: $o ).

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

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

thf(tp_ubforcartprodlem1,type,
    ubforcartprodlem1: $o ).

thf(tp_ubforcartprodlem2,type,
    ubforcartprodlem2: $o ).

thf(tp_ubforcartprodlem3,type,
    ubforcartprodlem3: $o ).

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

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

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

thf(tp_upairset2E,type,
    upairset2E: $o ).

thf(tp_upairset2IR,type,
    upairset2IR: $o ).

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

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

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

thf(tp_upairsetp,type,
    upairsetp: $i > $o ).

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

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

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

thf(ap2apEq1,definition,
    ( ap2apEq1
    = ( ! [A: $i,B: $i,Xf: $i] :
          ( ( in @ Xf @ ( funcSet @ A @ B ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ( ap @ A @ B @ Xf @ Xx )
                = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap2apEq1) ).

thf(ap2apEq2,definition,
    ( ap2apEq2
    = ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ( ap @ A @ B @ Xf @ Xx )
                = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap2apEq2) ).

thf(ap2p,definition,
    ( ap2p
    = ( ! [A: $i,B: $i,Xf: $i] :
          ( ( in @ Xf @ ( funcSet @ A @ B ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap2p) ).

thf(apProp,definition,
    ( apProp
    = ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in
                @ ( setunion
                  @ ( dsetconstr @ B
                    @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
                @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apProp) ).

thf(app,definition,
    ( app
    = ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',app) ).

thf(beta1,definition,
    ( beta1
    = ( ! [A: $i,B: $i,Xf: $i > $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( Xf @ Xx ) @ B ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ( ap @ A @ B
                  @ ( lam @ A @ B
                    @ ^ [Xy: $i] : ( Xf @ Xy ) )
                  @ Xx )
                = ( Xf @ Xx ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta1) ).

thf(beta2,definition,
    ( beta2
    = ( ! [A: $i,B: $i,Xf: $i > $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( Xf @ Xx ) @ B ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ( ap @ A @ B
                  @ ( lam @ A @ B
                    @ ^ [Xy: $i] : ( Xf @ Xy ) )
                  @ Xx )
                = ( Xf @ Xx ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta2) ).

thf(binintersectEL,definition,
    ( binintersectEL
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ ( binintersect @ A @ B ) )
         => ( in @ Xx @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectEL) ).

thf(binintersectER,definition,
    ( binintersectER
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ ( binintersect @ A @ B ) )
         => ( in @ Xx @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectER) ).

thf(binintersectI,definition,
    ( binintersectI
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ( in @ Xx @ B )
           => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectI) ).

thf(binintersectLsub,definition,
    ( binintersectLsub
    = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectLsub) ).

thf(binintersectRsub,definition,
    ( binintersectRsub
    = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectRsub) ).

thf(binintersectSubset1,definition,
    ( binintersectSubset1
    = ( ! [A: $i,B: $i] :
          ( ( ( binintersect @ A @ B )
            = A )
         => ( subset @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset1) ).

thf(binintersectSubset2,definition,
    ( binintersectSubset2
    = ( ! [A: $i,B: $i] :
          ( ( subset @ A @ B )
         => ( ( binintersect @ A @ B )
            = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset2) ).

thf(binintersectSubset3,definition,
    ( binintersectSubset3
    = ( ! [A: $i,B: $i] :
          ( ( ( binintersect @ A @ B )
            = B )
         => ( subset @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset3) ).

thf(binintersectSubset4,definition,
    ( binintersectSubset4
    = ( ! [A: $i,B: $i] :
          ( ( subset @ B @ A )
         => ( ( binintersect @ A @ B )
            = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset4) ).

thf(binintersectSubset5,definition,
    ( binintersectSubset5
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( subset @ C @ A )
         => ( ( subset @ C @ B )
           => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset5) ).

thf(binintersectTELcontra,definition,
    ( binintersectTELcontra
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ~ ( in @ Xx @ X )
                   => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectTELcontra) ).

thf(binintersectTERcontra,definition,
    ( binintersectTERcontra
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ~ ( in @ Xx @ Y )
                   => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectTERcontra) ).

thf(binintersectT_lem,definition,
    ( binintersectT_lem
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectT_lem) ).

thf(binunionE,definition,
    ( binunionE
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ ( binunion @ A @ B ) )
         => ( ( in @ Xx @ A )
            | ( in @ Xx @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionE) ).

thf(binunionEcases,definition,
    ( binunionEcases
    = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
          ( ( in @ Xx @ ( binunion @ A @ B ) )
         => ( ( ( in @ Xx @ A )
             => Xphi )
           => ( ( ( in @ Xx @ B )
               => Xphi )
             => Xphi ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionEcases) ).

thf(binunionIL,definition,
    ( binunionIL
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIL) ).

thf(binunionIR,definition,
    ( binunionIR
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ B )
         => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIR) ).

thf(binunionLsub,definition,
    ( binunionLsub
    = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionLsub) ).

thf(binunionRsub,definition,
    ( binunionRsub
    = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionRsub) ).

thf(binunionTILcontra,definition,
    ( binunionTILcontra
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
                   => ~ ( in @ Xx @ X ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionTILcontra) ).

thf(binunionTIRcontra,definition,
    ( binunionTIRcontra
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
                   => ~ ( in @ Xx @ Y ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionTIRcontra) ).

thf(binunionT_lem,definition,
    ( binunionT_lem
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionT_lem) ).

thf(breln,definition,
    ( breln
    = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln) ).

thf(brelnall1,definition,
    ( brelnall1
    = ( ! [A: $i,B: $i,R: $i] :
          ( ( breln @ A @ B @ R )
         => ! [Xphi: $i > $o] :
              ( ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ! [Xy: $i] :
                      ( ( in @ Xy @ B )
                     => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
                       => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ R )
                 => ( Xphi @ Xx ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',brelnall1) ).

thf(brelnall2,definition,
    ( brelnall2
    = ( ! [A: $i,B: $i,R: $i] :
          ( ( breln @ A @ B @ R )
         => ! [Xphi: $i > $o] :
              ( ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ! [Xy: $i] :
                      ( ( in @ Xy @ B )
                     => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
                       => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ R )
                 => ( Xphi @ Xx ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',brelnall2) ).

thf(bs114d,definition,
    ( bs114d
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( binintersect @ A @ ( binunion @ B @ C ) )
          = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bs114d) ).

thf(cartprodfstin,definition,
    ( cartprodfstin
    = ( ! [A: $i,B: $i,Xu: $i] :
          ( ( in @ Xu @ ( cartprod @ A @ B ) )
         => ( in @ ( kfst @ Xu ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodfstin) ).

thf(cartprodfstpairEq,definition,
    ( cartprodfstpairEq
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( ( kfst @ ( kpair @ Xx @ Xy ) )
                = Xx ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodfstpairEq) ).

thf(cartprodmempair,definition,
    ( cartprodmempair
    = ( ! [A: $i,B: $i,Xu: $i] :
          ( ( in @ Xu @ ( cartprod @ A @ B ) )
         => ( iskpair @ Xu ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair) ).

thf(cartprodmempair1,definition,
    ( cartprodmempair1
    = ( ! [A: $i,B: $i,Xu: $i] :
          ( ( in @ Xu @ ( cartprod @ A @ B ) )
         => ? [Xx: $i] :
              ( ( in @ Xx @ A )
              & ? [Xy: $i] :
                  ( ( in @ Xy @ B )
                  & ( Xu
                    = ( kpair @ Xx @ Xy ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair1) ).

thf(cartprodmempaircEq,definition,
    ( cartprodmempaircEq
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( ( kpair @ Xx @ Xy )
                = ( kpair @ Xx @ Xy ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempaircEq) ).

thf(cartprodpairin,definition,
    ( cartprodpairin
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairin) ).

thf(cartprodpairmemEL,definition,
    ( cartprodpairmemEL
    = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
          ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
         => ( in @ Xx @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairmemEL) ).

thf(cartprodpairmemER,definition,
    ( cartprodpairmemER
    = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
          ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
         => ( in @ Xy @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairmemER) ).

thf(cartprodpairsurjEq,definition,
    ( cartprodpairsurjEq
    = ( ! [A: $i,B: $i,Xu: $i] :
          ( ( in @ Xu @ ( cartprod @ A @ B ) )
         => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
            = Xu ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairsurjEq) ).

thf(cartprodsndin,definition,
    ( cartprodsndin
    = ( ! [A: $i,B: $i,Xu: $i] :
          ( ( in @ Xu @ ( cartprod @ A @ B ) )
         => ( in @ ( ksnd @ Xu ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodsndin) ).

thf(cartprodsndpairEq,definition,
    ( cartprodsndpairEq
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
                = Xy ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodsndpairEq) ).

thf(complementImpComplementIntersect,definition,
    ( complementImpComplementIntersect
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ( in @ Xx @ ( setminus @ A @ X ) )
                   => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementImpComplementIntersect) ).

thf(complementInPowersetComplementIntersect,definition,
    ( complementInPowersetComplementIntersect
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementInPowersetComplementIntersect) ).

thf(complementSubsetComplementIntersect,definition,
    ( complementSubsetComplementIntersect
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementSubsetComplementIntersect) ).

thf(complementTE1,definition,
    ( complementTE1
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
               => ( in @ Xx @ X ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementTE1) ).

thf(complementTI1,definition,
    ( complementTI1
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ( in @ Xx @ X )
               => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementTI1) ).

thf(complementT_lem,definition,
    ( complementT_lem
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementT_lem) ).

thf(complementTcontraSubset,definition,
    ( complementTcontraSubset
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( ( subset @ X @ ( setminus @ A @ Y ) )
               => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementTcontraSubset) ).

thf(complementTnotintersectT,definition,
    ( complementTnotintersectT
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ( in @ Xx @ ( setminus @ A @ X ) )
                   => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementTnotintersectT) ).

thf(contraSubsetComplement,definition,
    ( contraSubsetComplement
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( ( subset @ X @ ( setminus @ A @ Y ) )
               => ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ( ( in @ Xx @ Y )
                     => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contraSubsetComplement) ).

thf(contrasubsetT,definition,
    ( contrasubsetT
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ( subset @ X @ ( setminus @ A @ Y ) )
                   => ( ( in @ Xx @ Y )
                     => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contrasubsetT) ).

thf(contrasubsetT1,definition,
    ( contrasubsetT1
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ( subset @ X @ Y )
                   => ( ~ ( in @ Xx @ Y )
                     => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contrasubsetT1) ).

thf(contrasubsetT2,definition,
    ( contrasubsetT2
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( ( subset @ X @ Y )
               => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contrasubsetT2) ).

thf(contrasubsetT3,definition,
    ( contrasubsetT3
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
               => ( subset @ X @ Y ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contrasubsetT3) ).

thf(descr__Cong,definition,
    ( descr__Cong
    = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
          ( ! [Xx: $i,Xy: $i] :
              ( ( Xx = Xy )
             => ( ( Xphi @ Xx )
              <=> ( Xpsi @ Xy ) ) )
         => ( ( exu
              @ ^ [Xx: $i] : ( Xphi @ Xx ) )
           => ( ( exu
                @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
             => ( ( descr
                  @ ^ [Xx: $i] : ( Xphi @ Xx ) )
                = ( descr
                  @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descr__Cong) ).

thf(descrp,definition,
    ( descrp
    = ( ! [Xphi: $i > $o] :
          ( ( exu
            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
         => ( Xphi
            @ ( descr
              @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descrp) ).

thf(disjointsetsI1,definition,
    ( disjointsetsI1
    = ( ! [A: $i,B: $i] :
          ( ~ ? [Xx: $i] :
                ( ( in @ Xx @ A )
                & ( in @ Xx @ B ) )
         => ( ( binintersect @ A @ B )
            = emptyset ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjointsetsI1) ).

thf(doubleComplementE1,definition,
    ( doubleComplementE1
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
               => ( in @ Xx @ X ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementE1) ).

thf(doubleComplementEq,definition,
    ( doubleComplementEq
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ( X
            = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementEq) ).

thf(doubleComplementI1,definition,
    ( doubleComplementI1
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ( in @ Xx @ X )
               => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementI1) ).

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

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

thf(dpsetconstrEL1,definition,
    ( dpsetconstrEL1
    = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
          ( ( in @ ( kpair @ Xx @ Xy )
            @ ( dpsetconstr @ A @ B
              @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
         => ( in @ Xx @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrEL1) ).

thf(dpsetconstrEL2,definition,
    ( dpsetconstrEL2
    = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
          ( ( in @ ( kpair @ Xx @ Xy )
            @ ( dpsetconstr @ A @ B
              @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
         => ( in @ Xy @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrEL2) ).

thf(dpsetconstrER,definition,
    ( dpsetconstrER
    = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
          ( ( in @ ( kpair @ Xx @ Xy )
            @ ( dpsetconstr @ A @ B
              @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
         => ( Xphi @ Xx @ Xy ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrER) ).

thf(dpsetconstrERa,definition,
    ( dpsetconstrERa
    = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( ( in @ ( kpair @ Xx @ Xy )
                  @ ( dpsetconstr @ A @ B
                    @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
               => ( Xphi @ Xx @ Xy ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrERa) ).

thf(dpsetconstrI,definition,
    ( dpsetconstrI
    = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( ( Xphi @ Xx @ Xy )
               => ( in @ ( kpair @ Xx @ Xy )
                  @ ( dpsetconstr @ A @ B
                    @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrI) ).

thf(dpsetconstrSub,definition,
    ( dpsetconstrSub
    = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
          ( subset
          @ ( dpsetconstr @ A @ B
            @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
          @ ( cartprod @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrSub) ).

thf(dsetconstrEL,definition,
    ( dsetconstrEL
    = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
          ( ( in @ Xx
            @ ( dsetconstr @ A
              @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
         => ( in @ Xx @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL) ).

thf(dsetconstrER,definition,
    ( dsetconstrER
    = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
          ( ( in @ Xx
            @ ( dsetconstr @ A
              @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
         => ( Xphi @ Xx ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).

thf(dsetconstrI,definition,
    ( dsetconstrI
    = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ( Xphi @ Xx )
           => ( in @ Xx
              @ ( dsetconstr @ A
                @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).

thf(dsetconstr__Cong,definition,
    ( dsetconstr__Cong
    = ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ! [Xphi: $i > $o,Xpsi: $i > $o] :
              ( ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ! [Xy: $i] :
                      ( ( in @ Xy @ B )
                     => ( ( Xx = Xy )
                       => ( ( Xphi @ Xx )
                        <=> ( Xpsi @ Xy ) ) ) ) )
             => ( ( dsetconstr @ A
                  @ ^ [Xx: $i] : ( Xphi @ Xx ) )
                = ( dsetconstr @ B
                  @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstr__Cong) ).

thf(emptyE1,definition,
    ( emptyE1
    = ( ! [A: $i,Xphi: $i > $o] :
          ( ? [Xx: $i] :
              ( ( in @ Xx @ A )
              & ( Xphi @ Xx ) )
         => ( ( ( dsetconstr @ A
                @ ^ [Xx: $i] : ( Xphi @ Xx ) )
              = emptyset )
           => $false ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyE1) ).

thf(emptyI,definition,
    ( emptyI
    = ( ! [A: $i] :
          ( ! [Xx: $i] :
              ~ ( in @ Xx @ A )
         => ( A = emptyset ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyI) ).

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

thf(emptyinPowerset,definition,
    ( emptyinPowerset
    = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset) ).

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

thf(emptysetAx,definition,
    ( emptysetAx
    = ( ! [Xx: $i] :
          ~ ( in @ Xx @ emptyset ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetAx) ).

thf(emptysetE,definition,
    ( emptysetE
    = ( ! [Xx: $i] :
          ( ( in @ Xx @ emptyset )
         => ! [Xphi: $o] : Xphi ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).

thf(emptyset__Cong,definition,
    ( emptyset__Cong
    = ( emptyset = emptyset ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset__Cong) ).

thf(emptysetimpfalse,definition,
    ( emptysetimpfalse
    = ( ! [Xx: $i] :
          ( ( in @ Xx @ emptyset )
         => $false ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse) ).

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

thf(eqbreln,definition,
    ( eqbreln
    = ( ! [A: $i,B: $i,R: $i] :
          ( ( breln @ A @ B @ R )
         => ! [S: $i] :
              ( ( breln @ A @ B @ S )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ! [Xy: $i] :
                        ( ( in @ Xy @ B )
                       => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
                         => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
               => ( ! [Xx: $i] :
                      ( ( in @ Xx @ A )
                     => ! [Xy: $i] :
                          ( ( in @ Xy @ B )
                         => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
                           => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
                 => ( R = S ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqbreln) ).

thf(eqimpsubset1,definition,
    ( eqimpsubset1
    = ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ( subset @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset1) ).

thf(eqimpsubset2,definition,
    ( eqimpsubset2
    = ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ( subset @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset2) ).

thf(eqinunit,definition,
    ( eqinunit
    = ( ! [Xx: $i,Xy: $i] :
          ( ( Xx = Xy )
         => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit) ).

thf(eta1,definition,
    ( eta1
    = ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ( ( lam @ A @ B
              @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
            = Xf ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eta1) ).

thf(eta2,definition,
    ( eta2
    = ( ! [A: $i,B: $i,Xf: $i] :
          ( ( in @ Xf @ ( funcSet @ A @ B ) )
         => ( ( lam @ A @ B
              @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
            = Xf ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eta2) ).

thf(ex1,definition,
    ( ex1
    = ( ^ [A: $i,Xphi: $i > $o] :
          ( singleton
          @ ( dsetconstr @ A
            @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1) ).

thf(ex1E1,definition,
    ( ex1E1
    = ( ! [A: $i,Xphi: $i > $o] :
          ( ( ex1 @ A
            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
         => ? [Xx: $i] :
              ( ( in @ Xx @ A )
              & ( Xphi @ Xx ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1E1) ).

thf(ex1E2,definition,
    ( ex1E2
    = ( ! [A: $i,Xphi: $i > $o] :
          ( ( ex1 @ A
            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ! [Xy: $i] :
                  ( ( in @ Xy @ A )
                 => ( ( Xphi @ Xx )
                   => ( ( Xphi @ Xy )
                     => ( Xx = Xy ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1E2) ).

thf(ex1I,definition,
    ( ex1I
    = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ( Xphi @ Xx )
           => ( ! [Xy: $i] :
                  ( ( in @ Xy @ A )
                 => ( ( Xphi @ Xy )
                   => ( Xy = Xx ) ) )
             => ( ex1 @ A
                @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I) ).

thf(ex1I2,definition,
    ( ex1I2
    = ( ! [A: $i,Xphi: $i > $o] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ! [Xy: $i] :
                  ( ( in @ Xy @ A )
                 => ( ( Xphi @ Xx )
                   => ( ( Xphi @ Xy )
                     => ( Xx = Xy ) ) ) ) )
         => ( ? [Xx: $i] :
                ( ( in @ Xx @ A )
                & ( Xphi @ Xx ) )
           => ( ex1 @ A
              @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I2) ).

thf(exu,definition,
    ( exu
    = ( ^ [Xphi: $i > $o] :
        ? [Xx: $i] :
          ( ( Xphi @ Xx )
          & ! [Xy: $i] :
              ( ( Xphi @ Xy )
             => ( Xx = Xy ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu) ).

thf(exuE1,definition,
    ( exuE1
    = ( ! [Xphi: $i > $o] :
          ( ( exu
            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
         => ? [Xx: $i] :
              ( ( Xphi @ Xx )
              & ! [Xy: $i] :
                  ( ( Xphi @ Xy )
                 => ( Xx = Xy ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE1) ).

thf(exuE2,definition,
    ( exuE2
    = ( ! [Xphi: $i > $o] :
          ( ( exu
            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
         => ? [Xx: $i] :
            ! [Xy: $i] :
              ( ( Xphi @ Xy )
            <=> ( Xy = Xx ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE2) ).

thf(exuE3e,definition,
    ( exuE3e
    = ( ! [Xphi: $i > $o] :
          ( ( exu
            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
         => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3e) ).

thf(exuE3u,definition,
    ( exuE3u
    = ( ! [Xphi: $i > $o] :
          ( ( exu
            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
         => ! [Xx: $i,Xy: $i] :
              ( ( Xphi @ Xx )
             => ( ( Xphi @ Xy )
               => ( Xx = Xy ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3u) ).

thf(exuEu,definition,
    ( exuEu
    = ( ! [Xphi: $i > $o] :
          ( ( exu
            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
         => ! [Xx: $i,Xy: $i] :
              ( ( Xphi @ Xx )
             => ( ( Xphi @ Xy )
               => ( Xx = Xy ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuEu) ).

thf(exuI1,definition,
    ( exuI1
    = ( ! [Xphi: $i > $o] :
          ( ? [Xx: $i] :
              ( ( Xphi @ Xx )
              & ! [Xy: $i] :
                  ( ( Xphi @ Xy )
                 => ( Xx = Xy ) ) )
         => ( exu
            @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI1) ).

thf(exuI2,definition,
    ( exuI2
    = ( ! [Xphi: $i > $o] :
          ( ? [Xx: $i] :
            ! [Xy: $i] :
              ( ( Xphi @ Xy )
            <=> ( Xy = Xx ) )
         => ( exu
            @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI2) ).

thf(exuI3,definition,
    ( exuI3
    = ( ! [Xphi: $i > $o] :
          ( ? [Xx: $i] : ( Xphi @ Xx )
         => ( ! [Xx: $i,Xy: $i] :
                ( ( Xphi @ Xx )
               => ( ( Xphi @ Xy )
                 => ( Xx = Xy ) ) )
           => ( exu
              @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI3) ).

thf(exu__Cong,definition,
    ( exu__Cong
    = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
          ( ! [Xx: $i,Xy: $i] :
              ( ( Xx = Xy )
             => ( ( Xphi @ Xx )
              <=> ( Xpsi @ Xy ) ) )
         => ( ( exu
              @ ^ [Xx: $i] : ( Xphi @ Xx ) )
          <=> ( exu
              @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu__Cong) ).

thf(foundationAx,definition,
    ( foundationAx
    = ( ! [A: $i] :
          ( ? [Xx: $i] : ( in @ Xx @ A )
         => ? [B: $i] :
              ( ( in @ B @ A )
              & ~ ? [Xx: $i] :
                    ( ( in @ Xx @ B )
                    & ( in @ Xx @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',foundationAx) ).

thf(funcGraphProp1,definition,
    ( funcGraphProp1
    = ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp1) ).

thf(funcGraphProp2,definition,
    ( funcGraphProp2
    = ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ! [Xy: $i] :
                  ( ( in @ Xy @ B )
                 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
                   => ( ( ap @ A @ B @ Xf @ Xx )
                      = Xy ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp2) ).

thf(funcGraphProp3,definition,
    ( funcGraphProp3
    = ( ! [A: $i,B: $i,Xf: $i] :
          ( ( in @ Xf @ ( funcSet @ A @ B ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp3) ).

thf(funcGraphProp4,definition,
    ( funcGraphProp4
    = ( ! [A: $i,B: $i,Xf: $i] :
          ( ( in @ Xf @ ( funcSet @ A @ B ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ! [Xy: $i] :
                  ( ( in @ Xy @ B )
                 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
                   => ( ( ap @ A @ B @ Xf @ Xx )
                      = Xy ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp4) ).

thf(funcImageSingleton,definition,
    ( funcImageSingleton
    = ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( singleton
                @ ( dsetconstr @ B
                  @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcImageSingleton) ).

thf(funcext,definition,
    ( funcext
    = ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ! [Xg: $i] :
              ( ( func @ A @ B @ Xg )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ( ( ap @ A @ B @ Xf @ Xx )
                      = ( ap @ A @ B @ Xg @ Xx ) ) )
               => ( Xf = Xg ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcext) ).

thf(funcext2,definition,
    ( funcext2
    = ( ! [A: $i,B: $i,Xf: $i] :
          ( ( in @ Xf @ ( funcSet @ A @ B ) )
         => ! [Xg: $i] :
              ( ( in @ Xg @ ( funcSet @ A @ B ) )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ( ( ap @ A @ B @ Xf @ Xx )
                      = ( ap @ A @ B @ Xg @ Xx ) ) )
               => ( Xf = Xg ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcext2) ).

thf(funcextLem,definition,
    ( funcextLem
    = ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ! [Xg: $i] :
              ( ( func @ A @ B @ Xg )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ( ( ap @ A @ B @ Xf @ Xx )
                      = ( ap @ A @ B @ Xg @ Xx ) ) )
               => ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ! [Xy: $i] :
                        ( ( in @ Xy @ B )
                       => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
                         => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcextLem) ).

thf(funcinfuncset,definition,
    ( funcinfuncset
    = ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcinfuncset) ).

thf(ifSingleton,definition,
    ( ifSingleton
    = ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ A )
             => ( singleton
                @ ( dsetconstr @ A
                  @ ^ [Xz: $i] :
                      ( ( Xphi
                        & ( Xz = Xx ) )
                      | ( ~ Xphi
                        & ( Xz = Xy ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifSingleton) ).

thf(iffalse,definition,
    ( iffalse
    = ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ A )
             => ( ~ Xphi
               => ( ( if @ A @ Xphi @ Xx @ Xy )
                  = Xy ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iffalse) ).

thf(iffalseProp1,definition,
    ( iffalseProp1
    = ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ A )
             => ( ~ Xphi
               => ( in @ Xy
                  @ ( dsetconstr @ A
                    @ ^ [Xz: $i] :
                        ( ( Xphi
                          & ( Xz = Xx ) )
                        | ( ~ Xphi
                          & ( Xz = Xy ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iffalseProp1) ).

thf(iffalseProp2,definition,
    ( iffalseProp2
    = ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ A )
             => ( ~ Xphi
               => ( ( dsetconstr @ A
                    @ ^ [Xz: $i] :
                        ( ( Xphi
                          & ( Xz = Xx ) )
                        | ( ~ Xphi
                          & ( Xz = Xy ) ) ) )
                  = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iffalseProp2) ).

thf(ifp,definition,
    ( ifp
    = ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ A )
             => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifp) ).

thf(iftrue,definition,
    ( iftrue
    = ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ A )
             => ( Xphi
               => ( ( if @ A @ Xphi @ Xx @ Xy )
                  = Xx ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrue) ).

thf(iftrueProp1,definition,
    ( iftrueProp1
    = ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ A )
             => ( Xphi
               => ( in @ Xx
                  @ ( dsetconstr @ A
                    @ ^ [Xz: $i] :
                        ( ( Xphi
                          & ( Xz = Xx ) )
                        | ( ~ Xphi
                          & ( Xz = Xy ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrueProp1) ).

thf(iftrueProp2,definition,
    ( iftrueProp2
    = ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ A )
             => ( Xphi
               => ( ( dsetconstr @ A
                    @ ^ [Xz: $i] :
                        ( ( Xphi
                          & ( Xz = Xx ) )
                        | ( ~ Xphi
                          & ( Xz = Xy ) ) ) )
                  = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrueProp2) ).

thf(iftrueorfalse,definition,
    ( iftrueorfalse
    = ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ A )
             => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrueorfalse) ).

thf(inComplementUnionImpNotIn1,definition,
    ( inComplementUnionImpNotIn1
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
                   => ~ ( in @ Xx @ X ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inComplementUnionImpNotIn1) ).

thf(inCongP,definition,
    ( inCongP
    = ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ! [Xx: $i,Xy: $i] :
              ( ( Xx = Xy )
             => ( ( in @ Xx @ A )
               => ( in @ Xy @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inCongP) ).

thf(inIntersectImpInIntersectUnions,definition,
    ( inIntersectImpInIntersectUnions
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Z: $i] :
                  ( ( in @ Z @ ( powerset @ A ) )
                 => ! [Xx: $i] :
                      ( ( in @ Xx @ A )
                     => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
                       => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inIntersectImpInIntersectUnions) ).

thf(inIntersectImpInUnion,definition,
    ( inIntersectImpInUnion
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Z: $i] :
                  ( ( in @ Z @ ( powerset @ A ) )
                 => ! [Xx: $i] :
                      ( ( in @ Xx @ A )
                     => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
                       => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inIntersectImpInUnion) ).

thf(inIntersectImpInUnion2,definition,
    ( inIntersectImpInUnion2
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Z: $i] :
                  ( ( in @ Z @ ( powerset @ A ) )
                 => ! [Xx: $i] :
                      ( ( in @ Xx @ A )
                     => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
                       => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inIntersectImpInUnion2) ).

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

thf(in__Cong,definition,
    ( in__Cong
    = ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ! [Xx: $i,Xy: $i] :
              ( ( Xx = Xy )
             => ( ( in @ Xx @ A )
              <=> ( in @ Xy @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in__Cong) ).

thf(infuncsetfunc,definition,
    ( infuncsetfunc
    = ( ! [A: $i,B: $i,Xf: $i] :
          ( ( in @ Xf @ ( funcSet @ A @ B ) )
         => ( func @ A @ B @ Xf ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infuncsetfunc) ).

thf(intersectInPowersetIntersectUnions,definition,
    ( intersectInPowersetIntersectUnions
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Z: $i] :
                  ( ( in @ Z @ ( powerset @ A ) )
                 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersectInPowersetIntersectUnions) ).

thf(kfstpairEq,definition,
    ( kfstpairEq
    = ( ! [Xx: $i,Xy: $i] :
          ( ( kfst @ ( kpair @ Xx @ Xy ) )
          = Xx ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstpairEq) ).

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

thf(kpairiskpair,definition,
    ( kpairiskpair
    = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairiskpair) ).

thf(kpairp,definition,
    ( kpairp
    = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairp) ).

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

thf(ksndpairEq,definition,
    ( ksndpairEq
    = ( ! [Xx: $i,Xy: $i] :
          ( ( ksnd @ ( kpair @ Xx @ Xy ) )
          = Xy ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ksndpairEq) ).

thf(ksndsingleton,definition,
    ( ksndsingleton
    = ( ! [Xu: $i] :
          ( ( iskpair @ Xu )
         => ( singleton
            @ ( dsetconstr @ ( setunion @ Xu )
              @ ^ [Xx: $i] :
                  ( Xu
                  = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ksndsingleton) ).

thf(lam2lamEq,definition,
    ( lam2lamEq
    = ( ! [A: $i,B: $i,Xf: $i > $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( Xf @ Xx ) @ B ) )
         => ( ( lam @ A @ B
              @ ^ [Xx: $i] : ( Xf @ Xx ) )
            = ( lam @ A @ B
              @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lam2lamEq) ).

thf(lam2p,definition,
    ( lam2p
    = ( ! [A: $i,B: $i,Xf: $i > $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( Xf @ Xx ) @ B ) )
         => ( in
            @ ( lam @ A @ B
              @ ^ [Xx: $i] : ( Xf @ Xx ) )
            @ ( funcSet @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lam2p) ).

thf(lamProp,definition,
    ( lamProp
    = ( ! [A: $i,B: $i,Xf: $i > $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( Xf @ Xx ) @ B ) )
         => ( func @ A @ B
            @ ( dpsetconstr @ A @ B
              @ ^ [Xx: $i,Xy: $i] :
                  ( ( Xf @ Xx )
                  = Xy ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamProp) ).

thf(lamp,definition,
    ( lamp
    = ( ! [A: $i,B: $i,Xf: $i > $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( Xf @ Xx ) @ B ) )
         => ( func @ A @ B
            @ ( lam @ A @ B
              @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamp) ).

thf(noeltsimpempty,definition,
    ( noeltsimpempty
    = ( ! [A: $i] :
          ( ! [Xx: $i] :
              ~ ( in @ Xx @ A )
         => ( A = emptyset ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty) ).

thf(nonempty,definition,
    ( nonempty
    = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty) ).

thf(nonemptyE1,definition,
    ( nonemptyE1
    = ( ! [A: $i] :
          ( ( nonempty @ A )
         => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyE1) ).

thf(nonemptyI,definition,
    ( nonemptyI
    = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ( Xphi @ Xx )
           => ( nonempty
              @ ( dsetconstr @ A
                @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI) ).

thf(nonemptyI1,definition,
    ( nonemptyI1
    = ( ! [A: $i] :
          ( ? [Xx: $i] : ( in @ Xx @ A )
         => ( nonempty @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1) ).

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

thf(notdallE,definition,
    ( notdallE
    = ( ! [A: $i,Xphi: $i > $o] :
          ( ~ ! [Xx: $i] :
                ( ( in @ Xx @ A )
               => ( Xphi @ Xx ) )
         => ? [Xx: $i] :
              ( ( in @ Xx @ A )
              & ~ ( Xphi @ Xx ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdallE) ).

thf(notdexE,definition,
    ( notdexE
    = ( ! [A: $i,Xphi: $i > $o] :
          ( ~ ? [Xx: $i] :
                ( ( in @ Xx @ A )
                & ( Xphi @ Xx ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ~ ( Xphi @ Xx ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdexE) ).

thf(notequalI1,definition,
    ( notequalI1
    = ( ! [A: $i,B: $i] :
          ( ~ ( subset @ A @ B )
         => ( A != B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI1) ).

thf(notequalI2,definition,
    ( notequalI2
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ~ ( in @ Xx @ B )
           => ( A != B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI2) ).

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

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

thf(notsubsetI,definition,
    ( notsubsetI
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ~ ( in @ Xx @ B )
           => ~ ( subset @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notsubsetI) ).

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

thf(omegaIndAx,definition,
    ( omegaIndAx
    = ( ! [A: $i] :
          ( ( ( in @ emptyset @ A )
            & ! [Xx: $i] :
                ( ( ( in @ Xx @ omega )
                  & ( in @ Xx @ A ) )
               => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ omega )
             => ( in @ Xx @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaIndAx) ).

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

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

thf(powersetAx,definition,
    ( powersetAx
    = ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
        <=> ! [Xx: $i] :
              ( ( in @ Xx @ B )
             => ( in @ Xx @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetAx) ).

thf(powersetE,definition,
    ( powersetE
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ( ( in @ Xx @ B )
           => ( in @ Xx @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE) ).

thf(powersetE1,definition,
    ( powersetE1
    = ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ( subset @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE1) ).

thf(powersetI,definition,
    ( powersetI
    = ( ! [A: $i,B: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ B )
             => ( in @ Xx @ A ) )
         => ( in @ B @ ( powerset @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI) ).

thf(powersetI1,definition,
    ( powersetI1
    = ( ! [A: $i,B: $i] :
          ( ( subset @ B @ A )
         => ( in @ B @ ( powerset @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI1) ).

thf(powersetTE1,definition,
    ( powersetTE1
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ( in @ X @ ( powerset @ Y ) )
                   => ( ( in @ Xx @ X )
                     => ( in @ Xx @ Y ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetTE1) ).

thf(powersetTI1,definition,
    ( powersetTI1
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ( ( in @ Xx @ X )
                     => ( in @ Xx @ Y ) ) )
               => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetTI1) ).

thf(powersetT_lem,definition,
    ( powersetT_lem
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetT_lem) ).

thf(powerset__Cong,definition,
    ( powerset__Cong
    = ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ( ( powerset @ A )
            = ( powerset @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset__Cong) ).

thf(powersetsubset,definition,
    ( powersetsubset
    = ( ! [A: $i,B: $i] :
          ( ( subset @ A @ B )
         => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetsubset) ).

thf(prop2set2propI,definition,
    ( prop2set2propI
    = ( ! [Xphi: $o] :
          ( Xphi
         => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2set2propI) ).

thf(prop2setE,definition,
    ( prop2setE
    = ( ! [Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ ( prop2set @ Xphi ) )
         => Xphi ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE) ).

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

thf(quantDeMorgan1,definition,
    ( quantDeMorgan1
    = ( ! [A: $i,Xphi: $i > $o] :
          ( ~ ! [Xx: $i] :
                ( ( in @ Xx @ A )
               => ( Xphi @ Xx ) )
         => ? [Xx: $i] :
              ( ( in @ Xx @ A )
              & ~ ( Xphi @ Xx ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan1) ).

thf(quantDeMorgan2,definition,
    ( quantDeMorgan2
    = ( ! [A: $i,Xphi: $i > $o] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ~ ( Xphi @ Xx ) )
         => ~ ? [Xx: $i] :
                ( ( in @ Xx @ A )
                & ( Xphi @ Xx ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan2) ).

thf(quantDeMorgan3,definition,
    ( quantDeMorgan3
    = ( ! [A: $i,Xphi: $i > $o] :
          ( ~ ? [Xx: $i] :
                ( ( in @ Xx @ A )
                & ( Xphi @ Xx ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ~ ( Xphi @ Xx ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan3) ).

thf(quantDeMorgan4,definition,
    ( quantDeMorgan4
    = ( ! [A: $i,Xphi: $i > $o] :
          ( ? [Xx: $i] :
              ( ( in @ Xx @ A )
              & ~ ( Xphi @ Xx ) )
         => ~ ! [Xx: $i] :
                ( ( in @ Xx @ A )
               => ( Xphi @ Xx ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan4) ).

thf(replAx,definition,
    ( replAx
    = ( ! [Xphi: $i > $i > $o,A: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( exu
                @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
         => ? [B: $i] :
            ! [Xx: $i] :
              ( ( in @ Xx @ B )
            <=> ? [Xy: $i] :
                  ( ( in @ Xy @ A )
                  & ( Xphi @ Xy @ Xx ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replAx) ).

thf(secondinupair,definition,
    ( secondinupair
    = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',secondinupair) ).

thf(sepInPowerset,definition,
    ( sepInPowerset
    = ( ! [A: $i,Xphi: $i > $o] :
          ( in
          @ ( dsetconstr @ A
            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
          @ ( powerset @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepInPowerset) ).

thf(sepSubset,definition,
    ( sepSubset
    = ( ! [A: $i,Xphi: $i > $o] :
          ( subset
          @ ( dsetconstr @ A
            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
          @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepSubset) ).

thf(setOfPairsIsBReln,definition,
    ( setOfPairsIsBReln
    = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
          ( breln @ A @ B
          @ ( dpsetconstr @ A @ B
            @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setOfPairsIsBReln) ).

thf(setadjoinAx,definition,
    ( setadjoinAx
    = ( ! [Xx: $i,A: $i,Xy: $i] :
          ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
        <=> ( ( Xy = Xx )
            | ( in @ Xy @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinAx) ).

thf(setadjoinE,definition,
    ( setadjoinE
    = ( ! [Xx: $i,A: $i,Xy: $i] :
          ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
         => ! [Xphi: $o] :
              ( ( ( Xy = Xx )
               => Xphi )
             => ( ( ( in @ Xy @ A )
                 => Xphi )
               => Xphi ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinE) ).

thf(setadjoinIL,definition,
    ( setadjoinIL
    = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).

thf(setadjoinIR,definition,
    ( setadjoinIR
    = ( ! [Xx: $i,A: $i,Xy: $i] :
          ( ( in @ Xy @ A )
         => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIR) ).

thf(setadjoinOr,definition,
    ( setadjoinOr
    = ( ! [Xx: $i,A: $i,Xy: $i] :
          ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
         => ( ( Xy = Xx )
            | ( in @ Xy @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinOr) ).

thf(setadjoinSub,definition,
    ( setadjoinSub
    = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub) ).

thf(setadjoinSub2,definition,
    ( setadjoinSub2
    = ( ! [A: $i,Xx: $i,B: $i] :
          ( ( subset @ A @ B )
         => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub2) ).

thf(setadjoin__Cong,definition,
    ( setadjoin__Cong
    = ( ! [Xx: $i,Xy: $i] :
          ( ( Xx = Xy )
         => ! [Xz: $i,Xu: $i] :
              ( ( Xz = Xu )
             => ( ( setadjoin @ Xx @ Xz )
                = ( setadjoin @ Xy @ Xu ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoin__Cong) ).

thf(setbeta,definition,
    ( setbeta
    = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ( in @ Xx
              @ ( dsetconstr @ A
                @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
          <=> ( Xphi @ Xx ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setbeta) ).

thf(setext,definition,
    ( setext
    = ( ! [A: $i,B: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ Xx @ B ) )
         => ( ! [Xx: $i] :
                ( ( in @ Xx @ B )
               => ( in @ Xx @ A ) )
           => ( A = B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setext) ).

thf(setextAx,definition,
    ( setextAx
    = ( ! [A: $i,B: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
            <=> ( in @ Xx @ B ) )
         => ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextAx) ).

thf(setextT,definition,
    ( setextT
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ( ( in @ Xx @ X )
                     => ( in @ Xx @ Y ) ) )
               => ( ! [Xx: $i] :
                      ( ( in @ Xx @ A )
                     => ( ( in @ Xx @ Y )
                       => ( in @ Xx @ X ) ) )
                 => ( X = Y ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextT) ).

thf(setextsub,definition,
    ( setextsub
    = ( ! [A: $i,B: $i] :
          ( ( subset @ A @ B )
         => ( ( subset @ B @ A )
           => ( A = B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextsub) ).

thf(setminusEL,definition,
    ( setminusEL
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ ( setminus @ A @ B ) )
         => ( in @ Xx @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusEL) ).

thf(setminusELneg,definition,
    ( setminusELneg
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
         => ( ~ ( in @ Xx @ B )
           => ~ ( in @ Xx @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusELneg) ).

thf(setminusER,definition,
    ( setminusER
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ ( setminus @ A @ B ) )
         => ~ ( in @ Xx @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER) ).

thf(setminusERneg,definition,
    ( setminusERneg
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
         => ( ( in @ Xx @ A )
           => ( in @ Xx @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusERneg) ).

thf(setminusI,definition,
    ( setminusI
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ~ ( in @ Xx @ B )
           => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI) ).

thf(setminusILneg,definition,
    ( setminusILneg
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
         => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusILneg) ).

thf(setminusIRneg,definition,
    ( setminusIRneg
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ B )
         => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusIRneg) ).

thf(setminusLsub,definition,
    ( setminusLsub
    = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusLsub) ).

thf(setminusSubset1,definition,
    ( setminusSubset1
    = ( ! [A: $i,B: $i] :
          ( ( ( setminus @ A @ B )
            = emptyset )
         => ( subset @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset1) ).

thf(setminusSubset2,definition,
    ( setminusSubset2
    = ( ! [A: $i,B: $i] :
          ( ( subset @ A @ B )
         => ( ( setminus @ A @ B )
            = emptyset ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset2) ).

thf(setminusT_lem,definition,
    ( setminusT_lem
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusT_lem) ).

thf(setoftrueEq,definition,
    ( setoftrueEq
    = ( ! [A: $i] :
          ( ( dsetconstr @ A
            @ ^ [Xx: $i] : $true )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setoftrueEq) ).

thf(setukpairIL,definition,
    ( setukpairIL
    = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIL) ).

thf(setukpairIR,definition,
    ( setukpairIR
    = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIR) ).

thf(setukpairinjL,definition,
    ( setukpairinjL
    = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
          ( ( ( kpair @ Xx @ Xy )
            = ( kpair @ Xz @ Xu ) )
         => ( Xx = Xz ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL) ).

thf(setukpairinjL1,definition,
    ( setukpairinjL1
    = ( ! [Xx: $i,Xy: $i,Xz: $i] :
          ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
         => ( Xx = Xz ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL1) ).

thf(setukpairinjL2,definition,
    ( setukpairinjL2
    = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
          ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
         => ( Xx = Xz ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL2) ).

thf(setukpairinjR,definition,
    ( setukpairinjR
    = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
          ( ( ( kpair @ Xx @ Xy )
            = ( kpair @ Xz @ Xu ) )
         => ( Xy = Xu ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR) ).

thf(setukpairinjR1,definition,
    ( setukpairinjR1
    = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
          ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
         => ( ( Xz = Xu )
           => ( Xy = Xu ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR1) ).

thf(setukpairinjR11,definition,
    ( setukpairinjR11
    = ( ! [Xx: $i,Xy: $i] :
          ( ( Xx = Xy )
         => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
            = ( setadjoin @ Xx @ emptyset ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR11) ).

thf(setukpairinjR12,definition,
    ( setukpairinjR12
    = ( ! [Xx: $i,Xy: $i] :
          ( ( Xx = Xy )
         => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR12) ).

thf(setukpairinjR2,definition,
    ( setukpairinjR2
    = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
          ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
         => ( Xy = Xu ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR2) ).

thf(setunionAx,definition,
    ( setunionAx
    = ( ! [A: $i,Xx: $i] :
          ( ( in @ Xx @ ( setunion @ A ) )
        <=> ? [B: $i] :
              ( ( in @ Xx @ B )
              & ( in @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionAx) ).

thf(setunionE,definition,
    ( setunionE
    = ( ! [A: $i,Xx: $i] :
          ( ( in @ Xx @ ( setunion @ A ) )
         => ! [Xphi: $o] :
              ( ! [B: $i] :
                  ( ( in @ Xx @ B )
                 => ( ( in @ B @ A )
                   => Xphi ) )
             => Xphi ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE) ).

thf(setunionE2,definition,
    ( setunionE2
    = ( ! [A: $i,Xx: $i] :
          ( ( in @ Xx @ ( setunion @ A ) )
         => ? [X: $i] :
              ( ( in @ X @ A )
              & ( in @ Xx @ X ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE2) ).

thf(setunionI,definition,
    ( setunionI
    = ( ! [A: $i,Xx: $i,B: $i] :
          ( ( in @ Xx @ B )
         => ( ( in @ B @ A )
           => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionI) ).

thf(setunion__Cong,definition,
    ( setunion__Cong
    = ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ( ( setunion @ A )
            = ( setunion @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunion__Cong) ).

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

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

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

thf(singletoninpowerset,definition,
    ( singletoninpowerset
    = ( ! [A: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowerset) ).

thf(singletoninpowunion,definition,
    ( singletoninpowunion
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowunion) ).

thf(singletonprop,definition,
    ( singletonprop
    = ( ! [A: $i,Xphi: $i > $o] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ! [Xy: $i] :
                  ( ( in @ Xy @ A )
                 => ( ( Xphi @ Xx )
                   => ( ( Xphi @ Xy )
                     => ( Xx = Xy ) ) ) ) )
         => ( ? [Xx: $i] :
                ( ( in @ Xx @ A )
                & ( Xphi @ Xx ) )
           => ( singleton
              @ ( dsetconstr @ A
                @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonprop) ).

thf(singletonsswitch,definition,
    ( singletonsswitch
    = ( ! [Xx: $i,Xy: $i] :
          ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
         => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsswitch) ).

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

thf(singletonsuniq,definition,
    ( singletonsuniq
    = ( ! [Xx: $i,Xy: $i] :
          ( ( ( setadjoin @ Xx @ emptyset )
            = ( setadjoin @ Xy @ emptyset ) )
         => ( Xx = Xy ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsuniq) ).

thf(subPowSU,definition,
    ( subPowSU
    = ( ! [A: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subPowSU) ).

thf(subbreln,definition,
    ( subbreln
    = ( ! [A: $i,B: $i,R: $i] :
          ( ( breln @ A @ B @ R )
         => ! [S: $i] :
              ( ( breln @ A @ B @ S )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ! [Xy: $i] :
                        ( ( in @ Xy @ B )
                       => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
                         => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
               => ( subset @ R @ S ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subbreln) ).

thf(subset2powerset,definition,
    ( subset2powerset
    = ( ! [A: $i,B: $i] :
          ( ( subset @ A @ B )
         => ( in @ A @ ( powerset @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset2powerset) ).

thf(subsetE,definition,
    ( subsetE
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( subset @ A @ B )
         => ( ( in @ Xx @ A )
           => ( in @ Xx @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE) ).

thf(subsetE2,definition,
    ( subsetE2
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( subset @ A @ B )
         => ( ~ ( in @ Xx @ B )
           => ~ ( in @ Xx @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE2) ).

thf(subsetI1,definition,
    ( subsetI1
    = ( ! [A: $i,B: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ Xx @ B ) )
         => ( subset @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1) ).

thf(subsetI2,definition,
    ( subsetI2
    = ( ! [A: $i,B: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ Xx @ B ) )
         => ( subset @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2) ).

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

thf(subsetTI,definition,
    ( subsetTI
    = ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ( ( in @ Xx @ X )
                     => ( in @ Xx @ Y ) ) )
               => ( subset @ X @ Y ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTI) ).

thf(subsetTrans,definition,
    ( subsetTrans
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( subset @ A @ B )
         => ( ( subset @ B @ C )
           => ( subset @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTrans) ).

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

thf(symdiffE,definition,
    ( symdiffE
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ ( symdiff @ A @ B ) )
         => ! [Xphi: $o] :
              ( ( ( in @ Xx @ A )
               => ( ~ ( in @ Xx @ B )
                 => Xphi ) )
             => ( ( ~ ( in @ Xx @ A )
                 => ( ( in @ Xx @ B )
                   => Xphi ) )
               => Xphi ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffE) ).

thf(symdiffI1,definition,
    ( symdiffI1
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ~ ( in @ Xx @ B )
           => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI1) ).

thf(symdiffI2,definition,
    ( symdiffI2
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
         => ( ( in @ Xx @ B )
           => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI2) ).

thf(symdiffIneg1,definition,
    ( symdiffIneg1
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ( in @ Xx @ B )
           => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg1) ).

thf(symdiffIneg2,definition,
    ( symdiffIneg2
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
         => ( ~ ( in @ Xx @ B )
           => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg2) ).

thf(theeq,definition,
    ( theeq
    = ( ! [X: $i] :
          ( ( singleton @ X )
         => ! [Xx: $i] :
              ( ( in @ Xx @ X )
             => ( ( setunion @ X )
                = Xx ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theeq) ).

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

thf(ubforcartprodlem1,definition,
    ( ubforcartprodlem1
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem1) ).

thf(ubforcartprodlem2,definition,
    ( ubforcartprodlem2
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem2) ).

thf(ubforcartprodlem3,definition,
    ( ubforcartprodlem3
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem3) ).

thf(uniqinunit,definition,
    ( uniqinunit
    = ( ! [Xx: $i,Xy: $i] :
          ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
         => ( Xx = Xy ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).

thf(upairequniteq,definition,
    ( upairequniteq
    = ( ! [Xx: $i,Xy: $i,Xz: $i] :
          ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
            = ( setadjoin @ Xz @ emptyset ) )
         => ( Xx = Xy ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairequniteq) ).

thf(upairinpowunion,definition,
    ( upairinpowunion
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairinpowunion) ).

thf(upairset2E,definition,
    ( upairset2E
    = ( ! [Xx: $i,Xy: $i,Xz: $i] :
          ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
         => ( ( Xz = Xx )
            | ( Xz = Xy ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2E) ).

thf(upairset2IR,definition,
    ( upairset2IR
    = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2IR) ).

thf(upairsetE,definition,
    ( upairsetE
    = ( ! [Xx: $i,Xy: $i,Xz: $i] :
          ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
         => ( ( Xz = Xx )
            | ( Xz = Xy ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetE) ).

thf(upairsetIL,definition,
    ( upairsetIL
    = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIL) ).

thf(upairsetIR,definition,
    ( upairsetIR
    = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR) ).

thf(upairsubunion,definition,
    ( upairsubunion
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsubunion) ).

thf(vacuousDall,definition,
    ( vacuousDall
    = ( ! [Xphi: $i > $o,Xx: $i] :
          ( ( in @ Xx @ emptyset )
         => ( Xphi @ Xx ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vacuousDall) ).

thf(wellorderingAx,definition,
    ( wellorderingAx
    = ( ! [A: $i] :
        ? [B: $i] :
          ( ! [C: $i] :
              ( ( in @ C @ B )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ C )
                 => ( in @ Xx @ A ) ) )
          & ! [Xx: $i,Xy: $i] :
              ( ( ( in @ Xx @ A )
                & ( in @ Xy @ A ) )
             => ( ! [C: $i] :
                    ( ( in @ C @ B )
                   => ( ( in @ Xx @ C )
                    <=> ( in @ Xy @ C ) ) )
               => ( Xx = Xy ) ) )
          & ! [C: $i,D: $i] :
              ( ( ( in @ C @ B )
                & ( in @ D @ B ) )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ C )
                   => ( in @ Xx @ D ) )
                | ! [Xx: $i] :
                    ( ( in @ Xx @ D )
                   => ( in @ Xx @ C ) ) ) )
          & ! [C: $i] :
              ( ( ! [Xx: $i] :
                    ( ( in @ Xx @ C )
                   => ( in @ Xx @ A ) )
                & ? [Xx: $i] : ( in @ Xx @ C ) )
             => ? [D: $i,Xx: $i] :
                  ( ( in @ D @ B )
                  & ( in @ Xx @ C )
                  & ~ ? [Xy: $i] :
                        ( ( in @ Xy @ D )
                        & ( in @ Xy @ C ) )
                  & ! [E: $i] :
                      ( ( in @ E @ B )
                     => ( ! [Xy: $i] :
                            ( ( in @ Xy @ E )
                           => ( in @ Xy @ D ) )
                        | ( in @ Xx @ E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellorderingAx) ).

thf(1,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
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [Y: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ Y @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inComplementUnionImpInComplement1) ).

thf(2,negated_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
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [Y: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ Y @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ! [A: $i,B: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
            <=> ( in @ Xx @ B ) )
         => ( A = B ) )
     => ( ! [Xx: $i] :
            ~ ( in @ Xx @ emptyset )
       => ( ! [Xx: $i,A: $i,Xy: $i] :
              ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
            <=> ( ( Xy = Xx )
                | ( in @ Xy @ A ) ) )
         => ( ! [A: $i,B: $i] :
                ( ( in @ B @ ( powerset @ A ) )
              <=> ! [Xx: $i] :
                    ( ( in @ Xx @ B )
                   => ( in @ Xx @ A ) ) )
           => ( ! [A: $i,Xx: $i] :
                  ( ( in @ Xx @ ( setunion @ A ) )
                <=> ? [B: $i] :
                      ( ( in @ Xx @ B )
                      & ( in @ B @ A ) ) )
             => ( ( in @ emptyset @ omega )
               => ( ! [Xx: $i] :
                      ( ( in @ Xx @ omega )
                     => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) )
                 => ( ! [A: $i] :
                        ( ( ( in @ emptyset @ A )
                          & ! [Xx: $i] :
                              ( ( ( in @ Xx @ omega )
                                & ( in @ Xx @ A ) )
                             => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
                       => ! [Xx: $i] :
                            ( ( in @ Xx @ omega )
                           => ( in @ Xx @ A ) ) )
                   => ( ! [SY21: $i > $i > $o,SY22: $i] :
                          ( ! [SY23: $i] :
                              ( ( in @ SY23 @ SY22 )
                             => ? [SY25: $i] :
                                  ( ( SY21 @ SY23 @ SY25 )
                                  & ! [SY26: $i] :
                                      ( ( SY21 @ SY23 @ SY26 )
                                     => ( SY25 = SY26 ) ) ) )
                         => ? [B: $i] :
                            ! [Xx: $i] :
                              ( ( in @ Xx @ B )
                            <=> ? [Xy: $i] :
                                  ( ( in @ Xy @ SY22 )
                                  & ( SY21 @ Xy @ Xx ) ) ) )
                     => ( ! [A: $i] :
                            ( ? [Xx: $i] : ( in @ Xx @ A )
                           => ? [B: $i] :
                                ( ( in @ B @ A )
                                & ~ ? [Xx: $i] :
                                      ( ( in @ Xx @ B )
                                      & ( in @ Xx @ A ) ) ) )
                       => ( ! [A: $i] :
                            ? [B: $i] :
                              ( ! [C: $i] :
                                  ( ( in @ C @ B )
                                 => ! [Xx: $i] :
                                      ( ( in @ Xx @ C )
                                     => ( in @ Xx @ A ) ) )
                              & ! [Xx: $i,Xy: $i] :
                                  ( ( ( in @ Xx @ A )
                                    & ( in @ Xy @ A ) )
                                 => ( ! [C: $i] :
                                        ( ( in @ C @ B )
                                       => ( ( in @ Xx @ C )
                                        <=> ( in @ Xy @ C ) ) )
                                   => ( Xx = Xy ) ) )
                              & ! [C: $i,D: $i] :
                                  ( ( ( in @ C @ B )
                                    & ( in @ D @ B ) )
                                 => ( ! [Xx: $i] :
                                        ( ( in @ Xx @ C )
                                       => ( in @ Xx @ D ) )
                                    | ! [Xx: $i] :
                                        ( ( in @ Xx @ D )
                                       => ( in @ Xx @ C ) ) ) )
                              & ! [C: $i] :
                                  ( ( ! [Xx: $i] :
                                        ( ( in @ Xx @ C )
                                       => ( in @ Xx @ A ) )
                                    & ? [Xx: $i] : ( in @ Xx @ C ) )
                                 => ? [D: $i,Xx: $i] :
                                      ( ( in @ D @ B )
                                      & ( in @ Xx @ C )
                                      & ~ ? [Xy: $i] :
                                            ( ( in @ Xy @ D )
                                            & ( in @ Xy @ C ) )
                                      & ! [E: $i] :
                                          ( ( in @ E @ B )
                                         => ( ! [Xy: $i] :
                                                ( ( in @ Xy @ E )
                                               => ( in @ Xy @ D ) )
                                            | ( in @ Xx @ E ) ) ) ) ) )
                         => ( ! [SY53: $i > $o] :
                                ( ? [SY55: $i] :
                                    ( ( SY53 @ SY55 )
                                    & ! [SY56: $i] :
                                        ( ( SY53 @ SY56 )
                                       => ( SY55 = SY56 ) ) )
                               => ( SY53
                                  @ ( descr
                                    @ ^ [Xx: $i] : ( SY53 @ Xx ) ) ) )
                           => ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
                                  ( ( in @ Xx @ A )
                                 => ( ( Xphi @ Xx )
                                   => ( in @ Xx
                                      @ ( dsetconstr @ A
                                        @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) )
                             => ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
                                    ( ( in @ Xx
                                      @ ( dsetconstr @ A
                                        @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
                                   => ( in @ Xx @ A ) )
                               => ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
                                      ( ( in @ Xx
                                        @ ( dsetconstr @ A
                                          @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
                                     => ( Xphi @ Xx ) )
                                 => ( ! [SY70: $i > $o] :
                                        ( ? [SY72: $i] :
                                            ( ( SY70 @ SY72 )
                                            & ! [SY73: $i] :
                                                ( ( SY70 @ SY73 )
                                               => ( SY72 = SY73 ) ) )
                                       => ? [Xx: $i] :
                                            ( ( SY70 @ Xx )
                                            & ! [Xy: $i] :
                                                ( ( SY70 @ Xy )
                                               => ( Xx = Xy ) ) ) )
                                   => ( ! [Xphi: $o,Xx: $i] :
                                          ( ( in @ Xx @ ( prop2set @ Xphi ) )
                                         => Xphi )
                                     => ( ! [Xx: $i] :
                                            ( ( in @ Xx @ emptyset )
                                           => ! [Xphi: $o] : Xphi )
                                       => ( ! [Xx: $i] :
                                              ( ( in @ Xx @ emptyset )
                                             => $false )
                                         => ( ! [Xx: $i] :
                                                ~ ( in @ Xx @ emptyset )
                                           => ( ! [SY82: $i > $o] :
                                                  ( ? [SY84: $i] :
                                                      ( ( SY82 @ SY84 )
                                                      & ! [SY85: $i] :
                                                          ( ( SY82 @ SY85 )
                                                         => ( SY84 = SY85 ) ) )
                                                 => ? [Xx: $i] : ( SY82 @ Xx ) )
                                             => ( ! [A: $i,B: $i] :
                                                    ( ! [Xx: $i] :
                                                        ( ( in @ Xx @ A )
                                                       => ( in @ Xx @ B ) )
                                                   => ( ! [Xx: $i] :
                                                          ( ( in @ Xx @ B )
                                                         => ( in @ Xx @ A ) )
                                                     => ( A = B ) ) )
                                               => ( ! [A: $i] :
                                                      ( ! [Xx: $i] :
                                                          ~ ( in @ Xx @ A )
                                                     => ( A = emptyset ) )
                                                 => ( ! [A: $i] :
                                                        ( ! [Xx: $i] :
                                                            ~ ( in @ Xx @ A )
                                                       => ( A = emptyset ) )
                                                   => ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
                                                          ( ( in @ Xx @ A )
                                                         => ( ( in @ Xx
                                                              @ ( dsetconstr @ A
                                                                @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
                                                          <=> ( Xphi @ Xx ) ) )
                                                     => ( ! [SY99: $i] :
                                                            ( ( SY99 != emptyset )
                                                           => ? [Xx: $i] : ( in @ Xx @ SY99 ) )
                                                       => ( ! [SY101: $i,SY102: $i > $o,SY103: $i] :
                                                              ( ( in @ SY103 @ SY101 )
                                                             => ( ( SY102 @ SY103 )
                                                               => ( ( dsetconstr @ SY101
                                                                    @ ^ [Xy: $i] : ( SY102 @ Xy ) )
                                                                 != emptyset ) ) )
                                                         => ( ! [SY105: $i] :
                                                                ( ? [Xx: $i] : ( in @ Xx @ SY105 )
                                                               => ( SY105 != emptyset ) )
                                                           => ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) )
                                                             => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                               => ( ! [Xx: $i,A: $i,Xy: $i] :
                                                                      ( ( in @ Xy @ A )
                                                                     => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) )
                                                                 => ( ! [Xx: $i,A: $i,Xy: $i] :
                                                                        ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
                                                                       => ! [Xphi: $o] :
                                                                            ( ( ( Xy = Xx )
                                                                             => Xphi )
                                                                           => ( ( ( in @ Xy @ A )
                                                                               => Xphi )
                                                                             => Xphi ) ) )
                                                                   => ( ! [Xx: $i,A: $i,Xy: $i] :
                                                                          ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
                                                                         => ( ( Xy = Xx )
                                                                            | ( in @ Xy @ A ) ) )
                                                                     => ( ! [A: $i] :
                                                                            ( ( dsetconstr @ A
                                                                              @ ^ [Xx: $i] : $true )
                                                                            = A )
                                                                       => ( ! [A: $i,B: $i] :
                                                                              ( ! [Xx: $i] :
                                                                                  ( ( in @ Xx @ B )
                                                                                 => ( in @ Xx @ A ) )
                                                                             => ( in @ B @ ( powerset @ A ) ) )
                                                                         => ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) )
                                                                           => ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) )
                                                                             => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                    ( ( in @ B @ ( powerset @ A ) )
                                                                                   => ( ( in @ Xx @ B )
                                                                                     => ( in @ Xx @ A ) ) )
                                                                               => ( ! [A: $i,Xx: $i,B: $i] :
                                                                                      ( ( in @ Xx @ B )
                                                                                     => ( ( in @ B @ A )
                                                                                       => ( in @ Xx @ ( setunion @ A ) ) ) )
                                                                                 => ( ! [A: $i,Xx: $i] :
                                                                                        ( ( in @ Xx @ ( setunion @ A ) )
                                                                                       => ! [Xphi: $o] :
                                                                                            ( ! [B: $i] :
                                                                                                ( ( in @ Xx @ B )
                                                                                               => ( ( in @ B @ A )
                                                                                                 => Xphi ) )
                                                                                           => Xphi ) )
                                                                                   => ( ! [A: $i,Xx: $i] :
                                                                                          ( ( in @ Xx @ A )
                                                                                         => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) )
                                                                                     => ( ! [SY138: $i > $o] :
                                                                                            ( ? [SY140: $i] :
                                                                                                ( ( SY138 @ SY140 )
                                                                                                & ! [SY141: $i] :
                                                                                                    ( ( SY138 @ SY141 )
                                                                                                   => ( SY140 = SY141 ) ) )
                                                                                           => ? [Xx: $i] :
                                                                                              ! [Xy: $i] :
                                                                                                ( ( SY138 @ Xy )
                                                                                              <=> ( Xy = Xx ) ) )
                                                                                       => ( ! [SY144: $i] :
                                                                                              ( ( SY144 != emptyset )
                                                                                             => ? [Xx: $i] :
                                                                                                  ( ( in @ Xx @ SY144 )
                                                                                                  & $true ) )
                                                                                         => ( ! [Xx: $i,Xy: $i] :
                                                                                                ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
                                                                                               => ( Xx = Xy ) )
                                                                                           => ( ! [Xx: $i,Xy: $i] :
                                                                                                  ( ( Xx != Xy )
                                                                                                 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) )
                                                                                             => ( ! [Xx: $i,Xy: $i] :
                                                                                                    ( ( Xx = Xy )
                                                                                                   => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
                                                                                               => ( ! [Xx: $i,Xy: $i] :
                                                                                                      ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
                                                                                                     => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) )
                                                                                                 => ( ! [Xx: $i,Xy: $i,Xz: $i] :
                                                                                                        ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
                                                                                                       => ( ( Xz = Xx )
                                                                                                          | ( Xz = Xy ) ) )
                                                                                                   => ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
                                                                                                     => ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
                                                                                                       => ( ! [A: $i,Xphi: $i > $o] :
                                                                                                              ( ? [Xx: $i] :
                                                                                                                  ( ( in @ Xx @ A )
                                                                                                                  & ( Xphi @ Xx ) )
                                                                                                             => ( ( ( dsetconstr @ A
                                                                                                                    @ ^ [Xx: $i] : ( Xphi @ Xx ) )
                                                                                                                  = emptyset )
                                                                                                               => $false ) )
                                                                                                         => ( ! [Xphi: $i > $o,Xx: $i] :
                                                                                                                ( ( in @ Xx @ emptyset )
                                                                                                               => ( Xphi @ Xx ) )
                                                                                                           => ( ! [A: $i,Xphi: $i > $o] :
                                                                                                                  ( ~ ! [Xx: $i] :
                                                                                                                        ( ( in @ Xx @ A )
                                                                                                                       => ( Xphi @ Xx ) )
                                                                                                                 => ? [Xx: $i] :
                                                                                                                      ( ( in @ Xx @ A )
                                                                                                                      & ~ ( Xphi @ Xx ) ) )
                                                                                                             => ( ! [A: $i,Xphi: $i > $o] :
                                                                                                                    ( ! [Xx: $i] :
                                                                                                                        ( ( in @ Xx @ A )
                                                                                                                       => ~ ( Xphi @ Xx ) )
                                                                                                                   => ~ ? [Xx: $i] :
                                                                                                                          ( ( in @ Xx @ A )
                                                                                                                          & ( Xphi @ Xx ) ) )
                                                                                                               => ( ! [A: $i,Xphi: $i > $o] :
                                                                                                                      ( ~ ? [Xx: $i] :
                                                                                                                            ( ( in @ Xx @ A )
                                                                                                                            & ( Xphi @ Xx ) )
                                                                                                                     => ! [Xx: $i] :
                                                                                                                          ( ( in @ Xx @ A )
                                                                                                                         => ~ ( Xphi @ Xx ) ) )
                                                                                                                 => ( ! [A: $i,Xphi: $i > $o] :
                                                                                                                        ( ? [Xx: $i] :
                                                                                                                            ( ( in @ Xx @ A )
                                                                                                                            & ~ ( Xphi @ Xx ) )
                                                                                                                       => ~ ! [Xx: $i] :
                                                                                                                              ( ( in @ Xx @ A )
                                                                                                                             => ( Xphi @ Xx ) ) )
                                                                                                                   => ( ! [Xphi: $o] :
                                                                                                                          ( Xphi
                                                                                                                         => ( in @ emptyset @ ( prop2set @ Xphi ) ) )
                                                                                                                     => ( ! [Xphi: $o] :
                                                                                                                            ( Xphi
                                                                                                                           => ( set2prop @ ( prop2set @ Xphi ) ) )
                                                                                                                       => ( ! [A: $i,Xphi: $i > $o] :
                                                                                                                              ( ~ ? [Xx: $i] :
                                                                                                                                    ( ( in @ Xx @ A )
                                                                                                                                    & ( Xphi @ Xx ) )
                                                                                                                             => ! [Xx: $i] :
                                                                                                                                  ( ( in @ Xx @ A )
                                                                                                                                 => ~ ( Xphi @ Xx ) ) )
                                                                                                                         => ( ! [A: $i,Xphi: $i > $o] :
                                                                                                                                ( ~ ! [Xx: $i] :
                                                                                                                                      ( ( in @ Xx @ A )
                                                                                                                                     => ( Xphi @ Xx ) )
                                                                                                                               => ? [Xx: $i] :
                                                                                                                                    ( ( in @ Xx @ A )
                                                                                                                                    & ~ ( Xphi @ Xx ) ) )
                                                                                                                           => ( ! [SY193: $i > $o] :
                                                                                                                                  ( ? [Xx: $i] :
                                                                                                                                      ( ( SY193 @ Xx )
                                                                                                                                      & ! [Xy: $i] :
                                                                                                                                          ( ( SY193 @ Xy )
                                                                                                                                         => ( Xx = Xy ) ) )
                                                                                                                                 => ? [SY197: $i] :
                                                                                                                                      ( ( SY193 @ SY197 )
                                                                                                                                      & ! [SY198: $i] :
                                                                                                                                          ( ( SY193 @ SY198 )
                                                                                                                                         => ( SY197 = SY198 ) ) ) )
                                                                                                                             => ( ! [SY199: $i > $o] :
                                                                                                                                    ( ? [Xx: $i] : ( SY199 @ Xx )
                                                                                                                                   => ( ! [Xx: $i,Xy: $i] :
                                                                                                                                          ( ( SY199 @ Xx )
                                                                                                                                         => ( ( SY199 @ Xy )
                                                                                                                                           => ( Xx = Xy ) ) )
                                                                                                                                     => ? [SY204: $i] :
                                                                                                                                          ( ( SY199 @ SY204 )
                                                                                                                                          & ! [SY205: $i] :
                                                                                                                                              ( ( SY199 @ SY205 )
                                                                                                                                             => ( SY204 = SY205 ) ) ) ) )
                                                                                                                               => ( ! [SY206: $i > $o] :
                                                                                                                                      ( ? [Xx: $i] :
                                                                                                                                        ! [Xy: $i] :
                                                                                                                                          ( ( SY206 @ Xy )
                                                                                                                                        <=> ( Xy = Xx ) )
                                                                                                                                     => ? [SY210: $i] :
                                                                                                                                          ( ( SY206 @ SY210 )
                                                                                                                                          & ! [SY211: $i] :
                                                                                                                                              ( ( SY206 @ SY211 )
                                                                                                                                             => ( SY210 = SY211 ) ) ) )
                                                                                                                                 => ( ! [A: $i,B: $i] :
                                                                                                                                        ( ( A = B )
                                                                                                                                       => ! [Xx: $i,Xy: $i] :
                                                                                                                                            ( ( Xx = Xy )
                                                                                                                                           => ( ( in @ Xx @ A )
                                                                                                                                             => ( in @ Xy @ B ) ) ) )
                                                                                                                                   => ( ! [A: $i,B: $i] :
                                                                                                                                          ( ( A = B )
                                                                                                                                         => ! [Xx: $i,Xy: $i] :
                                                                                                                                              ( ( Xx = Xy )
                                                                                                                                             => ( ( in @ Xx @ A )
                                                                                                                                              <=> ( in @ Xy @ B ) ) ) )
                                                                                                                                     => ( ! [SY220: $i > $o] :
                                                                                                                                            ( ? [SY222: $i] :
                                                                                                                                                ( ( SY220 @ SY222 )
                                                                                                                                                & ! [SY223: $i] :
                                                                                                                                                    ( ( SY220 @ SY223 )
                                                                                                                                                   => ( SY222 = SY223 ) ) )
                                                                                                                                           => ! [Xx: $i,Xy: $i] :
                                                                                                                                                ( ( SY220 @ Xx )
                                                                                                                                               => ( ( SY220 @ Xy )
                                                                                                                                                 => ( Xx = Xy ) ) ) )
                                                                                                                                       => ( ! [SY226: $i > $o,SY227: $i > $o] :
                                                                                                                                              ( ! [Xx: $i,Xy: $i] :
                                                                                                                                                  ( ( Xx = Xy )
                                                                                                                                                 => ( ( SY226 @ Xx )
                                                                                                                                                  <=> ( SY227 @ Xy ) ) )
                                                                                                                                             => ( ? [SY231: $i] :
                                                                                                                                                    ( ( SY226 @ SY231 )
                                                                                                                                                    & ! [SY232: $i] :
                                                                                                                                                        ( ( SY226 @ SY232 )
                                                                                                                                                       => ( SY231 = SY232 ) ) )
                                                                                                                                              <=> ? [SY234: $i] :
                                                                                                                                                    ( ( SY227 @ SY234 )
                                                                                                                                                    & ! [SY235: $i] :
                                                                                                                                                        ( ( SY227 @ SY235 )
                                                                                                                                                       => ( SY234 = SY235 ) ) ) ) )
                                                                                                                                         => ( ( emptyset = emptyset )
                                                                                                                                           => ( ! [Xx: $i,Xy: $i] :
                                                                                                                                                  ( ( Xx = Xy )
                                                                                                                                                 => ! [Xz: $i,Xu: $i] :
                                                                                                                                                      ( ( Xz = Xu )
                                                                                                                                                     => ( ( setadjoin @ Xx @ Xz )
                                                                                                                                                        = ( setadjoin @ Xy @ Xu ) ) ) )
                                                                                                                                             => ( ! [A: $i,B: $i] :
                                                                                                                                                    ( ( A = B )
                                                                                                                                                   => ( ( powerset @ A )
                                                                                                                                                      = ( powerset @ B ) ) )
                                                                                                                                               => ( ! [A: $i,B: $i] :
                                                                                                                                                      ( ( A = B )
                                                                                                                                                     => ( ( setunion @ A )
                                                                                                                                                        = ( setunion @ B ) ) )
                                                                                                                                                 => ( ( omega = omega )
                                                                                                                                                   => ( ! [SY244: $i > $o] :
                                                                                                                                                          ( ? [SY246: $i] :
                                                                                                                                                              ( ( SY244 @ SY246 )
                                                                                                                                                              & ! [SY247: $i] :
                                                                                                                                                                  ( ( SY244 @ SY247 )
                                                                                                                                                                 => ( SY246 = SY247 ) ) )
                                                                                                                                                         => ! [Xx: $i,Xy: $i] :
                                                                                                                                                              ( ( SY244 @ Xx )
                                                                                                                                                             => ( ( SY244 @ Xy )
                                                                                                                                                               => ( Xx = Xy ) ) ) )
                                                                                                                                                     => ( ! [SY250: $i > $o,SY251: $i > $o] :
                                                                                                                                                            ( ! [Xx: $i,Xy: $i] :
                                                                                                                                                                ( ( Xx = Xy )
                                                                                                                                                               => ( ( SY250 @ Xx )
                                                                                                                                                                <=> ( SY251 @ Xy ) ) )
                                                                                                                                                           => ( ? [SY255: $i] :
                                                                                                                                                                  ( ( SY250 @ SY255 )
                                                                                                                                                                  & ! [SY256: $i] :
                                                                                                                                                                      ( ( SY250 @ SY256 )
                                                                                                                                                                     => ( SY255 = SY256 ) ) )
                                                                                                                                                             => ( ? [SY258: $i] :
                                                                                                                                                                    ( ( SY251 @ SY258 )
                                                                                                                                                                    & ! [SY259: $i] :
                                                                                                                                                                        ( ( SY251 @ SY259 )
                                                                                                                                                                       => ( SY258 = SY259 ) ) )
                                                                                                                                                               => ( ( descr
                                                                                                                                                                    @ ^ [Xx: $i] : ( SY250 @ Xx ) )
                                                                                                                                                                  = ( descr
                                                                                                                                                                    @ ^ [Xx: $i] : ( SY251 @ Xx ) ) ) ) ) )
                                                                                                                                                       => ( ! [A: $i,B: $i] :
                                                                                                                                                              ( ( A = B )
                                                                                                                                                             => ! [Xphi: $i > $o,Xpsi: $i > $o] :
                                                                                                                                                                  ( ! [Xx: $i] :
                                                                                                                                                                      ( ( in @ Xx @ A )
                                                                                                                                                                     => ! [Xy: $i] :
                                                                                                                                                                          ( ( in @ Xy @ B )
                                                                                                                                                                         => ( ( Xx = Xy )
                                                                                                                                                                           => ( ( Xphi @ Xx )
                                                                                                                                                                            <=> ( Xpsi @ Xy ) ) ) ) )
                                                                                                                                                                 => ( ( dsetconstr @ A
                                                                                                                                                                      @ ^ [Xx: $i] : ( Xphi @ Xx ) )
                                                                                                                                                                    = ( dsetconstr @ B
                                                                                                                                                                      @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) )
                                                                                                                                                         => ( ! [A: $i,B: $i] :
                                                                                                                                                                ( ! [Xx: $i] :
                                                                                                                                                                    ( ( in @ Xx @ A )
                                                                                                                                                                   => ( in @ Xx @ B ) )
                                                                                                                                                               => ( subset @ A @ B ) )
                                                                                                                                                           => ( ! [A: $i,B: $i] :
                                                                                                                                                                  ( ( A = B )
                                                                                                                                                                 => ( subset @ B @ A ) )
                                                                                                                                                             => ( ! [A: $i,B: $i] :
                                                                                                                                                                    ( ( A = B )
                                                                                                                                                                   => ( subset @ A @ B ) )
                                                                                                                                                               => ( ! [A: $i,B: $i] :
                                                                                                                                                                      ( ! [Xx: $i] :
                                                                                                                                                                          ( ( in @ Xx @ A )
                                                                                                                                                                         => ( in @ Xx @ B ) )
                                                                                                                                                                     => ( subset @ A @ B ) )
                                                                                                                                                                 => ( ! [A: $i] : ( subset @ emptyset @ A )
                                                                                                                                                                   => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                          ( ( subset @ A @ B )
                                                                                                                                                                         => ( ( in @ Xx @ A )
                                                                                                                                                                           => ( in @ Xx @ B ) ) )
                                                                                                                                                                     => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                            ( ( subset @ A @ B )
                                                                                                                                                                           => ( ~ ( in @ Xx @ B )
                                                                                                                                                                             => ~ ( in @ Xx @ A ) ) )
                                                                                                                                                                       => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                              ( ( in @ Xx @ A )
                                                                                                                                                                             => ( ~ ( in @ Xx @ B )
                                                                                                                                                                               => ~ ( subset @ A @ B ) ) )
                                                                                                                                                                         => ( ! [A: $i,B: $i] :
                                                                                                                                                                                ( ~ ( subset @ A @ B )
                                                                                                                                                                               => ( A != B ) )
                                                                                                                                                                           => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                                  ( ( in @ Xx @ A )
                                                                                                                                                                                 => ( ~ ( in @ Xx @ B )
                                                                                                                                                                                   => ( A != B ) ) )
                                                                                                                                                                             => ( ! [A: $i] : ( subset @ A @ A )
                                                                                                                                                                               => ( ! [A: $i,B: $i,C: $i] :
                                                                                                                                                                                      ( ( subset @ A @ B )
                                                                                                                                                                                     => ( ( subset @ B @ C )
                                                                                                                                                                                       => ( subset @ A @ C ) ) )
                                                                                                                                                                                 => ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) )
                                                                                                                                                                                   => ( ! [A: $i,Xx: $i,B: $i] :
                                                                                                                                                                                          ( ( subset @ A @ B )
                                                                                                                                                                                         => ( subset @ A @ ( setadjoin @ Xx @ B ) ) )
                                                                                                                                                                                     => ( ! [A: $i,B: $i] :
                                                                                                                                                                                            ( ( subset @ A @ B )
                                                                                                                                                                                           => ( in @ A @ ( powerset @ B ) ) )
                                                                                                                                                                                       => ( ! [A: $i,B: $i] :
                                                                                                                                                                                              ( ( subset @ A @ B )
                                                                                                                                                                                             => ( ( subset @ B @ A )
                                                                                                                                                                                               => ( A = B ) ) )
                                                                                                                                                                                         => ( ! [A: $i] :
                                                                                                                                                                                                ( ( subset @ A @ emptyset )
                                                                                                                                                                                               => ( A = emptyset ) )
                                                                                                                                                                                           => ( ! [A: $i,B: $i] :
                                                                                                                                                                                                  ( ( subset @ B @ A )
                                                                                                                                                                                                 => ( in @ B @ ( powerset @ A ) ) )
                                                                                                                                                                                             => ( ! [A: $i,B: $i] :
                                                                                                                                                                                                    ( ( in @ B @ ( powerset @ A ) )
                                                                                                                                                                                                   => ( subset @ B @ A ) )
                                                                                                                                                                                               => ( ! [A: $i] : ( in @ A @ ( powerset @ A ) )
                                                                                                                                                                                                 => ( ! [A: $i,B: $i] :
                                                                                                                                                                                                        ( ( subset @ A @ B )
                                                                                                                                                                                                       => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) )
                                                                                                                                                                                                   => ( ! [A: $i,Xphi: $i > $o] :
                                                                                                                                                                                                          ( in
                                                                                                                                                                                                          @ ( dsetconstr @ A
                                                                                                                                                                                                            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
                                                                                                                                                                                                          @ ( powerset @ A ) )
                                                                                                                                                                                                     => ( ! [A: $i,Xphi: $i > $o] :
                                                                                                                                                                                                            ( subset
                                                                                                                                                                                                            @ ( dsetconstr @ A
                                                                                                                                                                                                              @ ^ [Xx: $i] : ( Xphi @ Xx ) )
                                                                                                                                                                                                            @ A )
                                                                                                                                                                                                       => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                                                              ( ( in @ Xx @ A )
                                                                                                                                                                                                             => ( in @ Xx @ ( binunion @ A @ B ) ) )
                                                                                                                                                                                                         => ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
                                                                                                                                                                                                           => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                                                                  ( ( in @ Xx @ B )
                                                                                                                                                                                                                 => ( in @ Xx @ ( binunion @ A @ B ) ) )
                                                                                                                                                                                                             => ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
                                                                                                                                                                                                                    ( ( in @ Xx @ ( binunion @ A @ B ) )
                                                                                                                                                                                                                   => ( ( ( in @ Xx @ A )
                                                                                                                                                                                                                       => Xphi )
                                                                                                                                                                                                                     => ( ( ( in @ Xx @ B )
                                                                                                                                                                                                                         => Xphi )
                                                                                                                                                                                                                       => Xphi ) ) )
                                                                                                                                                                                                               => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                                                                      ( ( in @ Xx @ ( binunion @ A @ B ) )
                                                                                                                                                                                                                     => ( ( in @ Xx @ A )
                                                                                                                                                                                                                        | ( in @ Xx @ B ) ) )
                                                                                                                                                                                                                 => ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) )
                                                                                                                                                                                                                   => ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) )
                                                                                                                                                                                                                     => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                                                                            ( ( in @ Xx @ A )
                                                                                                                                                                                                                           => ( ( in @ Xx @ B )
                                                                                                                                                                                                                             => ( in @ Xx @ ( binintersect @ A @ B ) ) ) )
                                                                                                                                                                                                                       => ( ! [A: $i,B: $i,C: $i] :
                                                                                                                                                                                                                              ( ( subset @ C @ A )
                                                                                                                                                                                                                             => ( ( subset @ C @ B )
                                                                                                                                                                                                                               => ( subset @ C @ ( binintersect @ A @ B ) ) ) )
                                                                                                                                                                                                                         => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                                                                                ( ( in @ Xx @ ( binintersect @ A @ B ) )
                                                                                                                                                                                                                               => ( in @ Xx @ A ) )
                                                                                                                                                                                                                           => ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A )
                                                                                                                                                                                                                             => ( ! [A: $i,B: $i] :
                                                                                                                                                                                                                                    ( ( subset @ A @ B )
                                                                                                                                                                                                                                   => ( ( binintersect @ A @ B )
                                                                                                                                                                                                                                      = A ) )
                                                                                                                                                                                                                               => ( ! [A: $i,B: $i] :
                                                                                                                                                                                                                                      ( ( ( binintersect @ A @ B )
                                                                                                                                                                                                                                        = B )
                                                                                                                                                                                                                                     => ( subset @ B @ A ) )
                                                                                                                                                                                                                                 => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                                                                                        ( ( in @ Xx @ ( binintersect @ A @ B ) )
                                                                                                                                                                                                                                       => ( in @ Xx @ B ) )
                                                                                                                                                                                                                                   => ( ! [A: $i,B: $i] :
                                                                                                                                                                                                                                          ( ~ ? [Xx: $i] :
                                                                                                                                                                                                                                                ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                & ( in @ Xx @ B ) )
                                                                                                                                                                                                                                         => ( ( binintersect @ A @ B )
                                                                                                                                                                                                                                            = emptyset ) )
                                                                                                                                                                                                                                     => ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B )
                                                                                                                                                                                                                                       => ( ! [A: $i,B: $i] :
                                                                                                                                                                                                                                              ( ( subset @ B @ A )
                                                                                                                                                                                                                                             => ( ( binintersect @ A @ B )
                                                                                                                                                                                                                                                = B ) )
                                                                                                                                                                                                                                         => ( ! [A: $i,B: $i] :
                                                                                                                                                                                                                                                ( ( ( binintersect @ A @ B )
                                                                                                                                                                                                                                                  = A )
                                                                                                                                                                                                                                               => ( subset @ A @ B ) )
                                                                                                                                                                                                                                           => ( ! [A: $i,B: $i,C: $i] :
                                                                                                                                                                                                                                                  ( ( binintersect @ A @ ( binunion @ B @ C ) )
                                                                                                                                                                                                                                                  = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) )
                                                                                                                                                                                                                                             => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                                                                                                    ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                   => ( ~ ( in @ Xx @ B )
                                                                                                                                                                                                                                                     => ( in @ Xx @ ( setminus @ A @ B ) ) ) )
                                                                                                                                                                                                                                               => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                                                                                                      ( ( in @ Xx @ ( setminus @ A @ B ) )
                                                                                                                                                                                                                                                     => ( in @ Xx @ A ) )
                                                                                                                                                                                                                                                 => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                                                                                                        ( ( in @ Xx @ ( setminus @ A @ B ) )
                                                                                                                                                                                                                                                       => ~ ( in @ Xx @ B ) )
                                                                                                                                                                                                                                                   => ( ! [A: $i,B: $i] :
                                                                                                                                                                                                                                                          ( ( subset @ A @ B )
                                                                                                                                                                                                                                                         => ( ( setminus @ A @ B )
                                                                                                                                                                                                                                                            = emptyset ) )
                                                                                                                                                                                                                                                     => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                                                                                                            ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
                                                                                                                                                                                                                                                           => ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                             => ( in @ Xx @ B ) ) )
                                                                                                                                                                                                                                                       => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                                                                                                              ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
                                                                                                                                                                                                                                                             => ( ~ ( in @ Xx @ B )
                                                                                                                                                                                                                                                               => ~ ( in @ Xx @ A ) ) )
                                                                                                                                                                                                                                                         => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                                                                                                                ( ~ ( in @ Xx @ A )
                                                                                                                                                                                                                                                               => ~ ( in @ Xx @ ( setminus @ A @ B ) ) )
                                                                                                                                                                                                                                                           => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ Xx @ B )
                                                                                                                                                                                                                                                                 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) )
                                                                                                                                                                                                                                                             => ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A )
                                                                                                                                                                                                                                                               => ( ! [A: $i,B: $i] :
                                                                                                                                                                                                                                                                      ( ( ( setminus @ A @ B )
                                                                                                                                                                                                                                                                        = emptyset )
                                                                                                                                                                                                                                                                     => ( subset @ A @ B ) )
                                                                                                                                                                                                                                                                 => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ Xx @ ( symdiff @ A @ B ) )
                                                                                                                                                                                                                                                                       => ! [Xphi: $o] :
                                                                                                                                                                                                                                                                            ( ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                             => ( ~ ( in @ Xx @ B )
                                                                                                                                                                                                                                                                               => Xphi ) )
                                                                                                                                                                                                                                                                           => ( ( ~ ( in @ Xx @ A )
                                                                                                                                                                                                                                                                               => ( ( in @ Xx @ B )
                                                                                                                                                                                                                                                                                 => Xphi ) )
                                                                                                                                                                                                                                                                             => Xphi ) ) )
                                                                                                                                                                                                                                                                   => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                         => ( ~ ( in @ Xx @ B )
                                                                                                                                                                                                                                                                           => ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
                                                                                                                                                                                                                                                                     => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                                                                                                                            ( ~ ( in @ Xx @ A )
                                                                                                                                                                                                                                                                           => ( ( in @ Xx @ B )
                                                                                                                                                                                                                                                                             => ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
                                                                                                                                                                                                                                                                       => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                             => ( ( in @ Xx @ B )
                                                                                                                                                                                                                                                                               => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
                                                                                                                                                                                                                                                                         => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                                                                                                                                ( ~ ( in @ Xx @ A )
                                                                                                                                                                                                                                                                               => ( ~ ( in @ Xx @ B )
                                                                                                                                                                                                                                                                                 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
                                                                                                                                                                                                                                                                           => ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
                                                                                                                                                                                                                                                                             => ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                               => ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                 => ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                   => ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) )
                                                                                                                                                                                                                                                                                     => ( ! [A: $i,Xx: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                           => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) )
                                                                                                                                                                                                                                                                                       => ( ! [A: $i,Xx: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                             => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) )
                                                                                                                                                                                                                                                                                         => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                               => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) )
                                                                                                                                                                                                                                                                                           => ( ! [Xx: $i,Xy: $i,Xz: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                 => ( ( Xz = Xx )
                                                                                                                                                                                                                                                                                                    | ( Xz = Xy ) ) )
                                                                                                                                                                                                                                                                                             => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                   => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ Xy @ B )
                                                                                                                                                                                                                                                                                                       => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) )
                                                                                                                                                                                                                                                                                               => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                     => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ Xy @ B )
                                                                                                                                                                                                                                                                                                         => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
                                                                                                                                                                                                                                                                                                 => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                       => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ Xy @ B )
                                                                                                                                                                                                                                                                                                           => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
                                                                                                                                                                                                                                                                                                   => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                         => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ Xy @ B )
                                                                                                                                                                                                                                                                                                             => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                     => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                           => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ Xy @ B )
                                                                                                                                                                                                                                                                                                               => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                       => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                             => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ Xy @ B )
                                                                                                                                                                                                                                                                                                                 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) )
                                                                                                                                                                                                                                                                                                         => ( ! [A: $i,B: $i,Xu: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ Xu @ ( cartprod @ A @ B ) )
                                                                                                                                                                                                                                                                                                               => ? [Xx: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                    & ? [Xy: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( in @ Xy @ B )
                                                                                                                                                                                                                                                                                                                        & ( Xu
                                                                                                                                                                                                                                                                                                                          = ( kpair @ Xx @ Xy ) ) ) ) )
                                                                                                                                                                                                                                                                                                           => ( ! [A: $i,B: $i,Xu: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ Xu @ ( cartprod @ A @ B ) )
                                                                                                                                                                                                                                                                                                                 => ( iskpair @ Xu ) )
                                                                                                                                                                                                                                                                                                             => ( ! [A: $i,Xx: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ Xx @ ( setunion @ A ) )
                                                                                                                                                                                                                                                                                                                   => ? [X: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( in @ X @ A )
                                                                                                                                                                                                                                                                                                                        & ( in @ Xx @ X ) ) )
                                                                                                                                                                                                                                                                                                               => ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A )
                                                                                                                                                                                                                                                                                                                 => ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                   => ( ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
                                                                                                                                                                                                                                                                                                                          = Xx )
                                                                                                                                                                                                                                                                                                                     => ( ! [A: $i,Xphi: $i > $o] :
                                                                                                                                                                                                                                                                                                                            ( ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                               => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                    ( ( in @ Xy @ A )
                                                                                                                                                                                                                                                                                                                                   => ( ( Xphi @ Xx )
                                                                                                                                                                                                                                                                                                                                     => ( ( Xphi @ Xy )
                                                                                                                                                                                                                                                                                                                                       => ( Xx = Xy ) ) ) ) )
                                                                                                                                                                                                                                                                                                                           => ( ? [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                  & ( Xphi @ Xx ) )
                                                                                                                                                                                                                                                                                                                             => ( singleton
                                                                                                                                                                                                                                                                                                                                @ ( dsetconstr @ A
                                                                                                                                                                                                                                                                                                                                  @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) )
                                                                                                                                                                                                                                                                                                                       => ( ! [SY478: $i,SY479: $i > $o] :
                                                                                                                                                                                                                                                                                                                              ( ( singleton
                                                                                                                                                                                                                                                                                                                                @ ( dsetconstr @ SY478
                                                                                                                                                                                                                                                                                                                                  @ ^ [SY483: $i] : ( SY479 @ SY483 ) ) )
                                                                                                                                                                                                                                                                                                                             => ? [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( in @ Xx @ SY478 )
                                                                                                                                                                                                                                                                                                                                  & ( SY479 @ Xx ) ) )
                                                                                                                                                                                                                                                                                                                         => ( ! [SY485: $i,SY486: $i > $o,SY487: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( in @ SY487 @ SY485 )
                                                                                                                                                                                                                                                                                                                               => ( ( SY486 @ SY487 )
                                                                                                                                                                                                                                                                                                                                 => ( ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( in @ Xy @ SY485 )
                                                                                                                                                                                                                                                                                                                                       => ( ( SY486 @ Xy )
                                                                                                                                                                                                                                                                                                                                         => ( Xy = SY487 ) ) )
                                                                                                                                                                                                                                                                                                                                   => ( singleton
                                                                                                                                                                                                                                                                                                                                      @ ( dsetconstr @ SY485
                                                                                                                                                                                                                                                                                                                                        @ ^ [SY492: $i] : ( SY486 @ SY492 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                           => ( ! [SY493: $i,SY494: $i > $o] :
                                                                                                                                                                                                                                                                                                                                  ( ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                      ( ( in @ Xx @ SY493 )
                                                                                                                                                                                                                                                                                                                                     => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                          ( ( in @ Xy @ SY493 )
                                                                                                                                                                                                                                                                                                                                         => ( ( SY494 @ Xx )
                                                                                                                                                                                                                                                                                                                                           => ( ( SY494 @ Xy )
                                                                                                                                                                                                                                                                                                                                             => ( Xx = Xy ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                 => ( ? [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( in @ Xx @ SY493 )
                                                                                                                                                                                                                                                                                                                                        & ( SY494 @ Xx ) )
                                                                                                                                                                                                                                                                                                                                   => ( singleton
                                                                                                                                                                                                                                                                                                                                      @ ( dsetconstr @ SY493
                                                                                                                                                                                                                                                                                                                                        @ ^ [SY501: $i] : ( SY494 @ SY501 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                             => ( ! [Xx: $i,Xy: $i] :
                                                                                                                                                                                                                                                                                                                                    ( ( ( setadjoin @ Xx @ emptyset )
                                                                                                                                                                                                                                                                                                                                      = ( setadjoin @ Xy @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                   => ( Xx = Xy ) )
                                                                                                                                                                                                                                                                                                                               => ( ! [Xx: $i,Xy: $i,Xz: $i] :
                                                                                                                                                                                                                                                                                                                                      ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                     => ( Xx = Xz ) )
                                                                                                                                                                                                                                                                                                                                 => ( ! [Xu: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( iskpair @ Xu )
                                                                                                                                                                                                                                                                                                                                       => ( singleton
                                                                                                                                                                                                                                                                                                                                          @ ( dsetconstr @ ( setunion @ Xu )
                                                                                                                                                                                                                                                                                                                                            @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) )
                                                                                                                                                                                                                                                                                                                                   => ( ! [X: $i] :
                                                                                                                                                                                                                                                                                                                                          ( ( singleton @ X )
                                                                                                                                                                                                                                                                                                                                         => ( in @ ( setunion @ X ) @ X ) )
                                                                                                                                                                                                                                                                                                                                     => ( ! [Xx: $i,Xy: $i] :
                                                                                                                                                                                                                                                                                                                                            ( ( kfst @ ( kpair @ Xx @ Xy ) )
                                                                                                                                                                                                                                                                                                                                            = Xx )
                                                                                                                                                                                                                                                                                                                                       => ( ! [A: $i,B: $i,Xu: $i] :
                                                                                                                                                                                                                                                                                                                                              ( ( in @ Xu @ ( cartprod @ A @ B ) )
                                                                                                                                                                                                                                                                                                                                             => ( in @ ( kfst @ Xu ) @ A ) )
                                                                                                                                                                                                                                                                                                                                         => ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
                                                                                                                                                                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                               => ( Xx = Xz ) )
                                                                                                                                                                                                                                                                                                                                           => ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
                                                                                                                                                                                                                                                                                                                                                  ( ( ( kpair @ Xx @ Xy )
                                                                                                                                                                                                                                                                                                                                                    = ( kpair @ Xz @ Xu ) )
                                                                                                                                                                                                                                                                                                                                                 => ( Xx = Xz ) )
                                                                                                                                                                                                                                                                                                                                             => ( ! [Xx: $i,Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                    ( ( Xx = Xy )
                                                                                                                                                                                                                                                                                                                                                   => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                      = ( setadjoin @ Xx @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                               => ( ! [Xx: $i,Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                      ( ( Xx = Xy )
                                                                                                                                                                                                                                                                                                                                                     => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                                 => ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
                                                                                                                                                                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                                       => ( ( Xz = Xu )
                                                                                                                                                                                                                                                                                                                                                         => ( Xy = Xu ) ) )
                                                                                                                                                                                                                                                                                                                                                   => ( ! [Xx: $i,Xy: $i,Xz: $i] :
                                                                                                                                                                                                                                                                                                                                                          ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                            = ( setadjoin @ Xz @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                         => ( Xx = Xy ) )
                                                                                                                                                                                                                                                                                                                                                     => ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
                                                                                                                                                                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                                           => ( Xy = Xu ) )
                                                                                                                                                                                                                                                                                                                                                       => ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
                                                                                                                                                                                                                                                                                                                                                              ( ( ( kpair @ Xx @ Xy )
                                                                                                                                                                                                                                                                                                                                                                = ( kpair @ Xz @ Xu ) )
                                                                                                                                                                                                                                                                                                                                                             => ( Xy = Xu ) )
                                                                                                                                                                                                                                                                                                                                                         => ( ! [Xu: $i] :
                                                                                                                                                                                                                                                                                                                                                                ( ( iskpair @ Xu )
                                                                                                                                                                                                                                                                                                                                                               => ( singleton
                                                                                                                                                                                                                                                                                                                                                                  @ ( dsetconstr @ ( setunion @ Xu )
                                                                                                                                                                                                                                                                                                                                                                    @ ^ [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                        ( Xu
                                                                                                                                                                                                                                                                                                                                                                        = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                           => ( ! [Xx: $i,Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                  ( ( ksnd @ ( kpair @ Xx @ Xy ) )
                                                                                                                                                                                                                                                                                                                                                                  = Xy )
                                                                                                                                                                                                                                                                                                                                                             => ( ! [Xu: $i] :
                                                                                                                                                                                                                                                                                                                                                                    ( ( iskpair @ Xu )
                                                                                                                                                                                                                                                                                                                                                                   => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
                                                                                                                                                                                                                                                                                                                                                                      = Xu ) )
                                                                                                                                                                                                                                                                                                                                                               => ( ! [A: $i,B: $i,Xu: $i] :
                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ Xu @ ( cartprod @ A @ B ) )
                                                                                                                                                                                                                                                                                                                                                                     => ( in @ ( ksnd @ Xu ) @ B ) )
                                                                                                                                                                                                                                                                                                                                                                 => ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
                                                                                                                                                                                                                                                                                                                                                                       => ( in @ Xx @ A ) )
                                                                                                                                                                                                                                                                                                                                                                   => ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
                                                                                                                                                                                                                                                                                                                                                                         => ( in @ Xy @ B ) )
                                                                                                                                                                                                                                                                                                                                                                     => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                           => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ Xy @ B )
                                                                                                                                                                                                                                                                                                                                                                               => ( ( kpair @ Xx @ Xy )
                                                                                                                                                                                                                                                                                                                                                                                  = ( kpair @ Xx @ Xy ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                       => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                             => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ Xy @ B )
                                                                                                                                                                                                                                                                                                                                                                                 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
                                                                                                                                                                                                                                                                                                                                                                                    = Xx ) ) )
                                                                                                                                                                                                                                                                                                                                                                         => ( ! [A: $i,B: $i,Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                               => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ Xy @ B )
                                                                                                                                                                                                                                                                                                                                                                                   => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
                                                                                                                                                                                                                                                                                                                                                                                      = Xy ) ) )
                                                                                                                                                                                                                                                                                                                                                                           => ( ! [A: $i,B: $i,Xu: $i] :
                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ Xu @ ( cartprod @ A @ B ) )
                                                                                                                                                                                                                                                                                                                                                                                 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
                                                                                                                                                                                                                                                                                                                                                                                    = Xu ) )
                                                                                                                                                                                                                                                                                                                                                                             => ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                   => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ Xy @ B )
                                                                                                                                                                                                                                                                                                                                                                                       => ( ( Xphi @ Xx @ Xy )
                                                                                                                                                                                                                                                                                                                                                                                         => ( in @ ( kpair @ Xx @ Xy )
                                                                                                                                                                                                                                                                                                                                                                                            @ ( dpsetconstr @ A @ B
                                                                                                                                                                                                                                                                                                                                                                                              @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                               => ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
                                                                                                                                                                                                                                                                                                                                                                                      ( subset
                                                                                                                                                                                                                                                                                                                                                                                      @ ( dpsetconstr @ A @ B
                                                                                                                                                                                                                                                                                                                                                                                        @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
                                                                                                                                                                                                                                                                                                                                                                                      @ ( cartprod @ A @ B ) )
                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [SY585: $i,SY586: $i,SY587: $i > $i > $o] :
                                                                                                                                                                                                                                                                                                                                                                                        ( subset
                                                                                                                                                                                                                                                                                                                                                                                        @ ( dpsetconstr @ SY585 @ SY586
                                                                                                                                                                                                                                                                                                                                                                                          @ ^ [Xx: $i,Xy: $i] : ( SY587 @ Xx @ Xy ) )
                                                                                                                                                                                                                                                                                                                                                                                        @ ( cartprod @ SY585 @ SY586 ) )
                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                         => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ Xy @ B )
                                                                                                                                                                                                                                                                                                                                                                                             => ( ( in @ ( kpair @ Xx @ Xy )
                                                                                                                                                                                                                                                                                                                                                                                                  @ ( dpsetconstr @ A @ B
                                                                                                                                                                                                                                                                                                                                                                                                    @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
                                                                                                                                                                                                                                                                                                                                                                                               => ( Xphi @ Xx @ Xy ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ ( kpair @ Xx @ Xy )
                                                                                                                                                                                                                                                                                                                                                                                              @ ( dpsetconstr @ A @ B
                                                                                                                                                                                                                                                                                                                                                                                                @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
                                                                                                                                                                                                                                                                                                                                                                                           => ( in @ Xx @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ ( kpair @ Xx @ Xy )
                                                                                                                                                                                                                                                                                                                                                                                                @ ( dpsetconstr @ A @ B
                                                                                                                                                                                                                                                                                                                                                                                                  @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
                                                                                                                                                                                                                                                                                                                                                                                             => ( in @ Xy @ B ) )
                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ ( kpair @ Xx @ Xy )
                                                                                                                                                                                                                                                                                                                                                                                                  @ ( dpsetconstr @ A @ B
                                                                                                                                                                                                                                                                                                                                                                                                    @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
                                                                                                                                                                                                                                                                                                                                                                                               => ( Xphi @ Xx @ Xy ) )
                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [A: $i,B: $i,Xf: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                  ( ( func @ A @ B @ Xf )
                                                                                                                                                                                                                                                                                                                                                                                                 => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                     => ( singleton
                                                                                                                                                                                                                                                                                                                                                                                                        @ ( dsetconstr @ B
                                                                                                                                                                                                                                                                                                                                                                                                          @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [A: $i,B: $i,Xf: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                    ( ( func @ A @ B @ Xf )
                                                                                                                                                                                                                                                                                                                                                                                                   => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                       => ( in
                                                                                                                                                                                                                                                                                                                                                                                                          @ ( setunion
                                                                                                                                                                                                                                                                                                                                                                                                            @ ( dsetconstr @ B
                                                                                                                                                                                                                                                                                                                                                                                                              @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                          @ B ) ) )
                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [A: $i,B: $i,Xf: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                      ( ( func @ A @ B @ Xf )
                                                                                                                                                                                                                                                                                                                                                                                                     => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                         => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [A: $i,B: $i,Xf: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ Xf @ ( funcSet @ A @ B ) )
                                                                                                                                                                                                                                                                                                                                                                                                       => ( func @ A @ B @ Xf ) )
                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [A: $i,B: $i,Xf: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ Xf @ ( funcSet @ A @ B ) )
                                                                                                                                                                                                                                                                                                                                                                                                         => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                             => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [A: $i,B: $i,Xf: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                            ( ( func @ A @ B @ Xf )
                                                                                                                                                                                                                                                                                                                                                                                                           => ( in @ Xf @ ( funcSet @ A @ B ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [A: $i,B: $i,Xf: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                              ( ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                 => ( in @ ( Xf @ Xx ) @ B ) )
                                                                                                                                                                                                                                                                                                                                                                                                             => ( func @ A @ B
                                                                                                                                                                                                                                                                                                                                                                                                                @ ( dpsetconstr @ A @ B
                                                                                                                                                                                                                                                                                                                                                                                                                  @ ^ [Xx: $i,Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( Xf @ Xx )
                                                                                                                                                                                                                                                                                                                                                                                                                      = Xy ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [A: $i,B: $i,Xf: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                ( ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ ( Xf @ Xx ) @ B ) )
                                                                                                                                                                                                                                                                                                                                                                                                               => ( func @ A @ B
                                                                                                                                                                                                                                                                                                                                                                                                                  @ ( lam @ A @ B
                                                                                                                                                                                                                                                                                                                                                                                                                    @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [A: $i,B: $i,Xf: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                  ( ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                     => ( in @ ( Xf @ Xx ) @ B ) )
                                                                                                                                                                                                                                                                                                                                                                                                                 => ( in
                                                                                                                                                                                                                                                                                                                                                                                                                    @ ( lam @ A @ B
                                                                                                                                                                                                                                                                                                                                                                                                                      @ ^ [Xx: $i] : ( Xf @ Xx ) )
                                                                                                                                                                                                                                                                                                                                                                                                                    @ ( funcSet @ A @ B ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [SY661: $i,SY662: $i,SY663: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( subset @ SY663 @ ( cartprod @ SY661 @ SY662 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [Xphi: $i > $o] :
                                                                                                                                                                                                                                                                                                                                                                                                                        ( ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ Xx @ SY661 )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ Xy @ SY662 )
                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( in @ ( kpair @ Xx @ Xy ) @ SY663 )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ Xx @ SY663 )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ( Xphi @ Xx ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [SY671: $i,SY672: $i,SY673: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( subset @ SY673 @ ( cartprod @ SY671 @ SY672 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [Xphi: $i > $o] :
                                                                                                                                                                                                                                                                                                                                                                                                                          ( ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ Xx @ SY671 )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ Xy @ SY672 )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( in @ ( kpair @ Xx @ Xy ) @ SY673 )
                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ Xx @ SY673 )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ( Xphi @ Xx ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [SY681: $i,SY682: $i > $o] :
                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( singleton
                                                                                                                                                                                                                                                                                                                                                                                                                          @ ( dsetconstr @ SY681
                                                                                                                                                                                                                                                                                                                                                                                                                            @ ^ [SY686: $i] : ( SY682 @ SY686 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ Xx @ SY681 )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ Xy @ SY681 )
                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( SY682 @ Xx )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( SY682 @ Xy )
                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( Xx = Xy ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [A: $i,B: $i,Xf: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( func @ A @ B @ Xf )
                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [A: $i,B: $i,Xf: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ Xf @ ( funcSet @ A @ B ) )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                               => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [A: $i,B: $i,Xf: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( func @ A @ B @ Xf )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ Xy @ B )
                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( ap @ A @ B @ Xf @ Xx )
                                                                                                                                                                                                                                                                                                                                                                                                                                          = Xy ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [A: $i,B: $i,Xf: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( func @ A @ B @ Xf )
                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [Xg: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( func @ A @ B @ Xg )
                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( ap @ A @ B @ Xf @ Xx )
                                                                                                                                                                                                                                                                                                                                                                                                                                            = ( ap @ A @ B @ Xg @ Xx ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ Xy @ B )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [A: $i,B: $i,Xf: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ Xf @ ( funcSet @ A @ B ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ Xy @ B )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ( ap @ A @ B @ Xf @ Xx )
                                                                                                                                                                                                                                                                                                                                                                                                                                              = Xy ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [SY714: $i,SY715: $i,SY716: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( subset @ SY716 @ ( cartprod @ SY714 @ SY715 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [SY720: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( subset @ SY720 @ ( cartprod @ SY714 @ SY715 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ Xx @ SY714 )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ Xy @ SY715 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( in @ ( kpair @ Xx @ Xy ) @ SY716 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ ( kpair @ Xx @ Xy ) @ SY720 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( subset @ SY716 @ SY720 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [SY726: $i,SY727: $i,SY728: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( subset @ SY728 @ ( cartprod @ SY726 @ SY727 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [SY732: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( subset @ SY732 @ ( cartprod @ SY726 @ SY727 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ Xx @ SY726 )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ Xy @ SY727 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( in @ ( kpair @ Xx @ Xy ) @ SY728 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( in @ ( kpair @ Xx @ Xy ) @ SY732 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ Xx @ SY726 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ Xy @ SY727 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( in @ ( kpair @ Xx @ Xy ) @ SY732 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ ( kpair @ Xx @ Xy ) @ SY728 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( SY728 = SY732 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [A: $i,B: $i,Xf: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( func @ A @ B @ Xf )
                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [Xg: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( func @ A @ B @ Xg )
                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( ap @ A @ B @ Xf @ Xx )
                                                                                                                                                                                                                                                                                                                                                                                                                                                    = ( ap @ A @ B @ Xg @ Xx ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( Xf = Xg ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [A: $i,B: $i,Xf: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ Xf @ ( funcSet @ A @ B ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [Xg: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ Xg @ ( funcSet @ A @ B ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( ap @ A @ B @ Xf @ Xx )
                                                                                                                                                                                                                                                                                                                                                                                                                                                      = ( ap @ A @ B @ Xg @ Xx ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( Xf = Xg ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [A: $i,B: $i,Xf: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ Xf @ ( funcSet @ A @ B ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( ap @ A @ B @ Xf @ Xx )
                                                                                                                                                                                                                                                                                                                                                                                                                                                  = ( ap @ A @ B @ Xf @ Xx ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [A: $i,B: $i,Xf: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( func @ A @ B @ Xf )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( ap @ A @ B @ Xf @ Xx )
                                                                                                                                                                                                                                                                                                                                                                                                                                                    = ( ap @ A @ B @ Xf @ Xx ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [A: $i,B: $i,Xf: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ ( Xf @ Xx ) @ B ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( ap @ A @ B
                                                                                                                                                                                                                                                                                                                                                                                                                                                        @ ( lam @ A @ B
                                                                                                                                                                                                                                                                                                                                                                                                                                                          @ ^ [Xy: $i] : ( Xf @ Xy ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                        @ Xx )
                                                                                                                                                                                                                                                                                                                                                                                                                                                      = ( Xf @ Xx ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [A: $i,B: $i,Xf: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( func @ A @ B @ Xf )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( lam @ A @ B
                                                                                                                                                                                                                                                                                                                                                                                                                                                      @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                    = Xf ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [A: $i,B: $i,Xf: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ ( Xf @ Xx ) @ B ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( lam @ A @ B
                                                                                                                                                                                                                                                                                                                                                                                                                                                        @ ^ [Xx: $i] : ( Xf @ Xx ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                      = ( lam @ A @ B
                                                                                                                                                                                                                                                                                                                                                                                                                                                        @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [A: $i,B: $i,Xf: $i > $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( in @ ( Xf @ Xx ) @ B ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( ap @ A @ B
                                                                                                                                                                                                                                                                                                                                                                                                                                                              @ ( lam @ A @ B
                                                                                                                                                                                                                                                                                                                                                                                                                                                                @ ^ [Xy: $i] : ( Xf @ Xy ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                              @ Xx )
                                                                                                                                                                                                                                                                                                                                                                                                                                                            = ( Xf @ Xx ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [A: $i,B: $i,Xf: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ Xf @ ( funcSet @ A @ B ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( lam @ A @ B
                                                                                                                                                                                                                                                                                                                                                                                                                                                            @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                          = Xf ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [A: $i,Xphi: $o,Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ Xy @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ~ Xphi
                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( in @ Xy
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  @ ( dsetconstr @ A
                                                                                                                                                                                                                                                                                                                                                                                                                                                                    @ ^ [Xz: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( Xphi
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          & ( Xz = Xx ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        | ( ~ Xphi
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          & ( Xz = Xy ) ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [A: $i,Xphi: $o,Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ Xy @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ~ Xphi
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( dsetconstr @ A
                                                                                                                                                                                                                                                                                                                                                                                                                                                                      @ ^ [Xz: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( Xphi
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            & ( Xz = Xx ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          | ( ~ Xphi
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            & ( Xz = Xy ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                    = ( setadjoin @ Xy @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [A: $i,Xphi: $o,Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ Xy @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( Xphi
                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ Xx
                                                                                                                                                                                                                                                                                                                                                                                                                                                                      @ ( dsetconstr @ A
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        @ ^ [Xz: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( Xphi
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              & ( Xz = Xx ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            | ( ~ Xphi
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              & ( Xz = Xy ) ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [A: $i,Xphi: $o,Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ Xy @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( Xphi
                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( dsetconstr @ A
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          @ ^ [Xz: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( Xphi
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                & ( Xz = Xx ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | ( ~ Xphi
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                & ( Xz = Xy ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        = ( setadjoin @ Xx @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [A: $i,Xphi: $o,Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ Xy @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( singleton
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        @ ( dsetconstr @ A
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          @ ^ [Xz: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( Xphi
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                & ( Xz = Xx ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              | ( ~ Xphi
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                & ( Xz = Xy ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [A: $i,Xphi: $o,Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ Xy @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( singleton @ X )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ Xx @ X )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( setunion @ X )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            = Xx ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [A: $i,Xphi: $o,Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ Xy @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( Xphi
                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ( if @ A @ Xphi @ Xx @ Xy )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                = Xx ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [A: $i,Xphi: $o,Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ Xy @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ~ Xphi
                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( if @ A @ Xphi @ Xx @ Xy )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  = Xy ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [A: $i,Xphi: $o,Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ Xy @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [Y: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ Y @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [Y: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ Y @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [Y: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ Y @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [Y: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ Y @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( in @ Xx @ X )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ Xx @ Y ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( in @ Xx @ Y )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( in @ Xx @ X ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( X = Y ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [Y: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ Y @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( in @ Xx @ X )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( in @ Xx @ Y ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( subset @ X @ Y ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [Y: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ Y @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( in @ Xx @ X )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ Xx @ Y ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( in @ X @ ( powerset @ Y ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [Y: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ Y @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( in @ X @ ( powerset @ Y ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( in @ Xx @ X )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( in @ Xx @ Y ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( in @ Xx @ X )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ Xx @ X ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [Y: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ Y @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ~ ( in @ Xx @ X )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [Y: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ Y @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ~ ( in @ Xx @ Y )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [Y: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ Y @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( subset @ X @ ( setminus @ A @ Y ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( in @ Xx @ Y )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ~ ( in @ Xx @ X ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [Y: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ Y @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( subset @ X @ Y )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ~ ( in @ Xx @ Y )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ~ ( in @ Xx @ X ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [Y: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ Y @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( subset @ X @ Y )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [Y: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ Y @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( subset @ X @ Y ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( in @ Xx @ X )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ Xx @ X ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( X
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          = ( setminus @ A @ ( setminus @ A @ X ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [Y: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ Y @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( in @ Xx @ ( setminus @ A @ X ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [Y: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ Y @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( in @ Xx @ ( setminus @ A @ X ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [Y: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ Y @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [Y: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ Y @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [Y: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ Y @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( subset @ X @ ( setminus @ A @ Y ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ( in @ Xx @ Y )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [Y: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ Y @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( subset @ X @ ( setminus @ A @ Y ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [Y: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ Y @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ~ ( in @ Xx @ X ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [Y: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ Y @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ~ ( in @ Xx @ Y ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [Y: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ Y @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [Z: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ Z @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [Y: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ Y @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [Z: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ Z @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [Y: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ Y @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [Z: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ Z @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [Y: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ Y @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [Z: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ Z @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [Y: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ Y @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ~ ( in @ Xx @ X ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [A: $i,X: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [Y: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ Y @ ( powerset @ A ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ Xx @ A )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[2,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(4,plain,
    ( ( ! [A: $i,B: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
            <=> ( in @ Xx @ B ) )
         => ( A = B ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ! [Xx: $i] :
          ~ ( in @ Xx @ emptyset ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(6,plain,
    ( ( ! [Xx: $i,A: $i,Xy: $i] :
          ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
        <=> ( ( Xy = Xx )
            | ( in @ Xy @ A ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(7,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
        <=> ! [Xx: $i] :
              ( ( in @ Xx @ B )
             => ( in @ Xx @ A ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(8,plain,
    ( ( ! [A: $i,Xx: $i] :
          ( ( in @ Xx @ ( setunion @ A ) )
        <=> ? [B: $i] :
              ( ( in @ Xx @ B )
              & ( in @ B @ A ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(9,plain,
    ( ( in @ emptyset @ omega )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(10,plain,
    ( ( ! [Xx: $i] :
          ( ( in @ Xx @ omega )
         => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(11,plain,
    ( ( ! [A: $i] :
          ( ( ( in @ emptyset @ A )
            & ! [Xx: $i] :
                ( ( ( in @ Xx @ omega )
                  & ( in @ Xx @ A ) )
               => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ omega )
             => ( in @ Xx @ A ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(12,plain,
    ( ( ! [SY21: $i > $i > $o,SY22: $i] :
          ( ! [SY23: $i] :
              ( ( in @ SY23 @ SY22 )
             => ? [SY25: $i] :
                  ( ( SY21 @ SY23 @ SY25 )
                  & ! [SY26: $i] :
                      ( ( SY21 @ SY23 @ SY26 )
                     => ( SY25 = SY26 ) ) ) )
         => ? [B: $i] :
            ! [Xx: $i] :
              ( ( in @ Xx @ B )
            <=> ? [Xy: $i] :
                  ( ( in @ Xy @ SY22 )
                  & ( SY21 @ Xy @ Xx ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(13,plain,
    ( ( ! [A: $i] :
          ( ? [Xx: $i] : ( in @ Xx @ A )
         => ? [B: $i] :
              ( ( in @ B @ A )
              & ~ ? [Xx: $i] :
                    ( ( in @ Xx @ B )
                    & ( in @ Xx @ A ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(14,plain,
    ( ( ! [A: $i] :
        ? [B: $i] :
          ( ! [C: $i] :
              ( ( in @ C @ B )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ C )
                 => ( in @ Xx @ A ) ) )
          & ! [Xx: $i,Xy: $i] :
              ( ( ( in @ Xx @ A )
                & ( in @ Xy @ A ) )
             => ( ! [C: $i] :
                    ( ( in @ C @ B )
                   => ( ( in @ Xx @ C )
                    <=> ( in @ Xy @ C ) ) )
               => ( Xx = Xy ) ) )
          & ! [C: $i,D: $i] :
              ( ( ( in @ C @ B )
                & ( in @ D @ B ) )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ C )
                   => ( in @ Xx @ D ) )
                | ! [Xx: $i] :
                    ( ( in @ Xx @ D )
                   => ( in @ Xx @ C ) ) ) )
          & ! [C: $i] :
              ( ( ! [Xx: $i] :
                    ( ( in @ Xx @ C )
                   => ( in @ Xx @ A ) )
                & ? [Xx: $i] : ( in @ Xx @ C ) )
             => ? [D: $i,Xx: $i] :
                  ( ( in @ D @ B )
                  & ( in @ Xx @ C )
                  & ~ ? [Xy: $i] :
                        ( ( in @ Xy @ D )
                        & ( in @ Xy @ C ) )
                  & ! [E: $i] :
                      ( ( in @ E @ B )
                     => ( ! [Xy: $i] :
                            ( ( in @ Xy @ E )
                           => ( in @ Xy @ D ) )
                        | ( in @ Xx @ E ) ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(15,plain,
    ( ( ! [SY53: $i > $o] :
          ( ? [SY55: $i] :
              ( ( SY53 @ SY55 )
              & ! [SY56: $i] :
                  ( ( SY53 @ SY56 )
                 => ( SY55 = SY56 ) ) )
         => ( SY53
            @ ( descr
              @ ^ [Xx: $i] : ( SY53 @ Xx ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(16,plain,
    ( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ( Xphi @ Xx )
           => ( in @ Xx
              @ ( dsetconstr @ A
                @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(17,plain,
    ( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
          ( ( in @ Xx
            @ ( dsetconstr @ A
              @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
         => ( in @ Xx @ A ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(18,plain,
    ( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
          ( ( in @ Xx
            @ ( dsetconstr @ A
              @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
         => ( Xphi @ Xx ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(19,plain,
    ( ( ! [SY70: $i > $o] :
          ( ? [SY72: $i] :
              ( ( SY70 @ SY72 )
              & ! [SY73: $i] :
                  ( ( SY70 @ SY73 )
                 => ( SY72 = SY73 ) ) )
         => ? [Xx: $i] :
              ( ( SY70 @ Xx )
              & ! [Xy: $i] :
                  ( ( SY70 @ Xy )
                 => ( Xx = Xy ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(20,plain,
    ( ( ! [Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ ( prop2set @ Xphi ) )
         => Xphi ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(21,plain,
    ( ( ! [Xx: $i] :
          ( ( in @ Xx @ emptyset )
         => ! [Xphi: $o] : Xphi ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(22,plain,
    ( ( ! [Xx: $i] :
          ( ( in @ Xx @ emptyset )
         => $false ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(23,plain,
    ( ( ! [Xx: $i] :
          ~ ( in @ Xx @ emptyset ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(24,plain,
    ( ( ! [SY82: $i > $o] :
          ( ? [SY84: $i] :
              ( ( SY82 @ SY84 )
              & ! [SY85: $i] :
                  ( ( SY82 @ SY85 )
                 => ( SY84 = SY85 ) ) )
         => ? [Xx: $i] : ( SY82 @ Xx ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(25,plain,
    ( ( ! [A: $i,B: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ Xx @ B ) )
         => ( ! [Xx: $i] :
                ( ( in @ Xx @ B )
               => ( in @ Xx @ A ) )
           => ( A = B ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(26,plain,
    ( ( ! [A: $i] :
          ( ! [Xx: $i] :
              ~ ( in @ Xx @ A )
         => ( A = emptyset ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(27,plain,
    ( ( ! [A: $i] :
          ( ! [Xx: $i] :
              ~ ( in @ Xx @ A )
         => ( A = emptyset ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(28,plain,
    ( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ( in @ Xx
              @ ( dsetconstr @ A
                @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
          <=> ( Xphi @ Xx ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(29,plain,
    ( ( ! [SY99: $i] :
          ( ( SY99 != emptyset )
         => ? [Xx: $i] : ( in @ Xx @ SY99 ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(30,plain,
    ( ( ! [SY101: $i,SY102: $i > $o,SY103: $i] :
          ( ( in @ SY103 @ SY101 )
         => ( ( SY102 @ SY103 )
           => ( ( dsetconstr @ SY101
                @ ^ [Xy: $i] : ( SY102 @ Xy ) )
             != emptyset ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(31,plain,
    ( ( ! [SY105: $i] :
          ( ? [Xx: $i] : ( in @ Xx @ SY105 )
         => ( SY105 != emptyset ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(32,plain,
    ( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(33,plain,
    ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(34,plain,
    ( ( ! [Xx: $i,A: $i,Xy: $i] :
          ( ( in @ Xy @ A )
         => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(35,plain,
    ( ( ! [Xx: $i,A: $i,Xy: $i] :
          ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
         => ! [Xphi: $o] :
              ( ( ( Xy = Xx )
               => Xphi )
             => ( ( ( in @ Xy @ A )
                 => Xphi )
               => Xphi ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(36,plain,
    ( ( ! [Xx: $i,A: $i,Xy: $i] :
          ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
         => ( ( Xy = Xx )
            | ( in @ Xy @ A ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(37,plain,
    ( ( ! [A: $i] :
          ( ( dsetconstr @ A
            @ ^ [Xx: $i] : $true )
          = A ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(38,plain,
    ( ( ! [A: $i,B: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ B )
             => ( in @ Xx @ A ) )
         => ( in @ B @ ( powerset @ A ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(39,plain,
    ( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(40,plain,
    ( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(41,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ( ( in @ Xx @ B )
           => ( in @ Xx @ A ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(42,plain,
    ( ( ! [A: $i,Xx: $i,B: $i] :
          ( ( in @ Xx @ B )
         => ( ( in @ B @ A )
           => ( in @ Xx @ ( setunion @ A ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(43,plain,
    ( ( ! [A: $i,Xx: $i] :
          ( ( in @ Xx @ ( setunion @ A ) )
         => ! [Xphi: $o] :
              ( ! [B: $i] :
                  ( ( in @ Xx @ B )
                 => ( ( in @ B @ A )
                   => Xphi ) )
             => Xphi ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(44,plain,
    ( ( ! [A: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(45,plain,
    ( ( ! [SY138: $i > $o] :
          ( ? [SY140: $i] :
              ( ( SY138 @ SY140 )
              & ! [SY141: $i] :
                  ( ( SY138 @ SY141 )
                 => ( SY140 = SY141 ) ) )
         => ? [Xx: $i] :
            ! [Xy: $i] :
              ( ( SY138 @ Xy )
            <=> ( Xy = Xx ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(46,plain,
    ( ( ! [SY144: $i] :
          ( ( SY144 != emptyset )
         => ? [Xx: $i] :
              ( ( in @ Xx @ SY144 )
              & $true ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(47,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
         => ( Xx = Xy ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(48,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( Xx != Xy )
         => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(49,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( Xx = Xy )
         => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(50,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
         => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(51,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i] :
          ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
         => ( ( Xz = Xx )
            | ( Xz = Xy ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(52,plain,
    ( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(53,plain,
    ( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(54,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ? [Xx: $i] :
              ( ( in @ Xx @ A )
              & ( Xphi @ Xx ) )
         => ( ( ( dsetconstr @ A
                @ ^ [Xx: $i] : ( Xphi @ Xx ) )
              = emptyset )
           => $false ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(55,plain,
    ( ( ! [Xphi: $i > $o,Xx: $i] :
          ( ( in @ Xx @ emptyset )
         => ( Xphi @ Xx ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(56,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ~ ! [Xx: $i] :
                ( ( in @ Xx @ A )
               => ( Xphi @ Xx ) )
         => ? [Xx: $i] :
              ( ( in @ Xx @ A )
              & ~ ( Xphi @ Xx ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(57,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ~ ( Xphi @ Xx ) )
         => ~ ? [Xx: $i] :
                ( ( in @ Xx @ A )
                & ( Xphi @ Xx ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(58,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ~ ? [Xx: $i] :
                ( ( in @ Xx @ A )
                & ( Xphi @ Xx ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ~ ( Xphi @ Xx ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(59,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ? [Xx: $i] :
              ( ( in @ Xx @ A )
              & ~ ( Xphi @ Xx ) )
         => ~ ! [Xx: $i] :
                ( ( in @ Xx @ A )
               => ( Xphi @ Xx ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(60,plain,
    ( ( ! [Xphi: $o] :
          ( Xphi
         => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(61,plain,
    ( ( ! [Xphi: $o] :
          ( Xphi
         => ( set2prop @ ( prop2set @ Xphi ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(62,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ~ ? [Xx: $i] :
                ( ( in @ Xx @ A )
                & ( Xphi @ Xx ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ~ ( Xphi @ Xx ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(63,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ~ ! [Xx: $i] :
                ( ( in @ Xx @ A )
               => ( Xphi @ Xx ) )
         => ? [Xx: $i] :
              ( ( in @ Xx @ A )
              & ~ ( Xphi @ Xx ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(64,plain,
    ( ( ! [SY193: $i > $o] :
          ( ? [Xx: $i] :
              ( ( SY193 @ Xx )
              & ! [Xy: $i] :
                  ( ( SY193 @ Xy )
                 => ( Xx = Xy ) ) )
         => ? [SY197: $i] :
              ( ( SY193 @ SY197 )
              & ! [SY198: $i] :
                  ( ( SY193 @ SY198 )
                 => ( SY197 = SY198 ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(65,plain,
    ( ( ! [SY199: $i > $o] :
          ( ? [Xx: $i] : ( SY199 @ Xx )
         => ( ! [Xx: $i,Xy: $i] :
                ( ( SY199 @ Xx )
               => ( ( SY199 @ Xy )
                 => ( Xx = Xy ) ) )
           => ? [SY204: $i] :
                ( ( SY199 @ SY204 )
                & ! [SY205: $i] :
                    ( ( SY199 @ SY205 )
                   => ( SY204 = SY205 ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(66,plain,
    ( ( ! [SY206: $i > $o] :
          ( ? [Xx: $i] :
            ! [Xy: $i] :
              ( ( SY206 @ Xy )
            <=> ( Xy = Xx ) )
         => ? [SY210: $i] :
              ( ( SY206 @ SY210 )
              & ! [SY211: $i] :
                  ( ( SY206 @ SY211 )
                 => ( SY210 = SY211 ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(67,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ! [Xx: $i,Xy: $i] :
              ( ( Xx = Xy )
             => ( ( in @ Xx @ A )
               => ( in @ Xy @ B ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(68,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ! [Xx: $i,Xy: $i] :
              ( ( Xx = Xy )
             => ( ( in @ Xx @ A )
              <=> ( in @ Xy @ B ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(69,plain,
    ( ( ! [SY220: $i > $o] :
          ( ? [SY222: $i] :
              ( ( SY220 @ SY222 )
              & ! [SY223: $i] :
                  ( ( SY220 @ SY223 )
                 => ( SY222 = SY223 ) ) )
         => ! [Xx: $i,Xy: $i] :
              ( ( SY220 @ Xx )
             => ( ( SY220 @ Xy )
               => ( Xx = Xy ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(70,plain,
    ( ( ! [SY226: $i > $o,SY227: $i > $o] :
          ( ! [Xx: $i,Xy: $i] :
              ( ( Xx = Xy )
             => ( ( SY226 @ Xx )
              <=> ( SY227 @ Xy ) ) )
         => ( ? [SY231: $i] :
                ( ( SY226 @ SY231 )
                & ! [SY232: $i] :
                    ( ( SY226 @ SY232 )
                   => ( SY231 = SY232 ) ) )
          <=> ? [SY234: $i] :
                ( ( SY227 @ SY234 )
                & ! [SY235: $i] :
                    ( ( SY227 @ SY235 )
                   => ( SY234 = SY235 ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(71,plain,
    ( ( emptyset = emptyset )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(72,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( Xx = Xy )
         => ! [Xz: $i,Xu: $i] :
              ( ( Xz = Xu )
             => ( ( setadjoin @ Xx @ Xz )
                = ( setadjoin @ Xy @ Xu ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(73,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ( ( powerset @ A )
            = ( powerset @ B ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(74,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ( ( setunion @ A )
            = ( setunion @ B ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(75,plain,
    ( ( omega = omega )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(76,plain,
    ( ( ! [SY244: $i > $o] :
          ( ? [SY246: $i] :
              ( ( SY244 @ SY246 )
              & ! [SY247: $i] :
                  ( ( SY244 @ SY247 )
                 => ( SY246 = SY247 ) ) )
         => ! [Xx: $i,Xy: $i] :
              ( ( SY244 @ Xx )
             => ( ( SY244 @ Xy )
               => ( Xx = Xy ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(77,plain,
    ( ( ! [SY250: $i > $o,SY251: $i > $o] :
          ( ! [Xx: $i,Xy: $i] :
              ( ( Xx = Xy )
             => ( ( SY250 @ Xx )
              <=> ( SY251 @ Xy ) ) )
         => ( ? [SY255: $i] :
                ( ( SY250 @ SY255 )
                & ! [SY256: $i] :
                    ( ( SY250 @ SY256 )
                   => ( SY255 = SY256 ) ) )
           => ( ? [SY258: $i] :
                  ( ( SY251 @ SY258 )
                  & ! [SY259: $i] :
                      ( ( SY251 @ SY259 )
                     => ( SY258 = SY259 ) ) )
             => ( ( descr
                  @ ^ [Xx: $i] : ( SY250 @ Xx ) )
                = ( descr
                  @ ^ [Xx: $i] : ( SY251 @ Xx ) ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(78,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ! [Xphi: $i > $o,Xpsi: $i > $o] :
              ( ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ! [Xy: $i] :
                      ( ( in @ Xy @ B )
                     => ( ( Xx = Xy )
                       => ( ( Xphi @ Xx )
                        <=> ( Xpsi @ Xy ) ) ) ) )
             => ( ( dsetconstr @ A
                  @ ^ [Xx: $i] : ( Xphi @ Xx ) )
                = ( dsetconstr @ B
                  @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(79,plain,
    ( ( ! [A: $i,B: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ Xx @ B ) )
         => ( subset @ A @ B ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(80,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ( subset @ B @ A ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(81,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ( subset @ A @ B ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(82,plain,
    ( ( ! [A: $i,B: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ Xx @ B ) )
         => ( subset @ A @ B ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(83,plain,
    ( ( ! [A: $i] : ( subset @ emptyset @ A ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(84,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( subset @ A @ B )
         => ( ( in @ Xx @ A )
           => ( in @ Xx @ B ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(85,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( subset @ A @ B )
         => ( ~ ( in @ Xx @ B )
           => ~ ( in @ Xx @ A ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(86,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ~ ( in @ Xx @ B )
           => ~ ( subset @ A @ B ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(87,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( subset @ A @ B )
         => ( A != B ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(88,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ~ ( in @ Xx @ B )
           => ( A != B ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(89,plain,
    ( ( ! [A: $i] : ( subset @ A @ A ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(90,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( subset @ A @ B )
         => ( ( subset @ B @ C )
           => ( subset @ A @ C ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(91,plain,
    ( ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(92,plain,
    ( ( ! [A: $i,Xx: $i,B: $i] :
          ( ( subset @ A @ B )
         => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(93,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( subset @ A @ B )
         => ( in @ A @ ( powerset @ B ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(94,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( subset @ A @ B )
         => ( ( subset @ B @ A )
           => ( A = B ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(95,plain,
    ( ( ! [A: $i] :
          ( ( subset @ A @ emptyset )
         => ( A = emptyset ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(96,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( subset @ B @ A )
         => ( in @ B @ ( powerset @ A ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(97,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ( subset @ B @ A ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(98,plain,
    ( ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(99,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( subset @ A @ B )
         => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(100,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( in
          @ ( dsetconstr @ A
            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
          @ ( powerset @ A ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(101,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( subset
          @ ( dsetconstr @ A
            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
          @ A ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(102,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( in @ Xx @ ( binunion @ A @ B ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(103,plain,
    ( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(104,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ B )
         => ( in @ Xx @ ( binunion @ A @ B ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(105,plain,
    ( ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
          ( ( in @ Xx @ ( binunion @ A @ B ) )
         => ( ( ( in @ Xx @ A )
             => Xphi )
           => ( ( ( in @ Xx @ B )
               => Xphi )
             => Xphi ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(106,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ ( binunion @ A @ B ) )
         => ( ( in @ Xx @ A )
            | ( in @ Xx @ B ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(107,plain,
    ( ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(108,plain,
    ( ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(109,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ( in @ Xx @ B )
           => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(110,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( subset @ C @ A )
         => ( ( subset @ C @ B )
           => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(111,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ ( binintersect @ A @ B ) )
         => ( in @ Xx @ A ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(112,plain,
    ( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(113,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( subset @ A @ B )
         => ( ( binintersect @ A @ B )
            = A ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(114,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( binintersect @ A @ B )
            = B )
         => ( subset @ B @ A ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(115,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ ( binintersect @ A @ B ) )
         => ( in @ Xx @ B ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(116,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ? [Xx: $i] :
                ( ( in @ Xx @ A )
                & ( in @ Xx @ B ) )
         => ( ( binintersect @ A @ B )
            = emptyset ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(117,plain,
    ( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(118,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( subset @ B @ A )
         => ( ( binintersect @ A @ B )
            = B ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(119,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( binintersect @ A @ B )
            = A )
         => ( subset @ A @ B ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(120,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( binintersect @ A @ ( binunion @ B @ C ) )
          = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(121,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ~ ( in @ Xx @ B )
           => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(122,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ ( setminus @ A @ B ) )
         => ( in @ Xx @ A ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(123,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ ( setminus @ A @ B ) )
         => ~ ( in @ Xx @ B ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(124,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( subset @ A @ B )
         => ( ( setminus @ A @ B )
            = emptyset ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(125,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
         => ( ( in @ Xx @ A )
           => ( in @ Xx @ B ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(126,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
         => ( ~ ( in @ Xx @ B )
           => ~ ( in @ Xx @ A ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(127,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
         => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(128,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ B )
         => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(129,plain,
    ( ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(130,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( setminus @ A @ B )
            = emptyset )
         => ( subset @ A @ B ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(131,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ ( symdiff @ A @ B ) )
         => ! [Xphi: $o] :
              ( ( ( in @ Xx @ A )
               => ( ~ ( in @ Xx @ B )
                 => Xphi ) )
             => ( ( ~ ( in @ Xx @ A )
                 => ( ( in @ Xx @ B )
                   => Xphi ) )
               => Xphi ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(132,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ~ ( in @ Xx @ B )
           => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(133,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
         => ( ( in @ Xx @ B )
           => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(134,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ( in @ Xx @ B )
           => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(135,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
         => ( ~ ( in @ Xx @ B )
           => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(136,plain,
    ( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(137,plain,
    ( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(138,plain,
    ( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(139,plain,
    ( ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(140,plain,
    ( ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(141,plain,
    ( ( ! [A: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(142,plain,
    ( ( ! [A: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(143,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(144,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i] :
          ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
         => ( ( Xz = Xx )
            | ( Xz = Xy ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(145,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(146,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(147,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(148,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(149,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(150,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(151,plain,
    ( ( ! [A: $i,B: $i,Xu: $i] :
          ( ( in @ Xu @ ( cartprod @ A @ B ) )
         => ? [Xx: $i] :
              ( ( in @ Xx @ A )
              & ? [Xy: $i] :
                  ( ( in @ Xy @ B )
                  & ( Xu
                    = ( kpair @ Xx @ Xy ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(152,plain,
    ( ( ! [A: $i,B: $i,Xu: $i] :
          ( ( in @ Xu @ ( cartprod @ A @ B ) )
         => ( iskpair @ Xu ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(153,plain,
    ( ( ! [A: $i,Xx: $i] :
          ( ( in @ Xx @ ( setunion @ A ) )
         => ? [X: $i] :
              ( ( in @ X @ A )
              & ( in @ Xx @ X ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(154,plain,
    ( ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(155,plain,
    ( ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(156,plain,
    ( ( ! [Xx: $i] :
          ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
          = Xx ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(157,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ! [Xy: $i] :
                  ( ( in @ Xy @ A )
                 => ( ( Xphi @ Xx )
                   => ( ( Xphi @ Xy )
                     => ( Xx = Xy ) ) ) ) )
         => ( ? [Xx: $i] :
                ( ( in @ Xx @ A )
                & ( Xphi @ Xx ) )
           => ( singleton
              @ ( dsetconstr @ A
                @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(158,plain,
    ( ( ! [SY478: $i,SY479: $i > $o] :
          ( ( singleton
            @ ( dsetconstr @ SY478
              @ ^ [SY483: $i] : ( SY479 @ SY483 ) ) )
         => ? [Xx: $i] :
              ( ( in @ Xx @ SY478 )
              & ( SY479 @ Xx ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(159,plain,
    ( ( ! [SY485: $i,SY486: $i > $o,SY487: $i] :
          ( ( in @ SY487 @ SY485 )
         => ( ( SY486 @ SY487 )
           => ( ! [Xy: $i] :
                  ( ( in @ Xy @ SY485 )
                 => ( ( SY486 @ Xy )
                   => ( Xy = SY487 ) ) )
             => ( singleton
                @ ( dsetconstr @ SY485
                  @ ^ [SY492: $i] : ( SY486 @ SY492 ) ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(160,plain,
    ( ( ! [SY493: $i,SY494: $i > $o] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ SY493 )
             => ! [Xy: $i] :
                  ( ( in @ Xy @ SY493 )
                 => ( ( SY494 @ Xx )
                   => ( ( SY494 @ Xy )
                     => ( Xx = Xy ) ) ) ) )
         => ( ? [Xx: $i] :
                ( ( in @ Xx @ SY493 )
                & ( SY494 @ Xx ) )
           => ( singleton
              @ ( dsetconstr @ SY493
                @ ^ [SY501: $i] : ( SY494 @ SY501 ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(161,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( ( setadjoin @ Xx @ emptyset )
            = ( setadjoin @ Xy @ emptyset ) )
         => ( Xx = Xy ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(162,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i] :
          ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
         => ( Xx = Xz ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(163,plain,
    ( ( ! [Xu: $i] :
          ( ( iskpair @ Xu )
         => ( singleton
            @ ( dsetconstr @ ( setunion @ Xu )
              @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(164,plain,
    ( ( ! [X: $i] :
          ( ( singleton @ X )
         => ( in @ ( setunion @ X ) @ X ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(165,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( kfst @ ( kpair @ Xx @ Xy ) )
          = Xx ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(166,plain,
    ( ( ! [A: $i,B: $i,Xu: $i] :
          ( ( in @ Xu @ ( cartprod @ A @ B ) )
         => ( in @ ( kfst @ Xu ) @ A ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(167,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
          ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
         => ( Xx = Xz ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(168,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
          ( ( ( kpair @ Xx @ Xy )
            = ( kpair @ Xz @ Xu ) )
         => ( Xx = Xz ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(169,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( Xx = Xy )
         => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
            = ( setadjoin @ Xx @ emptyset ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(170,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( Xx = Xy )
         => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(171,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
          ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
         => ( ( Xz = Xu )
           => ( Xy = Xu ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(172,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i] :
          ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
            = ( setadjoin @ Xz @ emptyset ) )
         => ( Xx = Xy ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(173,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
          ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
         => ( Xy = Xu ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(174,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
          ( ( ( kpair @ Xx @ Xy )
            = ( kpair @ Xz @ Xu ) )
         => ( Xy = Xu ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(175,plain,
    ( ( ! [Xu: $i] :
          ( ( iskpair @ Xu )
         => ( singleton
            @ ( dsetconstr @ ( setunion @ Xu )
              @ ^ [Xx: $i] :
                  ( Xu
                  = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(176,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( ksnd @ ( kpair @ Xx @ Xy ) )
          = Xy ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(177,plain,
    ( ( ! [Xu: $i] :
          ( ( iskpair @ Xu )
         => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
            = Xu ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(178,plain,
    ( ( ! [A: $i,B: $i,Xu: $i] :
          ( ( in @ Xu @ ( cartprod @ A @ B ) )
         => ( in @ ( ksnd @ Xu ) @ B ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(179,plain,
    ( ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
          ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
         => ( in @ Xx @ A ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(180,plain,
    ( ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
          ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
         => ( in @ Xy @ B ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(181,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( ( kpair @ Xx @ Xy )
                = ( kpair @ Xx @ Xy ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(182,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( ( kfst @ ( kpair @ Xx @ Xy ) )
                = Xx ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(183,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
                = Xy ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(184,plain,
    ( ( ! [A: $i,B: $i,Xu: $i] :
          ( ( in @ Xu @ ( cartprod @ A @ B ) )
         => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
            = Xu ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(185,plain,
    ( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( ( Xphi @ Xx @ Xy )
               => ( in @ ( kpair @ Xx @ Xy )
                  @ ( dpsetconstr @ A @ B
                    @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(186,plain,
    ( ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
          ( subset
          @ ( dpsetconstr @ A @ B
            @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
          @ ( cartprod @ A @ B ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(187,plain,
    ( ( ! [SY585: $i,SY586: $i,SY587: $i > $i > $o] :
          ( subset
          @ ( dpsetconstr @ SY585 @ SY586
            @ ^ [Xx: $i,Xy: $i] : ( SY587 @ Xx @ Xy ) )
          @ ( cartprod @ SY585 @ SY586 ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(188,plain,
    ( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( ( in @ ( kpair @ Xx @ Xy )
                  @ ( dpsetconstr @ A @ B
                    @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
               => ( Xphi @ Xx @ Xy ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(189,plain,
    ( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
          ( ( in @ ( kpair @ Xx @ Xy )
            @ ( dpsetconstr @ A @ B
              @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
         => ( in @ Xx @ A ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(190,plain,
    ( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
          ( ( in @ ( kpair @ Xx @ Xy )
            @ ( dpsetconstr @ A @ B
              @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
         => ( in @ Xy @ B ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(191,plain,
    ( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
          ( ( in @ ( kpair @ Xx @ Xy )
            @ ( dpsetconstr @ A @ B
              @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
         => ( Xphi @ Xx @ Xy ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(192,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( singleton
                @ ( dsetconstr @ B
                  @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(193,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in
                @ ( setunion
                  @ ( dsetconstr @ B
                    @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
                @ B ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(194,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(195,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( in @ Xf @ ( funcSet @ A @ B ) )
         => ( func @ A @ B @ Xf ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(196,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( in @ Xf @ ( funcSet @ A @ B ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(197,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ( in @ Xf @ ( funcSet @ A @ B ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(198,plain,
    ( ( ! [A: $i,B: $i,Xf: $i > $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( Xf @ Xx ) @ B ) )
         => ( func @ A @ B
            @ ( dpsetconstr @ A @ B
              @ ^ [Xx: $i,Xy: $i] :
                  ( ( Xf @ Xx )
                  = Xy ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(199,plain,
    ( ( ! [A: $i,B: $i,Xf: $i > $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( Xf @ Xx ) @ B ) )
         => ( func @ A @ B
            @ ( lam @ A @ B
              @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(200,plain,
    ( ( ! [A: $i,B: $i,Xf: $i > $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( Xf @ Xx ) @ B ) )
         => ( in
            @ ( lam @ A @ B
              @ ^ [Xx: $i] : ( Xf @ Xx ) )
            @ ( funcSet @ A @ B ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(201,plain,
    ( ( ! [SY661: $i,SY662: $i,SY663: $i] :
          ( ( subset @ SY663 @ ( cartprod @ SY661 @ SY662 ) )
         => ! [Xphi: $i > $o] :
              ( ! [Xx: $i] :
                  ( ( in @ Xx @ SY661 )
                 => ! [Xy: $i] :
                      ( ( in @ Xy @ SY662 )
                     => ( ( in @ ( kpair @ Xx @ Xy ) @ SY663 )
                       => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ SY663 )
                 => ( Xphi @ Xx ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(202,plain,
    ( ( ! [SY671: $i,SY672: $i,SY673: $i] :
          ( ( subset @ SY673 @ ( cartprod @ SY671 @ SY672 ) )
         => ! [Xphi: $i > $o] :
              ( ! [Xx: $i] :
                  ( ( in @ Xx @ SY671 )
                 => ! [Xy: $i] :
                      ( ( in @ Xy @ SY672 )
                     => ( ( in @ ( kpair @ Xx @ Xy ) @ SY673 )
                       => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ SY673 )
                 => ( Xphi @ Xx ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(203,plain,
    ( ( ! [SY681: $i,SY682: $i > $o] :
          ( ( singleton
            @ ( dsetconstr @ SY681
              @ ^ [SY686: $i] : ( SY682 @ SY686 ) ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ SY681 )
             => ! [Xy: $i] :
                  ( ( in @ Xy @ SY681 )
                 => ( ( SY682 @ Xx )
                   => ( ( SY682 @ Xy )
                     => ( Xx = Xy ) ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(204,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(205,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( in @ Xf @ ( funcSet @ A @ B ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(206,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ! [Xy: $i] :
                  ( ( in @ Xy @ B )
                 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
                   => ( ( ap @ A @ B @ Xf @ Xx )
                      = Xy ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(207,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ! [Xg: $i] :
              ( ( func @ A @ B @ Xg )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ( ( ap @ A @ B @ Xf @ Xx )
                      = ( ap @ A @ B @ Xg @ Xx ) ) )
               => ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ! [Xy: $i] :
                        ( ( in @ Xy @ B )
                       => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
                         => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(208,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( in @ Xf @ ( funcSet @ A @ B ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ! [Xy: $i] :
                  ( ( in @ Xy @ B )
                 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
                   => ( ( ap @ A @ B @ Xf @ Xx )
                      = Xy ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(209,plain,
    ( ( ! [SY714: $i,SY715: $i,SY716: $i] :
          ( ( subset @ SY716 @ ( cartprod @ SY714 @ SY715 ) )
         => ! [SY720: $i] :
              ( ( subset @ SY720 @ ( cartprod @ SY714 @ SY715 ) )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ SY714 )
                   => ! [Xy: $i] :
                        ( ( in @ Xy @ SY715 )
                       => ( ( in @ ( kpair @ Xx @ Xy ) @ SY716 )
                         => ( in @ ( kpair @ Xx @ Xy ) @ SY720 ) ) ) )
               => ( subset @ SY716 @ SY720 ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(210,plain,
    ( ( ! [SY726: $i,SY727: $i,SY728: $i] :
          ( ( subset @ SY728 @ ( cartprod @ SY726 @ SY727 ) )
         => ! [SY732: $i] :
              ( ( subset @ SY732 @ ( cartprod @ SY726 @ SY727 ) )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ SY726 )
                   => ! [Xy: $i] :
                        ( ( in @ Xy @ SY727 )
                       => ( ( in @ ( kpair @ Xx @ Xy ) @ SY728 )
                         => ( in @ ( kpair @ Xx @ Xy ) @ SY732 ) ) ) )
               => ( ! [Xx: $i] :
                      ( ( in @ Xx @ SY726 )
                     => ! [Xy: $i] :
                          ( ( in @ Xy @ SY727 )
                         => ( ( in @ ( kpair @ Xx @ Xy ) @ SY732 )
                           => ( in @ ( kpair @ Xx @ Xy ) @ SY728 ) ) ) )
                 => ( SY728 = SY732 ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(211,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ! [Xg: $i] :
              ( ( func @ A @ B @ Xg )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ( ( ap @ A @ B @ Xf @ Xx )
                      = ( ap @ A @ B @ Xg @ Xx ) ) )
               => ( Xf = Xg ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(212,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( in @ Xf @ ( funcSet @ A @ B ) )
         => ! [Xg: $i] :
              ( ( in @ Xg @ ( funcSet @ A @ B ) )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ( ( ap @ A @ B @ Xf @ Xx )
                      = ( ap @ A @ B @ Xg @ Xx ) ) )
               => ( Xf = Xg ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(213,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( in @ Xf @ ( funcSet @ A @ B ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ( ap @ A @ B @ Xf @ Xx )
                = ( ap @ A @ B @ Xf @ Xx ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(214,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ( ap @ A @ B @ Xf @ Xx )
                = ( ap @ A @ B @ Xf @ Xx ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(215,plain,
    ( ( ! [A: $i,B: $i,Xf: $i > $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( Xf @ Xx ) @ B ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ( ap @ A @ B
                  @ ( lam @ A @ B
                    @ ^ [Xy: $i] : ( Xf @ Xy ) )
                  @ Xx )
                = ( Xf @ Xx ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(216,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ( ( lam @ A @ B
              @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
            = Xf ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(217,plain,
    ( ( ! [A: $i,B: $i,Xf: $i > $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( Xf @ Xx ) @ B ) )
         => ( ( lam @ A @ B
              @ ^ [Xx: $i] : ( Xf @ Xx ) )
            = ( lam @ A @ B
              @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(218,plain,
    ( ( ! [A: $i,B: $i,Xf: $i > $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( Xf @ Xx ) @ B ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ( ap @ A @ B
                  @ ( lam @ A @ B
                    @ ^ [Xy: $i] : ( Xf @ Xy ) )
                  @ Xx )
                = ( Xf @ Xx ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(219,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( in @ Xf @ ( funcSet @ A @ B ) )
         => ( ( lam @ A @ B
              @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
            = Xf ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(220,plain,
    ( ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ A )
             => ( ~ Xphi
               => ( in @ Xy
                  @ ( dsetconstr @ A
                    @ ^ [Xz: $i] :
                        ( ( Xphi
                          & ( Xz = Xx ) )
                        | ( ~ Xphi
                          & ( Xz = Xy ) ) ) ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(221,plain,
    ( ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ A )
             => ( ~ Xphi
               => ( ( dsetconstr @ A
                    @ ^ [Xz: $i] :
                        ( ( Xphi
                          & ( Xz = Xx ) )
                        | ( ~ Xphi
                          & ( Xz = Xy ) ) ) )
                  = ( setadjoin @ Xy @ emptyset ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(222,plain,
    ( ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ A )
             => ( Xphi
               => ( in @ Xx
                  @ ( dsetconstr @ A
                    @ ^ [Xz: $i] :
                        ( ( Xphi
                          & ( Xz = Xx ) )
                        | ( ~ Xphi
                          & ( Xz = Xy ) ) ) ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(223,plain,
    ( ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ A )
             => ( Xphi
               => ( ( dsetconstr @ A
                    @ ^ [Xz: $i] :
                        ( ( Xphi
                          & ( Xz = Xx ) )
                        | ( ~ Xphi
                          & ( Xz = Xy ) ) ) )
                  = ( setadjoin @ Xx @ emptyset ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(224,plain,
    ( ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ A )
             => ( singleton
                @ ( dsetconstr @ A
                  @ ^ [Xz: $i] :
                      ( ( Xphi
                        & ( Xz = Xx ) )
                      | ( ~ Xphi
                        & ( Xz = Xy ) ) ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(225,plain,
    ( ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ A )
             => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(226,plain,
    ( ( ! [X: $i] :
          ( ( singleton @ X )
         => ! [Xx: $i] :
              ( ( in @ Xx @ X )
             => ( ( setunion @ X )
                = Xx ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(227,plain,
    ( ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ A )
             => ( Xphi
               => ( ( if @ A @ Xphi @ Xx @ Xy )
                  = Xx ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(228,plain,
    ( ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ A )
             => ( ~ Xphi
               => ( ( if @ A @ Xphi @ Xx @ Xy )
                  = Xy ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(229,plain,
    ( ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ A )
             => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(230,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(231,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(232,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(233,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(234,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(235,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ( ( in @ Xx @ X )
                     => ( in @ Xx @ Y ) ) )
               => ( ! [Xx: $i] :
                      ( ( in @ Xx @ A )
                     => ( ( in @ Xx @ Y )
                       => ( in @ Xx @ X ) ) )
                 => ( X = Y ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(236,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ( ( in @ Xx @ X )
                     => ( in @ Xx @ Y ) ) )
               => ( subset @ X @ Y ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(237,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ( ( in @ Xx @ X )
                     => ( in @ Xx @ Y ) ) )
               => ( in @ X @ ( powerset @ Y ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(238,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ( in @ X @ ( powerset @ Y ) )
                   => ( ( in @ Xx @ X )
                     => ( in @ Xx @ Y ) ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(239,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ( in @ Xx @ X )
               => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(240,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
               => ( in @ Xx @ X ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(241,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ~ ( in @ Xx @ X )
                   => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(242,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ~ ( in @ Xx @ Y )
                   => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(243,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ( subset @ X @ ( setminus @ A @ Y ) )
                   => ( ( in @ Xx @ Y )
                     => ~ ( in @ Xx @ X ) ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(244,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ( subset @ X @ Y )
                   => ( ~ ( in @ Xx @ Y )
                     => ~ ( in @ Xx @ X ) ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(245,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( ( subset @ X @ Y )
               => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(246,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
               => ( subset @ X @ Y ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(247,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ( in @ Xx @ X )
               => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(248,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
               => ( in @ Xx @ X ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(249,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(250,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(251,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ( X
            = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(252,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ( in @ Xx @ ( setminus @ A @ X ) )
                   => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(253,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ( in @ Xx @ ( setminus @ A @ X ) )
                   => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(254,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(255,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(256,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( ( subset @ X @ ( setminus @ A @ Y ) )
               => ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ( ( in @ Xx @ Y )
                     => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(257,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( ( subset @ X @ ( setminus @ A @ Y ) )
               => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(258,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
                   => ~ ( in @ Xx @ X ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(259,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
                   => ~ ( in @ Xx @ Y ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(260,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Z: $i] :
                  ( ( in @ Z @ ( powerset @ A ) )
                 => ! [Xx: $i] :
                      ( ( in @ Xx @ A )
                     => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
                       => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(261,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Z: $i] :
                  ( ( in @ Z @ ( powerset @ A ) )
                 => ! [Xx: $i] :
                      ( ( in @ Xx @ A )
                     => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
                       => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(262,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Z: $i] :
                  ( ( in @ Z @ ( powerset @ A ) )
                 => ! [Xx: $i] :
                      ( ( in @ Xx @ A )
                     => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
                       => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(263,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Z: $i] :
                  ( ( in @ Z @ ( powerset @ A ) )
                 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(264,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
                   => ~ ( in @ Xx @ X ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(265,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
                   => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) )
    = $false ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(266,plain,
    ( ( ~ ! [A: $i,X: $i] :
            ( ( in @ X @ ( powerset @ A ) )
           => ! [Y: $i] :
                ( ( in @ Y @ ( powerset @ A ) )
               => ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
                     => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[265]) ).

thf(267,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
                   => ~ ( in @ Xx @ X ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[264]) ).

thf(268,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Z: $i] :
                  ( ( in @ Z @ ( powerset @ A ) )
                 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[263]) ).

thf(269,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Z: $i] :
                  ( ( in @ Z @ ( powerset @ A ) )
                 => ! [Xx: $i] :
                      ( ( in @ Xx @ A )
                     => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
                       => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[262]) ).

thf(270,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Z: $i] :
                  ( ( in @ Z @ ( powerset @ A ) )
                 => ! [Xx: $i] :
                      ( ( in @ Xx @ A )
                     => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
                       => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[261]) ).

thf(271,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Z: $i] :
                  ( ( in @ Z @ ( powerset @ A ) )
                 => ! [Xx: $i] :
                      ( ( in @ Xx @ A )
                     => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
                       => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[260]) ).

thf(272,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
                   => ~ ( in @ Xx @ Y ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[259]) ).

thf(273,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
                   => ~ ( in @ Xx @ X ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[258]) ).

thf(274,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( ( subset @ X @ ( setminus @ A @ Y ) )
               => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[257]) ).

thf(275,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( ( subset @ X @ ( setminus @ A @ Y ) )
               => ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ( ( in @ Xx @ Y )
                     => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[256]) ).

thf(276,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[255]) ).

thf(277,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[254]) ).

thf(278,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ( in @ Xx @ ( setminus @ A @ X ) )
                   => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[253]) ).

thf(279,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ( in @ Xx @ ( setminus @ A @ X ) )
                   => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[252]) ).

thf(280,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ( X
            = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[251]) ).

thf(281,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[250]) ).

thf(282,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[249]) ).

thf(283,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
               => ( in @ Xx @ X ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[248]) ).

thf(284,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ( in @ Xx @ X )
               => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[247]) ).

thf(285,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
               => ( subset @ X @ Y ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[246]) ).

thf(286,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( ( subset @ X @ Y )
               => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[245]) ).

thf(287,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ( subset @ X @ Y )
                   => ( ~ ( in @ Xx @ Y )
                     => ~ ( in @ Xx @ X ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[244]) ).

thf(288,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ( subset @ X @ ( setminus @ A @ Y ) )
                   => ( ( in @ Xx @ Y )
                     => ~ ( in @ Xx @ X ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[243]) ).

thf(289,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ~ ( in @ Xx @ Y )
                   => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[242]) ).

thf(290,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ~ ( in @ Xx @ X )
                   => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[241]) ).

thf(291,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
               => ( in @ Xx @ X ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[240]) ).

thf(292,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ( in @ Xx @ X )
               => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[239]) ).

thf(293,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ( ( in @ X @ ( powerset @ Y ) )
                   => ( ( in @ Xx @ X )
                     => ( in @ Xx @ Y ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[238]) ).

thf(294,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ( ( in @ Xx @ X )
                     => ( in @ Xx @ Y ) ) )
               => ( in @ X @ ( powerset @ Y ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[237]) ).

thf(295,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ( ( in @ Xx @ X )
                     => ( in @ Xx @ Y ) ) )
               => ( subset @ X @ Y ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[236]) ).

thf(296,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ( ( in @ Xx @ X )
                     => ( in @ Xx @ Y ) ) )
               => ( ! [Xx: $i] :
                      ( ( in @ Xx @ A )
                     => ( ( in @ Xx @ Y )
                       => ( in @ Xx @ X ) ) )
                 => ( X = Y ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[235]) ).

thf(297,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[234]) ).

thf(298,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[233]) ).

thf(299,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[232]) ).

thf(300,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[231]) ).

thf(301,plain,
    ( ( ! [A: $i,X: $i] :
          ( ( in @ X @ ( powerset @ A ) )
         => ! [Y: $i] :
              ( ( in @ Y @ ( powerset @ A ) )
             => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[230]) ).

thf(302,plain,
    ( ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ A )
             => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[229]) ).

thf(303,plain,
    ( ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ A )
             => ( ~ Xphi
               => ( ( if @ A @ Xphi @ Xx @ Xy )
                  = Xy ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[228]) ).

thf(304,plain,
    ( ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ A )
             => ( Xphi
               => ( ( if @ A @ Xphi @ Xx @ Xy )
                  = Xx ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[227]) ).

thf(305,plain,
    ( ( ! [X: $i] :
          ( ( singleton @ X )
         => ! [Xx: $i] :
              ( ( in @ Xx @ X )
             => ( ( setunion @ X )
                = Xx ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[226]) ).

thf(306,plain,
    ( ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ A )
             => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[225]) ).

thf(307,plain,
    ( ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ A )
             => ( singleton
                @ ( dsetconstr @ A
                  @ ^ [Xz: $i] :
                      ( ( Xphi
                        & ( Xz = Xx ) )
                      | ( ~ Xphi
                        & ( Xz = Xy ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[224]) ).

thf(308,plain,
    ( ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ A )
             => ( Xphi
               => ( ( dsetconstr @ A
                    @ ^ [Xz: $i] :
                        ( ( Xphi
                          & ( Xz = Xx ) )
                        | ( ~ Xphi
                          & ( Xz = Xy ) ) ) )
                  = ( setadjoin @ Xx @ emptyset ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[223]) ).

thf(309,plain,
    ( ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ A )
             => ( Xphi
               => ( in @ Xx
                  @ ( dsetconstr @ A
                    @ ^ [Xz: $i] :
                        ( ( Xphi
                          & ( Xz = Xx ) )
                        | ( ~ Xphi
                          & ( Xz = Xy ) ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[222]) ).

thf(310,plain,
    ( ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ A )
             => ( ~ Xphi
               => ( ( dsetconstr @ A
                    @ ^ [Xz: $i] :
                        ( ( Xphi
                          & ( Xz = Xx ) )
                        | ( ~ Xphi
                          & ( Xz = Xy ) ) ) )
                  = ( setadjoin @ Xy @ emptyset ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[221]) ).

thf(311,plain,
    ( ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ A )
             => ( ~ Xphi
               => ( in @ Xy
                  @ ( dsetconstr @ A
                    @ ^ [Xz: $i] :
                        ( ( Xphi
                          & ( Xz = Xx ) )
                        | ( ~ Xphi
                          & ( Xz = Xy ) ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[220]) ).

thf(312,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( in @ Xf @ ( funcSet @ A @ B ) )
         => ( ( lam @ A @ B
              @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
            = Xf ) ) )
    = $true ),
    inference(copy,[status(thm)],[219]) ).

thf(313,plain,
    ( ( ! [A: $i,B: $i,Xf: $i > $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( Xf @ Xx ) @ B ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ( ap @ A @ B
                  @ ( lam @ A @ B
                    @ ^ [Xy: $i] : ( Xf @ Xy ) )
                  @ Xx )
                = ( Xf @ Xx ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[218]) ).

thf(314,plain,
    ( ( ! [A: $i,B: $i,Xf: $i > $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( Xf @ Xx ) @ B ) )
         => ( ( lam @ A @ B
              @ ^ [Xx: $i] : ( Xf @ Xx ) )
            = ( lam @ A @ B
              @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[217]) ).

thf(315,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ( ( lam @ A @ B
              @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
            = Xf ) ) )
    = $true ),
    inference(copy,[status(thm)],[216]) ).

thf(316,plain,
    ( ( ! [A: $i,B: $i,Xf: $i > $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( Xf @ Xx ) @ B ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ( ap @ A @ B
                  @ ( lam @ A @ B
                    @ ^ [Xy: $i] : ( Xf @ Xy ) )
                  @ Xx )
                = ( Xf @ Xx ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[215]) ).

thf(317,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ( ap @ A @ B @ Xf @ Xx )
                = ( ap @ A @ B @ Xf @ Xx ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[214]) ).

thf(318,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( in @ Xf @ ( funcSet @ A @ B ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( ( ap @ A @ B @ Xf @ Xx )
                = ( ap @ A @ B @ Xf @ Xx ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[213]) ).

thf(319,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( in @ Xf @ ( funcSet @ A @ B ) )
         => ! [Xg: $i] :
              ( ( in @ Xg @ ( funcSet @ A @ B ) )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ( ( ap @ A @ B @ Xf @ Xx )
                      = ( ap @ A @ B @ Xg @ Xx ) ) )
               => ( Xf = Xg ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[212]) ).

thf(320,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ! [Xg: $i] :
              ( ( func @ A @ B @ Xg )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ( ( ap @ A @ B @ Xf @ Xx )
                      = ( ap @ A @ B @ Xg @ Xx ) ) )
               => ( Xf = Xg ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[211]) ).

thf(321,plain,
    ( ( ! [SY726: $i,SY727: $i,SY728: $i] :
          ( ( subset @ SY728 @ ( cartprod @ SY726 @ SY727 ) )
         => ! [SY732: $i] :
              ( ( subset @ SY732 @ ( cartprod @ SY726 @ SY727 ) )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ SY726 )
                   => ! [Xy: $i] :
                        ( ( in @ Xy @ SY727 )
                       => ( ( in @ ( kpair @ Xx @ Xy ) @ SY728 )
                         => ( in @ ( kpair @ Xx @ Xy ) @ SY732 ) ) ) )
               => ( ! [Xx: $i] :
                      ( ( in @ Xx @ SY726 )
                     => ! [Xy: $i] :
                          ( ( in @ Xy @ SY727 )
                         => ( ( in @ ( kpair @ Xx @ Xy ) @ SY732 )
                           => ( in @ ( kpair @ Xx @ Xy ) @ SY728 ) ) ) )
                 => ( SY728 = SY732 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[210]) ).

thf(322,plain,
    ( ( ! [SY714: $i,SY715: $i,SY716: $i] :
          ( ( subset @ SY716 @ ( cartprod @ SY714 @ SY715 ) )
         => ! [SY720: $i] :
              ( ( subset @ SY720 @ ( cartprod @ SY714 @ SY715 ) )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ SY714 )
                   => ! [Xy: $i] :
                        ( ( in @ Xy @ SY715 )
                       => ( ( in @ ( kpair @ Xx @ Xy ) @ SY716 )
                         => ( in @ ( kpair @ Xx @ Xy ) @ SY720 ) ) ) )
               => ( subset @ SY716 @ SY720 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[209]) ).

thf(323,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( in @ Xf @ ( funcSet @ A @ B ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ! [Xy: $i] :
                  ( ( in @ Xy @ B )
                 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
                   => ( ( ap @ A @ B @ Xf @ Xx )
                      = Xy ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[208]) ).

thf(324,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ! [Xg: $i] :
              ( ( func @ A @ B @ Xg )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ( ( ap @ A @ B @ Xf @ Xx )
                      = ( ap @ A @ B @ Xg @ Xx ) ) )
               => ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ! [Xy: $i] :
                        ( ( in @ Xy @ B )
                       => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
                         => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[207]) ).

thf(325,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ! [Xy: $i] :
                  ( ( in @ Xy @ B )
                 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
                   => ( ( ap @ A @ B @ Xf @ Xx )
                      = Xy ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[206]) ).

thf(326,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( in @ Xf @ ( funcSet @ A @ B ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[205]) ).

thf(327,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[204]) ).

thf(328,plain,
    ( ( ! [SY681: $i,SY682: $i > $o] :
          ( ( singleton
            @ ( dsetconstr @ SY681
              @ ^ [SY686: $i] : ( SY682 @ SY686 ) ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ SY681 )
             => ! [Xy: $i] :
                  ( ( in @ Xy @ SY681 )
                 => ( ( SY682 @ Xx )
                   => ( ( SY682 @ Xy )
                     => ( Xx = Xy ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[203]) ).

thf(329,plain,
    ( ( ! [SY671: $i,SY672: $i,SY673: $i] :
          ( ( subset @ SY673 @ ( cartprod @ SY671 @ SY672 ) )
         => ! [Xphi: $i > $o] :
              ( ! [Xx: $i] :
                  ( ( in @ Xx @ SY671 )
                 => ! [Xy: $i] :
                      ( ( in @ Xy @ SY672 )
                     => ( ( in @ ( kpair @ Xx @ Xy ) @ SY673 )
                       => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ SY673 )
                 => ( Xphi @ Xx ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[202]) ).

thf(330,plain,
    ( ( ! [SY661: $i,SY662: $i,SY663: $i] :
          ( ( subset @ SY663 @ ( cartprod @ SY661 @ SY662 ) )
         => ! [Xphi: $i > $o] :
              ( ! [Xx: $i] :
                  ( ( in @ Xx @ SY661 )
                 => ! [Xy: $i] :
                      ( ( in @ Xy @ SY662 )
                     => ( ( in @ ( kpair @ Xx @ Xy ) @ SY663 )
                       => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ SY663 )
                 => ( Xphi @ Xx ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[201]) ).

thf(331,plain,
    ( ( ! [A: $i,B: $i,Xf: $i > $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( Xf @ Xx ) @ B ) )
         => ( in
            @ ( lam @ A @ B
              @ ^ [Xx: $i] : ( Xf @ Xx ) )
            @ ( funcSet @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[200]) ).

thf(332,plain,
    ( ( ! [A: $i,B: $i,Xf: $i > $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( Xf @ Xx ) @ B ) )
         => ( func @ A @ B
            @ ( lam @ A @ B
              @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[199]) ).

thf(333,plain,
    ( ( ! [A: $i,B: $i,Xf: $i > $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( Xf @ Xx ) @ B ) )
         => ( func @ A @ B
            @ ( dpsetconstr @ A @ B
              @ ^ [Xx: $i,Xy: $i] :
                  ( ( Xf @ Xx )
                  = Xy ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[198]) ).

thf(334,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ( in @ Xf @ ( funcSet @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[197]) ).

thf(335,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( in @ Xf @ ( funcSet @ A @ B ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[196]) ).

thf(336,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( in @ Xf @ ( funcSet @ A @ B ) )
         => ( func @ A @ B @ Xf ) ) )
    = $true ),
    inference(copy,[status(thm)],[195]) ).

thf(337,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[194]) ).

thf(338,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in
                @ ( setunion
                  @ ( dsetconstr @ B
                    @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
                @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[193]) ).

thf(339,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( singleton
                @ ( dsetconstr @ B
                  @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[192]) ).

thf(340,plain,
    ( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
          ( ( in @ ( kpair @ Xx @ Xy )
            @ ( dpsetconstr @ A @ B
              @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
         => ( Xphi @ Xx @ Xy ) ) )
    = $true ),
    inference(copy,[status(thm)],[191]) ).

thf(341,plain,
    ( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
          ( ( in @ ( kpair @ Xx @ Xy )
            @ ( dpsetconstr @ A @ B
              @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
         => ( in @ Xy @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[190]) ).

thf(342,plain,
    ( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
          ( ( in @ ( kpair @ Xx @ Xy )
            @ ( dpsetconstr @ A @ B
              @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
         => ( in @ Xx @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[189]) ).

thf(343,plain,
    ( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( ( in @ ( kpair @ Xx @ Xy )
                  @ ( dpsetconstr @ A @ B
                    @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
               => ( Xphi @ Xx @ Xy ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[188]) ).

thf(344,plain,
    ( ( ! [SY585: $i,SY586: $i,SY587: $i > $i > $o] :
          ( subset
          @ ( dpsetconstr @ SY585 @ SY586
            @ ^ [Xx: $i,Xy: $i] : ( SY587 @ Xx @ Xy ) )
          @ ( cartprod @ SY585 @ SY586 ) ) )
    = $true ),
    inference(copy,[status(thm)],[187]) ).

thf(345,plain,
    ( ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
          ( subset
          @ ( dpsetconstr @ A @ B
            @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
          @ ( cartprod @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[186]) ).

thf(346,plain,
    ( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( ( Xphi @ Xx @ Xy )
               => ( in @ ( kpair @ Xx @ Xy )
                  @ ( dpsetconstr @ A @ B
                    @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[185]) ).

thf(347,plain,
    ( ( ! [A: $i,B: $i,Xu: $i] :
          ( ( in @ Xu @ ( cartprod @ A @ B ) )
         => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
            = Xu ) ) )
    = $true ),
    inference(copy,[status(thm)],[184]) ).

thf(348,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
                = Xy ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[183]) ).

thf(349,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( ( kfst @ ( kpair @ Xx @ Xy ) )
                = Xx ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[182]) ).

thf(350,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( ( kpair @ Xx @ Xy )
                = ( kpair @ Xx @ Xy ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[181]) ).

thf(351,plain,
    ( ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
          ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
         => ( in @ Xy @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[180]) ).

thf(352,plain,
    ( ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
          ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
         => ( in @ Xx @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[179]) ).

thf(353,plain,
    ( ( ! [A: $i,B: $i,Xu: $i] :
          ( ( in @ Xu @ ( cartprod @ A @ B ) )
         => ( in @ ( ksnd @ Xu ) @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[178]) ).

thf(354,plain,
    ( ( ! [Xu: $i] :
          ( ( iskpair @ Xu )
         => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
            = Xu ) ) )
    = $true ),
    inference(copy,[status(thm)],[177]) ).

thf(355,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( ksnd @ ( kpair @ Xx @ Xy ) )
          = Xy ) )
    = $true ),
    inference(copy,[status(thm)],[176]) ).

thf(356,plain,
    ( ( ! [Xu: $i] :
          ( ( iskpair @ Xu )
         => ( singleton
            @ ( dsetconstr @ ( setunion @ Xu )
              @ ^ [Xx: $i] :
                  ( Xu
                  = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[175]) ).

thf(357,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
          ( ( ( kpair @ Xx @ Xy )
            = ( kpair @ Xz @ Xu ) )
         => ( Xy = Xu ) ) )
    = $true ),
    inference(copy,[status(thm)],[174]) ).

thf(358,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
          ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
         => ( Xy = Xu ) ) )
    = $true ),
    inference(copy,[status(thm)],[173]) ).

thf(359,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i] :
          ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
            = ( setadjoin @ Xz @ emptyset ) )
         => ( Xx = Xy ) ) )
    = $true ),
    inference(copy,[status(thm)],[172]) ).

thf(360,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
          ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
         => ( ( Xz = Xu )
           => ( Xy = Xu ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[171]) ).

thf(361,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( Xx = Xy )
         => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[170]) ).

thf(362,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( Xx = Xy )
         => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
            = ( setadjoin @ Xx @ emptyset ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[169]) ).

thf(363,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
          ( ( ( kpair @ Xx @ Xy )
            = ( kpair @ Xz @ Xu ) )
         => ( Xx = Xz ) ) )
    = $true ),
    inference(copy,[status(thm)],[168]) ).

thf(364,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
          ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
         => ( Xx = Xz ) ) )
    = $true ),
    inference(copy,[status(thm)],[167]) ).

thf(365,plain,
    ( ( ! [A: $i,B: $i,Xu: $i] :
          ( ( in @ Xu @ ( cartprod @ A @ B ) )
         => ( in @ ( kfst @ Xu ) @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[166]) ).

thf(366,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( kfst @ ( kpair @ Xx @ Xy ) )
          = Xx ) )
    = $true ),
    inference(copy,[status(thm)],[165]) ).

thf(367,plain,
    ( ( ! [X: $i] :
          ( ( singleton @ X )
         => ( in @ ( setunion @ X ) @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[164]) ).

thf(368,plain,
    ( ( ! [Xu: $i] :
          ( ( iskpair @ Xu )
         => ( singleton
            @ ( dsetconstr @ ( setunion @ Xu )
              @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[163]) ).

thf(369,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i] :
          ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
         => ( Xx = Xz ) ) )
    = $true ),
    inference(copy,[status(thm)],[162]) ).

thf(370,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( ( setadjoin @ Xx @ emptyset )
            = ( setadjoin @ Xy @ emptyset ) )
         => ( Xx = Xy ) ) )
    = $true ),
    inference(copy,[status(thm)],[161]) ).

thf(371,plain,
    ( ( ! [SY493: $i,SY494: $i > $o] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ SY493 )
             => ! [Xy: $i] :
                  ( ( in @ Xy @ SY493 )
                 => ( ( SY494 @ Xx )
                   => ( ( SY494 @ Xy )
                     => ( Xx = Xy ) ) ) ) )
         => ( ? [Xx: $i] :
                ( ( in @ Xx @ SY493 )
                & ( SY494 @ Xx ) )
           => ( singleton
              @ ( dsetconstr @ SY493
                @ ^ [SY501: $i] : ( SY494 @ SY501 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[160]) ).

thf(372,plain,
    ( ( ! [SY485: $i,SY486: $i > $o,SY487: $i] :
          ( ( in @ SY487 @ SY485 )
         => ( ( SY486 @ SY487 )
           => ( ! [Xy: $i] :
                  ( ( in @ Xy @ SY485 )
                 => ( ( SY486 @ Xy )
                   => ( Xy = SY487 ) ) )
             => ( singleton
                @ ( dsetconstr @ SY485
                  @ ^ [SY492: $i] : ( SY486 @ SY492 ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[159]) ).

thf(373,plain,
    ( ( ! [SY478: $i,SY479: $i > $o] :
          ( ( singleton
            @ ( dsetconstr @ SY478
              @ ^ [SY483: $i] : ( SY479 @ SY483 ) ) )
         => ? [Xx: $i] :
              ( ( in @ Xx @ SY478 )
              & ( SY479 @ Xx ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[158]) ).

thf(374,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ! [Xy: $i] :
                  ( ( in @ Xy @ A )
                 => ( ( Xphi @ Xx )
                   => ( ( Xphi @ Xy )
                     => ( Xx = Xy ) ) ) ) )
         => ( ? [Xx: $i] :
                ( ( in @ Xx @ A )
                & ( Xphi @ Xx ) )
           => ( singleton
              @ ( dsetconstr @ A
                @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[157]) ).

thf(375,plain,
    ( ( ! [Xx: $i] :
          ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
          = Xx ) )
    = $true ),
    inference(copy,[status(thm)],[156]) ).

thf(376,plain,
    ( ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[155]) ).

thf(377,plain,
    ( ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) )
    = $true ),
    inference(copy,[status(thm)],[154]) ).

thf(378,plain,
    ( ( ! [A: $i,Xx: $i] :
          ( ( in @ Xx @ ( setunion @ A ) )
         => ? [X: $i] :
              ( ( in @ X @ A )
              & ( in @ Xx @ X ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[153]) ).

thf(379,plain,
    ( ( ! [A: $i,B: $i,Xu: $i] :
          ( ( in @ Xu @ ( cartprod @ A @ B ) )
         => ( iskpair @ Xu ) ) )
    = $true ),
    inference(copy,[status(thm)],[152]) ).

thf(380,plain,
    ( ( ! [A: $i,B: $i,Xu: $i] :
          ( ( in @ Xu @ ( cartprod @ A @ B ) )
         => ? [Xx: $i] :
              ( ( in @ Xx @ A )
              & ? [Xy: $i] :
                  ( ( in @ Xy @ B )
                  & ( Xu
                    = ( kpair @ Xx @ Xy ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[151]) ).

thf(381,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[150]) ).

thf(382,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[149]) ).

thf(383,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[148]) ).

thf(384,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[147]) ).

thf(385,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[146]) ).

thf(386,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[145]) ).

thf(387,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i] :
          ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
         => ( ( Xz = Xx )
            | ( Xz = Xy ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[144]) ).

thf(388,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[143]) ).

thf(389,plain,
    ( ( ! [A: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[142]) ).

thf(390,plain,
    ( ( ! [A: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[141]) ).

thf(391,plain,
    ( ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) )
    = $true ),
    inference(copy,[status(thm)],[140]) ).

thf(392,plain,
    ( ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[139]) ).

thf(393,plain,
    ( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[138]) ).

thf(394,plain,
    ( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[137]) ).

thf(395,plain,
    ( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[136]) ).

thf(396,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
         => ( ~ ( in @ Xx @ B )
           => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[135]) ).

thf(397,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ( in @ Xx @ B )
           => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[134]) ).

thf(398,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
         => ( ( in @ Xx @ B )
           => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[133]) ).

thf(399,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ~ ( in @ Xx @ B )
           => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[132]) ).

thf(400,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ ( symdiff @ A @ B ) )
         => ! [Xphi: $o] :
              ( ( ( in @ Xx @ A )
               => ( ~ ( in @ Xx @ B )
                 => Xphi ) )
             => ( ( ~ ( in @ Xx @ A )
                 => ( ( in @ Xx @ B )
                   => Xphi ) )
               => Xphi ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[131]) ).

thf(401,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( setminus @ A @ B )
            = emptyset )
         => ( subset @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[130]) ).

thf(402,plain,
    ( ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) )
    = $true ),
    inference(copy,[status(thm)],[129]) ).

thf(403,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ B )
         => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[128]) ).

thf(404,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
         => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[127]) ).

thf(405,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
         => ( ~ ( in @ Xx @ B )
           => ~ ( in @ Xx @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[126]) ).

thf(406,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
         => ( ( in @ Xx @ A )
           => ( in @ Xx @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[125]) ).

thf(407,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( subset @ A @ B )
         => ( ( setminus @ A @ B )
            = emptyset ) ) )
    = $true ),
    inference(copy,[status(thm)],[124]) ).

thf(408,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ ( setminus @ A @ B ) )
         => ~ ( in @ Xx @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[123]) ).

thf(409,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ ( setminus @ A @ B ) )
         => ( in @ Xx @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[122]) ).

thf(410,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ~ ( in @ Xx @ B )
           => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[121]) ).

thf(411,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( binintersect @ A @ ( binunion @ B @ C ) )
          = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[120]) ).

thf(412,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( binintersect @ A @ B )
            = A )
         => ( subset @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[119]) ).

thf(413,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( subset @ B @ A )
         => ( ( binintersect @ A @ B )
            = B ) ) )
    = $true ),
    inference(copy,[status(thm)],[118]) ).

thf(414,plain,
    ( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) )
    = $true ),
    inference(copy,[status(thm)],[117]) ).

thf(415,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ? [Xx: $i] :
                ( ( in @ Xx @ A )
                & ( in @ Xx @ B ) )
         => ( ( binintersect @ A @ B )
            = emptyset ) ) )
    = $true ),
    inference(copy,[status(thm)],[116]) ).

thf(416,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ ( binintersect @ A @ B ) )
         => ( in @ Xx @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[115]) ).

thf(417,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( binintersect @ A @ B )
            = B )
         => ( subset @ B @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[114]) ).

thf(418,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( subset @ A @ B )
         => ( ( binintersect @ A @ B )
            = A ) ) )
    = $true ),
    inference(copy,[status(thm)],[113]) ).

thf(419,plain,
    ( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) )
    = $true ),
    inference(copy,[status(thm)],[112]) ).

thf(420,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ ( binintersect @ A @ B ) )
         => ( in @ Xx @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[111]) ).

thf(421,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( subset @ C @ A )
         => ( ( subset @ C @ B )
           => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[110]) ).

thf(422,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ( in @ Xx @ B )
           => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[109]) ).

thf(423,plain,
    ( ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[108]) ).

thf(424,plain,
    ( ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[107]) ).

thf(425,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ ( binunion @ A @ B ) )
         => ( ( in @ Xx @ A )
            | ( in @ Xx @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[106]) ).

thf(426,plain,
    ( ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
          ( ( in @ Xx @ ( binunion @ A @ B ) )
         => ( ( ( in @ Xx @ A )
             => Xphi )
           => ( ( ( in @ Xx @ B )
               => Xphi )
             => Xphi ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[105]) ).

thf(427,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ B )
         => ( in @ Xx @ ( binunion @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[104]) ).

thf(428,plain,
    ( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[103]) ).

thf(429,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( in @ Xx @ ( binunion @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[102]) ).

thf(430,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( subset
          @ ( dsetconstr @ A
            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
          @ A ) )
    = $true ),
    inference(copy,[status(thm)],[101]) ).

thf(431,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( in
          @ ( dsetconstr @ A
            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
          @ ( powerset @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[100]) ).

thf(432,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( subset @ A @ B )
         => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[99]) ).

thf(433,plain,
    ( ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[98]) ).

thf(434,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ( subset @ B @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[97]) ).

thf(435,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( subset @ B @ A )
         => ( in @ B @ ( powerset @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[96]) ).

thf(436,plain,
    ( ( ! [A: $i] :
          ( ( subset @ A @ emptyset )
         => ( A = emptyset ) ) )
    = $true ),
    inference(copy,[status(thm)],[95]) ).

thf(437,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( subset @ A @ B )
         => ( ( subset @ B @ A )
           => ( A = B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[94]) ).

thf(438,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( subset @ A @ B )
         => ( in @ A @ ( powerset @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[93]) ).

thf(439,plain,
    ( ( ! [A: $i,Xx: $i,B: $i] :
          ( ( subset @ A @ B )
         => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[92]) ).

thf(440,plain,
    ( ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[91]) ).

thf(441,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ( subset @ A @ B )
         => ( ( subset @ B @ C )
           => ( subset @ A @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[90]) ).

thf(442,plain,
    ( ( ! [A: $i] : ( subset @ A @ A ) )
    = $true ),
    inference(copy,[status(thm)],[89]) ).

thf(443,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ~ ( in @ Xx @ B )
           => ( A != B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[88]) ).

thf(444,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( subset @ A @ B )
         => ( A != B ) ) )
    = $true ),
    inference(copy,[status(thm)],[87]) ).

thf(445,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ~ ( in @ Xx @ B )
           => ~ ( subset @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[86]) ).

thf(446,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( subset @ A @ B )
         => ( ~ ( in @ Xx @ B )
           => ~ ( in @ Xx @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[85]) ).

thf(447,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( subset @ A @ B )
         => ( ( in @ Xx @ A )
           => ( in @ Xx @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[84]) ).

thf(448,plain,
    ( ( ! [A: $i] : ( subset @ emptyset @ A ) )
    = $true ),
    inference(copy,[status(thm)],[83]) ).

thf(449,plain,
    ( ( ! [A: $i,B: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ Xx @ B ) )
         => ( subset @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[82]) ).

thf(450,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ( subset @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[81]) ).

thf(451,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ( subset @ B @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[80]) ).

thf(452,plain,
    ( ( ! [A: $i,B: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ Xx @ B ) )
         => ( subset @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[79]) ).

thf(453,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ! [Xphi: $i > $o,Xpsi: $i > $o] :
              ( ! [Xx: $i] :
                  ( ( in @ Xx @ A )
                 => ! [Xy: $i] :
                      ( ( in @ Xy @ B )
                     => ( ( Xx = Xy )
                       => ( ( Xphi @ Xx )
                        <=> ( Xpsi @ Xy ) ) ) ) )
             => ( ( dsetconstr @ A
                  @ ^ [Xx: $i] : ( Xphi @ Xx ) )
                = ( dsetconstr @ B
                  @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[78]) ).

thf(454,plain,
    ( ( ! [SY250: $i > $o,SY251: $i > $o] :
          ( ! [Xx: $i,Xy: $i] :
              ( ( Xx = Xy )
             => ( ( SY250 @ Xx )
              <=> ( SY251 @ Xy ) ) )
         => ( ? [SY255: $i] :
                ( ( SY250 @ SY255 )
                & ! [SY256: $i] :
                    ( ( SY250 @ SY256 )
                   => ( SY255 = SY256 ) ) )
           => ( ? [SY258: $i] :
                  ( ( SY251 @ SY258 )
                  & ! [SY259: $i] :
                      ( ( SY251 @ SY259 )
                     => ( SY258 = SY259 ) ) )
             => ( ( descr
                  @ ^ [Xx: $i] : ( SY250 @ Xx ) )
                = ( descr
                  @ ^ [Xx: $i] : ( SY251 @ Xx ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[77]) ).

thf(455,plain,
    ( ( ! [SY244: $i > $o] :
          ( ? [SY246: $i] :
              ( ( SY244 @ SY246 )
              & ! [SY247: $i] :
                  ( ( SY244 @ SY247 )
                 => ( SY246 = SY247 ) ) )
         => ! [Xx: $i,Xy: $i] :
              ( ( SY244 @ Xx )
             => ( ( SY244 @ Xy )
               => ( Xx = Xy ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[76]) ).

thf(456,plain,
    ( ( omega = omega )
    = $true ),
    inference(copy,[status(thm)],[75]) ).

thf(457,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ( ( setunion @ A )
            = ( setunion @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[74]) ).

thf(458,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ( ( powerset @ A )
            = ( powerset @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[73]) ).

thf(459,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( Xx = Xy )
         => ! [Xz: $i,Xu: $i] :
              ( ( Xz = Xu )
             => ( ( setadjoin @ Xx @ Xz )
                = ( setadjoin @ Xy @ Xu ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[72]) ).

thf(460,plain,
    ( ( emptyset = emptyset )
    = $true ),
    inference(copy,[status(thm)],[71]) ).

thf(461,plain,
    ( ( ! [SY226: $i > $o,SY227: $i > $o] :
          ( ! [Xx: $i,Xy: $i] :
              ( ( Xx = Xy )
             => ( ( SY226 @ Xx )
              <=> ( SY227 @ Xy ) ) )
         => ( ? [SY231: $i] :
                ( ( SY226 @ SY231 )
                & ! [SY232: $i] :
                    ( ( SY226 @ SY232 )
                   => ( SY231 = SY232 ) ) )
          <=> ? [SY234: $i] :
                ( ( SY227 @ SY234 )
                & ! [SY235: $i] :
                    ( ( SY227 @ SY235 )
                   => ( SY234 = SY235 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[70]) ).

thf(462,plain,
    ( ( ! [SY220: $i > $o] :
          ( ? [SY222: $i] :
              ( ( SY220 @ SY222 )
              & ! [SY223: $i] :
                  ( ( SY220 @ SY223 )
                 => ( SY222 = SY223 ) ) )
         => ! [Xx: $i,Xy: $i] :
              ( ( SY220 @ Xx )
             => ( ( SY220 @ Xy )
               => ( Xx = Xy ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[69]) ).

thf(463,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ! [Xx: $i,Xy: $i] :
              ( ( Xx = Xy )
             => ( ( in @ Xx @ A )
              <=> ( in @ Xy @ B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[68]) ).

thf(464,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A = B )
         => ! [Xx: $i,Xy: $i] :
              ( ( Xx = Xy )
             => ( ( in @ Xx @ A )
               => ( in @ Xy @ B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[67]) ).

thf(465,plain,
    ( ( ! [SY206: $i > $o] :
          ( ? [Xx: $i] :
            ! [Xy: $i] :
              ( ( SY206 @ Xy )
            <=> ( Xy = Xx ) )
         => ? [SY210: $i] :
              ( ( SY206 @ SY210 )
              & ! [SY211: $i] :
                  ( ( SY206 @ SY211 )
                 => ( SY210 = SY211 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[66]) ).

thf(466,plain,
    ( ( ! [SY199: $i > $o] :
          ( ? [Xx: $i] : ( SY199 @ Xx )
         => ( ! [Xx: $i,Xy: $i] :
                ( ( SY199 @ Xx )
               => ( ( SY199 @ Xy )
                 => ( Xx = Xy ) ) )
           => ? [SY204: $i] :
                ( ( SY199 @ SY204 )
                & ! [SY205: $i] :
                    ( ( SY199 @ SY205 )
                   => ( SY204 = SY205 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[65]) ).

thf(467,plain,
    ( ( ! [SY193: $i > $o] :
          ( ? [Xx: $i] :
              ( ( SY193 @ Xx )
              & ! [Xy: $i] :
                  ( ( SY193 @ Xy )
                 => ( Xx = Xy ) ) )
         => ? [SY197: $i] :
              ( ( SY193 @ SY197 )
              & ! [SY198: $i] :
                  ( ( SY193 @ SY198 )
                 => ( SY197 = SY198 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[64]) ).

thf(468,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ~ ! [Xx: $i] :
                ( ( in @ Xx @ A )
               => ( Xphi @ Xx ) )
         => ? [Xx: $i] :
              ( ( in @ Xx @ A )
              & ~ ( Xphi @ Xx ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[63]) ).

thf(469,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ~ ? [Xx: $i] :
                ( ( in @ Xx @ A )
                & ( Xphi @ Xx ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ~ ( Xphi @ Xx ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[62]) ).

thf(470,plain,
    ( ( ! [Xphi: $o] :
          ( Xphi
         => ( set2prop @ ( prop2set @ Xphi ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[61]) ).

thf(471,plain,
    ( ( ! [Xphi: $o] :
          ( Xphi
         => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[60]) ).

thf(472,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ? [Xx: $i] :
              ( ( in @ Xx @ A )
              & ~ ( Xphi @ Xx ) )
         => ~ ! [Xx: $i] :
                ( ( in @ Xx @ A )
               => ( Xphi @ Xx ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[59]) ).

thf(473,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ~ ? [Xx: $i] :
                ( ( in @ Xx @ A )
                & ( Xphi @ Xx ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ~ ( Xphi @ Xx ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[58]) ).

thf(474,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ~ ( Xphi @ Xx ) )
         => ~ ? [Xx: $i] :
                ( ( in @ Xx @ A )
                & ( Xphi @ Xx ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[57]) ).

thf(475,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ~ ! [Xx: $i] :
                ( ( in @ Xx @ A )
               => ( Xphi @ Xx ) )
         => ? [Xx: $i] :
              ( ( in @ Xx @ A )
              & ~ ( Xphi @ Xx ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[56]) ).

thf(476,plain,
    ( ( ! [Xphi: $i > $o,Xx: $i] :
          ( ( in @ Xx @ emptyset )
         => ( Xphi @ Xx ) ) )
    = $true ),
    inference(copy,[status(thm)],[55]) ).

thf(477,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ? [Xx: $i] :
              ( ( in @ Xx @ A )
              & ( Xphi @ Xx ) )
         => ( ( ( dsetconstr @ A
                @ ^ [Xx: $i] : ( Xphi @ Xx ) )
              = emptyset )
           => $false ) ) )
    = $true ),
    inference(copy,[status(thm)],[54]) ).

thf(478,plain,
    ( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[53]) ).

thf(479,plain,
    ( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[52]) ).

thf(480,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i] :
          ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
         => ( ( Xz = Xx )
            | ( Xz = Xy ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[51]) ).

thf(481,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
         => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[50]) ).

thf(482,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( Xx = Xy )
         => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[49]) ).

thf(483,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( Xx != Xy )
         => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[48]) ).

thf(484,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
         => ( Xx = Xy ) ) )
    = $true ),
    inference(copy,[status(thm)],[47]) ).

thf(485,plain,
    ( ( ! [SY144: $i] :
          ( ( SY144 != emptyset )
         => ? [Xx: $i] :
              ( ( in @ Xx @ SY144 )
              & $true ) ) )
    = $true ),
    inference(copy,[status(thm)],[46]) ).

thf(486,plain,
    ( ( ! [SY138: $i > $o] :
          ( ? [SY140: $i] :
              ( ( SY138 @ SY140 )
              & ! [SY141: $i] :
                  ( ( SY138 @ SY141 )
                 => ( SY140 = SY141 ) ) )
         => ? [Xx: $i] :
            ! [Xy: $i] :
              ( ( SY138 @ Xy )
            <=> ( Xy = Xx ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[45]) ).

thf(487,plain,
    ( ( ! [A: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[44]) ).

thf(488,plain,
    ( ( ! [A: $i,Xx: $i] :
          ( ( in @ Xx @ ( setunion @ A ) )
         => ! [Xphi: $o] :
              ( ! [B: $i] :
                  ( ( in @ Xx @ B )
                 => ( ( in @ B @ A )
                   => Xphi ) )
             => Xphi ) ) )
    = $true ),
    inference(copy,[status(thm)],[43]) ).

thf(489,plain,
    ( ( ! [A: $i,Xx: $i,B: $i] :
          ( ( in @ Xx @ B )
         => ( ( in @ B @ A )
           => ( in @ Xx @ ( setunion @ A ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[42]) ).

thf(490,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ( ( in @ Xx @ B )
           => ( in @ Xx @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[41]) ).

thf(491,plain,
    ( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[40]) ).

thf(492,plain,
    ( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[39]) ).

thf(493,plain,
    ( ( ! [A: $i,B: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ B )
             => ( in @ Xx @ A ) )
         => ( in @ B @ ( powerset @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[38]) ).

thf(494,plain,
    ( ( ! [A: $i] :
          ( ( dsetconstr @ A
            @ ^ [Xx: $i] : $true )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[37]) ).

thf(495,plain,
    ( ( ! [Xx: $i,A: $i,Xy: $i] :
          ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
         => ( ( Xy = Xx )
            | ( in @ Xy @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[36]) ).

thf(496,plain,
    ( ( ! [Xx: $i,A: $i,Xy: $i] :
          ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
         => ! [Xphi: $o] :
              ( ( ( Xy = Xx )
               => Xphi )
             => ( ( ( in @ Xy @ A )
                 => Xphi )
               => Xphi ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[35]) ).

thf(497,plain,
    ( ( ! [Xx: $i,A: $i,Xy: $i] :
          ( ( in @ Xy @ A )
         => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[34]) ).

thf(498,plain,
    ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
    = $true ),
    inference(copy,[status(thm)],[33]) ).

thf(499,plain,
    ( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
    = $true ),
    inference(copy,[status(thm)],[32]) ).

thf(500,plain,
    ( ( ! [SY105: $i] :
          ( ? [Xx: $i] : ( in @ Xx @ SY105 )
         => ( SY105 != emptyset ) ) )
    = $true ),
    inference(copy,[status(thm)],[31]) ).

thf(501,plain,
    ( ( ! [SY101: $i,SY102: $i > $o,SY103: $i] :
          ( ( in @ SY103 @ SY101 )
         => ( ( SY102 @ SY103 )
           => ( ( dsetconstr @ SY101
                @ ^ [Xy: $i] : ( SY102 @ Xy ) )
             != emptyset ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[30]) ).

thf(502,plain,
    ( ( ! [SY99: $i] :
          ( ( SY99 != emptyset )
         => ? [Xx: $i] : ( in @ Xx @ SY99 ) ) )
    = $true ),
    inference(copy,[status(thm)],[29]) ).

thf(503,plain,
    ( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ( in @ Xx
              @ ( dsetconstr @ A
                @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
          <=> ( Xphi @ Xx ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[28]) ).

thf(504,plain,
    ( ( ! [A: $i] :
          ( ! [Xx: $i] :
              ~ ( in @ Xx @ A )
         => ( A = emptyset ) ) )
    = $true ),
    inference(copy,[status(thm)],[27]) ).

thf(505,plain,
    ( ( ! [A: $i] :
          ( ! [Xx: $i] :
              ~ ( in @ Xx @ A )
         => ( A = emptyset ) ) )
    = $true ),
    inference(copy,[status(thm)],[26]) ).

thf(506,plain,
    ( ( ! [A: $i,B: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ Xx @ B ) )
         => ( ! [Xx: $i] :
                ( ( in @ Xx @ B )
               => ( in @ Xx @ A ) )
           => ( A = B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[25]) ).

thf(507,plain,
    ( ( ! [SY82: $i > $o] :
          ( ? [SY84: $i] :
              ( ( SY82 @ SY84 )
              & ! [SY85: $i] :
                  ( ( SY82 @ SY85 )
                 => ( SY84 = SY85 ) ) )
         => ? [Xx: $i] : ( SY82 @ Xx ) ) )
    = $true ),
    inference(copy,[status(thm)],[24]) ).

thf(508,plain,
    ( ( ! [Xx: $i] :
          ~ ( in @ Xx @ emptyset ) )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(509,plain,
    ( ( ! [Xx: $i] :
          ( ( in @ Xx @ emptyset )
         => $false ) )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(510,plain,
    ( ( ! [Xx: $i] :
          ( ( in @ Xx @ emptyset )
         => ! [Xphi: $o] : Xphi ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(511,plain,
    ( ( ! [Xphi: $o,Xx: $i] :
          ( ( in @ Xx @ ( prop2set @ Xphi ) )
         => Xphi ) )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(512,plain,
    ( ( ! [SY70: $i > $o] :
          ( ? [SY72: $i] :
              ( ( SY70 @ SY72 )
              & ! [SY73: $i] :
                  ( ( SY70 @ SY73 )
                 => ( SY72 = SY73 ) ) )
         => ? [Xx: $i] :
              ( ( SY70 @ Xx )
              & ! [Xy: $i] :
                  ( ( SY70 @ Xy )
                 => ( Xx = Xy ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[19]) ).

thf(513,plain,
    ( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
          ( ( in @ Xx
            @ ( dsetconstr @ A
              @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
         => ( Xphi @ Xx ) ) )
    = $true ),
    inference(copy,[status(thm)],[18]) ).

thf(514,plain,
    ( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
          ( ( in @ Xx
            @ ( dsetconstr @ A
              @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
         => ( in @ Xx @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[17]) ).

thf(515,plain,
    ( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ( Xphi @ Xx )
           => ( in @ Xx
              @ ( dsetconstr @ A
                @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(516,plain,
    ( ( ! [SY53: $i > $o] :
          ( ? [SY55: $i] :
              ( ( SY53 @ SY55 )
              & ! [SY56: $i] :
                  ( ( SY53 @ SY56 )
                 => ( SY55 = SY56 ) ) )
         => ( SY53
            @ ( descr
              @ ^ [Xx: $i] : ( SY53 @ Xx ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(517,plain,
    ( ( ! [A: $i] :
        ? [B: $i] :
          ( ! [C: $i] :
              ( ( in @ C @ B )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ C )
                 => ( in @ Xx @ A ) ) )
          & ! [Xx: $i,Xy: $i] :
              ( ( ( in @ Xx @ A )
                & ( in @ Xy @ A ) )
             => ( ! [C: $i] :
                    ( ( in @ C @ B )
                   => ( ( in @ Xx @ C )
                    <=> ( in @ Xy @ C ) ) )
               => ( Xx = Xy ) ) )
          & ! [C: $i,D: $i] :
              ( ( ( in @ C @ B )
                & ( in @ D @ B ) )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ C )
                   => ( in @ Xx @ D ) )
                | ! [Xx: $i] :
                    ( ( in @ Xx @ D )
                   => ( in @ Xx @ C ) ) ) )
          & ! [C: $i] :
              ( ( ! [Xx: $i] :
                    ( ( in @ Xx @ C )
                   => ( in @ Xx @ A ) )
                & ? [Xx: $i] : ( in @ Xx @ C ) )
             => ? [D: $i,Xx: $i] :
                  ( ( in @ D @ B )
                  & ( in @ Xx @ C )
                  & ~ ? [Xy: $i] :
                        ( ( in @ Xy @ D )
                        & ( in @ Xy @ C ) )
                  & ! [E: $i] :
                      ( ( in @ E @ B )
                     => ( ! [Xy: $i] :
                            ( ( in @ Xy @ E )
                           => ( in @ Xy @ D ) )
                        | ( in @ Xx @ E ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(518,plain,
    ( ( ! [A: $i] :
          ( ? [Xx: $i] : ( in @ Xx @ A )
         => ? [B: $i] :
              ( ( in @ B @ A )
              & ~ ? [Xx: $i] :
                    ( ( in @ Xx @ B )
                    & ( in @ Xx @ A ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(519,plain,
    ( ( ! [SY21: $i > $i > $o,SY22: $i] :
          ( ! [SY23: $i] :
              ( ( in @ SY23 @ SY22 )
             => ? [SY25: $i] :
                  ( ( SY21 @ SY23 @ SY25 )
                  & ! [SY26: $i] :
                      ( ( SY21 @ SY23 @ SY26 )
                     => ( SY25 = SY26 ) ) ) )
         => ? [B: $i] :
            ! [Xx: $i] :
              ( ( in @ Xx @ B )
            <=> ? [Xy: $i] :
                  ( ( in @ Xy @ SY22 )
                  & ( SY21 @ Xy @ Xx ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[12]) ).

thf(520,plain,
    ( ( ! [A: $i] :
          ( ( ( in @ emptyset @ A )
            & ! [Xx: $i] :
                ( ( ( in @ Xx @ omega )
                  & ( in @ Xx @ A ) )
               => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ omega )
             => ( in @ Xx @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(521,plain,
    ( ( ! [Xx: $i] :
          ( ( in @ Xx @ omega )
         => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(522,plain,
    ( ( in @ emptyset @ omega )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(523,plain,
    ( ( ! [A: $i,Xx: $i] :
          ( ( in @ Xx @ ( setunion @ A ) )
        <=> ? [B: $i] :
              ( ( in @ Xx @ B )
              & ( in @ B @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[8]) ).

thf(524,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
        <=> ! [Xx: $i] :
              ( ( in @ Xx @ B )
             => ( in @ Xx @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[7]) ).

thf(525,plain,
    ( ( ! [Xx: $i,A: $i,Xy: $i] :
          ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
        <=> ( ( Xy = Xx )
            | ( in @ Xy @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6]) ).

thf(526,plain,
    ( ( ! [Xx: $i] :
          ~ ( in @ Xx @ emptyset ) )
    = $true ),
    inference(copy,[status(thm)],[5]) ).

thf(527,plain,
    ( ( ! [A: $i,B: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
            <=> ( in @ Xx @ B ) )
         => ( A = B ) ) )
    = $true ),
    inference(copy,[status(thm)],[4]) ).

thf(528,plain,
    ( ( ~ ! [A: $i,X: $i] :
            ( ( in @ X @ ( powerset @ A ) )
           => ! [Y: $i] :
                ( ( in @ Y @ ( powerset @ A ) )
               => ! [Xx: $i] :
                    ( ( in @ Xx @ A )
                   => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
                     => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[266]) ).

thf(529,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
          | ( func @ SX0 @ SX1 @ SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[336,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(530,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ~ ~ ! [SX2: $i] :
                    ~ ~ ( ~ ( in @ SX2 @ SX0 )
                        | ~ ( SX1 @ SX2 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ SX0 )
              | ~ ( SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[469,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(531,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ! [SX3: $i] :
                  ( ~ ( in @ SX3 @ SX0 )
                  | ~ ( subset @ SX1 @ SX2 )
                  | ~ ~ ( in @ SX3 @ SX2 )
                  | ~ ( in @ SX3 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[287,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(532,plain,
    ( ( ! [SX0: $i > $o] :
          ( ~ ~ ! [SX1: $i] :
                  ~ ~ ( ~ ( SX0 @ SX1 )
                      | ~ ! [SX2: $i] :
                            ( ~ ( SX0 @ SX2 )
                            | ( SX1 = SX2 ) ) )
          | ~ ! [SX1: $i] :
                ~ ! [SX2: $i] :
                    ~ ( ~ ( ~ ( SX0 @ SX2 )
                          | ( SX2 = SX1 ) )
                      | ~ ( ( SX2 != SX1 )
                          | ( SX0 @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[486,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(533,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( func @ SX0 @ SX1 @ SX2 )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX0 )
              | ( in @ ( kpair @ SX3 @ ( ap @ SX0 @ SX1 @ SX2 @ SX3 ) ) @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[327,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(534,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( in @ SX0 @ emptyset )
          | ! [SX1: $o] : SX1 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[510,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(535,plain,
    ( ( ! [SX0: $i,SX1: $o,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX0 )
              | ~ ~ SX1
              | ( in @ SX3
                @ ( dsetconstr @ SX0
                  @ ^ [SX4: $i] :
                      ( ~ ( ~ SX1
                          | ( SX4 != SX2 ) )
                      | ~ ( ~ ~ SX1
                          | ( SX4 != SX3 ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[311,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(536,plain,
    ( ( ! [SX0: $i > $o] :
          ( ~ ~ ! [SX1: $i] :
                  ~ ~ ( ~ ( SX0 @ SX1 )
                      | ~ ! [SX2: $i] :
                            ( ~ ( SX0 @ SX2 )
                            | ( SX1 = SX2 ) ) )
          | ! [SX1: $i,SX2: $i] :
              ( ~ ( SX0 @ SX1 )
              | ~ ( SX0 @ SX2 )
              | ( SX1 = SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[455,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(537,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
                | ! [SX2: $i] :
                    ( ~ ( in @ SX2 @ SX1 )
                    | ( in @ SX2 @ SX0 ) ) )
            | ~ ( ~ ! [SX2: $i] :
                      ( ~ ( in @ SX2 @ SX1 )
                      | ( in @ SX2 @ SX0 ) )
                | ( in @ SX1 @ ( powerset @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[524,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(538,plain,
    ( ( ! [SX0: $i > $o] :
          ( ~ ~ ! [SX1: $i] :
                  ~ ~ ( ~ ( SX0 @ SX1 )
                      | ~ ! [SX2: $i] :
                            ( ~ ( SX0 @ SX2 )
                            | ( SX1 = SX2 ) ) )
          | ! [SX1: $i,SX2: $i] :
              ( ~ ( SX0 @ SX1 )
              | ~ ( SX0 @ SX2 )
              | ( SX1 = SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[462,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(539,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ! [SX3: $i] :
                  ( ~ ( in @ SX3 @ SX0 )
                  | ~ ( in @ SX3 @ ( setminus @ SX0 @ ( binunion @ SX1 @ SX2 ) ) )
                  | ~ ( in @ SX3 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[267,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(540,plain,
    ( ( ! [SX0: $o] :
          ( ~ SX0
          | ( in @ emptyset @ ( prop2set @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[471,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(541,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ~ ! [SX2: $i] :
                  ~ ~ ( ~ ( in @ SX2 @ SX0 )
                      | ~ ~ ( SX1 @ SX2 ) )
          | ~ ! [SX2: $i] :
                ( ~ ( in @ SX2 @ SX0 )
                | ( SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[472,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(542,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
          | ~ ( in @ SX2 @ SX0 )
          | ( in @ SX2 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[406,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(543,plain,
    ( ( ! [SX0: $i > $o] :
          ( ~ ~ ! [SX1: $i] :
                  ~ ~ ( ~ ( SX0 @ SX1 )
                      | ~ ! [SX2: $i] :
                            ( ~ ( SX0 @ SX2 )
                            | ( SX1 = SX2 ) ) )
          | ~ ! [SX1: $i] :
                ~ ~ ( ~ ( SX0 @ SX1 )
                    | ~ ! [SX2: $i] :
                          ( ~ ( SX0 @ SX2 )
                          | ( SX1 = SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[467,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(544,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ~ ~ ( in @ SX2 @ SX1 )
          | ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[410,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(545,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX1 )
              | ( in @ ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[383,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(546,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ! [SX2: $i] :
                ~ ( ~ ( ~ ( in @ SX2 @ SX0 )
                      | ( in @ SX2 @ SX1 ) )
                  | ~ ( ~ ( in @ SX2 @ SX1 )
                      | ( in @ SX2 @ SX0 ) ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[527,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(547,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ~ ~ ! [SX2: $i] :
                    ~ ~ ( ~ ( in @ SX2 @ SX0 )
                        | ~ ( SX1 @ SX2 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ SX0 )
              | ~ ( SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[473,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(548,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( subset @ SX0 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[450,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(549,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ( in @ ( powerset @ SX1 ) @ ( powerset @ ( powerset @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[299,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(550,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ~ ( in @ SX2 @ SX0 )
          | ~ ~ ( in @ SX2 @ SX1 )
          | ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[396,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(551,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i > $i > $o,SX3: $i,SX4: $i] :
          ( ~ ( in @ ( kpair @ SX3 @ SX4 )
              @ ( dpsetconstr @ SX0 @ SX1
                @ ^ [SX5: $i,SX6: $i] : ( SX2 @ SX5 @ SX6 ) ) )
          | ( in @ SX4 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[341,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(552,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( subset @ SX0 @ emptyset )
          | ( SX0 = emptyset ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[436,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(553,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) )
          | ( SX0 = SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[369,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(554,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
           != ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) )
          | ( SX1 = SX3 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[358,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(555,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ~ ( in @ SX2 @ SX1 )
          | ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[397,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(556,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ~ ( in @ ( kpair @ SX2 @ SX3 ) @ ( cartprod @ SX0 @ SX1 ) )
          | ( in @ SX2 @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[352,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(557,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX1 )
              | ( ( kpair @ SX2 @ SX3 )
                = ( kpair @ SX2 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[350,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(558,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
          | ! [SX3: $i > $o] :
              ( ~ ! [SX4: $i] :
                    ( ~ ( in @ SX4 @ SX0 )
                    | ! [SX5: $i] :
                        ( ~ ( in @ SX5 @ SX1 )
                        | ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 )
                        | ( SX3 @ ( kpair @ SX4 @ SX5 ) ) ) )
              | ! [SX4: $i] :
                  ( ~ ( in @ SX4 @ SX2 )
                  | ( SX3 @ SX4 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[329,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(559,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( singleton @ SX0 )
          | ( in @ ( setunion @ SX0 ) @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[367,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(560,plain,
    ( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ~ ( SX1 @ SX2 )
          | ( ( dsetconstr @ SX0
              @ ^ [SX3: $i] : ( SX1 @ SX3 ) )
           != emptyset ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[501,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(561,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ emptyset ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[361,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(562,plain,
    ( ( ! [SX0: $i,SX1: $o,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX0 )
              | ~ SX1
              | ( in @ SX2
                @ ( dsetconstr @ SX0
                  @ ^ [SX4: $i] :
                      ( ~ ( ~ SX1
                          | ( SX4 != SX2 ) )
                      | ~ ( ~ ~ SX1
                          | ( SX4 != SX3 ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[309,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(563,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( func @ SX0 @ SX1 @ SX2 )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX0 )
              | ( in
                @ ( setunion
                  @ ( dsetconstr @ SX1
                    @ ^ [SX4: $i] : ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 ) ) )
                @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[338,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(564,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( subset @ SX1 @ SX0 )
          | ( ( binintersect @ SX0 @ SX1 )
            = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[413,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(565,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ( subset @ ( setminus @ SX0 @ ( setminus @ SX0 @ SX1 ) ) @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[281,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(566,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( subset @ SX0 @ SX1 )
          | ( ( binintersect @ SX0 @ SX1 )
            = SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[418,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(567,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ~ ( subset @ SX1 @ ( setminus @ SX0 @ SX2 ) )
              | ( subset @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[274,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(568,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ ( funcSet @ SX0 @ SX1 ) )
              | ~ ! [SX4: $i] :
                    ( ~ ( in @ SX4 @ SX0 )
                    | ( ( ap @ SX0 @ SX1 @ SX2 @ SX4 )
                      = ( ap @ SX0 @ SX1 @ SX3 @ SX4 ) ) )
              | ( SX2 = SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[319,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(569,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
          | ~ ~ ( in @ SX2 @ SX1 )
          | ~ ( in @ SX2 @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[405,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(570,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
                | ( SX2 = SX0 )
                | ( in @ SX2 @ SX1 ) )
            | ~ ( ~ ( ( SX2 = SX0 )
                    | ( in @ SX2 @ SX1 ) )
                | ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[525,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(571,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ! [SX3: $i] :
                  ( ~ ( in @ SX3 @ ( powerset @ SX0 ) )
                  | ! [SX4: $i] :
                      ( ~ ( in @ SX4 @ SX0 )
                      | ~ ( in @ SX4 @ ( binintersect @ SX1 @ SX2 ) )
                      | ( in @ SX4 @ ( binintersect @ ( binunion @ SX1 @ SX3 ) @ ( binunion @ SX2 @ SX3 ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[269,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(572,plain,
    ( ( ! [SX0: $i > $o,SX1: $i > $o] :
          ( ~ ! [SX2: $i,SX3: $i] :
                ( ( SX2 != SX3 )
                | ~ ( ~ ( ~ ( SX0 @ SX2 )
                        | ( SX1 @ SX3 ) )
                    | ~ ( ~ ( SX1 @ SX3 )
                        | ( SX0 @ SX2 ) ) ) )
          | ~ ~ ! [SX2: $i] :
                  ~ ~ ( ~ ( SX0 @ SX2 )
                      | ~ ! [SX3: $i] :
                            ( ~ ( SX0 @ SX3 )
                            | ( SX2 = SX3 ) ) )
          | ~ ~ ! [SX2: $i] :
                  ~ ~ ( ~ ( SX1 @ SX2 )
                      | ~ ! [SX3: $i] :
                            ( ~ ( SX1 @ SX3 )
                            | ( SX2 = SX3 ) ) )
          | ( ( descr
              @ ^ [SX2: $i] : ( SX0 @ SX2 ) )
            = ( descr
              @ ^ [SX2: $i] : ( SX1 @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[454,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(573,plain,
    ( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ~ ( SX1 @ SX2 )
          | ( in @ SX2
            @ ( dsetconstr @ SX0
              @ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[515,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(574,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( subset @ SX1 @ SX0 )
          | ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[435,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(575,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ~ ! [SX3: $i] :
                    ( ~ ( in @ SX3 @ SX0 )
                    | ~ ( in @ SX3 @ SX1 )
                    | ( in @ SX3 @ SX2 ) )
              | ~ ! [SX3: $i] :
                    ( ~ ( in @ SX3 @ SX0 )
                    | ~ ( in @ SX3 @ SX2 )
                    | ( in @ SX3 @ SX1 ) )
              | ( SX1 = SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[296,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(576,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ! [SX2: $i] :
                ( ~ ( in @ SX2 @ SX0 )
                | ( in @ SX2 @ SX1 ) )
          | ~ ! [SX2: $i] :
                ( ~ ( in @ SX2 @ SX1 )
                | ( in @ SX2 @ SX0 ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[506,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(577,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i > $i > $o,SX3: $i] :
          ( ~ ( in @ SX3 @ SX0 )
          | ! [SX4: $i] :
              ( ~ ( in @ SX4 @ SX1 )
              | ~ ( in @ ( kpair @ SX3 @ SX4 )
                  @ ( dpsetconstr @ SX0 @ SX1
                    @ ^ [SX5: $i,SX6: $i] : ( SX2 @ SX5 @ SX6 ) ) )
              | ( SX2 @ SX3 @ SX4 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[343,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(578,plain,
    ( ( ! [SX0: $i] :
          ( ~ ! [SX1: $i] :
                ~ ( in @ SX1 @ SX0 )
          | ( SX0 = emptyset ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[504,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(579,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ~ ! [SX2: $i] :
                  ( ~ ( in @ SX2 @ SX0 )
                  | ( SX1 @ SX2 ) )
          | ~ ! [SX2: $i] :
                ~ ~ ( ~ ( in @ SX2 @ SX0 )
                    | ~ ~ ( SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[475,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(580,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $o] :
          ( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
          | ~ ( ~ ( in @ SX2 @ SX0 )
              | SX3 )
          | ~ ( ~ ( in @ SX2 @ SX1 )
              | SX3 )
          | SX3 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[426,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(581,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX1 @ SX2 )
          | ~ ( in @ SX2 @ SX0 )
          | ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[489,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(582,plain,
    ( ( ! [SX0: $i] :
          ( ~ ~ ( ~ ( in @ emptyset @ SX0 )
                | ~ ! [SX1: $i] :
                      ( ~ ~ ( ~ ( in @ SX1 @ omega )
                            | ~ ( in @ SX1 @ SX0 ) )
                      | ( in @ ( setadjoin @ SX1 @ SX1 ) @ SX0 ) ) )
          | ! [SX1: $i] :
              ( ~ ( in @ SX1 @ omega )
              | ( in @ SX1 @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[520,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(583,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
            | ! [SX2: $i] :
                ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
                | ! [SX3: $i] :
                    ( ~ ( in @ SX3 @ SX0 )
                    | ~ ( in @ SX3 @ ( setminus @ SX0 @ ( binunion @ SX1 @ SX2 ) ) )
                    | ( in @ SX3 @ ( setminus @ SX0 @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[528,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(584,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ~ ( subset @ SX1 @ ( setminus @ SX0 @ SX2 ) )
              | ! [SX3: $i] :
                  ( ~ ( in @ SX3 @ SX0 )
                  | ~ ( in @ SX3 @ SX2 )
                  | ( in @ SX3 @ ( setminus @ SX0 @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[275,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(585,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ~ ! [SX2: $i] :
                  ~ ~ ( ~ ( in @ SX2 @ SX0 )
                      | ~ ( SX1 @ SX2 ) )
          | ( ( dsetconstr @ SX0
              @ ^ [SX2: $i] : ( SX1 @ SX2 ) )
           != emptyset )
          | $false ) )
    = $true ),
    inference(unfold_def,[status(thm)],[477,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(586,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ! [SX2: $i] :
                ( ~ ( in @ SX2 @ SX0 )
                | ( in @ SX2 @ SX1 ) )
          | ( subset @ SX0 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[452,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(587,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ( in @ ( binintersect @ SX1 @ SX2 ) @ ( powerset @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[301,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(588,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ! [SX2: $i,SX3: $i] :
              ( ( SX2 != SX3 )
              | ~ ( in @ SX2 @ SX0 )
              | ( in @ SX3 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[464,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(589,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i > $i > $o,SX3: $i,SX4: $i] :
          ( ~ ( in @ ( kpair @ SX3 @ SX4 )
              @ ( dpsetconstr @ SX0 @ SX1
                @ ^ [SX5: $i,SX6: $i] : ( SX2 @ SX5 @ SX6 ) ) )
          | ( SX2 @ SX3 @ SX4 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[340,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(590,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ( ( kpair @ SX0 @ SX1 )
           != ( kpair @ SX2 @ SX3 ) )
          | ( SX0 = SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[363,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(591,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( subset @ SX0 @ SX1 )
          | ~ ( in @ SX2 @ SX0 )
          | ( in @ SX2 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[447,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(592,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( func @ SX0 @ SX1 @ SX2 )
          | ! [SX3: $i] :
              ( ~ ( func @ SX0 @ SX1 @ SX3 )
              | ~ ! [SX4: $i] :
                    ( ~ ( in @ SX4 @ SX0 )
                    | ( ( ap @ SX0 @ SX1 @ SX2 @ SX4 )
                      = ( ap @ SX0 @ SX1 @ SX3 @ SX4 ) ) )
              | ! [SX4: $i] :
                  ( ~ ( in @ SX4 @ SX0 )
                  | ! [SX5: $i] :
                      ( ~ ( in @ SX5 @ SX1 )
                      | ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX3 )
                      | ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[324,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(593,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( iskpair @ SX0 )
          | ( singleton
            @ ( dsetconstr @ ( setunion @ SX0 )
              @ ^ [SX1: $i] : ( in @ ( setadjoin @ SX1 @ emptyset ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[368,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(594,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
          | ~ ! [SX3: $i] :
                ~ ~ ( ~ ( in @ SX3 @ SX0 )
                    | ~ ~ ! [SX4: $i] :
                            ~ ~ ( ~ ( in @ SX4 @ SX1 )
                                | ( SX2
                                 != ( kpair @ SX3 @ SX4 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[380,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(595,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ! [SX3: $i] :
                  ( ~ ( in @ SX3 @ SX0 )
                  | ~ ( in @ SX1 @ ( powerset @ SX2 ) )
                  | ~ ( in @ SX3 @ SX1 )
                  | ( in @ SX3 @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[293,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(596,plain,
    ( ( ! [SX0: $i] :
          ( ~ ! [SX1: $i] :
                ~ ( in @ SX1 @ SX0 )
          | ( SX0 = emptyset ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[505,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(597,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
          | ( SX2 = SX0 )
          | ( in @ SX2 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[495,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(598,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ! [SX2: $i] :
                ( ~ ( in @ SX2 @ SX0 )
                | ! [SX3: $i] :
                    ( ~ ( in @ SX3 @ SX0 )
                    | ~ ( SX1 @ SX2 )
                    | ~ ( SX1 @ SX3 )
                    | ( SX2 = SX3 ) ) )
          | ~ ~ ! [SX2: $i] :
                  ~ ~ ( ~ ( in @ SX2 @ SX0 )
                      | ~ ( SX1 @ SX2 ) )
          | ( singleton
            @ ( dsetconstr @ SX0
              @ ^ [SX2: $i] : ( SX1 @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[374,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(599,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i > $i > $o,SX3: $i,SX4: $i] :
          ( ~ ( in @ ( kpair @ SX3 @ SX4 )
              @ ( dpsetconstr @ SX0 @ SX1
                @ ^ [SX5: $i,SX6: $i] : ( SX2 @ SX5 @ SX6 ) ) )
          | ( in @ SX3 @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[342,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(600,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( ( SX0 != SX1 ) )
          | ~ ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[483,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(601,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i > $i] :
          ( ~ ! [SX3: $i] :
                ( ~ ( in @ SX3 @ SX0 )
                | ( in @ ( SX2 @ SX3 ) @ SX1 ) )
          | ( ( lam @ SX0 @ SX1
              @ ^ [SX3: $i] : ( SX2 @ SX3 ) )
            = ( lam @ SX0 @ SX1
              @ ^ [SX3: $i] : ( SX2 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[314,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(602,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ( in @ ( setadjoin @ SX2 @ emptyset ) @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[388,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(603,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i > $i] :
          ( ~ ! [SX3: $i] :
                ( ~ ( in @ SX3 @ SX0 )
                | ( in @ ( SX2 @ SX3 ) @ SX1 ) )
          | ( in
            @ ( lam @ SX0 @ SX1
              @ ^ [SX3: $i] : ( SX2 @ SX3 ) )
            @ ( funcSet @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[331,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(604,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( ( setunion @ SX0 )
            = ( setunion @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[457,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(605,plain,
    ( ( ! [SX0: $i] :
          ~ ! [SX1: $i] :
              ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX2: $i] :
                                    ( ~ ( in @ SX2 @ SX1 )
                                    | ! [SX3: $i] :
                                        ( ~ ( in @ SX3 @ SX2 )
                                        | ( in @ SX3 @ SX0 ) ) )
                              | ~ ! [SX2: $i,SX3: $i] :
                                    ( ~ ~ ( ~ ( in @ SX2 @ SX0 )
                                          | ~ ( in @ SX3 @ SX0 ) )
                                    | ~ ! [SX4: $i] :
                                          ( ~ ( in @ SX4 @ SX1 )
                                          | ~ ( ~ ( ~ ( in @ SX2 @ SX4 )
                                                  | ( in @ SX3 @ SX4 ) )
                                              | ~ ( ~ ( in @ SX3 @ SX4 )
                                                  | ( in @ SX2 @ SX4 ) ) ) )
                                    | ( SX2 = SX3 ) ) )
                        | ~ ! [SX2: $i,SX3: $i] :
                              ( ~ ~ ( ~ ( in @ SX2 @ SX1 )
                                    | ~ ( in @ SX3 @ SX1 ) )
                              | ! [SX4: $i] :
                                  ( ~ ( in @ SX4 @ SX2 )
                                  | ( in @ SX4 @ SX3 ) )
                              | ! [SX4: $i] :
                                  ( ~ ( in @ SX4 @ SX3 )
                                  | ( in @ SX4 @ SX2 ) ) ) )
                  | ~ ! [SX2: $i] :
                        ( ~ ~ ( ~ ! [SX3: $i] :
                                    ( ~ ( in @ SX3 @ SX2 )
                                    | ( in @ SX3 @ SX0 ) )
                              | ~ ~ ! [SX3: $i] :
                                      ~ ( in @ SX3 @ SX2 ) )
                        | ~ ! [SX3: $i] :
                              ~ ~ ! [SX4: $i] :
                                    ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SX1 )
                                                    | ~ ( in @ SX4 @ SX2 ) )
                                              | ~ ~ ~ ! [SX5: $i] :
                                                        ~ ~ ( ~ ( in @ SX5 @ SX3 )
                                                            | ~ ( in @ SX5 @ SX2 ) ) )
                                        | ~ ! [SX5: $i] :
                                              ( ~ ( in @ SX5 @ SX1 )
                                              | ! [SX6: $i] :
                                                  ( ~ ( in @ SX6 @ SX5 )
                                                  | ( in @ SX6 @ SX3 ) )
                                              | ( in @ SX4 @ SX5 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[517,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(606,plain,
    ( ( ! [SX0: $i] :
          ( ~ ~ ! [SX1: $i] :
                  ~ ( in @ SX1 @ SX0 )
          | ~ ! [SX1: $i] :
                ~ ~ ( ~ ( in @ SX1 @ SX0 )
                    | ~ ~ ~ ! [SX2: $i] :
                              ~ ~ ( ~ ( in @ SX2 @ SX1 )
                                  | ~ ( in @ SX2 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[518,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(607,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
          | ( in @ SX2 @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[420,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(608,plain,
    ( ( ! [SX0: $i > $o] :
          ( ~ ~ ! [SX1: $i] :
                  ~ ~ ( ~ ( SX0 @ SX1 )
                      | ~ ! [SX2: $i] :
                            ( ~ ( SX0 @ SX2 )
                            | ( SX1 = SX2 ) ) )
          | ~ ! [SX1: $i] :
                ~ ( SX0 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[507,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(609,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ~ ~ ! [SX2: $i] :
                    ~ ~ ( ~ ( in @ SX2 @ SX0 )
                        | ~ ( in @ SX2 @ SX1 ) )
          | ( ( binintersect @ SX0 @ SX1 )
            = emptyset ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[415,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(610,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( subset @ SX0 @ SX1 )
          | ( ( setminus @ SX0 @ SX1 )
            = emptyset ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[407,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(611,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( in @ SX0 @ emptyset )
          | $false ) )
    = $true ),
    inference(unfold_def,[status(thm)],[509,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(612,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ! [SX3: $i] :
                  ( ~ ( in @ SX3 @ SX0 )
                  | ~ ~ ( in @ SX3 @ ( binunion @ SX1 @ SX2 ) )
                  | ~ ( in @ SX3 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[273,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(613,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( iskpair @ SX0 )
          | ( singleton
            @ ( dsetconstr @ ( setunion @ SX0 )
              @ ^ [SX1: $i] :
                  ( SX0
                  = ( kpair @ ( kfst @ SX0 ) @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[356,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(614,plain,
    ( ( ! [SX0: $i,SX1: $o,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX0 )
              | ~ ~ SX1
              | ( ( if @ SX0 @ SX1 @ SX2 @ SX3 )
                = SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[303,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(615,plain,
    ( ( ! [SX0: $i > $o,SX1: $i] :
          ( ~ ( in @ SX1 @ emptyset )
          | ( SX0 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[476,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(616,plain,
    ( ( ! [SX0: $o] :
          ( ~ SX0
          | ( set2prop @ ( prop2set @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[470,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(617,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ SX0 )
              | ~ ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
              | ( in @ SX2 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[291,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(618,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ( subset @ ( setminus @ SX0 @ SX1 ) @ ( setminus @ SX0 @ ( binintersect @ SX1 @ SX2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[277,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(619,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( subset @ SX0 @ SX1 )
          | ~ ~ ( in @ SX2 @ SX1 )
          | ~ ( in @ SX2 @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[446,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(620,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i > $i] :
          ( ~ ! [SX3: $i] :
                ( ~ ( in @ SX3 @ SX0 )
                | ( in @ ( SX2 @ SX3 ) @ SX1 ) )
          | ( func @ SX0 @ SX1
            @ ( dpsetconstr @ SX0 @ SX1
              @ ^ [SX3: $i,SX4: $i] :
                  ( ( SX2 @ SX3 )
                  = SX4 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[333,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(621,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ! [SX2: $i] :
                ( ~ ( in @ SX2 @ SX0 )
                | ! [SX3: $i] :
                    ( ~ ( in @ SX3 @ SX0 )
                    | ~ ( SX1 @ SX2 )
                    | ~ ( SX1 @ SX3 )
                    | ( SX2 = SX3 ) ) )
          | ~ ~ ! [SX2: $i] :
                  ~ ~ ( ~ ( in @ SX2 @ SX0 )
                      | ~ ( SX1 @ SX2 ) )
          | ( singleton
            @ ( dsetconstr @ SX0
              @ ^ [SX2: $i] : ( SX1 @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[371,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(622,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ~ ( in @ SX2 @ SX0 )
          | ~ ( in @ SX2 @ SX1 )
          | ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[398,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(623,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) )
          | ( SX2 = SX0 )
          | ( SX2 = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[387,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(624,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ( in @ ( setminus @ SX0 @ SX1 ) @ ( powerset @ ( setminus @ SX0 @ ( binintersect @ SX1 @ SX2 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[276,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(625,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ SX0 )
              | ~ ( in @ SX2 @ SX1 )
              | ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[292,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(626,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ( SX1
            = ( setminus @ SX0 @ ( setminus @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[280,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(627,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( ( powerset @ SX0 )
            = ( powerset @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[458,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(628,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ~ ( subset @ SX1 @ SX2 )
              | ( subset @ ( setminus @ SX0 @ SX2 ) @ ( setminus @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[286,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(629,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( func @ SX0 @ SX1 @ SX2 )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX0 )
              | ( ( ap @ SX0 @ SX1 @ SX2 @ SX3 )
                = ( ap @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[317,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(630,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) )
          | ( SX2 = SX0 )
          | ( SX2 = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[480,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(631,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
          | ! [SX3: $i > $o] :
              ( ~ ! [SX4: $i] :
                    ( ~ ( in @ SX4 @ SX0 )
                    | ! [SX5: $i] :
                        ( ~ ( in @ SX5 @ SX1 )
                        | ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 )
                        | ( SX3 @ ( kpair @ SX4 @ SX5 ) ) ) )
              | ! [SX4: $i] :
                  ( ~ ( in @ SX4 @ SX2 )
                  | ( SX3 @ SX4 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[330,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(632,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ~ ( in @ SX2 @ SX1 )
          | ( in @ SX2 @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[490,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(633,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ! [SX3: $i] :
                  ( ~ ( in @ SX3 @ SX0 )
                  | ~ ~ ( in @ SX3 @ SX2 )
                  | ~ ( in @ SX3 @ ( binintersect @ SX1 @ SX2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[289,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(634,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ SX0 )
          | ( in @ ( setadjoin @ SX1 @ emptyset ) @ ( powerset @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[389,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(635,plain,
    ( ( ! [SX0: $o,SX1: $i] :
          ( ~ ( in @ SX1 @ ( prop2set @ SX0 ) )
          | SX0 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[511,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(636,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX1 )
              | ( in @ ( kpair @ SX2 @ SX3 ) @ ( cartprod @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[381,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(637,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
          | ( in @ ( ksnd @ SX2 ) @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[353,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(638,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ( singleton
              @ ( dsetconstr @ SX0
                @ ^ [SX2: $i] : ( SX1 @ SX2 ) ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ SX0 )
              | ! [SX3: $i] :
                  ( ~ ( in @ SX3 @ SX0 )
                  | ~ ( SX1 @ SX2 )
                  | ~ ( SX1 @ SX3 )
                  | ( SX2 = SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[328,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(639,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ( subset @ SX1 @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[434,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(640,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX1 )
              | ( ( kfst @ ( kpair @ SX2 @ SX3 ) )
                = SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[349,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(641,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ( in @ ( setminus @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[297,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(642,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ( ( kpair @ SX0 @ SX1 )
           != ( kpair @ SX2 @ SX3 ) )
          | ( SX1 = SX3 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[357,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(643,plain,
    ( ( ! [SX0: $i > $i > $o,SX1: $i] :
          ( ~ ! [SX2: $i] :
                ( ~ ( in @ SX2 @ SX1 )
                | ~ ! [SX3: $i] :
                      ~ ~ ( ~ ( SX0 @ SX2 @ SX3 )
                          | ~ ! [SX4: $i] :
                                ( ~ ( SX0 @ SX2 @ SX4 )
                                | ( SX3 = SX4 ) ) ) )
          | ~ ! [SX2: $i] :
                ~ ! [SX3: $i] :
                    ~ ( ~ ( ~ ( in @ SX3 @ SX2 )
                          | ~ ! [SX4: $i] :
                                ~ ~ ( ~ ( in @ SX4 @ SX1 )
                                    | ~ ( SX0 @ SX4 @ SX3 ) ) )
                      | ~ ( ~ ~ ! [SX4: $i] :
                                  ~ ~ ( ~ ( in @ SX4 @ SX1 )
                                      | ~ ( SX0 @ SX4 @ SX3 ) )
                          | ( in @ SX3 @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[519,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(644,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ! [SX2: $i] :
                ( ~ ( in @ SX2 @ SX0 )
                | ( in @ SX2 @ SX1 ) )
          | ( subset @ SX0 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[449,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(645,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( subset @ SX0 @ SX1 )
          | ~ ( subset @ SX1 @ SX0 )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[437,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(646,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[429,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(647,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ! [SX3: $i] :
                  ( ~ ( in @ SX3 @ SX0 )
                  | ~ ~ ( in @ SX3 @ ( binunion @ SX1 @ SX2 ) )
                  | ~ ( in @ SX3 @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[272,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(648,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ! [SX2: $i,SX3: $i] :
              ( ( SX2 != SX3 )
              | ( ( setadjoin @ SX0 @ SX2 )
                = ( setadjoin @ SX1 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[459,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(649,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( iskpair @ SX0 )
          | ( ( kpair @ ( kfst @ SX0 ) @ ( ksnd @ SX0 ) )
            = SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[354,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(650,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ SX1 )
          | ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[427,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(651,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( subset @ SX1 @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[451,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(652,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ! [SX3: $i] :
                  ( ~ ( in @ SX3 @ SX0 )
                  | ~ ~ ( in @ SX3 @ SX1 )
                  | ~ ( in @ SX3 @ ( binintersect @ SX1 @ SX2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[290,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(653,plain,
    ( ( ! [SX0: $i > $o] :
          ( ~ ~ ! [SX1: $i] :
                  ~ ~ ( ~ ( SX0 @ SX1 )
                      | ~ ! [SX2: $i] :
                            ( ~ ( SX0 @ SX2 )
                            | ( SX1 = SX2 ) ) )
          | ( SX0
            @ ( descr
              @ ^ [SX1: $i] : ( SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[516,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(654,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
          | ~ ( in @ SX2 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[408,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(655,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ( subset @ SX1 @ ( setminus @ SX0 @ ( setminus @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[282,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(656,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ~ ! [SX2: $i] :
                  ( ~ ( in @ SX2 @ SX0 )
                  | ( SX1 @ SX2 ) )
          | ~ ! [SX2: $i] :
                ~ ~ ( ~ ( in @ SX2 @ SX0 )
                    | ~ ~ ( SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[468,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(657,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ! [SX3: $i] :
                  ( ~ ( in @ SX3 @ SX0 )
                  | ~ ( in @ SX3 @ ( setminus @ SX0 @ SX1 ) )
                  | ( in @ SX3 @ ( setminus @ SX0 @ ( binintersect @ SX1 @ SX2 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[278,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(658,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ( in @ ( binunion @ SX1 @ SX2 ) @ ( powerset @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[300,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(659,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( subset @ SX0 @ SX1 )
          | ( in @ SX0 @ ( powerset @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[438,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(660,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( setminus @ SX0 @ SX1 )
           != emptyset )
          | ( subset @ SX0 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[401,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(661,plain,
    ( ( ! [SX0: $i > $o] :
          ( ~ ~ ! [SX1: $i] :
                  ~ ( SX0 @ SX1 )
          | ~ ! [SX1: $i,SX2: $i] :
                ( ~ ( SX0 @ SX1 )
                | ~ ( SX0 @ SX2 )
                | ( SX1 = SX2 ) )
          | ~ ! [SX1: $i] :
                ~ ~ ( ~ ( SX0 @ SX1 )
                    | ~ ! [SX2: $i] :
                          ( ~ ( SX0 @ SX2 )
                          | ( SX1 = SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[466,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(662,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ~ ~ ( in @ SX2 @ SX1 )
          | ~ ( subset @ SX0 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[445,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(663,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ! [SX3: $i] :
                  ( ~ ( in @ SX3 @ ( powerset @ SX0 ) )
                  | ( in @ ( binintersect @ SX1 @ SX2 ) @ ( powerset @ ( binintersect @ ( binunion @ SX1 @ SX3 ) @ ( binunion @ SX2 @ SX3 ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[268,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(664,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
          | ! [SX3: $i] :
              ( ~ ( subset @ SX3 @ ( cartprod @ SX0 @ SX1 ) )
              | ~ ! [SX4: $i] :
                    ( ~ ( in @ SX4 @ SX0 )
                    | ! [SX5: $i] :
                        ( ~ ( in @ SX5 @ SX1 )
                        | ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 )
                        | ( in @ ( kpair @ SX4 @ SX5 ) @ SX3 ) ) )
              | ( subset @ SX2 @ SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[322,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(665,plain,
    ( ( ! [SX0: $i,SX1: $o,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX0 )
              | ~ SX1
              | ( ( if @ SX0 @ SX1 @ SX2 @ SX3 )
                = SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[304,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(666,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i > $i] :
          ( ~ ! [SX3: $i] :
                ( ~ ( in @ SX3 @ SX0 )
                | ( in @ ( SX2 @ SX3 ) @ SX1 ) )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX0 )
              | ( ( ap @ SX0 @ SX1
                  @ ( lam @ SX0 @ SX1
                    @ ^ [SX4: $i] : ( SX2 @ SX4 ) )
                  @ SX3 )
                = ( SX2 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[316,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(667,plain,
    ( ( ! [SX0: $i] :
          ( ~ ~ ! [SX1: $i] :
                  ~ ( in @ SX1 @ SX0 )
          | ( SX0 != emptyset ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[500,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(668,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
          | ( ( kpair @ ( kfst @ SX2 ) @ ( ksnd @ SX2 ) )
            = SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[347,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(669,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
          | ( ( lam @ SX0 @ SX1
              @ ^ [SX3: $i] : ( ap @ SX0 @ SX1 @ SX2 @ SX3 ) )
            = SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[312,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(670,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
           != ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) )
          | ( SX2 != SX3 )
          | ( SX1 = SX3 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[360,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(671,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ~ ( in @ ( kpair @ SX2 @ SX3 ) @ ( cartprod @ SX0 @ SX1 ) )
          | ( in @ SX3 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[351,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(672,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( func @ SX0 @ SX1 @ SX2 )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX0 )
              | ( in @ ( ap @ SX0 @ SX1 @ SX2 @ SX3 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[337,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(673,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ! [SX3: $i] :
                  ( ~ ( in @ SX3 @ SX0 )
                  | ~ ( subset @ SX1 @ ( setminus @ SX0 @ SX2 ) )
                  | ~ ( in @ SX3 @ SX2 )
                  | ~ ( in @ SX3 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[288,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(674,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i > $i > $o,SX3: $i] :
          ( ~ ( in @ SX3 @ SX0 )
          | ! [SX4: $i] :
              ( ~ ( in @ SX4 @ SX1 )
              | ~ ( SX2 @ SX3 @ SX4 )
              | ( in @ ( kpair @ SX3 @ SX4 )
                @ ( dpsetconstr @ SX0 @ SX1
                  @ ^ [SX5: $i,SX6: $i] : ( SX2 @ SX5 @ SX6 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[346,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(675,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ~ ~ ( in @ SX2 @ SX1 )
          | ( SX0 != SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[443,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(676,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ~ ( in @ SX2 @ SX1 )
          | ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[422,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(677,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ! [SX2: $i] :
                ( ~ ( in @ SX2 @ SX1 )
                | ( in @ SX2 @ SX0 ) )
          | ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[493,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(678,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ SX0 )
              | ~ ( in @ SX2 @ SX1 )
              | ( in @ SX2 @ ( setminus @ SX0 @ ( setminus @ SX0 @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[284,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(679,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
          | ( in @ SX2 @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[409,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(680,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
          | ( iskpair @ SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[379,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(681,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( func @ SX0 @ SX1 @ SX2 )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX0 )
              | ! [SX4: $i] :
                  ( ~ ( in @ SX4 @ SX1 )
                  | ~ ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 )
                  | ( ( ap @ SX0 @ SX1 @ SX2 @ SX3 )
                    = SX4 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[325,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(682,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ( in @ ( setminus @ SX1 @ SX2 ) @ ( powerset @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[298,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(683,plain,
    ( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
          ( ~ ( in @ SX2
              @ ( dsetconstr @ SX0
                @ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
          | ( in @ SX2 @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[514,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(684,plain,
    ( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ~ ( ~ ( ~ ( in @ SX2
                      @ ( dsetconstr @ SX0
                        @ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
                  | ( SX1 @ SX2 ) )
              | ~ ( ~ ( SX1 @ SX2 )
                  | ( in @ SX2
                    @ ( dsetconstr @ SX0
                      @ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[503,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(685,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ SX1 )
          | ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[497,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(686,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( func @ SX0 @ SX1 @ SX2 )
          | ! [SX3: $i] :
              ( ~ ( func @ SX0 @ SX1 @ SX3 )
              | ~ ! [SX4: $i] :
                    ( ~ ( in @ SX4 @ SX0 )
                    | ( ( ap @ SX0 @ SX1 @ SX2 @ SX4 )
                      = ( ap @ SX0 @ SX1 @ SX3 @ SX4 ) ) )
              | ( SX2 = SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[320,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(687,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ! [SX3: $i] :
                  ( ~ ( in @ SX3 @ ( powerset @ SX0 ) )
                  | ! [SX4: $i] :
                      ( ~ ( in @ SX4 @ SX0 )
                      | ~ ( in @ SX4 @ ( binintersect @ SX1 @ SX2 ) )
                      | ( in @ SX4 @ ( binunion @ SX1 @ SX3 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[271,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(688,plain,
    ( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
          ( ~ ( in @ SX2
              @ ( dsetconstr @ SX0
                @ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
          | ( SX1 @ SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[513,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(689,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ! [SX2: $i,SX3: $i] :
              ( ( SX2 != SX3 )
              | ~ ( ~ ( ~ ( in @ SX2 @ SX0 )
                      | ( in @ SX3 @ SX1 ) )
                  | ~ ( ~ ( in @ SX3 @ SX1 )
                      | ( in @ SX2 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[463,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(690,plain,
    ( ( ! [SX0: $i,SX1: $o,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX0 )
              | ( singleton
                @ ( dsetconstr @ SX0
                  @ ^ [SX4: $i] :
                      ( ~ ( ~ SX1
                          | ( SX4 != SX2 ) )
                      | ~ ( ~ ~ SX1
                          | ( SX4 != SX3 ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[307,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(691,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( binintersect @ SX0 @ SX1 )
           != SX0 )
          | ( subset @ SX0 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[412,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(692,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX1 )
              | ( in @ ( kpair @ SX2 @ SX3 ) @ ( powerset @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[382,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(693,plain,
    ( ( ! [SX0: $i,SX1: $o,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX0 )
              | ( in @ ( if @ SX0 @ SX1 @ SX2 @ SX3 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[306,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(694,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX0 )
              | ! [SX4: $i] :
                  ( ~ ( in @ SX4 @ SX1 )
                  | ~ ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 )
                  | ( ( ap @ SX0 @ SX1 @ SX2 @ SX3 )
                    = SX4 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[323,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(695,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i > $i] :
          ( ~ ! [SX3: $i] :
                ( ~ ( in @ SX3 @ SX0 )
                | ( in @ ( SX2 @ SX3 ) @ SX1 ) )
          | ( func @ SX0 @ SX1
            @ ( lam @ SX0 @ SX1
              @ ^ [SX3: $i] : ( SX2 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[332,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(696,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ! [SX2: $i] :
                ( ~ ( in @ SX2 @ SX0 )
                | ~ ( SX1 @ SX2 ) )
          | ~ ~ ! [SX2: $i] :
                  ~ ~ ( ~ ( in @ SX2 @ SX0 )
                      | ~ ( SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[474,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(697,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( setadjoin @ SX0 @ emptyset )
           != ( setadjoin @ SX1 @ emptyset ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[370,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(698,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX0 )
              | ( in @ ( ap @ SX0 @ SX1 @ SX2 @ SX3 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[335,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(699,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( ( SX0 != emptyset ) )
          | ~ ! [SX1: $i] :
                ~ ( in @ SX1 @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[502,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(700,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
          | ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[481,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(701,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
                | ~ ! [SX2: $i] :
                      ~ ~ ( ~ ( in @ SX1 @ SX2 )
                          | ~ ( in @ SX2 @ SX0 ) ) )
            | ~ ( ~ ~ ! [SX2: $i] :
                        ~ ~ ( ~ ( in @ SX1 @ SX2 )
                            | ~ ( in @ SX2 @ SX0 ) )
                | ( in @ SX1 @ ( setunion @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[523,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(702,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) )
          | ! [SX3: $o] :
              ( ~ ( ~ ( in @ SX2 @ SX0 )
                  | ~ ~ ( in @ SX2 @ SX1 )
                  | SX3 )
              | ~ ( ~ ~ ( in @ SX2 @ SX0 )
                  | ~ ( in @ SX2 @ SX1 )
                  | SX3 )
              | SX3 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[400,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(703,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ~ ( subset @ SX0 @ SX1 )
          | ( SX0 != SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[444,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(704,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
          | ~ ! [SX2: $i] :
                ~ ~ ( ~ ( in @ SX2 @ SX0 )
                    | ~ ( in @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[378,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(705,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ! [SX2: $i > $o,SX3: $i > $o] :
              ( ~ ! [SX4: $i] :
                    ( ~ ( in @ SX4 @ SX0 )
                    | ! [SX5: $i] :
                        ( ~ ( in @ SX5 @ SX1 )
                        | ( SX4 != SX5 )
                        | ~ ( ~ ( ~ ( SX2 @ SX4 )
                                | ( SX3 @ SX5 ) )
                            | ~ ( ~ ( SX3 @ SX5 )
                                | ( SX2 @ SX4 ) ) ) ) )
              | ( ( dsetconstr @ SX0
                  @ ^ [SX4: $i] : ( SX2 @ SX4 ) )
                = ( dsetconstr @ SX1
                  @ ^ [SX4: $i] : ( SX3 @ SX4 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[453,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(706,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
          | ! [SX3: $o] :
              ( ~ ( ( SX2 != SX0 )
                  | SX3 )
              | ~ ( ~ ( in @ SX2 @ SX1 )
                  | SX3 )
              | SX3 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[496,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(707,plain,
    ( ( ! [SX0: $i > $o] :
          ( ~ ~ ! [SX1: $i] :
                  ~ ~ ( ~ ( SX0 @ SX1 )
                      | ~ ! [SX2: $i] :
                            ( ~ ( SX0 @ SX2 )
                            | ( SX1 = SX2 ) ) )
          | ~ ! [SX1: $i] :
                ~ ~ ( ~ ( SX0 @ SX1 )
                    | ~ ! [SX2: $i] :
                          ( ~ ( SX0 @ SX2 )
                          | ( SX1 = SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[512,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(708,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX0 )
              | ( ( ap @ SX0 @ SX1 @ SX2 @ SX3 )
                = ( ap @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[318,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(709,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ SX0 )
              | ~ ( in @ SX2 @ ( setminus @ SX0 @ ( setminus @ SX0 @ SX1 ) ) )
              | ( in @ SX2 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[283,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(710,plain,
    ( ( ! [SX0: $i > $o,SX1: $i > $o] :
          ( ~ ! [SX2: $i,SX3: $i] :
                ( ( SX2 != SX3 )
                | ~ ( ~ ( ~ ( SX0 @ SX2 )
                        | ( SX1 @ SX3 ) )
                    | ~ ( ~ ( SX1 @ SX3 )
                        | ( SX0 @ SX2 ) ) ) )
          | ~ ( ~ ( ~ ~ ! [SX2: $i] :
                          ~ ~ ( ~ ( SX0 @ SX2 )
                              | ~ ! [SX3: $i] :
                                    ( ~ ( SX0 @ SX3 )
                                    | ( SX2 = SX3 ) ) )
                  | ~ ! [SX2: $i] :
                        ~ ~ ( ~ ( SX1 @ SX2 )
                            | ~ ! [SX3: $i] :
                                  ( ~ ( SX1 @ SX3 )
                                  | ( SX2 = SX3 ) ) ) )
              | ~ ( ~ ~ ! [SX2: $i] :
                          ~ ~ ( ~ ( SX1 @ SX2 )
                              | ~ ! [SX3: $i] :
                                    ( ~ ( SX1 @ SX3 )
                                    | ( SX2 = SX3 ) ) )
                  | ~ ! [SX2: $i] :
                        ~ ~ ( ~ ( SX0 @ SX2 )
                            | ~ ! [SX3: $i] :
                                  ( ~ ( SX0 @ SX3 )
                                  | ( SX2 = SX3 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[461,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(711,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ( singleton
              @ ( dsetconstr @ SX0
                @ ^ [SX2: $i] : ( SX1 @ SX2 ) ) )
          | ~ ! [SX2: $i] :
                ~ ~ ( ~ ( in @ SX2 @ SX0 )
                    | ~ ( SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[373,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(712,plain,
    ( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ~ ( SX1 @ SX2 )
          | ~ ! [SX3: $i] :
                ( ~ ( in @ SX3 @ SX0 )
                | ~ ( SX1 @ SX3 )
                | ( SX3 = SX2 ) )
          | ( singleton
            @ ( dsetconstr @ SX0
              @ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[372,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(713,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
            = ( setadjoin @ SX0 @ emptyset ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[362,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(714,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX1 )
              | ( subset @ ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[384,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(715,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX1 )
              | ( ( ksnd @ ( kpair @ SX2 @ SX3 ) )
                = SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[348,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(716,plain,
    ( ( ! [SX0: $i,SX1: $o,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX0 )
              | ~ SX1
              | ( ( dsetconstr @ SX0
                  @ ^ [SX4: $i] :
                      ( ~ ( ~ SX1
                          | ( SX4 != SX2 ) )
                      | ~ ( ~ ~ SX1
                          | ( SX4 != SX3 ) ) ) )
                = ( setadjoin @ SX2 @ emptyset ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[308,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(717,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
          | ! [SX3: $i] :
              ( ~ ( subset @ SX3 @ ( cartprod @ SX0 @ SX1 ) )
              | ~ ! [SX4: $i] :
                    ( ~ ( in @ SX4 @ SX0 )
                    | ! [SX5: $i] :
                        ( ~ ( in @ SX5 @ SX1 )
                        | ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 )
                        | ( in @ ( kpair @ SX4 @ SX5 ) @ SX3 ) ) )
              | ~ ! [SX4: $i] :
                    ( ~ ( in @ SX4 @ SX0 )
                    | ! [SX5: $i] :
                        ( ~ ( in @ SX5 @ SX1 )
                        | ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX3 )
                        | ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 ) ) )
              | ( SX2 = SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[321,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(718,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( func @ SX0 @ SX1 @ SX2 )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX0 )
              | ( singleton
                @ ( dsetconstr @ SX1
                  @ ^ [SX4: $i] : ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[339,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(719,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ SX0 )
          | ( subset @ ( setadjoin @ SX1 @ emptyset ) @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[390,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(720,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( ( SX0 != emptyset ) )
          | ~ ! [SX1: $i] :
                ~ ~ ( ~ ( in @ SX1 @ SX0 )
                    | ~ $true ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[485,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(721,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( subset @ SX2 @ SX0 )
          | ~ ( subset @ SX2 @ SX1 )
          | ( subset @ SX2 @ ( binintersect @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[421,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(722,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ~ ~ ( in @ SX2 @ SX1 )
          | ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[399,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(723,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ~ ( subset @ ( setminus @ SX0 @ SX2 ) @ ( setminus @ SX0 @ SX1 ) )
              | ( subset @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[285,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(724,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ! [SX3: $i] :
                  ( ~ ( in @ SX3 @ ( powerset @ SX0 ) )
                  | ! [SX4: $i] :
                      ( ~ ( in @ SX4 @ SX0 )
                      | ~ ( in @ SX4 @ ( binintersect @ SX1 @ SX2 ) )
                      | ( in @ SX4 @ ( binunion @ SX2 @ SX3 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[270,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(725,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ SX0 )
          | ( in @ SX1 @ ( powerset @ ( setunion @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[487,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(726,plain,
    ( ( ! [SX0: $i,SX1: $o,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX0 )
              | ~ ~ SX1
              | ( ( dsetconstr @ SX0
                  @ ^ [SX4: $i] :
                      ( ~ ( ~ SX1
                          | ( SX4 != SX2 ) )
                      | ~ ( ~ ~ SX1
                          | ( SX4 != SX3 ) ) ) )
                = ( setadjoin @ SX3 @ emptyset ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[310,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(727,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ~ ! [SX3: $i] :
                    ( ~ ( in @ SX3 @ SX0 )
                    | ~ ( in @ SX3 @ SX1 )
                    | ( in @ SX3 @ SX2 ) )
              | ( in @ SX1 @ ( powerset @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[294,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(728,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( func @ SX0 @ SX1 @ SX2 )
          | ( ( lam @ SX0 @ SX1
              @ ^ [SX3: $i] : ( ap @ SX0 @ SX1 @ SX2 @ SX3 ) )
            = SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[315,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(729,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( binintersect @ SX0 @ SX1 )
           != SX1 )
          | ( subset @ SX1 @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[417,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(730,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
          | ( in @ ( kfst @ SX2 ) @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[365,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(731,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[482,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(732,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( subset @ SX0 @ SX1 )
          | ~ ( subset @ SX1 @ SX2 )
          | ( subset @ SX0 @ SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[441,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(733,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ( ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
           != ( setadjoin @ SX2 @ emptyset ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[359,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(734,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( subset @ SX0 @ SX1 )
          | ( subset @ ( powerset @ SX0 ) @ ( powerset @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[432,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(735,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
           != ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) )
          | ( SX0 = SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[364,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(736,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( func @ SX0 @ SX1 @ SX2 )
          | ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[334,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(737,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
          | ( in @ SX2 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[416,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(738,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ~ ( in @ SX2 @ SX0 )
          | ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[404,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(739,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ~ ! [SX3: $i] :
                    ( ~ ( in @ SX3 @ SX0 )
                    | ~ ( in @ SX3 @ SX1 )
                    | ( in @ SX3 @ SX2 ) )
              | ( subset @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[295,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(740,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i > $i] :
          ( ~ ! [SX3: $i] :
                ( ~ ( in @ SX3 @ SX0 )
                | ( in @ ( SX2 @ SX3 ) @ SX1 ) )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX0 )
              | ( ( ap @ SX0 @ SX1
                  @ ( lam @ SX0 @ SX1
                    @ ^ [SX4: $i] : ( SX2 @ SX4 ) )
                  @ SX3 )
                = ( SX2 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[313,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(741,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX0 )
              | ( in @ ( kpair @ SX3 @ ( ap @ SX0 @ SX1 @ SX2 @ SX3 ) ) @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[326,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(742,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ! [SX3: $i] :
                  ( ~ ( in @ SX3 @ SX0 )
                  | ~ ( in @ SX3 @ ( setminus @ SX0 @ SX1 ) )
                  | ~ ( in @ SX3 @ ( binintersect @ SX1 @ SX2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[279,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(743,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( in @ SX0 @ omega )
          | ( in @ ( setadjoin @ SX0 @ SX0 ) @ omega ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[521,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(744,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[484,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(745,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ SX1 )
          | ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[403,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(746,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( singleton @ SX0 )
          | ! [SX1: $i] :
              ( ~ ( in @ SX1 @ SX0 )
              | ( ( setunion @ SX0 )
                = SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[305,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(747,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX1 )
              | ( in @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[385,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(748,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
          | ( in @ SX2 @ SX0 )
          | ( in @ SX2 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[425,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(749,plain,
    ( ( ! [SX0: $i > $o] :
          ( ~ ~ ! [SX1: $i] :
                  ~ ! [SX2: $i] :
                      ~ ( ~ ( ~ ( SX0 @ SX2 )
                            | ( SX2 = SX1 ) )
                        | ~ ( ( SX2 != SX1 )
                            | ( SX0 @ SX2 ) ) )
          | ~ ! [SX1: $i] :
                ~ ~ ( ~ ( SX0 @ SX1 )
                    | ~ ! [SX2: $i] :
                          ( ~ ( SX0 @ SX2 )
                          | ( SX1 = SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[465,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(750,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( subset @ SX0 @ SX2 )
          | ( subset @ SX0 @ ( setadjoin @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[439,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(751,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
          | ! [SX2: $o] :
              ( ~ ! [SX3: $i] :
                    ( ~ ( in @ SX1 @ SX3 )
                    | ~ ( in @ SX3 @ SX0 )
                    | SX2 )
              | SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[488,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(752,plain,
    ( ( ! [SX0: $i,SX1: $o,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX0 )
              | ( in @ ( if @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[302,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(753,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ SX1 )
              | ( subset @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ ( binunion @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[386,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).

thf(754,plain,
    ! [SV1: $i] :
      ( ( ! [SY1855: $i,SY1856: $i > $i > $o] :
            ( subset
            @ ( dpsetconstr @ SV1 @ SY1855
              @ ^ [Xx: $i,Xy: $i] : ( SY1856 @ Xx @ Xy ) )
            @ ( cartprod @ SV1 @ SY1855 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[344]) ).

thf(755,plain,
    ! [SV2: $i] :
      ( ( ! [SY1859: $i,SY1860: $i > $i > $o] :
            ( subset
            @ ( dpsetconstr @ SV2 @ SY1859
              @ ^ [Xx: $i,Xy: $i] : ( SY1860 @ Xx @ Xy ) )
            @ ( cartprod @ SV2 @ SY1859 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[345]) ).

thf(756,plain,
    ! [SV3: $i] :
      ( ( ! [SY1863: $i] :
            ( ( ksnd @ ( kpair @ SV3 @ SY1863 ) )
            = SY1863 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[355]) ).

thf(757,plain,
    ! [SV4: $i] :
      ( ( ! [SY1864: $i] :
            ( ( kfst @ ( kpair @ SV4 @ SY1864 ) )
            = SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[366]) ).

thf(758,plain,
    ! [SV5: $i] :
      ( ( ( setunion @ ( setadjoin @ SV5 @ emptyset ) )
        = SV5 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[375]) ).

thf(759,plain,
    ! [SV6: $i] :
      ( ( subset @ SV6 @ ( setunion @ ( setadjoin @ SV6 @ emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[376]) ).

thf(760,plain,
    ! [SV7: $i] :
      ( ( subset @ ( setunion @ ( setadjoin @ SV7 @ emptyset ) ) @ SV7 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[377]) ).

thf(761,plain,
    ! [SV8: $i] :
      ( ( ! [SY1865: $i] : ( iskpair @ ( kpair @ SV8 @ SY1865 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[391]) ).

thf(762,plain,
    ! [SV9: $i] :
      ( ( ! [SY1866: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ SV9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV9 @ ( setadjoin @ SY1866 @ emptyset ) ) @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[392]) ).

thf(763,plain,
    ! [SV10: $i] :
      ( ( ! [SY1867: $i] : ( in @ SY1867 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV10 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV10 @ ( setadjoin @ SY1867 @ emptyset ) ) @ emptyset ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[393]) ).

thf(764,plain,
    ! [SV11: $i] :
      ( ( ! [SY1868: $i] : ( in @ SV11 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV11 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV11 @ ( setadjoin @ SY1868 @ emptyset ) ) @ emptyset ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[394]) ).

thf(765,plain,
    ! [SV12: $i] :
      ( ( ! [SY1869: $i] : ( in @ SY1869 @ ( setadjoin @ SV12 @ ( setadjoin @ SY1869 @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[395]) ).

thf(766,plain,
    ! [SV13: $i] :
      ( ( ! [SY1870: $i] : ( subset @ ( setminus @ SV13 @ SY1870 ) @ SV13 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[402]) ).

thf(767,plain,
    ! [SV14: $i] :
      ( ( ! [SY1871: $i,SY1872: $i] :
            ( ( binintersect @ SV14 @ ( binunion @ SY1871 @ SY1872 ) )
            = ( binunion @ ( binintersect @ SV14 @ SY1871 ) @ ( binintersect @ SV14 @ SY1872 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[411]) ).

thf(768,plain,
    ! [SV15: $i] :
      ( ( ! [SY1873: $i] : ( subset @ ( binintersect @ SV15 @ SY1873 ) @ SY1873 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[414]) ).

thf(769,plain,
    ! [SV16: $i] :
      ( ( ! [SY1874: $i] : ( subset @ ( binintersect @ SV16 @ SY1874 ) @ SV16 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[419]) ).

thf(770,plain,
    ! [SV17: $i] :
      ( ( ! [SY1875: $i] : ( subset @ SY1875 @ ( binunion @ SV17 @ SY1875 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[423]) ).

thf(771,plain,
    ! [SV18: $i] :
      ( ( ! [SY1876: $i] : ( subset @ SV18 @ ( binunion @ SV18 @ SY1876 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[424]) ).

thf(772,plain,
    ! [SV19: $i] :
      ( ( ! [SY1877: $i] : ( in @ SY1877 @ ( setadjoin @ SV19 @ ( setadjoin @ SY1877 @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[428]) ).

thf(773,plain,
    ! [SV20: $i] :
      ( ( ! [SY1878: $i > $o] :
            ( subset
            @ ( dsetconstr @ SV20
              @ ^ [Xx: $i] : ( SY1878 @ Xx ) )
            @ SV20 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[430]) ).

thf(774,plain,
    ! [SV21: $i] :
      ( ( ! [SY1880: $i > $o] :
            ( in
            @ ( dsetconstr @ SV21
              @ ^ [Xx: $i] : ( SY1880 @ Xx ) )
            @ ( powerset @ SV21 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[431]) ).

thf(775,plain,
    ! [SV22: $i] :
      ( ( in @ SV22 @ ( powerset @ SV22 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[433]) ).

thf(776,plain,
    ! [SV23: $i] :
      ( ( ! [SY1882: $i] : ( subset @ SY1882 @ ( setadjoin @ SV23 @ SY1882 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[440]) ).

thf(777,plain,
    ! [SV24: $i] :
      ( ( subset @ SV24 @ SV24 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[442]) ).

thf(778,plain,
    ! [SV25: $i] :
      ( ( subset @ emptyset @ SV25 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[448]) ).

thf(779,plain,
    ! [SV26: $i] :
      ( ( ! [SY1883: $i] : ( in @ SY1883 @ ( setadjoin @ SV26 @ ( setadjoin @ SY1883 @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[478]) ).

thf(780,plain,
    ! [SV27: $i] :
      ( ( ! [SY1884: $i] : ( in @ SV27 @ ( setadjoin @ SV27 @ ( setadjoin @ SY1884 @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[479]) ).

thf(781,plain,
    ! [SV28: $i] :
      ( ( in @ emptyset @ ( powerset @ SV28 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[491]) ).

thf(782,plain,
    ! [SV29: $i] :
      ( ( in @ emptyset @ ( powerset @ SV29 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[492]) ).

thf(783,plain,
    ! [SV30: $i] :
      ( ( ( dsetconstr @ SV30
          @ ^ [Xx: $i] : $true )
        = SV30 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[494]) ).

thf(784,plain,
    ! [SV31: $i] :
      ( ( ! [SY1886: $i] : ( in @ SV31 @ ( setadjoin @ SV31 @ SY1886 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[499]) ).

thf(785,plain,
    ! [SV32: $i] :
      ( ( ~ ( in @ SV32 @ emptyset ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[508]) ).

thf(786,plain,
    ! [SV33: $i] :
      ( ( ~ ( in @ SV33 @ emptyset ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[526]) ).

thf(787,plain,
    ! [SV34: $i] :
      ( ( ! [SY1887: $i,SY1888: $i] :
            ( ~ ( in @ SY1888 @ ( funcSet @ SV34 @ SY1887 ) )
            | ( func @ SV34 @ SY1887 @ SY1888 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[529]) ).

thf(788,plain,
    ! [SV35: $i] :
      ( ( ! [SY1889: $i > $o] :
            ( ~ ~ ~ ! [SY1890: $i] :
                      ~ ~ ( ~ ( in @ SY1890 @ SV35 )
                          | ~ ( SY1889 @ SY1890 ) )
            | ! [SY1891: $i] :
                ( ~ ( in @ SY1891 @ SV35 )
                | ~ ( SY1889 @ SY1891 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[530]) ).

thf(789,plain,
    ! [SV36: $i] :
      ( ( ! [SY1892: $i] :
            ( ~ ( in @ SY1892 @ ( powerset @ SV36 ) )
            | ! [SY1893: $i] :
                ( ~ ( in @ SY1893 @ ( powerset @ SV36 ) )
                | ! [SY1894: $i] :
                    ( ~ ( in @ SY1894 @ SV36 )
                    | ~ ( subset @ SY1892 @ SY1893 )
                    | ~ ~ ( in @ SY1894 @ SY1893 )
                    | ~ ( in @ SY1894 @ SY1892 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[531]) ).

thf(790,plain,
    ! [SV37: $i > $o] :
      ( ( ~ ~ ! [SY1895: $i] :
                ~ ~ ( ~ ( SV37 @ SY1895 )
                    | ~ ! [SY1896: $i] :
                          ( ~ ( SV37 @ SY1896 )
                          | ( SY1895 = SY1896 ) ) )
        | ~ ! [SY1897: $i] :
              ~ ! [SY1898: $i] :
                  ~ ( ~ ( ~ ( SV37 @ SY1898 )
                        | ( SY1898 = SY1897 ) )
                    | ~ ( ( SY1898 != SY1897 )
                        | ( SV37 @ SY1898 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[532]) ).

thf(791,plain,
    ! [SV38: $i] :
      ( ( ! [SY1899: $i,SY1900: $i] :
            ( ~ ( func @ SV38 @ SY1899 @ SY1900 )
            | ! [SY1901: $i] :
                ( ~ ( in @ SY1901 @ SV38 )
                | ( in @ ( kpair @ SY1901 @ ( ap @ SV38 @ SY1899 @ SY1900 @ SY1901 ) ) @ SY1900 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[533]) ).

thf(792,plain,
    ! [SV39: $i] :
      ( ( ~ ( in @ SV39 @ emptyset )
        | ! [SX1: $o] : SX1 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[534]) ).

thf(793,plain,
    ! [SV40: $i] :
      ( ( ! [SY1903: $o,SY1904: $i] :
            ( ~ ( in @ SY1904 @ SV40 )
            | ! [SY1905: $i] :
                ( ~ ( in @ SY1905 @ SV40 )
                | ~ ~ SY1903
                | ( in @ SY1905
                  @ ( dsetconstr @ SV40
                    @ ^ [SX4: $i] :
                        ( ~ ( ~ SY1903
                            | ( SX4 != SY1904 ) )
                        | ~ ( ~ ~ SY1903
                            | ( SX4 != SY1905 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[535]) ).

thf(794,plain,
    ! [SV41: $i > $o] :
      ( ( ~ ~ ! [SY1907: $i] :
                ~ ~ ( ~ ( SV41 @ SY1907 )
                    | ~ ! [SY1908: $i] :
                          ( ~ ( SV41 @ SY1908 )
                          | ( SY1907 = SY1908 ) ) )
        | ! [SY1909: $i,SY1910: $i] :
            ( ~ ( SV41 @ SY1909 )
            | ~ ( SV41 @ SY1910 )
            | ( SY1909 = SY1910 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[536]) ).

thf(795,plain,
    ! [SV42: $i] :
      ( ( ! [SY1911: $i] :
            ~ ( ~ ( ~ ( in @ SY1911 @ ( powerset @ SV42 ) )
                  | ! [SY1912: $i] :
                      ( ~ ( in @ SY1912 @ SY1911 )
                      | ( in @ SY1912 @ SV42 ) ) )
              | ~ ( ~ ! [SY1913: $i] :
                        ( ~ ( in @ SY1913 @ SY1911 )
                        | ( in @ SY1913 @ SV42 ) )
                  | ( in @ SY1911 @ ( powerset @ SV42 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[537]) ).

thf(796,plain,
    ! [SV43: $i > $o] :
      ( ( ~ ~ ! [SY1914: $i] :
                ~ ~ ( ~ ( SV43 @ SY1914 )
                    | ~ ! [SY1915: $i] :
                          ( ~ ( SV43 @ SY1915 )
                          | ( SY1914 = SY1915 ) ) )
        | ! [SY1916: $i,SY1917: $i] :
            ( ~ ( SV43 @ SY1916 )
            | ~ ( SV43 @ SY1917 )
            | ( SY1916 = SY1917 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[538]) ).

thf(797,plain,
    ! [SV44: $i] :
      ( ( ! [SY1918: $i] :
            ( ~ ( in @ SY1918 @ ( powerset @ SV44 ) )
            | ! [SY1919: $i] :
                ( ~ ( in @ SY1919 @ ( powerset @ SV44 ) )
                | ! [SY1920: $i] :
                    ( ~ ( in @ SY1920 @ SV44 )
                    | ~ ( in @ SY1920 @ ( setminus @ SV44 @ ( binunion @ SY1918 @ SY1919 ) ) )
                    | ~ ( in @ SY1920 @ SY1918 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[539]) ).

thf(798,plain,
    ! [SV45: $o] :
      ( ( ~ SV45
        | ( in @ emptyset @ ( prop2set @ SV45 ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[540]) ).

thf(799,plain,
    ( ( ~ $true
      | ( in @ emptyset @ ( prop2set @ $true ) ) )
    = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[540]) ).

thf(800,plain,
    ( ( ~ $false
      | ( in @ emptyset @ ( prop2set @ $false ) ) )
    = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[540]) ).

thf(801,plain,
    ! [SV46: $i] :
      ( ( ! [SY1921: $i > $o] :
            ( ~ ~ ! [SY1922: $i] :
                    ~ ~ ( ~ ( in @ SY1922 @ SV46 )
                        | ~ ~ ( SY1921 @ SY1922 ) )
            | ~ ! [SY1923: $i] :
                  ( ~ ( in @ SY1923 @ SV46 )
                  | ( SY1921 @ SY1923 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[541]) ).

thf(802,plain,
    ! [SV47: $i] :
      ( ( ! [SY1924: $i,SY1925: $i] :
            ( ~ ~ ( in @ SY1925 @ ( setminus @ SV47 @ SY1924 ) )
            | ~ ( in @ SY1925 @ SV47 )
            | ( in @ SY1925 @ SY1924 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[542]) ).

thf(803,plain,
    ! [SV48: $i > $o] :
      ( ( ~ ~ ! [SY1926: $i] :
                ~ ~ ( ~ ( SV48 @ SY1926 )
                    | ~ ! [SY1927: $i] :
                          ( ~ ( SV48 @ SY1927 )
                          | ( SY1926 = SY1927 ) ) )
        | ~ ! [SY1928: $i] :
              ~ ~ ( ~ ( SV48 @ SY1928 )
                  | ~ ! [SY1929: $i] :
                        ( ~ ( SV48 @ SY1929 )
                        | ( SY1928 = SY1929 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[543]) ).

thf(804,plain,
    ! [SV49: $i] :
      ( ( ! [SY1930: $i,SY1931: $i] :
            ( ~ ( in @ SY1931 @ SV49 )
            | ~ ~ ( in @ SY1931 @ SY1930 )
            | ( in @ SY1931 @ ( setminus @ SV49 @ SY1930 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[544]) ).

thf(805,plain,
    ! [SV50: $i] :
      ( ( ! [SY1932: $i,SY1933: $i] :
            ( ~ ( in @ SY1933 @ SV50 )
            | ! [SY1934: $i] :
                ( ~ ( in @ SY1934 @ SY1932 )
                | ( in @ ( setadjoin @ ( setadjoin @ SY1933 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1933 @ ( setadjoin @ SY1934 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV50 @ SY1932 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[545]) ).

thf(806,plain,
    ! [SV51: $i] :
      ( ( ! [SY1935: $i] :
            ( ~ ! [SY1936: $i] :
                  ~ ( ~ ( ~ ( in @ SY1936 @ SV51 )
                        | ( in @ SY1936 @ SY1935 ) )
                    | ~ ( ~ ( in @ SY1936 @ SY1935 )
                        | ( in @ SY1936 @ SV51 ) ) )
            | ( SV51 = SY1935 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[546]) ).

thf(807,plain,
    ! [SV52: $i] :
      ( ( ! [SY1937: $i > $o] :
            ( ~ ~ ~ ! [SY1938: $i] :
                      ~ ~ ( ~ ( in @ SY1938 @ SV52 )
                          | ~ ( SY1937 @ SY1938 ) )
            | ! [SY1939: $i] :
                ( ~ ( in @ SY1939 @ SV52 )
                | ~ ( SY1937 @ SY1939 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[547]) ).

thf(808,plain,
    ! [SV53: $i] :
      ( ( ! [SY1940: $i] :
            ( ( SV53 != SY1940 )
            | ( subset @ SV53 @ SY1940 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[548]) ).

thf(809,plain,
    ! [SV54: $i] :
      ( ( ! [SY1941: $i] :
            ( ~ ( in @ SY1941 @ ( powerset @ SV54 ) )
            | ( in @ ( powerset @ SY1941 ) @ ( powerset @ ( powerset @ SV54 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[549]) ).

thf(810,plain,
    ! [SV55: $i] :
      ( ( ! [SY1942: $i,SY1943: $i] :
            ( ~ ~ ( in @ SY1943 @ SV55 )
            | ~ ~ ( in @ SY1943 @ SY1942 )
            | ~ ( in @ SY1943 @ ( symdiff @ SV55 @ SY1942 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[550]) ).

thf(811,plain,
    ! [SV56: $i] :
      ( ( ! [SY1944: $i,SY1945: $i > $i > $o,SY1946: $i,SY1947: $i] :
            ( ~ ( in @ ( kpair @ SY1946 @ SY1947 )
                @ ( dpsetconstr @ SV56 @ SY1944
                  @ ^ [SX5: $i,SX6: $i] : ( SY1945 @ SX5 @ SX6 ) ) )
            | ( in @ SY1947 @ SY1944 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[551]) ).

thf(812,plain,
    ! [SV57: $i] :
      ( ( ~ ( subset @ SV57 @ emptyset )
        | ( SV57 = emptyset ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[552]) ).

thf(813,plain,
    ! [SV58: $i] :
      ( ( ! [SY1950: $i,SY1951: $i] :
            ( ~ ( in @ ( setadjoin @ SY1951 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV58 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV58 @ ( setadjoin @ SY1950 @ emptyset ) ) @ emptyset ) ) )
            | ( SV58 = SY1951 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[553]) ).

thf(814,plain,
    ! [SV59: $i] :
      ( ( ! [SY1952: $i,SY1953: $i,SY1954: $i] :
            ( ( ( setadjoin @ ( setadjoin @ SV59 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV59 @ ( setadjoin @ SY1952 @ emptyset ) ) @ emptyset ) )
             != ( setadjoin @ ( setadjoin @ SY1953 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1953 @ ( setadjoin @ SY1954 @ emptyset ) ) @ emptyset ) ) )
            | ( SY1952 = SY1954 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[554]) ).

thf(815,plain,
    ! [SV60: $i] :
      ( ( ! [SY1955: $i,SY1956: $i] :
            ( ~ ( in @ SY1956 @ SV60 )
            | ~ ( in @ SY1956 @ SY1955 )
            | ~ ( in @ SY1956 @ ( symdiff @ SV60 @ SY1955 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[555]) ).

thf(816,plain,
    ! [SV61: $i] :
      ( ( ! [SY1957: $i,SY1958: $i,SY1959: $i] :
            ( ~ ( in @ ( kpair @ SY1958 @ SY1959 ) @ ( cartprod @ SV61 @ SY1957 ) )
            | ( in @ SY1958 @ SV61 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[556]) ).

thf(817,plain,
    ! [SV62: $i] :
      ( ( ! [SY1960: $i,SY1961: $i] :
            ( ~ ( in @ SY1961 @ SV62 )
            | ! [SX3: $i] :
                ( ~ ( in @ SX3 @ SY1960 )
                | ( ( kpair @ SY1961 @ SX3 )
                  = ( kpair @ SY1961 @ SX3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[557]) ).

thf(818,plain,
    ! [SV63: $i] :
      ( ( ! [SY1963: $i,SY1964: $i] :
            ( ~ ( subset @ SY1964 @ ( cartprod @ SV63 @ SY1963 ) )
            | ! [SY1965: $i > $o] :
                ( ~ ! [SY1966: $i] :
                      ( ~ ( in @ SY1966 @ SV63 )
                      | ! [SX5: $i] :
                          ( ~ ( in @ SX5 @ SY1963 )
                          | ~ ( in @ ( kpair @ SY1966 @ SX5 ) @ SY1964 )
                          | ( SY1965 @ ( kpair @ SY1966 @ SX5 ) ) ) )
                | ! [SX4: $i] :
                    ( ~ ( in @ SX4 @ SY1964 )
                    | ( SY1965 @ SX4 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[558]) ).

thf(819,plain,
    ! [SV64: $i] :
      ( ( ~ ( singleton @ SV64 )
        | ( in @ ( setunion @ SV64 ) @ SV64 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[559]) ).

thf(820,plain,
    ! [SV65: $i] :
      ( ( ! [SY1969: $i > $o,SY1970: $i] :
            ( ~ ( in @ SY1970 @ SV65 )
            | ~ ( SY1969 @ SY1970 )
            | ( ( dsetconstr @ SV65
                @ ^ [SX3: $i] : ( SY1969 @ SX3 ) )
             != emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[560]) ).

thf(821,plain,
    ! [SV66: $i] :
      ( ( ! [SY1972: $i] :
            ( ( SV66 != SY1972 )
            | ( ( setadjoin @ ( setadjoin @ SV66 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV66 @ ( setadjoin @ SY1972 @ emptyset ) ) @ emptyset ) )
              = ( setadjoin @ ( setadjoin @ SV66 @ emptyset ) @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[561]) ).

thf(822,plain,
    ! [SV67: $i] :
      ( ( ! [SY1973: $o,SY1974: $i] :
            ( ~ ( in @ SY1974 @ SV67 )
            | ! [SY1975: $i] :
                ( ~ ( in @ SY1975 @ SV67 )
                | ~ SY1973
                | ( in @ SY1974
                  @ ( dsetconstr @ SV67
                    @ ^ [SX4: $i] :
                        ( ~ ( ~ SY1973
                            | ( SX4 != SY1974 ) )
                        | ~ ( ~ ~ SY1973
                            | ( SX4 != SY1975 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[562]) ).

thf(823,plain,
    ! [SV68: $i] :
      ( ( ! [SY1977: $i,SY1978: $i] :
            ( ~ ( func @ SV68 @ SY1977 @ SY1978 )
            | ! [SY1979: $i] :
                ( ~ ( in @ SY1979 @ SV68 )
                | ( in
                  @ ( setunion
                    @ ( dsetconstr @ SY1977
                      @ ^ [SX4: $i] : ( in @ ( kpair @ SY1979 @ SX4 ) @ SY1978 ) ) )
                  @ SY1977 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[563]) ).

thf(824,plain,
    ! [SV69: $i] :
      ( ( ! [SY1981: $i] :
            ( ~ ( subset @ SY1981 @ SV69 )
            | ( ( binintersect @ SV69 @ SY1981 )
              = SY1981 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[564]) ).

thf(825,plain,
    ! [SV70: $i] :
      ( ( ! [SY1982: $i] :
            ( ~ ( in @ SY1982 @ ( powerset @ SV70 ) )
            | ( subset @ ( setminus @ SV70 @ ( setminus @ SV70 @ SY1982 ) ) @ SY1982 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[565]) ).

thf(826,plain,
    ! [SV71: $i] :
      ( ( ! [SY1983: $i] :
            ( ~ ( subset @ SV71 @ SY1983 )
            | ( ( binintersect @ SV71 @ SY1983 )
              = SV71 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[566]) ).

thf(827,plain,
    ! [SV72: $i] :
      ( ( ! [SY1984: $i] :
            ( ~ ( in @ SY1984 @ ( powerset @ SV72 ) )
            | ! [SY1985: $i] :
                ( ~ ( in @ SY1985 @ ( powerset @ SV72 ) )
                | ~ ( subset @ SY1984 @ ( setminus @ SV72 @ SY1985 ) )
                | ( subset @ SY1985 @ ( setminus @ SV72 @ SY1984 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[567]) ).

thf(828,plain,
    ! [SV73: $i] :
      ( ( ! [SY1986: $i,SY1987: $i] :
            ( ~ ( in @ SY1987 @ ( funcSet @ SV73 @ SY1986 ) )
            | ! [SY1988: $i] :
                ( ~ ( in @ SY1988 @ ( funcSet @ SV73 @ SY1986 ) )
                | ~ ! [SY1989: $i] :
                      ( ~ ( in @ SY1989 @ SV73 )
                      | ( ( ap @ SV73 @ SY1986 @ SY1987 @ SY1989 )
                        = ( ap @ SV73 @ SY1986 @ SY1988 @ SY1989 ) ) )
                | ( SY1987 = SY1988 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[568]) ).

thf(829,plain,
    ! [SV74: $i] :
      ( ( ! [SY1990: $i,SY1991: $i] :
            ( ~ ~ ( in @ SY1991 @ ( setminus @ SV74 @ SY1990 ) )
            | ~ ~ ( in @ SY1991 @ SY1990 )
            | ~ ( in @ SY1991 @ SV74 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[569]) ).

thf(830,plain,
    ! [SV75: $i] :
      ( ( ! [SY1992: $i,SY1993: $i] :
            ~ ( ~ ( ~ ( in @ SY1993 @ ( setadjoin @ SV75 @ SY1992 ) )
                  | ( SY1993 = SV75 )
                  | ( in @ SY1993 @ SY1992 ) )
              | ~ ( ~ ( ( SY1993 = SV75 )
                      | ( in @ SY1993 @ SY1992 ) )
                  | ( in @ SY1993 @ ( setadjoin @ SV75 @ SY1992 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[570]) ).

thf(831,plain,
    ! [SV76: $i] :
      ( ( ! [SY1994: $i] :
            ( ~ ( in @ SY1994 @ ( powerset @ SV76 ) )
            | ! [SY1995: $i] :
                ( ~ ( in @ SY1995 @ ( powerset @ SV76 ) )
                | ! [SY1996: $i] :
                    ( ~ ( in @ SY1996 @ ( powerset @ SV76 ) )
                    | ! [SY1997: $i] :
                        ( ~ ( in @ SY1997 @ SV76 )
                        | ~ ( in @ SY1997 @ ( binintersect @ SY1994 @ SY1995 ) )
                        | ( in @ SY1997 @ ( binintersect @ ( binunion @ SY1994 @ SY1996 ) @ ( binunion @ SY1995 @ SY1996 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[571]) ).

thf(832,plain,
    ! [SV77: $i > $o] :
      ( ( ! [SY1998: $i > $o] :
            ( ~ ! [SY1999: $i,SY2000: $i] :
                  ( ( SY1999 != SY2000 )
                  | ~ ( ~ ( ~ ( SV77 @ SY1999 )
                          | ( SY1998 @ SY2000 ) )
                      | ~ ( ~ ( SY1998 @ SY2000 )
                          | ( SV77 @ SY1999 ) ) ) )
            | ~ ~ ! [SY2001: $i] :
                    ~ ~ ( ~ ( SV77 @ SY2001 )
                        | ~ ! [SY2002: $i] :
                              ( ~ ( SV77 @ SY2002 )
                              | ( SY2001 = SY2002 ) ) )
            | ~ ~ ! [SX2: $i] :
                    ~ ~ ( ~ ( SY1998 @ SX2 )
                        | ~ ! [SX3: $i] :
                              ( ~ ( SY1998 @ SX3 )
                              | ( SX2 = SX3 ) ) )
            | ( ( descr
                @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
              = ( descr
                @ ^ [SX2: $i] : ( SY1998 @ SX2 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[572]) ).

thf(833,plain,
    ! [SV78: $i] :
      ( ( ! [SY2007: $i > $o,SY2008: $i] :
            ( ~ ( in @ SY2008 @ SV78 )
            | ~ ( SY2007 @ SY2008 )
            | ( in @ SY2008
              @ ( dsetconstr @ SV78
                @ ^ [SX3: $i] : ( SY2007 @ SX3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[573]) ).

thf(834,plain,
    ! [SV79: $i] :
      ( ( ! [SY2010: $i] :
            ( ~ ( subset @ SY2010 @ SV79 )
            | ( in @ SY2010 @ ( powerset @ SV79 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[574]) ).

thf(835,plain,
    ! [SV80: $i] :
      ( ( ! [SY2011: $i] :
            ( ~ ( in @ SY2011 @ ( powerset @ SV80 ) )
            | ! [SY2012: $i] :
                ( ~ ( in @ SY2012 @ ( powerset @ SV80 ) )
                | ~ ! [SY2013: $i] :
                      ( ~ ( in @ SY2013 @ SV80 )
                      | ~ ( in @ SY2013 @ SY2011 )
                      | ( in @ SY2013 @ SY2012 ) )
                | ~ ! [SY2014: $i] :
                      ( ~ ( in @ SY2014 @ SV80 )
                      | ~ ( in @ SY2014 @ SY2012 )
                      | ( in @ SY2014 @ SY2011 ) )
                | ( SY2011 = SY2012 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[575]) ).

thf(836,plain,
    ! [SV81: $i] :
      ( ( ! [SY2015: $i] :
            ( ~ ! [SY2016: $i] :
                  ( ~ ( in @ SY2016 @ SV81 )
                  | ( in @ SY2016 @ SY2015 ) )
            | ~ ! [SY2017: $i] :
                  ( ~ ( in @ SY2017 @ SY2015 )
                  | ( in @ SY2017 @ SV81 ) )
            | ( SV81 = SY2015 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[576]) ).

thf(837,plain,
    ! [SV82: $i] :
      ( ( ! [SY2018: $i,SY2019: $i > $i > $o,SY2020: $i] :
            ( ~ ( in @ SY2020 @ SV82 )
            | ! [SY2021: $i] :
                ( ~ ( in @ SY2021 @ SY2018 )
                | ~ ( in @ ( kpair @ SY2020 @ SY2021 )
                    @ ( dpsetconstr @ SV82 @ SY2018
                      @ ^ [SX5: $i,SX6: $i] : ( SY2019 @ SX5 @ SX6 ) ) )
                | ( SY2019 @ SY2020 @ SY2021 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[577]) ).

thf(838,plain,
    ! [SV83: $i] :
      ( ( ~ ! [SY2024: $i] :
              ~ ( in @ SY2024 @ SV83 )
        | ( SV83 = emptyset ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[578]) ).

thf(839,plain,
    ! [SV84: $i] :
      ( ( ! [SY2025: $i > $o] :
            ( ~ ~ ! [SY2026: $i] :
                    ( ~ ( in @ SY2026 @ SV84 )
                    | ( SY2025 @ SY2026 ) )
            | ~ ! [SY2027: $i] :
                  ~ ~ ( ~ ( in @ SY2027 @ SV84 )
                      | ~ ~ ( SY2025 @ SY2027 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[579]) ).

thf(840,plain,
    ! [SV85: $i] :
      ( ( ! [SY2028: $i,SY2029: $i,SY2030: $o] :
            ( ~ ( in @ SY2029 @ ( binunion @ SV85 @ SY2028 ) )
            | ~ ( ~ ( in @ SY2029 @ SV85 )
                | SY2030 )
            | ~ ( ~ ( in @ SY2029 @ SY2028 )
                | SY2030 )
            | SY2030 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[580]) ).

thf(841,plain,
    ! [SV86: $i] :
      ( ( ! [SY2031: $i,SY2032: $i] :
            ( ~ ( in @ SY2031 @ SY2032 )
            | ~ ( in @ SY2032 @ SV86 )
            | ( in @ SY2031 @ ( setunion @ SV86 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[581]) ).

thf(842,plain,
    ! [SV87: $i] :
      ( ( ~ ~ ( ~ ( in @ emptyset @ SV87 )
              | ~ ! [SY2033: $i] :
                    ( ~ ~ ( ~ ( in @ SY2033 @ omega )
                          | ~ ( in @ SY2033 @ SV87 ) )
                    | ( in @ ( setadjoin @ SY2033 @ SY2033 ) @ SV87 ) ) )
        | ! [SY2034: $i] :
            ( ~ ( in @ SY2034 @ omega )
            | ( in @ SY2034 @ SV87 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[582]) ).

thf(843,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ! [SX3: $i] :
                  ( ~ ( in @ SX3 @ SX0 )
                  | ~ ( in @ SX3 @ ( setminus @ SX0 @ ( binunion @ SX1 @ SX2 ) ) )
                  | ( in @ SX3 @ ( setminus @ SX0 @ SX1 ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[583]) ).

thf(844,plain,
    ! [SV88: $i] :
      ( ( ! [SY2035: $i] :
            ( ~ ( in @ SY2035 @ ( powerset @ SV88 ) )
            | ! [SY2036: $i] :
                ( ~ ( in @ SY2036 @ ( powerset @ SV88 ) )
                | ~ ( subset @ SY2035 @ ( setminus @ SV88 @ SY2036 ) )
                | ! [SY2037: $i] :
                    ( ~ ( in @ SY2037 @ SV88 )
                    | ~ ( in @ SY2037 @ SY2036 )
                    | ( in @ SY2037 @ ( setminus @ SV88 @ SY2035 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[584]) ).

thf(845,plain,
    ! [SV89: $i] :
      ( ( ! [SY2038: $i > $o] :
            ( ~ ~ ! [SY2039: $i] :
                    ~ ~ ( ~ ( in @ SY2039 @ SV89 )
                        | ~ ( SY2038 @ SY2039 ) )
            | ( ( dsetconstr @ SV89
                @ ^ [SX2: $i] : ( SY2038 @ SX2 ) )
             != emptyset )
            | $false ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[585]) ).

thf(846,plain,
    ! [SV90: $i] :
      ( ( ! [SY2041: $i] :
            ( ~ ! [SY2042: $i] :
                  ( ~ ( in @ SY2042 @ SV90 )
                  | ( in @ SY2042 @ SY2041 ) )
            | ( subset @ SV90 @ SY2041 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[586]) ).

thf(847,plain,
    ! [SV91: $i] :
      ( ( ! [SY2043: $i] :
            ( ~ ( in @ SY2043 @ ( powerset @ SV91 ) )
            | ! [SY2044: $i] :
                ( ~ ( in @ SY2044 @ ( powerset @ SV91 ) )
                | ( in @ ( binintersect @ SY2043 @ SY2044 ) @ ( powerset @ SV91 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[587]) ).

thf(848,plain,
    ! [SV92: $i] :
      ( ( ! [SY2045: $i] :
            ( ( SV92 != SY2045 )
            | ! [SY2046: $i,SY2047: $i] :
                ( ( SY2046 != SY2047 )
                | ~ ( in @ SY2046 @ SV92 )
                | ( in @ SY2047 @ SY2045 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[588]) ).

thf(849,plain,
    ! [SV93: $i] :
      ( ( ! [SY2048: $i,SY2049: $i > $i > $o,SY2050: $i,SY2051: $i] :
            ( ~ ( in @ ( kpair @ SY2050 @ SY2051 )
                @ ( dpsetconstr @ SV93 @ SY2048
                  @ ^ [SX5: $i,SX6: $i] : ( SY2049 @ SX5 @ SX6 ) ) )
            | ( SY2049 @ SY2050 @ SY2051 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[589]) ).

thf(850,plain,
    ! [SV94: $i] :
      ( ( ! [SY2054: $i,SY2055: $i,SY2056: $i] :
            ( ( ( kpair @ SV94 @ SY2054 )
             != ( kpair @ SY2055 @ SY2056 ) )
            | ( SV94 = SY2055 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[590]) ).

thf(851,plain,
    ! [SV95: $i] :
      ( ( ! [SY2057: $i,SY2058: $i] :
            ( ~ ( subset @ SV95 @ SY2057 )
            | ~ ( in @ SY2058 @ SV95 )
            | ( in @ SY2058 @ SY2057 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[591]) ).

thf(852,plain,
    ! [SV96: $i] :
      ( ( ! [SY2059: $i,SY2060: $i] :
            ( ~ ( func @ SV96 @ SY2059 @ SY2060 )
            | ! [SY2061: $i] :
                ( ~ ( func @ SV96 @ SY2059 @ SY2061 )
                | ~ ! [SY2062: $i] :
                      ( ~ ( in @ SY2062 @ SV96 )
                      | ( ( ap @ SV96 @ SY2059 @ SY2060 @ SY2062 )
                        = ( ap @ SV96 @ SY2059 @ SY2061 @ SY2062 ) ) )
                | ! [SY2063: $i] :
                    ( ~ ( in @ SY2063 @ SV96 )
                    | ! [SX5: $i] :
                        ( ~ ( in @ SX5 @ SY2059 )
                        | ~ ( in @ ( kpair @ SY2063 @ SX5 ) @ SY2061 )
                        | ( in @ ( kpair @ SY2063 @ SX5 ) @ SY2060 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[592]) ).

thf(853,plain,
    ! [SV97: $i] :
      ( ( ~ ( iskpair @ SV97 )
        | ( singleton
          @ ( dsetconstr @ ( setunion @ SV97 )
            @ ^ [SY2065: $i] : ( in @ ( setadjoin @ SY2065 @ emptyset ) @ SV97 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[593]) ).

thf(854,plain,
    ! [SV98: $i] :
      ( ( ! [SY2066: $i,SY2067: $i] :
            ( ~ ( in @ SY2067 @ ( cartprod @ SV98 @ SY2066 ) )
            | ~ ! [SY2068: $i] :
                  ~ ~ ( ~ ( in @ SY2068 @ SV98 )
                      | ~ ~ ! [SX4: $i] :
                              ~ ~ ( ~ ( in @ SX4 @ SY2066 )
                                  | ( SY2067
                                   != ( kpair @ SY2068 @ SX4 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[594]) ).

thf(855,plain,
    ! [SV99: $i] :
      ( ( ! [SY2070: $i] :
            ( ~ ( in @ SY2070 @ ( powerset @ SV99 ) )
            | ! [SY2071: $i] :
                ( ~ ( in @ SY2071 @ ( powerset @ SV99 ) )
                | ! [SY2072: $i] :
                    ( ~ ( in @ SY2072 @ SV99 )
                    | ~ ( in @ SY2070 @ ( powerset @ SY2071 ) )
                    | ~ ( in @ SY2072 @ SY2070 )
                    | ( in @ SY2072 @ SY2071 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[595]) ).

thf(856,plain,
    ! [SV100: $i] :
      ( ( ~ ! [SY2073: $i] :
              ~ ( in @ SY2073 @ SV100 )
        | ( SV100 = emptyset ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[596]) ).

thf(857,plain,
    ! [SV101: $i] :
      ( ( ! [SY2074: $i,SY2075: $i] :
            ( ~ ( in @ SY2075 @ ( setadjoin @ SV101 @ SY2074 ) )
            | ( SY2075 = SV101 )
            | ( in @ SY2075 @ SY2074 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[597]) ).

thf(858,plain,
    ! [SV102: $i] :
      ( ( ! [SY2076: $i > $o] :
            ( ~ ! [SY2077: $i] :
                  ( ~ ( in @ SY2077 @ SV102 )
                  | ! [SY2078: $i] :
                      ( ~ ( in @ SY2078 @ SV102 )
                      | ~ ( SY2076 @ SY2077 )
                      | ~ ( SY2076 @ SY2078 )
                      | ( SY2077 = SY2078 ) ) )
            | ~ ~ ! [SY2079: $i] :
                    ~ ~ ( ~ ( in @ SY2079 @ SV102 )
                        | ~ ( SY2076 @ SY2079 ) )
            | ( singleton
              @ ( dsetconstr @ SV102
                @ ^ [SX2: $i] : ( SY2076 @ SX2 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[598]) ).

thf(859,plain,
    ! [SV103: $i] :
      ( ( ! [SY2081: $i,SY2082: $i > $i > $o,SY2083: $i,SY2084: $i] :
            ( ~ ( in @ ( kpair @ SY2083 @ SY2084 )
                @ ( dpsetconstr @ SV103 @ SY2081
                  @ ^ [SX5: $i,SX6: $i] : ( SY2082 @ SX5 @ SX6 ) ) )
            | ( in @ SY2083 @ SV103 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[599]) ).

thf(860,plain,
    ! [SV104: $i] :
      ( ( ! [SY2087: $i] :
            ( ~ ( ( SV104 != SY2087 ) )
            | ~ ( in @ SY2087 @ ( setadjoin @ SV104 @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[600]) ).

thf(861,plain,
    ! [SV105: $i] :
      ( ( ! [SY2088: $i,SY2089: $i > $i] :
            ( ~ ! [SY2090: $i] :
                  ( ~ ( in @ SY2090 @ SV105 )
                  | ( in @ ( SY2089 @ SY2090 ) @ SY2088 ) )
            | ( ( lam @ SV105 @ SY2088
                @ ^ [SX3: $i] : ( SY2089 @ SX3 ) )
              = ( lam @ SV105 @ SY2088
                @ ^ [SX3: $i] : ( SY2089 @ SX3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[601]) ).

thf(862,plain,
    ! [SV106: $i] :
      ( ( ! [SY2093: $i,SY2094: $i] :
            ( ~ ( in @ SY2094 @ SV106 )
            | ( in @ ( setadjoin @ SY2094 @ emptyset ) @ ( powerset @ ( binunion @ SV106 @ SY2093 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[602]) ).

thf(863,plain,
    ! [SV107: $i] :
      ( ( ! [SY2095: $i,SY2096: $i > $i] :
            ( ~ ! [SY2097: $i] :
                  ( ~ ( in @ SY2097 @ SV107 )
                  | ( in @ ( SY2096 @ SY2097 ) @ SY2095 ) )
            | ( in
              @ ( lam @ SV107 @ SY2095
                @ ^ [SX3: $i] : ( SY2096 @ SX3 ) )
              @ ( funcSet @ SV107 @ SY2095 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[603]) ).

thf(864,plain,
    ! [SV108: $i] :
      ( ( ! [SY2099: $i] :
            ( ( SV108 != SY2099 )
            | ( ( setunion @ SV108 )
              = ( setunion @ SY2099 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[604]) ).

thf(865,plain,
    ! [SV109: $i] :
      ( ( ~ ! [SY2100: $i] :
              ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY2101: $i] :
                                    ( ~ ( in @ SY2101 @ SY2100 )
                                    | ! [SY2102: $i] :
                                        ( ~ ( in @ SY2102 @ SY2101 )
                                        | ( in @ SY2102 @ SV109 ) ) )
                              | ~ ! [SY2103: $i,SY2104: $i] :
                                    ( ~ ~ ( ~ ( in @ SY2103 @ SV109 )
                                          | ~ ( in @ SY2104 @ SV109 ) )
                                    | ~ ! [SX4: $i] :
                                          ( ~ ( in @ SX4 @ SY2100 )
                                          | ~ ( ~ ( ~ ( in @ SY2103 @ SX4 )
                                                  | ( in @ SY2104 @ SX4 ) )
                                              | ~ ( ~ ( in @ SY2104 @ SX4 )
                                                  | ( in @ SY2103 @ SX4 ) ) ) )
                                    | ( SY2103 = SY2104 ) ) )
                        | ~ ! [SX2: $i,SX3: $i] :
                              ( ~ ~ ( ~ ( in @ SX2 @ SY2100 )
                                    | ~ ( in @ SX3 @ SY2100 ) )
                              | ! [SX4: $i] :
                                  ( ~ ( in @ SX4 @ SX2 )
                                  | ( in @ SX4 @ SX3 ) )
                              | ! [SX4: $i] :
                                  ( ~ ( in @ SX4 @ SX3 )
                                  | ( in @ SX4 @ SX2 ) ) ) )
                  | ~ ! [SY2110: $i] :
                        ( ~ ~ ( ~ ! [SY2111: $i] :
                                    ( ~ ( in @ SY2111 @ SY2110 )
                                    | ( in @ SY2111 @ SV109 ) )
                              | ~ ~ ! [SX3: $i] :
                                      ~ ( in @ SX3 @ SY2110 ) )
                        | ~ ! [SX3: $i] :
                              ~ ~ ! [SX4: $i] :
                                    ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY2100 )
                                                    | ~ ( in @ SX4 @ SY2110 ) )
                                              | ~ ~ ~ ! [SX5: $i] :
                                                        ~ ~ ( ~ ( in @ SX5 @ SX3 )
                                                            | ~ ( in @ SX5 @ SY2110 ) ) )
                                        | ~ ! [SX5: $i] :
                                              ( ~ ( in @ SX5 @ SY2100 )
                                              | ! [SX6: $i] :
                                                  ( ~ ( in @ SX6 @ SX5 )
                                                  | ( in @ SX6 @ SX3 ) )
                                              | ( in @ SX4 @ SX5 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[605]) ).

thf(866,plain,
    ! [SV110: $i] :
      ( ( ~ ~ ! [SY2118: $i] :
                ~ ( in @ SY2118 @ SV110 )
        | ~ ! [SY2119: $i] :
              ~ ~ ( ~ ( in @ SY2119 @ SV110 )
                  | ~ ~ ~ ! [SY2120: $i] :
                            ~ ~ ( ~ ( in @ SY2120 @ SY2119 )
                                | ~ ( in @ SY2120 @ SV110 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[606]) ).

thf(867,plain,
    ! [SV111: $i] :
      ( ( ! [SY2121: $i,SY2122: $i] :
            ( ~ ( in @ SY2122 @ ( binintersect @ SV111 @ SY2121 ) )
            | ( in @ SY2122 @ SV111 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[607]) ).

thf(868,plain,
    ! [SV112: $i > $o] :
      ( ( ~ ~ ! [SY2123: $i] :
                ~ ~ ( ~ ( SV112 @ SY2123 )
                    | ~ ! [SY2124: $i] :
                          ( ~ ( SV112 @ SY2124 )
                          | ( SY2123 = SY2124 ) ) )
        | ~ ! [SY2125: $i] :
              ~ ( SV112 @ SY2125 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[608]) ).

thf(869,plain,
    ! [SV113: $i] :
      ( ( ! [SY2126: $i] :
            ( ~ ~ ~ ! [SY2127: $i] :
                      ~ ~ ( ~ ( in @ SY2127 @ SV113 )
                          | ~ ( in @ SY2127 @ SY2126 ) )
            | ( ( binintersect @ SV113 @ SY2126 )
              = emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[609]) ).

thf(870,plain,
    ! [SV114: $i] :
      ( ( ! [SY2128: $i] :
            ( ~ ( subset @ SV114 @ SY2128 )
            | ( ( setminus @ SV114 @ SY2128 )
              = emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[610]) ).

thf(871,plain,
    ! [SV115: $i] :
      ( ( ~ ( in @ SV115 @ emptyset )
        | $false )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[611]) ).

thf(872,plain,
    ! [SV116: $i] :
      ( ( ! [SY2129: $i] :
            ( ~ ( in @ SY2129 @ ( powerset @ SV116 ) )
            | ! [SY2130: $i] :
                ( ~ ( in @ SY2130 @ ( powerset @ SV116 ) )
                | ! [SY2131: $i] :
                    ( ~ ( in @ SY2131 @ SV116 )
                    | ~ ~ ( in @ SY2131 @ ( binunion @ SY2129 @ SY2130 ) )
                    | ~ ( in @ SY2131 @ SY2129 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[612]) ).

thf(873,plain,
    ! [SV117: $i] :
      ( ( ~ ( iskpair @ SV117 )
        | ( singleton
          @ ( dsetconstr @ ( setunion @ SV117 )
            @ ^ [SY2132: $i] :
                ( SV117
                = ( kpair @ ( kfst @ SV117 ) @ SY2132 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[613]) ).

thf(874,plain,
    ! [SV118: $i] :
      ( ( ! [SY2133: $o,SY2134: $i] :
            ( ~ ( in @ SY2134 @ SV118 )
            | ! [SY2135: $i] :
                ( ~ ( in @ SY2135 @ SV118 )
                | ~ ~ SY2133
                | ( ( if @ SV118 @ SY2133 @ SY2134 @ SY2135 )
                  = SY2135 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[614]) ).

thf(875,plain,
    ! [SV119: $i > $o] :
      ( ( ! [SY2136: $i] :
            ( ~ ( in @ SY2136 @ emptyset )
            | ( SV119 @ SY2136 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[615]) ).

thf(876,plain,
    ! [SV120: $o] :
      ( ( ~ SV120
        | ( set2prop @ ( prop2set @ SV120 ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[616]) ).

thf(877,plain,
    ( ( ~ $true
      | ( set2prop @ ( prop2set @ $true ) ) )
    = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[616]) ).

thf(878,plain,
    ( ( ~ $false
      | ( set2prop @ ( prop2set @ $false ) ) )
    = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[616]) ).

thf(879,plain,
    ! [SV121: $i] :
      ( ( ! [SY2137: $i] :
            ( ~ ( in @ SY2137 @ ( powerset @ SV121 ) )
            | ! [SY2138: $i] :
                ( ~ ( in @ SY2138 @ SV121 )
                | ~ ~ ( in @ SY2138 @ ( setminus @ SV121 @ SY2137 ) )
                | ( in @ SY2138 @ SY2137 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[617]) ).

thf(880,plain,
    ! [SV122: $i] :
      ( ( ! [SY2139: $i] :
            ( ~ ( in @ SY2139 @ ( powerset @ SV122 ) )
            | ! [SY2140: $i] :
                ( ~ ( in @ SY2140 @ ( powerset @ SV122 ) )
                | ( subset @ ( setminus @ SV122 @ SY2139 ) @ ( setminus @ SV122 @ ( binintersect @ SY2139 @ SY2140 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[618]) ).

thf(881,plain,
    ! [SV123: $i] :
      ( ( ! [SY2141: $i,SY2142: $i] :
            ( ~ ( subset @ SV123 @ SY2141 )
            | ~ ~ ( in @ SY2142 @ SY2141 )
            | ~ ( in @ SY2142 @ SV123 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[619]) ).

thf(882,plain,
    ! [SV124: $i] :
      ( ( ! [SY2143: $i,SY2144: $i > $i] :
            ( ~ ! [SY2145: $i] :
                  ( ~ ( in @ SY2145 @ SV124 )
                  | ( in @ ( SY2144 @ SY2145 ) @ SY2143 ) )
            | ( func @ SV124 @ SY2143
              @ ( dpsetconstr @ SV124 @ SY2143
                @ ^ [SX3: $i,SX4: $i] :
                    ( ( SY2144 @ SX3 )
                    = SX4 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[620]) ).

thf(883,plain,
    ! [SV125: $i] :
      ( ( ! [SY2148: $i > $o] :
            ( ~ ! [SY2149: $i] :
                  ( ~ ( in @ SY2149 @ SV125 )
                  | ! [SY2150: $i] :
                      ( ~ ( in @ SY2150 @ SV125 )
                      | ~ ( SY2148 @ SY2149 )
                      | ~ ( SY2148 @ SY2150 )
                      | ( SY2149 = SY2150 ) ) )
            | ~ ~ ! [SY2151: $i] :
                    ~ ~ ( ~ ( in @ SY2151 @ SV125 )
                        | ~ ( SY2148 @ SY2151 ) )
            | ( singleton
              @ ( dsetconstr @ SV125
                @ ^ [SX2: $i] : ( SY2148 @ SX2 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[621]) ).

thf(884,plain,
    ! [SV126: $i] :
      ( ( ! [SY2153: $i,SY2154: $i] :
            ( ~ ~ ( in @ SY2154 @ SV126 )
            | ~ ( in @ SY2154 @ SY2153 )
            | ( in @ SY2154 @ ( symdiff @ SV126 @ SY2153 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[622]) ).

thf(885,plain,
    ! [SV127: $i] :
      ( ( ! [SY2155: $i,SY2156: $i] :
            ( ~ ( in @ SY2156 @ ( setadjoin @ SV127 @ ( setadjoin @ SY2155 @ emptyset ) ) )
            | ( SY2156 = SV127 )
            | ( SY2156 = SY2155 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[623]) ).

thf(886,plain,
    ! [SV128: $i] :
      ( ( ! [SY2157: $i] :
            ( ~ ( in @ SY2157 @ ( powerset @ SV128 ) )
            | ! [SY2158: $i] :
                ( ~ ( in @ SY2158 @ ( powerset @ SV128 ) )
                | ( in @ ( setminus @ SV128 @ SY2157 ) @ ( powerset @ ( setminus @ SV128 @ ( binintersect @ SY2157 @ SY2158 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[624]) ).

thf(887,plain,
    ! [SV129: $i] :
      ( ( ! [SY2159: $i] :
            ( ~ ( in @ SY2159 @ ( powerset @ SV129 ) )
            | ! [SY2160: $i] :
                ( ~ ( in @ SY2160 @ SV129 )
                | ~ ( in @ SY2160 @ SY2159 )
                | ~ ( in @ SY2160 @ ( setminus @ SV129 @ SY2159 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[625]) ).

thf(888,plain,
    ! [SV130: $i] :
      ( ( ! [SY2161: $i] :
            ( ~ ( in @ SY2161 @ ( powerset @ SV130 ) )
            | ( SY2161
              = ( setminus @ SV130 @ ( setminus @ SV130 @ SY2161 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[626]) ).

thf(889,plain,
    ! [SV131: $i] :
      ( ( ! [SY2162: $i] :
            ( ( SV131 != SY2162 )
            | ( ( powerset @ SV131 )
              = ( powerset @ SY2162 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[627]) ).

thf(890,plain,
    ! [SV132: $i] :
      ( ( ! [SY2163: $i] :
            ( ~ ( in @ SY2163 @ ( powerset @ SV132 ) )
            | ! [SY2164: $i] :
                ( ~ ( in @ SY2164 @ ( powerset @ SV132 ) )
                | ~ ( subset @ SY2163 @ SY2164 )
                | ( subset @ ( setminus @ SV132 @ SY2164 ) @ ( setminus @ SV132 @ SY2163 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[628]) ).

thf(891,plain,
    ! [SV133: $i] :
      ( ( ! [SY2165: $i,SY2166: $i] :
            ( ~ ( func @ SV133 @ SY2165 @ SY2166 )
            | ! [SY2167: $i] :
                ( ~ ( in @ SY2167 @ SV133 )
                | ( ( ap @ SV133 @ SY2165 @ SY2166 @ SY2167 )
                  = ( ap @ SV133 @ SY2165 @ SY2166 @ SY2167 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[629]) ).

thf(892,plain,
    ! [SV134: $i] :
      ( ( ! [SY2168: $i,SY2169: $i] :
            ( ~ ( in @ SY2169 @ ( setadjoin @ SV134 @ ( setadjoin @ SY2168 @ emptyset ) ) )
            | ( SY2169 = SV134 )
            | ( SY2169 = SY2168 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[630]) ).

thf(893,plain,
    ! [SV135: $i] :
      ( ( ! [SY2170: $i,SY2171: $i] :
            ( ~ ( subset @ SY2171 @ ( cartprod @ SV135 @ SY2170 ) )
            | ! [SY2172: $i > $o] :
                ( ~ ! [SY2173: $i] :
                      ( ~ ( in @ SY2173 @ SV135 )
                      | ! [SX5: $i] :
                          ( ~ ( in @ SX5 @ SY2170 )
                          | ~ ( in @ ( kpair @ SY2173 @ SX5 ) @ SY2171 )
                          | ( SY2172 @ ( kpair @ SY2173 @ SX5 ) ) ) )
                | ! [SX4: $i] :
                    ( ~ ( in @ SX4 @ SY2171 )
                    | ( SY2172 @ SX4 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[631]) ).

thf(894,plain,
    ! [SV136: $i] :
      ( ( ! [SY2176: $i,SY2177: $i] :
            ( ~ ( in @ SY2176 @ ( powerset @ SV136 ) )
            | ~ ( in @ SY2177 @ SY2176 )
            | ( in @ SY2177 @ SV136 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[632]) ).

thf(895,plain,
    ! [SV137: $i] :
      ( ( ! [SY2178: $i] :
            ( ~ ( in @ SY2178 @ ( powerset @ SV137 ) )
            | ! [SY2179: $i] :
                ( ~ ( in @ SY2179 @ ( powerset @ SV137 ) )
                | ! [SY2180: $i] :
                    ( ~ ( in @ SY2180 @ SV137 )
                    | ~ ~ ( in @ SY2180 @ SY2179 )
                    | ~ ( in @ SY2180 @ ( binintersect @ SY2178 @ SY2179 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[633]) ).

thf(896,plain,
    ! [SV138: $i] :
      ( ( ! [SY2181: $i] :
            ( ~ ( in @ SY2181 @ SV138 )
            | ( in @ ( setadjoin @ SY2181 @ emptyset ) @ ( powerset @ SV138 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[634]) ).

thf(897,plain,
    ! [SV139: $o] :
      ( ( ! [SY2182: $i] :
            ( ~ ( in @ SY2182 @ ( prop2set @ SV139 ) )
            | SV139 ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[635]) ).

thf(898,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( in @ SX0 @ ( prop2set @ $true ) )
          | $true ) )
    = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[635]) ).

thf(899,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( in @ SX0 @ ( prop2set @ $false ) )
          | $false ) )
    = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[635]) ).

thf(900,plain,
    ! [SV140: $i] :
      ( ( ! [SY2183: $i,SY2184: $i] :
            ( ~ ( in @ SY2184 @ SV140 )
            | ! [SY2185: $i] :
                ( ~ ( in @ SY2185 @ SY2183 )
                | ( in @ ( kpair @ SY2184 @ SY2185 ) @ ( cartprod @ SV140 @ SY2183 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[636]) ).

thf(901,plain,
    ! [SV141: $i] :
      ( ( ! [SY2186: $i,SY2187: $i] :
            ( ~ ( in @ SY2187 @ ( cartprod @ SV141 @ SY2186 ) )
            | ( in @ ( ksnd @ SY2187 ) @ SY2186 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[637]) ).

thf(902,plain,
    ! [SV142: $i] :
      ( ( ! [SY2188: $i > $o] :
            ( ~ ( singleton
                @ ( dsetconstr @ SV142
                  @ ^ [SX2: $i] : ( SY2188 @ SX2 ) ) )
            | ! [SY2190: $i] :
                ( ~ ( in @ SY2190 @ SV142 )
                | ! [SY2191: $i] :
                    ( ~ ( in @ SY2191 @ SV142 )
                    | ~ ( SY2188 @ SY2190 )
                    | ~ ( SY2188 @ SY2191 )
                    | ( SY2190 = SY2191 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[638]) ).

thf(903,plain,
    ! [SV143: $i] :
      ( ( ! [SY2192: $i] :
            ( ~ ( in @ SY2192 @ ( powerset @ SV143 ) )
            | ( subset @ SY2192 @ SV143 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[639]) ).

thf(904,plain,
    ! [SV144: $i] :
      ( ( ! [SY2193: $i,SY2194: $i] :
            ( ~ ( in @ SY2194 @ SV144 )
            | ! [SX3: $i] :
                ( ~ ( in @ SX3 @ SY2193 )
                | ( ( kfst @ ( kpair @ SY2194 @ SX3 ) )
                  = SY2194 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[640]) ).

thf(905,plain,
    ! [SV145: $i] :
      ( ( ! [SY2196: $i] :
            ( ~ ( in @ SY2196 @ ( powerset @ SV145 ) )
            | ( in @ ( setminus @ SV145 @ SY2196 ) @ ( powerset @ SV145 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[641]) ).

thf(906,plain,
    ! [SV146: $i] :
      ( ( ! [SY2197: $i,SY2198: $i,SY2199: $i] :
            ( ( ( kpair @ SV146 @ SY2197 )
             != ( kpair @ SY2198 @ SY2199 ) )
            | ( SY2197 = SY2199 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[642]) ).

thf(907,plain,
    ! [SV147: $i > $i > $o] :
      ( ( ! [SY2200: $i] :
            ( ~ ! [SY2201: $i] :
                  ( ~ ( in @ SY2201 @ SY2200 )
                  | ~ ! [SY2202: $i] :
                        ~ ~ ( ~ ( SV147 @ SY2201 @ SY2202 )
                            | ~ ! [SY2203: $i] :
                                  ( ~ ( SV147 @ SY2201 @ SY2203 )
                                  | ( SY2202 = SY2203 ) ) ) )
            | ~ ! [SY2204: $i] :
                  ~ ! [SY2205: $i] :
                      ~ ( ~ ( ~ ( in @ SY2205 @ SY2204 )
                            | ~ ! [SY2206: $i] :
                                  ~ ~ ( ~ ( in @ SY2206 @ SY2200 )
                                      | ~ ( SV147 @ SY2206 @ SY2205 ) ) )
                        | ~ ( ~ ~ ! [SY2207: $i] :
                                    ~ ~ ( ~ ( in @ SY2207 @ SY2200 )
                                        | ~ ( SV147 @ SY2207 @ SY2205 ) )
                            | ( in @ SY2205 @ SY2204 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[643]) ).

thf(908,plain,
    ! [SV148: $i] :
      ( ( ! [SY2208: $i] :
            ( ~ ! [SY2209: $i] :
                  ( ~ ( in @ SY2209 @ SV148 )
                  | ( in @ SY2209 @ SY2208 ) )
            | ( subset @ SV148 @ SY2208 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[644]) ).

thf(909,plain,
    ! [SV149: $i] :
      ( ( ! [SY2210: $i] :
            ( ~ ( subset @ SV149 @ SY2210 )
            | ~ ( subset @ SY2210 @ SV149 )
            | ( SV149 = SY2210 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[645]) ).

thf(910,plain,
    ! [SV150: $i] :
      ( ( ! [SY2211: $i,SY2212: $i] :
            ( ~ ( in @ SY2212 @ SV150 )
            | ( in @ SY2212 @ ( binunion @ SV150 @ SY2211 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[646]) ).

thf(911,plain,
    ! [SV151: $i] :
      ( ( ! [SY2213: $i] :
            ( ~ ( in @ SY2213 @ ( powerset @ SV151 ) )
            | ! [SY2214: $i] :
                ( ~ ( in @ SY2214 @ ( powerset @ SV151 ) )
                | ! [SY2215: $i] :
                    ( ~ ( in @ SY2215 @ SV151 )
                    | ~ ~ ( in @ SY2215 @ ( binunion @ SY2213 @ SY2214 ) )
                    | ~ ( in @ SY2215 @ SY2214 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[647]) ).

thf(912,plain,
    ! [SV152: $i] :
      ( ( ! [SY2216: $i] :
            ( ( SV152 != SY2216 )
            | ! [SY2217: $i,SY2218: $i] :
                ( ( SY2217 != SY2218 )
                | ( ( setadjoin @ SV152 @ SY2217 )
                  = ( setadjoin @ SY2216 @ SY2218 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[648]) ).

thf(913,plain,
    ! [SV153: $i] :
      ( ( ~ ( iskpair @ SV153 )
        | ( ( kpair @ ( kfst @ SV153 ) @ ( ksnd @ SV153 ) )
          = SV153 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[649]) ).

thf(914,plain,
    ! [SV154: $i] :
      ( ( ! [SY2219: $i,SY2220: $i] :
            ( ~ ( in @ SY2220 @ SY2219 )
            | ( in @ SY2220 @ ( binunion @ SV154 @ SY2219 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[650]) ).

thf(915,plain,
    ! [SV155: $i] :
      ( ( ! [SY2221: $i] :
            ( ( SV155 != SY2221 )
            | ( subset @ SY2221 @ SV155 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[651]) ).

thf(916,plain,
    ! [SV156: $i] :
      ( ( ! [SY2222: $i] :
            ( ~ ( in @ SY2222 @ ( powerset @ SV156 ) )
            | ! [SY2223: $i] :
                ( ~ ( in @ SY2223 @ ( powerset @ SV156 ) )
                | ! [SY2224: $i] :
                    ( ~ ( in @ SY2224 @ SV156 )
                    | ~ ~ ( in @ SY2224 @ SY2222 )
                    | ~ ( in @ SY2224 @ ( binintersect @ SY2222 @ SY2223 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[652]) ).

thf(917,plain,
    ! [SV157: $i > $o] :
      ( ( ~ ~ ! [SY2225: $i] :
                ~ ~ ( ~ ( SV157 @ SY2225 )
                    | ~ ! [SY2226: $i] :
                          ( ~ ( SV157 @ SY2226 )
                          | ( SY2225 = SY2226 ) ) )
        | ( SV157
          @ ( descr
            @ ^ [SY2227: $i] : ( SV157 @ SY2227 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[653]) ).

thf(918,plain,
    ! [SV158: $i] :
      ( ( ! [SY2228: $i,SY2229: $i] :
            ( ~ ( in @ SY2229 @ ( setminus @ SV158 @ SY2228 ) )
            | ~ ( in @ SY2229 @ SY2228 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[654]) ).

thf(919,plain,
    ! [SV159: $i] :
      ( ( ! [SY2230: $i] :
            ( ~ ( in @ SY2230 @ ( powerset @ SV159 ) )
            | ( subset @ SY2230 @ ( setminus @ SV159 @ ( setminus @ SV159 @ SY2230 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[655]) ).

thf(920,plain,
    ! [SV160: $i] :
      ( ( ! [SY2231: $i > $o] :
            ( ~ ~ ! [SY2232: $i] :
                    ( ~ ( in @ SY2232 @ SV160 )
                    | ( SY2231 @ SY2232 ) )
            | ~ ! [SY2233: $i] :
                  ~ ~ ( ~ ( in @ SY2233 @ SV160 )
                      | ~ ~ ( SY2231 @ SY2233 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[656]) ).

thf(921,plain,
    ! [SV161: $i] :
      ( ( ! [SY2234: $i] :
            ( ~ ( in @ SY2234 @ ( powerset @ SV161 ) )
            | ! [SY2235: $i] :
                ( ~ ( in @ SY2235 @ ( powerset @ SV161 ) )
                | ! [SY2236: $i] :
                    ( ~ ( in @ SY2236 @ SV161 )
                    | ~ ( in @ SY2236 @ ( setminus @ SV161 @ SY2234 ) )
                    | ( in @ SY2236 @ ( setminus @ SV161 @ ( binintersect @ SY2234 @ SY2235 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[657]) ).

thf(922,plain,
    ! [SV162: $i] :
      ( ( ! [SY2237: $i] :
            ( ~ ( in @ SY2237 @ ( powerset @ SV162 ) )
            | ! [SY2238: $i] :
                ( ~ ( in @ SY2238 @ ( powerset @ SV162 ) )
                | ( in @ ( binunion @ SY2237 @ SY2238 ) @ ( powerset @ SV162 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[658]) ).

thf(923,plain,
    ! [SV163: $i] :
      ( ( ! [SY2239: $i] :
            ( ~ ( subset @ SV163 @ SY2239 )
            | ( in @ SV163 @ ( powerset @ SY2239 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[659]) ).

thf(924,plain,
    ! [SV164: $i] :
      ( ( ! [SY2240: $i] :
            ( ( ( setminus @ SV164 @ SY2240 )
             != emptyset )
            | ( subset @ SV164 @ SY2240 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[660]) ).

thf(925,plain,
    ! [SV165: $i > $o] :
      ( ( ~ ~ ! [SY2241: $i] :
                ~ ( SV165 @ SY2241 )
        | ~ ! [SY2242: $i,SY2243: $i] :
              ( ~ ( SV165 @ SY2242 )
              | ~ ( SV165 @ SY2243 )
              | ( SY2242 = SY2243 ) )
        | ~ ! [SY2244: $i] :
              ~ ~ ( ~ ( SV165 @ SY2244 )
                  | ~ ! [SY2245: $i] :
                        ( ~ ( SV165 @ SY2245 )
                        | ( SY2244 = SY2245 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[661]) ).

thf(926,plain,
    ! [SV166: $i] :
      ( ( ! [SY2246: $i,SY2247: $i] :
            ( ~ ( in @ SY2247 @ SV166 )
            | ~ ~ ( in @ SY2247 @ SY2246 )
            | ~ ( subset @ SV166 @ SY2246 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[662]) ).

thf(927,plain,
    ! [SV167: $i] :
      ( ( ! [SY2248: $i] :
            ( ~ ( in @ SY2248 @ ( powerset @ SV167 ) )
            | ! [SY2249: $i] :
                ( ~ ( in @ SY2249 @ ( powerset @ SV167 ) )
                | ! [SY2250: $i] :
                    ( ~ ( in @ SY2250 @ ( powerset @ SV167 ) )
                    | ( in @ ( binintersect @ SY2248 @ SY2249 ) @ ( powerset @ ( binintersect @ ( binunion @ SY2248 @ SY2250 ) @ ( binunion @ SY2249 @ SY2250 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[663]) ).

thf(928,plain,
    ! [SV168: $i] :
      ( ( ! [SY2251: $i,SY2252: $i] :
            ( ~ ( subset @ SY2252 @ ( cartprod @ SV168 @ SY2251 ) )
            | ! [SY2253: $i] :
                ( ~ ( subset @ SY2253 @ ( cartprod @ SV168 @ SY2251 ) )
                | ~ ! [SY2254: $i] :
                      ( ~ ( in @ SY2254 @ SV168 )
                      | ! [SX5: $i] :
                          ( ~ ( in @ SX5 @ SY2251 )
                          | ~ ( in @ ( kpair @ SY2254 @ SX5 ) @ SY2252 )
                          | ( in @ ( kpair @ SY2254 @ SX5 ) @ SY2253 ) ) )
                | ( subset @ SY2252 @ SY2253 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[664]) ).

thf(929,plain,
    ! [SV169: $i] :
      ( ( ! [SY2256: $o,SY2257: $i] :
            ( ~ ( in @ SY2257 @ SV169 )
            | ! [SY2258: $i] :
                ( ~ ( in @ SY2258 @ SV169 )
                | ~ SY2256
                | ( ( if @ SV169 @ SY2256 @ SY2257 @ SY2258 )
                  = SY2257 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[665]) ).

thf(930,plain,
    ! [SV170: $i] :
      ( ( ! [SY2259: $i,SY2260: $i > $i] :
            ( ~ ! [SY2261: $i] :
                  ( ~ ( in @ SY2261 @ SV170 )
                  | ( in @ ( SY2260 @ SY2261 ) @ SY2259 ) )
            | ! [SY2262: $i] :
                ( ~ ( in @ SY2262 @ SV170 )
                | ( ( ap @ SV170 @ SY2259
                    @ ( lam @ SV170 @ SY2259
                      @ ^ [SX4: $i] : ( SY2260 @ SX4 ) )
                    @ SY2262 )
                  = ( SY2260 @ SY2262 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[666]) ).

thf(931,plain,
    ! [SV171: $i] :
      ( ( ~ ~ ! [SY2264: $i] :
                ~ ( in @ SY2264 @ SV171 )
        | ( SV171 != emptyset ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[667]) ).

thf(932,plain,
    ! [SV172: $i] :
      ( ( ! [SY2265: $i,SY2266: $i] :
            ( ~ ( in @ SY2266 @ ( cartprod @ SV172 @ SY2265 ) )
            | ( ( kpair @ ( kfst @ SY2266 ) @ ( ksnd @ SY2266 ) )
              = SY2266 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[668]) ).

thf(933,plain,
    ! [SV173: $i] :
      ( ( ! [SY2267: $i,SY2268: $i] :
            ( ~ ( in @ SY2268 @ ( funcSet @ SV173 @ SY2267 ) )
            | ( ( lam @ SV173 @ SY2267
                @ ^ [SY2269: $i] : ( ap @ SV173 @ SY2267 @ SY2268 @ SY2269 ) )
              = SY2268 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[669]) ).

thf(934,plain,
    ! [SV174: $i] :
      ( ( ! [SY2270: $i,SY2271: $i,SY2272: $i] :
            ( ( ( setadjoin @ ( setadjoin @ SV174 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV174 @ ( setadjoin @ SY2270 @ emptyset ) ) @ emptyset ) )
             != ( setadjoin @ ( setadjoin @ SY2271 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2271 @ ( setadjoin @ SY2272 @ emptyset ) ) @ emptyset ) ) )
            | ( SY2271 != SY2272 )
            | ( SY2270 = SY2272 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[670]) ).

thf(935,plain,
    ! [SV175: $i] :
      ( ( ! [SY2273: $i,SY2274: $i,SY2275: $i] :
            ( ~ ( in @ ( kpair @ SY2274 @ SY2275 ) @ ( cartprod @ SV175 @ SY2273 ) )
            | ( in @ SY2275 @ SY2273 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[671]) ).

thf(936,plain,
    ! [SV176: $i] :
      ( ( ! [SY2276: $i,SY2277: $i] :
            ( ~ ( func @ SV176 @ SY2276 @ SY2277 )
            | ! [SY2278: $i] :
                ( ~ ( in @ SY2278 @ SV176 )
                | ( in @ ( ap @ SV176 @ SY2276 @ SY2277 @ SY2278 ) @ SY2276 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[672]) ).

thf(937,plain,
    ! [SV177: $i] :
      ( ( ! [SY2279: $i] :
            ( ~ ( in @ SY2279 @ ( powerset @ SV177 ) )
            | ! [SY2280: $i] :
                ( ~ ( in @ SY2280 @ ( powerset @ SV177 ) )
                | ! [SY2281: $i] :
                    ( ~ ( in @ SY2281 @ SV177 )
                    | ~ ( subset @ SY2279 @ ( setminus @ SV177 @ SY2280 ) )
                    | ~ ( in @ SY2281 @ SY2280 )
                    | ~ ( in @ SY2281 @ SY2279 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[673]) ).

thf(938,plain,
    ! [SV178: $i] :
      ( ( ! [SY2282: $i,SY2283: $i > $i > $o,SY2284: $i] :
            ( ~ ( in @ SY2284 @ SV178 )
            | ! [SY2285: $i] :
                ( ~ ( in @ SY2285 @ SY2282 )
                | ~ ( SY2283 @ SY2284 @ SY2285 )
                | ( in @ ( kpair @ SY2284 @ SY2285 )
                  @ ( dpsetconstr @ SV178 @ SY2282
                    @ ^ [SX5: $i,SX6: $i] : ( SY2283 @ SX5 @ SX6 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[674]) ).

thf(939,plain,
    ! [SV179: $i] :
      ( ( ! [SY2288: $i,SY2289: $i] :
            ( ~ ( in @ SY2289 @ SV179 )
            | ~ ~ ( in @ SY2289 @ SY2288 )
            | ( SV179 != SY2288 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[675]) ).

thf(940,plain,
    ! [SV180: $i] :
      ( ( ! [SY2290: $i,SY2291: $i] :
            ( ~ ( in @ SY2291 @ SV180 )
            | ~ ( in @ SY2291 @ SY2290 )
            | ( in @ SY2291 @ ( binintersect @ SV180 @ SY2290 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[676]) ).

thf(941,plain,
    ! [SV181: $i] :
      ( ( ! [SY2292: $i] :
            ( ~ ! [SY2293: $i] :
                  ( ~ ( in @ SY2293 @ SY2292 )
                  | ( in @ SY2293 @ SV181 ) )
            | ( in @ SY2292 @ ( powerset @ SV181 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[677]) ).

thf(942,plain,
    ! [SV182: $i] :
      ( ( ! [SY2294: $i] :
            ( ~ ( in @ SY2294 @ ( powerset @ SV182 ) )
            | ! [SY2295: $i] :
                ( ~ ( in @ SY2295 @ SV182 )
                | ~ ( in @ SY2295 @ SY2294 )
                | ( in @ SY2295 @ ( setminus @ SV182 @ ( setminus @ SV182 @ SY2294 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[678]) ).

thf(943,plain,
    ! [SV183: $i] :
      ( ( ! [SY2296: $i,SY2297: $i] :
            ( ~ ( in @ SY2297 @ ( setminus @ SV183 @ SY2296 ) )
            | ( in @ SY2297 @ SV183 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[679]) ).

thf(944,plain,
    ! [SV184: $i] :
      ( ( ! [SY2298: $i,SY2299: $i] :
            ( ~ ( in @ SY2299 @ ( cartprod @ SV184 @ SY2298 ) )
            | ( iskpair @ SY2299 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[680]) ).

thf(945,plain,
    ! [SV185: $i] :
      ( ( ! [SY2300: $i,SY2301: $i] :
            ( ~ ( func @ SV185 @ SY2300 @ SY2301 )
            | ! [SY2302: $i] :
                ( ~ ( in @ SY2302 @ SV185 )
                | ! [SY2303: $i] :
                    ( ~ ( in @ SY2303 @ SY2300 )
                    | ~ ( in @ ( kpair @ SY2302 @ SY2303 ) @ SY2301 )
                    | ( ( ap @ SV185 @ SY2300 @ SY2301 @ SY2302 )
                      = SY2303 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[681]) ).

thf(946,plain,
    ! [SV186: $i] :
      ( ( ! [SY2304: $i] :
            ( ~ ( in @ SY2304 @ ( powerset @ SV186 ) )
            | ! [SY2305: $i] :
                ( ~ ( in @ SY2305 @ ( powerset @ SV186 ) )
                | ( in @ ( setminus @ SY2304 @ SY2305 ) @ ( powerset @ SV186 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[682]) ).

thf(947,plain,
    ! [SV187: $i] :
      ( ( ! [SY2306: $i > $o,SY2307: $i] :
            ( ~ ( in @ SY2307
                @ ( dsetconstr @ SV187
                  @ ^ [SX3: $i] : ( SY2306 @ SX3 ) ) )
            | ( in @ SY2307 @ SV187 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[683]) ).

thf(948,plain,
    ! [SV188: $i] :
      ( ( ! [SY2309: $i > $o,SY2310: $i] :
            ( ~ ( in @ SY2310 @ SV188 )
            | ~ ( ~ ( ~ ( in @ SY2310
                        @ ( dsetconstr @ SV188
                          @ ^ [SX3: $i] : ( SY2309 @ SX3 ) ) )
                    | ( SY2309 @ SY2310 ) )
                | ~ ( ~ ( SY2309 @ SY2310 )
                    | ( in @ SY2310
                      @ ( dsetconstr @ SV188
                        @ ^ [SX3: $i] : ( SY2309 @ SX3 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[684]) ).

thf(949,plain,
    ! [SV189: $i] :
      ( ( ! [SY2313: $i,SY2314: $i] :
            ( ~ ( in @ SY2314 @ SY2313 )
            | ( in @ SY2314 @ ( setadjoin @ SV189 @ SY2313 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[685]) ).

thf(950,plain,
    ! [SV190: $i] :
      ( ( ! [SY2315: $i,SY2316: $i] :
            ( ~ ( func @ SV190 @ SY2315 @ SY2316 )
            | ! [SY2317: $i] :
                ( ~ ( func @ SV190 @ SY2315 @ SY2317 )
                | ~ ! [SY2318: $i] :
                      ( ~ ( in @ SY2318 @ SV190 )
                      | ( ( ap @ SV190 @ SY2315 @ SY2316 @ SY2318 )
                        = ( ap @ SV190 @ SY2315 @ SY2317 @ SY2318 ) ) )
                | ( SY2316 = SY2317 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[686]) ).

thf(951,plain,
    ! [SV191: $i] :
      ( ( ! [SY2319: $i] :
            ( ~ ( in @ SY2319 @ ( powerset @ SV191 ) )
            | ! [SY2320: $i] :
                ( ~ ( in @ SY2320 @ ( powerset @ SV191 ) )
                | ! [SY2321: $i] :
                    ( ~ ( in @ SY2321 @ ( powerset @ SV191 ) )
                    | ! [SY2322: $i] :
                        ( ~ ( in @ SY2322 @ SV191 )
                        | ~ ( in @ SY2322 @ ( binintersect @ SY2319 @ SY2320 ) )
                        | ( in @ SY2322 @ ( binunion @ SY2319 @ SY2321 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[687]) ).

thf(952,plain,
    ! [SV192: $i] :
      ( ( ! [SY2323: $i > $o,SY2324: $i] :
            ( ~ ( in @ SY2324
                @ ( dsetconstr @ SV192
                  @ ^ [SX3: $i] : ( SY2323 @ SX3 ) ) )
            | ( SY2323 @ SY2324 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[688]) ).

thf(953,plain,
    ! [SV193: $i] :
      ( ( ! [SY2326: $i] :
            ( ( SV193 != SY2326 )
            | ! [SY2327: $i,SY2328: $i] :
                ( ( SY2327 != SY2328 )
                | ~ ( ~ ( ~ ( in @ SY2327 @ SV193 )
                        | ( in @ SY2328 @ SY2326 ) )
                    | ~ ( ~ ( in @ SY2328 @ SY2326 )
                        | ( in @ SY2327 @ SV193 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[689]) ).

thf(954,plain,
    ! [SV194: $i] :
      ( ( ! [SY2329: $o,SY2330: $i] :
            ( ~ ( in @ SY2330 @ SV194 )
            | ! [SY2331: $i] :
                ( ~ ( in @ SY2331 @ SV194 )
                | ( singleton
                  @ ( dsetconstr @ SV194
                    @ ^ [SX4: $i] :
                        ( ~ ( ~ SY2329
                            | ( SX4 != SY2330 ) )
                        | ~ ( ~ ~ SY2329
                            | ( SX4 != SY2331 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[690]) ).

thf(955,plain,
    ! [SV195: $i] :
      ( ( ! [SY2333: $i] :
            ( ( ( binintersect @ SV195 @ SY2333 )
             != SV195 )
            | ( subset @ SV195 @ SY2333 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[691]) ).

thf(956,plain,
    ! [SV196: $i] :
      ( ( ! [SY2334: $i,SY2335: $i] :
            ( ~ ( in @ SY2335 @ SV196 )
            | ! [SY2336: $i] :
                ( ~ ( in @ SY2336 @ SY2334 )
                | ( in @ ( kpair @ SY2335 @ SY2336 ) @ ( powerset @ ( powerset @ ( binunion @ SV196 @ SY2334 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[692]) ).

thf(957,plain,
    ! [SV197: $i] :
      ( ( ! [SY2337: $o,SY2338: $i] :
            ( ~ ( in @ SY2338 @ SV197 )
            | ! [SY2339: $i] :
                ( ~ ( in @ SY2339 @ SV197 )
                | ( in @ ( if @ SV197 @ SY2337 @ SY2338 @ SY2339 ) @ SV197 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[693]) ).

thf(958,plain,
    ! [SV198: $i] :
      ( ( ! [SY2340: $i,SY2341: $i] :
            ( ~ ( in @ SY2341 @ ( funcSet @ SV198 @ SY2340 ) )
            | ! [SY2342: $i] :
                ( ~ ( in @ SY2342 @ SV198 )
                | ! [SY2343: $i] :
                    ( ~ ( in @ SY2343 @ SY2340 )
                    | ~ ( in @ ( kpair @ SY2342 @ SY2343 ) @ SY2341 )
                    | ( ( ap @ SV198 @ SY2340 @ SY2341 @ SY2342 )
                      = SY2343 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[694]) ).

thf(959,plain,
    ! [SV199: $i] :
      ( ( ! [SY2344: $i,SY2345: $i > $i] :
            ( ~ ! [SY2346: $i] :
                  ( ~ ( in @ SY2346 @ SV199 )
                  | ( in @ ( SY2345 @ SY2346 ) @ SY2344 ) )
            | ( func @ SV199 @ SY2344
              @ ( lam @ SV199 @ SY2344
                @ ^ [SX3: $i] : ( SY2345 @ SX3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[695]) ).

thf(960,plain,
    ! [SV200: $i] :
      ( ( ! [SY2348: $i > $o] :
            ( ~ ! [SY2349: $i] :
                  ( ~ ( in @ SY2349 @ SV200 )
                  | ~ ( SY2348 @ SY2349 ) )
            | ~ ~ ! [SY2350: $i] :
                    ~ ~ ( ~ ( in @ SY2350 @ SV200 )
                        | ~ ( SY2348 @ SY2350 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[696]) ).

thf(961,plain,
    ! [SV201: $i] :
      ( ( ! [SY2351: $i] :
            ( ( ( setadjoin @ SV201 @ emptyset )
             != ( setadjoin @ SY2351 @ emptyset ) )
            | ( SV201 = SY2351 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[697]) ).

thf(962,plain,
    ! [SV202: $i] :
      ( ( ! [SY2352: $i,SY2353: $i] :
            ( ~ ( in @ SY2353 @ ( funcSet @ SV202 @ SY2352 ) )
            | ! [SY2354: $i] :
                ( ~ ( in @ SY2354 @ SV202 )
                | ( in @ ( ap @ SV202 @ SY2352 @ SY2353 @ SY2354 ) @ SY2352 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[698]) ).

thf(963,plain,
    ! [SV203: $i] :
      ( ( ~ ( ( SV203 != emptyset ) )
        | ~ ! [SY2355: $i] :
              ~ ( in @ SY2355 @ SV203 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[699]) ).

thf(964,plain,
    ! [SV204: $i] :
      ( ( ! [SY2356: $i] :
            ( ~ ( in @ SV204 @ ( setadjoin @ SY2356 @ emptyset ) )
            | ( in @ SY2356 @ ( setadjoin @ SV204 @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[700]) ).

thf(965,plain,
    ! [SV205: $i] :
      ( ( ! [SY2357: $i] :
            ~ ( ~ ( ~ ( in @ SY2357 @ ( setunion @ SV205 ) )
                  | ~ ! [SY2358: $i] :
                        ~ ~ ( ~ ( in @ SY2357 @ SY2358 )
                            | ~ ( in @ SY2358 @ SV205 ) ) )
              | ~ ( ~ ~ ! [SY2359: $i] :
                          ~ ~ ( ~ ( in @ SY2357 @ SY2359 )
                              | ~ ( in @ SY2359 @ SV205 ) )
                  | ( in @ SY2357 @ ( setunion @ SV205 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[701]) ).

thf(966,plain,
    ! [SV206: $i] :
      ( ( ! [SY2360: $i,SY2361: $i] :
            ( ~ ( in @ SY2361 @ ( symdiff @ SV206 @ SY2360 ) )
            | ! [SY2362: $o] :
                ( ~ ( ~ ( in @ SY2361 @ SV206 )
                    | ~ ~ ( in @ SY2361 @ SY2360 )
                    | SY2362 )
                | ~ ( ~ ~ ( in @ SY2361 @ SV206 )
                    | ~ ( in @ SY2361 @ SY2360 )
                    | SY2362 )
                | SY2362 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[702]) ).

thf(967,plain,
    ! [SV207: $i] :
      ( ( ! [SY2363: $i] :
            ( ~ ~ ( subset @ SV207 @ SY2363 )
            | ( SV207 != SY2363 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[703]) ).

thf(968,plain,
    ! [SV208: $i] :
      ( ( ! [SY2364: $i] :
            ( ~ ( in @ SY2364 @ ( setunion @ SV208 ) )
            | ~ ! [SY2365: $i] :
                  ~ ~ ( ~ ( in @ SY2365 @ SV208 )
                      | ~ ( in @ SY2364 @ SY2365 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[704]) ).

thf(969,plain,
    ! [SV209: $i] :
      ( ( ! [SY2366: $i] :
            ( ( SV209 != SY2366 )
            | ! [SY2367: $i > $o,SY2368: $i > $o] :
                ( ~ ! [SY2369: $i] :
                      ( ~ ( in @ SY2369 @ SV209 )
                      | ! [SX5: $i] :
                          ( ~ ( in @ SX5 @ SY2366 )
                          | ( SY2369 != SX5 )
                          | ~ ( ~ ( ~ ( SY2367 @ SY2369 )
                                  | ( SY2368 @ SX5 ) )
                              | ~ ( ~ ( SY2368 @ SX5 )
                                  | ( SY2367 @ SY2369 ) ) ) ) )
                | ( ( dsetconstr @ SV209
                    @ ^ [SX4: $i] : ( SY2367 @ SX4 ) )
                  = ( dsetconstr @ SY2366
                    @ ^ [SX4: $i] : ( SY2368 @ SX4 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[705]) ).

thf(970,plain,
    ! [SV210: $i] :
      ( ( ! [SY2373: $i,SY2374: $i] :
            ( ~ ( in @ SY2374 @ ( setadjoin @ SV210 @ SY2373 ) )
            | ! [SY2375: $o] :
                ( ~ ( ( SY2374 != SV210 )
                    | SY2375 )
                | ~ ( ~ ( in @ SY2374 @ SY2373 )
                    | SY2375 )
                | SY2375 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[706]) ).

thf(971,plain,
    ! [SV211: $i > $o] :
      ( ( ~ ~ ! [SY2376: $i] :
                ~ ~ ( ~ ( SV211 @ SY2376 )
                    | ~ ! [SY2377: $i] :
                          ( ~ ( SV211 @ SY2377 )
                          | ( SY2376 = SY2377 ) ) )
        | ~ ! [SY2378: $i] :
              ~ ~ ( ~ ( SV211 @ SY2378 )
                  | ~ ! [SY2379: $i] :
                        ( ~ ( SV211 @ SY2379 )
                        | ( SY2378 = SY2379 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[707]) ).

thf(972,plain,
    ! [SV212: $i] :
      ( ( ! [SY2380: $i,SY2381: $i] :
            ( ~ ( in @ SY2381 @ ( funcSet @ SV212 @ SY2380 ) )
            | ! [SY2382: $i] :
                ( ~ ( in @ SY2382 @ SV212 )
                | ( ( ap @ SV212 @ SY2380 @ SY2381 @ SY2382 )
                  = ( ap @ SV212 @ SY2380 @ SY2381 @ SY2382 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[708]) ).

thf(973,plain,
    ! [SV213: $i] :
      ( ( ! [SY2383: $i] :
            ( ~ ( in @ SY2383 @ ( powerset @ SV213 ) )
            | ! [SY2384: $i] :
                ( ~ ( in @ SY2384 @ SV213 )
                | ~ ( in @ SY2384 @ ( setminus @ SV213 @ ( setminus @ SV213 @ SY2383 ) ) )
                | ( in @ SY2384 @ SY2383 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[709]) ).

thf(974,plain,
    ! [SV214: $i > $o] :
      ( ( ! [SY2385: $i > $o] :
            ( ~ ! [SY2386: $i,SY2387: $i] :
                  ( ( SY2386 != SY2387 )
                  | ~ ( ~ ( ~ ( SV214 @ SY2386 )
                          | ( SY2385 @ SY2387 ) )
                      | ~ ( ~ ( SY2385 @ SY2387 )
                          | ( SV214 @ SY2386 ) ) ) )
            | ~ ( ~ ( ~ ~ ! [SY2388: $i] :
                            ~ ~ ( ~ ( SV214 @ SY2388 )
                                | ~ ! [SY2389: $i] :
                                      ( ~ ( SV214 @ SY2389 )
                                      | ( SY2388 = SY2389 ) ) )
                    | ~ ! [SX2: $i] :
                          ~ ~ ( ~ ( SY2385 @ SX2 )
                              | ~ ! [SX3: $i] :
                                    ( ~ ( SY2385 @ SX3 )
                                    | ( SX2 = SX3 ) ) ) )
                | ~ ( ~ ~ ! [SX2: $i] :
                            ~ ~ ( ~ ( SY2385 @ SX2 )
                                | ~ ! [SX3: $i] :
                                      ( ~ ( SY2385 @ SX3 )
                                      | ( SX2 = SX3 ) ) )
                    | ~ ! [SY2394: $i] :
                          ~ ~ ( ~ ( SV214 @ SY2394 )
                              | ~ ! [SY2395: $i] :
                                    ( ~ ( SV214 @ SY2395 )
                                    | ( SY2394 = SY2395 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[710]) ).

thf(975,plain,
    ! [SV215: $i] :
      ( ( ! [SY2396: $i > $o] :
            ( ~ ( singleton
                @ ( dsetconstr @ SV215
                  @ ^ [SX2: $i] : ( SY2396 @ SX2 ) ) )
            | ~ ! [SY2398: $i] :
                  ~ ~ ( ~ ( in @ SY2398 @ SV215 )
                      | ~ ( SY2396 @ SY2398 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[711]) ).

thf(976,plain,
    ! [SV216: $i] :
      ( ( ! [SY2399: $i > $o,SY2400: $i] :
            ( ~ ( in @ SY2400 @ SV216 )
            | ~ ( SY2399 @ SY2400 )
            | ~ ! [SY2401: $i] :
                  ( ~ ( in @ SY2401 @ SV216 )
                  | ~ ( SY2399 @ SY2401 )
                  | ( SY2401 = SY2400 ) )
            | ( singleton
              @ ( dsetconstr @ SV216
                @ ^ [SX3: $i] : ( SY2399 @ SX3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[712]) ).

thf(977,plain,
    ! [SV217: $i] :
      ( ( ! [SY2403: $i] :
            ( ( SV217 != SY2403 )
            | ( ( setadjoin @ SV217 @ ( setadjoin @ SY2403 @ emptyset ) )
              = ( setadjoin @ SV217 @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[713]) ).

thf(978,plain,
    ! [SV218: $i] :
      ( ( ! [SY2404: $i,SY2405: $i] :
            ( ~ ( in @ SY2405 @ SV218 )
            | ! [SY2406: $i] :
                ( ~ ( in @ SY2406 @ SY2404 )
                | ( subset @ ( setadjoin @ ( setadjoin @ SY2405 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2405 @ ( setadjoin @ SY2406 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV218 @ SY2404 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[714]) ).

thf(979,plain,
    ! [SV219: $i] :
      ( ( ! [SY2407: $i,SY2408: $i] :
            ( ~ ( in @ SY2408 @ SV219 )
            | ! [SX3: $i] :
                ( ~ ( in @ SX3 @ SY2407 )
                | ( ( ksnd @ ( kpair @ SY2408 @ SX3 ) )
                  = SX3 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[715]) ).

thf(980,plain,
    ! [SV220: $i] :
      ( ( ! [SY2410: $o,SY2411: $i] :
            ( ~ ( in @ SY2411 @ SV220 )
            | ! [SY2412: $i] :
                ( ~ ( in @ SY2412 @ SV220 )
                | ~ SY2410
                | ( ( dsetconstr @ SV220
                    @ ^ [SX4: $i] :
                        ( ~ ( ~ SY2410
                            | ( SX4 != SY2411 ) )
                        | ~ ( ~ ~ SY2410
                            | ( SX4 != SY2412 ) ) ) )
                  = ( setadjoin @ SY2411 @ emptyset ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[716]) ).

thf(981,plain,
    ! [SV221: $i] :
      ( ( ! [SY2414: $i,SY2415: $i] :
            ( ~ ( subset @ SY2415 @ ( cartprod @ SV221 @ SY2414 ) )
            | ! [SY2416: $i] :
                ( ~ ( subset @ SY2416 @ ( cartprod @ SV221 @ SY2414 ) )
                | ~ ! [SY2417: $i] :
                      ( ~ ( in @ SY2417 @ SV221 )
                      | ! [SX5: $i] :
                          ( ~ ( in @ SX5 @ SY2414 )
                          | ~ ( in @ ( kpair @ SY2417 @ SX5 ) @ SY2415 )
                          | ( in @ ( kpair @ SY2417 @ SX5 ) @ SY2416 ) ) )
                | ~ ! [SY2419: $i] :
                      ( ~ ( in @ SY2419 @ SV221 )
                      | ! [SX5: $i] :
                          ( ~ ( in @ SX5 @ SY2414 )
                          | ~ ( in @ ( kpair @ SY2419 @ SX5 ) @ SY2416 )
                          | ( in @ ( kpair @ SY2419 @ SX5 ) @ SY2415 ) ) )
                | ( SY2415 = SY2416 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[717]) ).

thf(982,plain,
    ! [SV222: $i] :
      ( ( ! [SY2421: $i,SY2422: $i] :
            ( ~ ( func @ SV222 @ SY2421 @ SY2422 )
            | ! [SY2423: $i] :
                ( ~ ( in @ SY2423 @ SV222 )
                | ( singleton
                  @ ( dsetconstr @ SY2421
                    @ ^ [SX4: $i] : ( in @ ( kpair @ SY2423 @ SX4 ) @ SY2422 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[718]) ).

thf(983,plain,
    ! [SV223: $i] :
      ( ( ! [SY2425: $i] :
            ( ~ ( in @ SY2425 @ SV223 )
            | ( subset @ ( setadjoin @ SY2425 @ emptyset ) @ SV223 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[719]) ).

thf(984,plain,
    ! [SV224: $i] :
      ( ( ~ ( ( SV224 != emptyset ) )
        | ~ ! [SY2426: $i] :
              ~ ~ ( ~ ( in @ SY2426 @ SV224 )
                  | ~ $true ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[720]) ).

thf(985,plain,
    ! [SV225: $i] :
      ( ( ! [SY2427: $i,SY2428: $i] :
            ( ~ ( subset @ SY2428 @ SV225 )
            | ~ ( subset @ SY2428 @ SY2427 )
            | ( subset @ SY2428 @ ( binintersect @ SV225 @ SY2427 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[721]) ).

thf(986,plain,
    ! [SV226: $i] :
      ( ( ! [SY2429: $i,SY2430: $i] :
            ( ~ ( in @ SY2430 @ SV226 )
            | ~ ~ ( in @ SY2430 @ SY2429 )
            | ( in @ SY2430 @ ( symdiff @ SV226 @ SY2429 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[722]) ).

thf(987,plain,
    ! [SV227: $i] :
      ( ( ! [SY2431: $i] :
            ( ~ ( in @ SY2431 @ ( powerset @ SV227 ) )
            | ! [SY2432: $i] :
                ( ~ ( in @ SY2432 @ ( powerset @ SV227 ) )
                | ~ ( subset @ ( setminus @ SV227 @ SY2432 ) @ ( setminus @ SV227 @ SY2431 ) )
                | ( subset @ SY2431 @ SY2432 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[723]) ).

thf(988,plain,
    ! [SV228: $i] :
      ( ( ! [SY2433: $i] :
            ( ~ ( in @ SY2433 @ ( powerset @ SV228 ) )
            | ! [SY2434: $i] :
                ( ~ ( in @ SY2434 @ ( powerset @ SV228 ) )
                | ! [SY2435: $i] :
                    ( ~ ( in @ SY2435 @ ( powerset @ SV228 ) )
                    | ! [SY2436: $i] :
                        ( ~ ( in @ SY2436 @ SV228 )
                        | ~ ( in @ SY2436 @ ( binintersect @ SY2433 @ SY2434 ) )
                        | ( in @ SY2436 @ ( binunion @ SY2434 @ SY2435 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[724]) ).

thf(989,plain,
    ! [SV229: $i] :
      ( ( ! [SY2437: $i] :
            ( ~ ( in @ SY2437 @ SV229 )
            | ( in @ SY2437 @ ( powerset @ ( setunion @ SV229 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[725]) ).

thf(990,plain,
    ! [SV230: $i] :
      ( ( ! [SY2438: $o,SY2439: $i] :
            ( ~ ( in @ SY2439 @ SV230 )
            | ! [SY2440: $i] :
                ( ~ ( in @ SY2440 @ SV230 )
                | ~ ~ SY2438
                | ( ( dsetconstr @ SV230
                    @ ^ [SX4: $i] :
                        ( ~ ( ~ SY2438
                            | ( SX4 != SY2439 ) )
                        | ~ ( ~ ~ SY2438
                            | ( SX4 != SY2440 ) ) ) )
                  = ( setadjoin @ SY2440 @ emptyset ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[726]) ).

thf(991,plain,
    ! [SV231: $i] :
      ( ( ! [SY2442: $i] :
            ( ~ ( in @ SY2442 @ ( powerset @ SV231 ) )
            | ! [SY2443: $i] :
                ( ~ ( in @ SY2443 @ ( powerset @ SV231 ) )
                | ~ ! [SY2444: $i] :
                      ( ~ ( in @ SY2444 @ SV231 )
                      | ~ ( in @ SY2444 @ SY2442 )
                      | ( in @ SY2444 @ SY2443 ) )
                | ( in @ SY2442 @ ( powerset @ SY2443 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[727]) ).

thf(992,plain,
    ! [SV232: $i] :
      ( ( ! [SY2445: $i,SY2446: $i] :
            ( ~ ( func @ SV232 @ SY2445 @ SY2446 )
            | ( ( lam @ SV232 @ SY2445
                @ ^ [SY2447: $i] : ( ap @ SV232 @ SY2445 @ SY2446 @ SY2447 ) )
              = SY2446 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[728]) ).

thf(993,plain,
    ! [SV233: $i] :
      ( ( ! [SY2448: $i] :
            ( ( ( binintersect @ SV233 @ SY2448 )
             != SY2448 )
            | ( subset @ SY2448 @ SV233 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[729]) ).

thf(994,plain,
    ! [SV234: $i] :
      ( ( ! [SY2449: $i,SY2450: $i] :
            ( ~ ( in @ SY2450 @ ( cartprod @ SV234 @ SY2449 ) )
            | ( in @ ( kfst @ SY2450 ) @ SV234 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[730]) ).

thf(995,plain,
    ! [SV235: $i] :
      ( ( ! [SY2451: $i] :
            ( ( SV235 != SY2451 )
            | ( in @ SV235 @ ( setadjoin @ SY2451 @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[731]) ).

thf(996,plain,
    ! [SV236: $i] :
      ( ( ! [SY2452: $i,SY2453: $i] :
            ( ~ ( subset @ SV236 @ SY2452 )
            | ~ ( subset @ SY2452 @ SY2453 )
            | ( subset @ SV236 @ SY2453 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[732]) ).

thf(997,plain,
    ! [SV237: $i] :
      ( ( ! [SY2454: $i,SY2455: $i] :
            ( ( ( setadjoin @ SV237 @ ( setadjoin @ SY2454 @ emptyset ) )
             != ( setadjoin @ SY2455 @ emptyset ) )
            | ( SV237 = SY2454 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[733]) ).

thf(998,plain,
    ! [SV238: $i] :
      ( ( ! [SY2456: $i] :
            ( ~ ( subset @ SV238 @ SY2456 )
            | ( subset @ ( powerset @ SV238 ) @ ( powerset @ SY2456 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[734]) ).

thf(999,plain,
    ! [SV239: $i] :
      ( ( ! [SY2457: $i,SY2458: $i,SY2459: $i] :
            ( ( ( setadjoin @ ( setadjoin @ SV239 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV239 @ ( setadjoin @ SY2457 @ emptyset ) ) @ emptyset ) )
             != ( setadjoin @ ( setadjoin @ SY2458 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2458 @ ( setadjoin @ SY2459 @ emptyset ) ) @ emptyset ) ) )
            | ( SV239 = SY2458 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[735]) ).

thf(1000,plain,
    ! [SV240: $i] :
      ( ( ! [SY2460: $i,SY2461: $i] :
            ( ~ ( func @ SV240 @ SY2460 @ SY2461 )
            | ( in @ SY2461 @ ( funcSet @ SV240 @ SY2460 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[736]) ).

thf(1001,plain,
    ! [SV241: $i] :
      ( ( ! [SY2462: $i,SY2463: $i] :
            ( ~ ( in @ SY2463 @ ( binintersect @ SV241 @ SY2462 ) )
            | ( in @ SY2463 @ SY2462 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[737]) ).

thf(1002,plain,
    ! [SV242: $i] :
      ( ( ! [SY2464: $i,SY2465: $i] :
            ( ~ ~ ( in @ SY2465 @ SV242 )
            | ~ ( in @ SY2465 @ ( setminus @ SV242 @ SY2464 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[738]) ).

thf(1003,plain,
    ! [SV243: $i] :
      ( ( ! [SY2466: $i] :
            ( ~ ( in @ SY2466 @ ( powerset @ SV243 ) )
            | ! [SY2467: $i] :
                ( ~ ( in @ SY2467 @ ( powerset @ SV243 ) )
                | ~ ! [SY2468: $i] :
                      ( ~ ( in @ SY2468 @ SV243 )
                      | ~ ( in @ SY2468 @ SY2466 )
                      | ( in @ SY2468 @ SY2467 ) )
                | ( subset @ SY2466 @ SY2467 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[739]) ).

thf(1004,plain,
    ! [SV244: $i] :
      ( ( ! [SY2469: $i,SY2470: $i > $i] :
            ( ~ ! [SY2471: $i] :
                  ( ~ ( in @ SY2471 @ SV244 )
                  | ( in @ ( SY2470 @ SY2471 ) @ SY2469 ) )
            | ! [SY2472: $i] :
                ( ~ ( in @ SY2472 @ SV244 )
                | ( ( ap @ SV244 @ SY2469
                    @ ( lam @ SV244 @ SY2469
                      @ ^ [SX4: $i] : ( SY2470 @ SX4 ) )
                    @ SY2472 )
                  = ( SY2470 @ SY2472 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[740]) ).

thf(1005,plain,
    ! [SV245: $i] :
      ( ( ! [SY2474: $i,SY2475: $i] :
            ( ~ ( in @ SY2475 @ ( funcSet @ SV245 @ SY2474 ) )
            | ! [SY2476: $i] :
                ( ~ ( in @ SY2476 @ SV245 )
                | ( in @ ( kpair @ SY2476 @ ( ap @ SV245 @ SY2474 @ SY2475 @ SY2476 ) ) @ SY2475 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[741]) ).

thf(1006,plain,
    ! [SV246: $i] :
      ( ( ! [SY2477: $i] :
            ( ~ ( in @ SY2477 @ ( powerset @ SV246 ) )
            | ! [SY2478: $i] :
                ( ~ ( in @ SY2478 @ ( powerset @ SV246 ) )
                | ! [SY2479: $i] :
                    ( ~ ( in @ SY2479 @ SV246 )
                    | ~ ( in @ SY2479 @ ( setminus @ SV246 @ SY2477 ) )
                    | ~ ( in @ SY2479 @ ( binintersect @ SY2477 @ SY2478 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[742]) ).

thf(1007,plain,
    ! [SV247: $i] :
      ( ( ~ ( in @ SV247 @ omega )
        | ( in @ ( setadjoin @ SV247 @ SV247 ) @ omega ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[743]) ).

thf(1008,plain,
    ! [SV248: $i] :
      ( ( ! [SY2480: $i] :
            ( ~ ( in @ SV248 @ ( setadjoin @ SY2480 @ emptyset ) )
            | ( SV248 = SY2480 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[744]) ).

thf(1009,plain,
    ! [SV249: $i] :
      ( ( ! [SY2481: $i,SY2482: $i] :
            ( ~ ( in @ SY2482 @ SY2481 )
            | ~ ( in @ SY2482 @ ( setminus @ SV249 @ SY2481 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[745]) ).

thf(1010,plain,
    ! [SV250: $i] :
      ( ( ~ ( singleton @ SV250 )
        | ! [SY2483: $i] :
            ( ~ ( in @ SY2483 @ SV250 )
            | ( ( setunion @ SV250 )
              = SY2483 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[746]) ).

thf(1011,plain,
    ! [SV251: $i] :
      ( ( ! [SY2484: $i,SY2485: $i] :
            ( ~ ( in @ SY2485 @ SV251 )
            | ! [SY2486: $i] :
                ( ~ ( in @ SY2486 @ SY2484 )
                | ( in @ ( setadjoin @ SY2485 @ ( setadjoin @ SY2486 @ emptyset ) ) @ ( powerset @ ( binunion @ SV251 @ SY2484 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[747]) ).

thf(1012,plain,
    ! [SV252: $i] :
      ( ( ! [SY2487: $i,SY2488: $i] :
            ( ~ ( in @ SY2488 @ ( binunion @ SV252 @ SY2487 ) )
            | ( in @ SY2488 @ SV252 )
            | ( in @ SY2488 @ SY2487 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[748]) ).

thf(1013,plain,
    ! [SV253: $i > $o] :
      ( ( ~ ~ ! [SY2489: $i] :
                ~ ! [SY2490: $i] :
                    ~ ( ~ ( ~ ( SV253 @ SY2490 )
                          | ( SY2490 = SY2489 ) )
                      | ~ ( ( SY2490 != SY2489 )
                          | ( SV253 @ SY2490 ) ) )
        | ~ ! [SY2491: $i] :
              ~ ~ ( ~ ( SV253 @ SY2491 )
                  | ~ ! [SY2492: $i] :
                        ( ~ ( SV253 @ SY2492 )
                        | ( SY2491 = SY2492 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[749]) ).

thf(1014,plain,
    ! [SV254: $i] :
      ( ( ! [SY2493: $i,SY2494: $i] :
            ( ~ ( subset @ SV254 @ SY2494 )
            | ( subset @ SV254 @ ( setadjoin @ SY2493 @ SY2494 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[750]) ).

thf(1015,plain,
    ! [SV255: $i] :
      ( ( ! [SY2495: $i] :
            ( ~ ( in @ SY2495 @ ( setunion @ SV255 ) )
            | ! [SY2496: $o] :
                ( ~ ! [SY2497: $i] :
                      ( ~ ( in @ SY2495 @ SY2497 )
                      | ~ ( in @ SY2497 @ SV255 )
                      | SY2496 )
                | SY2496 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[751]) ).

thf(1016,plain,
    ! [SV256: $i] :
      ( ( ! [SY2498: $o,SY2499: $i] :
            ( ~ ( in @ SY2499 @ SV256 )
            | ! [SY2500: $i] :
                ( ~ ( in @ SY2500 @ SV256 )
                | ( in @ ( if @ SV256 @ SY2498 @ SY2499 @ SY2500 ) @ ( setadjoin @ SY2499 @ ( setadjoin @ SY2500 @ emptyset ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[752]) ).

thf(1017,plain,
    ! [SV257: $i] :
      ( ( ! [SY2501: $i,SY2502: $i] :
            ( ~ ( in @ SY2502 @ SV257 )
            | ! [SY2503: $i] :
                ( ~ ( in @ SY2503 @ SY2501 )
                | ( subset @ ( setadjoin @ SY2502 @ ( setadjoin @ SY2503 @ emptyset ) ) @ ( binunion @ SV257 @ SY2501 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[753]) ).

thf(1018,plain,
    ! [SV258: $i,SV1: $i] :
      ( ( ! [SY2504: $i > $i > $o] :
            ( subset
            @ ( dpsetconstr @ SV1 @ SV258
              @ ^ [Xx: $i,Xy: $i] : ( SY2504 @ Xx @ Xy ) )
            @ ( cartprod @ SV1 @ SV258 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[754]) ).

thf(1019,plain,
    ! [SV259: $i,SV2: $i] :
      ( ( ! [SY2507: $i > $i > $o] :
            ( subset
            @ ( dpsetconstr @ SV2 @ SV259
              @ ^ [Xx: $i,Xy: $i] : ( SY2507 @ Xx @ Xy ) )
            @ ( cartprod @ SV2 @ SV259 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[755]) ).

thf(1020,plain,
    ! [SV260: $i,SV3: $i] :
      ( ( ( ksnd @ ( kpair @ SV3 @ SV260 ) )
        = SV260 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[756]) ).

thf(1021,plain,
    ! [SV261: $i,SV4: $i] :
      ( ( ( kfst @ ( kpair @ SV4 @ SV261 ) )
        = SV4 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[757]) ).

thf(1022,plain,
    ! [SV262: $i,SV8: $i] :
      ( ( iskpair @ ( kpair @ SV8 @ SV262 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[761]) ).

thf(1023,plain,
    ! [SV263: $i,SV9: $i] :
      ( ( iskpair @ ( setadjoin @ ( setadjoin @ SV9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV9 @ ( setadjoin @ SV263 @ emptyset ) ) @ emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[762]) ).

thf(1024,plain,
    ! [SV10: $i,SV264: $i] :
      ( ( in @ SV264 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV10 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV10 @ ( setadjoin @ SV264 @ emptyset ) ) @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[763]) ).

thf(1025,plain,
    ! [SV265: $i,SV11: $i] :
      ( ( in @ SV11 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV11 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV11 @ ( setadjoin @ SV265 @ emptyset ) ) @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[764]) ).

thf(1026,plain,
    ! [SV12: $i,SV266: $i] :
      ( ( in @ SV266 @ ( setadjoin @ SV12 @ ( setadjoin @ SV266 @ emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[765]) ).

thf(1027,plain,
    ! [SV267: $i,SV13: $i] :
      ( ( subset @ ( setminus @ SV13 @ SV267 ) @ SV13 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[766]) ).

thf(1028,plain,
    ! [SV268: $i,SV14: $i] :
      ( ( ! [SY2510: $i] :
            ( ( binintersect @ SV14 @ ( binunion @ SV268 @ SY2510 ) )
            = ( binunion @ ( binintersect @ SV14 @ SV268 ) @ ( binintersect @ SV14 @ SY2510 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[767]) ).

thf(1029,plain,
    ! [SV269: $i,SV15: $i] :
      ( ( subset @ ( binintersect @ SV15 @ SV269 ) @ SV269 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[768]) ).

thf(1030,plain,
    ! [SV270: $i,SV16: $i] :
      ( ( subset @ ( binintersect @ SV16 @ SV270 ) @ SV16 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[769]) ).

thf(1031,plain,
    ! [SV17: $i,SV271: $i] :
      ( ( subset @ SV271 @ ( binunion @ SV17 @ SV271 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[770]) ).

thf(1032,plain,
    ! [SV272: $i,SV18: $i] :
      ( ( subset @ SV18 @ ( binunion @ SV18 @ SV272 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[771]) ).

thf(1033,plain,
    ! [SV19: $i,SV273: $i] :
      ( ( in @ SV273 @ ( setadjoin @ SV19 @ ( setadjoin @ SV273 @ emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[772]) ).

thf(1034,plain,
    ! [SV274: $i > $o,SV20: $i] :
      ( ( subset
        @ ( dsetconstr @ SV20
          @ ^ [SY2511: $i] : ( SV274 @ SY2511 ) )
        @ SV20 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[773]) ).

thf(1035,plain,
    ! [SV275: $i > $o,SV21: $i] :
      ( ( in
        @ ( dsetconstr @ SV21
          @ ^ [SY2512: $i] : ( SV275 @ SY2512 ) )
        @ ( powerset @ SV21 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[774]) ).

thf(1036,plain,
    ! [SV23: $i,SV276: $i] :
      ( ( subset @ SV276 @ ( setadjoin @ SV23 @ SV276 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[776]) ).

thf(1037,plain,
    ! [SV26: $i,SV277: $i] :
      ( ( in @ SV277 @ ( setadjoin @ SV26 @ ( setadjoin @ SV277 @ emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[779]) ).

thf(1038,plain,
    ! [SV278: $i,SV27: $i] :
      ( ( in @ SV27 @ ( setadjoin @ SV27 @ ( setadjoin @ SV278 @ emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[780]) ).

thf(1039,plain,
    ! [SV279: $i,SV31: $i] :
      ( ( in @ SV31 @ ( setadjoin @ SV31 @ SV279 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[784]) ).

thf(1040,plain,
    ! [SV32: $i] :
      ( ( in @ SV32 @ emptyset )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[785]) ).

thf(1041,plain,
    ! [SV33: $i] :
      ( ( in @ SV33 @ emptyset )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[786]) ).

thf(1042,plain,
    ! [SV280: $i,SV34: $i] :
      ( ( ! [SY2513: $i] :
            ( ~ ( in @ SY2513 @ ( funcSet @ SV34 @ SV280 ) )
            | ( func @ SV34 @ SV280 @ SY2513 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[787]) ).

thf(1043,plain,
    ! [SV281: $i > $o,SV35: $i] :
      ( ( ~ ~ ~ ! [SY2514: $i] :
                  ~ ~ ( ~ ( in @ SY2514 @ SV35 )
                      | ~ ( SV281 @ SY2514 ) )
        | ! [SY2515: $i] :
            ( ~ ( in @ SY2515 @ SV35 )
            | ~ ( SV281 @ SY2515 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[788]) ).

thf(1044,plain,
    ! [SV36: $i,SV282: $i] :
      ( ( ~ ( in @ SV282 @ ( powerset @ SV36 ) )
        | ! [SY2516: $i] :
            ( ~ ( in @ SY2516 @ ( powerset @ SV36 ) )
            | ! [SY2517: $i] :
                ( ~ ( in @ SY2517 @ SV36 )
                | ~ ( subset @ SV282 @ SY2516 )
                | ~ ~ ( in @ SY2517 @ SY2516 )
                | ~ ( in @ SY2517 @ SV282 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[789]) ).

thf(1045,plain,
    ! [SV37: $i > $o] :
      ( ( ( ~ ~ ! [SY1895: $i] :
                  ~ ~ ( ~ ( SV37 @ SY1895 )
                      | ~ ! [SY1896: $i] :
                            ( ~ ( SV37 @ SY1896 )
                            | ( SY1895 = SY1896 ) ) ) )
        = $true )
      | ( ( ~ ! [SY1897: $i] :
                ~ ! [SY1898: $i] :
                    ~ ( ~ ( ~ ( SV37 @ SY1898 )
                          | ( SY1898 = SY1897 ) )
                      | ~ ( ( SY1898 != SY1897 )
                          | ( SV37 @ SY1898 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[790]) ).

thf(1046,plain,
    ! [SV283: $i,SV38: $i] :
      ( ( ! [SY2518: $i] :
            ( ~ ( func @ SV38 @ SV283 @ SY2518 )
            | ! [SY2519: $i] :
                ( ~ ( in @ SY2519 @ SV38 )
                | ( in @ ( kpair @ SY2519 @ ( ap @ SV38 @ SV283 @ SY2518 @ SY2519 ) ) @ SY2518 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[791]) ).

thf(1047,plain,
    ! [SV39: $i] :
      ( ( ( ~ ( in @ SV39 @ emptyset ) )
        = $true )
      | ( ( ! [SX1: $o] : SX1 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[792]) ).

thf(1048,plain,
    ! [SV284: $o,SV40: $i] :
      ( ( ! [SY2520: $i] :
            ( ~ ( in @ SY2520 @ SV40 )
            | ! [SY2521: $i] :
                ( ~ ( in @ SY2521 @ SV40 )
                | ~ ~ SV284
                | ( in @ SY2521
                  @ ( dsetconstr @ SV40
                    @ ^ [SY2522: $i] :
                        ( ~ ( ~ SV284
                            | ( SY2522 != SY2520 ) )
                        | ~ ( ~ ~ SV284
                            | ( SY2522 != SY2521 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[793]) ).

thf(1049,plain,
    ! [SV40: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV40 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV40 )
                | ~ ~ $true
                | ( in @ SX1
                  @ ( dsetconstr @ SV40
                    @ ^ [SX2: $i] :
                        ( ~ ( ~ $true
                            | ( SX2 != SX0 ) )
                        | ~ ( ~ ~ $true
                            | ( SX2 != SX1 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[793]) ).

thf(1050,plain,
    ! [SV40: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV40 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV40 )
                | ~ ~ $false
                | ( in @ SX1
                  @ ( dsetconstr @ SV40
                    @ ^ [SX2: $i] :
                        ( ~ ( ~ $false
                            | ( SX2 != SX0 ) )
                        | ~ ( ~ ~ $false
                            | ( SX2 != SX1 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[793]) ).

thf(1051,plain,
    ! [SV41: $i > $o] :
      ( ( ( ~ ~ ! [SY1907: $i] :
                  ~ ~ ( ~ ( SV41 @ SY1907 )
                      | ~ ! [SY1908: $i] :
                            ( ~ ( SV41 @ SY1908 )
                            | ( SY1907 = SY1908 ) ) ) )
        = $true )
      | ( ( ! [SY1909: $i,SY1910: $i] :
              ( ~ ( SV41 @ SY1909 )
              | ~ ( SV41 @ SY1910 )
              | ( SY1909 = SY1910 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[794]) ).

thf(1052,plain,
    ! [SV42: $i,SV285: $i] :
      ( ( ~ ( ~ ( ~ ( in @ SV285 @ ( powerset @ SV42 ) )
                | ! [SY2523: $i] :
                    ( ~ ( in @ SY2523 @ SV285 )
                    | ( in @ SY2523 @ SV42 ) ) )
            | ~ ( ~ ! [SY2524: $i] :
                      ( ~ ( in @ SY2524 @ SV285 )
                      | ( in @ SY2524 @ SV42 ) )
                | ( in @ SV285 @ ( powerset @ SV42 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[795]) ).

thf(1053,plain,
    ! [SV43: $i > $o] :
      ( ( ( ~ ~ ! [SY1914: $i] :
                  ~ ~ ( ~ ( SV43 @ SY1914 )
                      | ~ ! [SY1915: $i] :
                            ( ~ ( SV43 @ SY1915 )
                            | ( SY1914 = SY1915 ) ) ) )
        = $true )
      | ( ( ! [SY1916: $i,SY1917: $i] :
              ( ~ ( SV43 @ SY1916 )
              | ~ ( SV43 @ SY1917 )
              | ( SY1916 = SY1917 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[796]) ).

thf(1054,plain,
    ! [SV44: $i,SV286: $i] :
      ( ( ~ ( in @ SV286 @ ( powerset @ SV44 ) )
        | ! [SY2525: $i] :
            ( ~ ( in @ SY2525 @ ( powerset @ SV44 ) )
            | ! [SY2526: $i] :
                ( ~ ( in @ SY2526 @ SV44 )
                | ~ ( in @ SY2526 @ ( setminus @ SV44 @ ( binunion @ SV286 @ SY2525 ) ) )
                | ~ ( in @ SY2526 @ SV286 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[797]) ).

thf(1055,plain,
    ! [SV45: $o] :
      ( ( ( ~ SV45 ) = $true )
      | ( ( in @ emptyset @ ( prop2set @ SV45 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[798]) ).

thf(1056,plain,
    ( ( ( ~ $true ) = $true )
    | ( ( in @ emptyset @ ( prop2set @ $true ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[799]) ).

thf(1057,plain,
    ( ( ( ~ $false ) = $true )
    | ( ( in @ emptyset @ ( prop2set @ $false ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[800]) ).

thf(1058,plain,
    ! [SV287: $i > $o,SV46: $i] :
      ( ( ~ ~ ! [SY2527: $i] :
                ~ ~ ( ~ ( in @ SY2527 @ SV46 )
                    | ~ ~ ( SV287 @ SY2527 ) )
        | ~ ! [SY2528: $i] :
              ( ~ ( in @ SY2528 @ SV46 )
              | ( SV287 @ SY2528 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[801]) ).

thf(1059,plain,
    ! [SV288: $i,SV47: $i] :
      ( ( ! [SY2529: $i] :
            ( ~ ~ ( in @ SY2529 @ ( setminus @ SV47 @ SV288 ) )
            | ~ ( in @ SY2529 @ SV47 )
            | ( in @ SY2529 @ SV288 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[802]) ).

thf(1060,plain,
    ! [SV48: $i > $o] :
      ( ( ( ~ ~ ! [SY1926: $i] :
                  ~ ~ ( ~ ( SV48 @ SY1926 )
                      | ~ ! [SY1927: $i] :
                            ( ~ ( SV48 @ SY1927 )
                            | ( SY1926 = SY1927 ) ) ) )
        = $true )
      | ( ( ~ ! [SY1928: $i] :
                ~ ~ ( ~ ( SV48 @ SY1928 )
                    | ~ ! [SY1929: $i] :
                          ( ~ ( SV48 @ SY1929 )
                          | ( SY1928 = SY1929 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[803]) ).

thf(1061,plain,
    ! [SV289: $i,SV49: $i] :
      ( ( ! [SY2530: $i] :
            ( ~ ( in @ SY2530 @ SV49 )
            | ~ ~ ( in @ SY2530 @ SV289 )
            | ( in @ SY2530 @ ( setminus @ SV49 @ SV289 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[804]) ).

thf(1062,plain,
    ! [SV290: $i,SV50: $i] :
      ( ( ! [SY2531: $i] :
            ( ~ ( in @ SY2531 @ SV50 )
            | ! [SY2532: $i] :
                ( ~ ( in @ SY2532 @ SV290 )
                | ( in @ ( setadjoin @ ( setadjoin @ SY2531 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2531 @ ( setadjoin @ SY2532 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV50 @ SV290 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[805]) ).

thf(1063,plain,
    ! [SV291: $i,SV51: $i] :
      ( ( ~ ! [SY2533: $i] :
              ~ ( ~ ( ~ ( in @ SY2533 @ SV51 )
                    | ( in @ SY2533 @ SV291 ) )
                | ~ ( ~ ( in @ SY2533 @ SV291 )
                    | ( in @ SY2533 @ SV51 ) ) )
        | ( SV51 = SV291 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[806]) ).

thf(1064,plain,
    ! [SV292: $i > $o,SV52: $i] :
      ( ( ~ ~ ~ ! [SY2534: $i] :
                  ~ ~ ( ~ ( in @ SY2534 @ SV52 )
                      | ~ ( SV292 @ SY2534 ) )
        | ! [SY2535: $i] :
            ( ~ ( in @ SY2535 @ SV52 )
            | ~ ( SV292 @ SY2535 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[807]) ).

thf(1065,plain,
    ! [SV293: $i,SV53: $i] :
      ( ( ( SV53 != SV293 )
        | ( subset @ SV53 @ SV293 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[808]) ).

thf(1066,plain,
    ! [SV54: $i,SV294: $i] :
      ( ( ~ ( in @ SV294 @ ( powerset @ SV54 ) )
        | ( in @ ( powerset @ SV294 ) @ ( powerset @ ( powerset @ SV54 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[809]) ).

thf(1067,plain,
    ! [SV295: $i,SV55: $i] :
      ( ( ! [SY2536: $i] :
            ( ~ ~ ( in @ SY2536 @ SV55 )
            | ~ ~ ( in @ SY2536 @ SV295 )
            | ~ ( in @ SY2536 @ ( symdiff @ SV55 @ SV295 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[810]) ).

thf(1068,plain,
    ! [SV296: $i,SV56: $i] :
      ( ( ! [SY2537: $i > $i > $o,SY2538: $i,SY2539: $i] :
            ( ~ ( in @ ( kpair @ SY2538 @ SY2539 )
                @ ( dpsetconstr @ SV56 @ SV296
                  @ ^ [SX5: $i,SX6: $i] : ( SY2537 @ SX5 @ SX6 ) ) )
            | ( in @ SY2539 @ SV296 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[811]) ).

thf(1069,plain,
    ! [SV57: $i] :
      ( ( ( ~ ( subset @ SV57 @ emptyset ) )
        = $true )
      | ( ( SV57 = emptyset )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[812]) ).

thf(1070,plain,
    ! [SV297: $i,SV58: $i] :
      ( ( ! [SY2542: $i] :
            ( ~ ( in @ ( setadjoin @ SY2542 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV58 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV58 @ ( setadjoin @ SV297 @ emptyset ) ) @ emptyset ) ) )
            | ( SV58 = SY2542 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[813]) ).

thf(1071,plain,
    ! [SV298: $i,SV59: $i] :
      ( ( ! [SY2543: $i,SY2544: $i] :
            ( ( ( setadjoin @ ( setadjoin @ SV59 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV59 @ ( setadjoin @ SV298 @ emptyset ) ) @ emptyset ) )
             != ( setadjoin @ ( setadjoin @ SY2543 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2543 @ ( setadjoin @ SY2544 @ emptyset ) ) @ emptyset ) ) )
            | ( SV298 = SY2544 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[814]) ).

thf(1072,plain,
    ! [SV299: $i,SV60: $i] :
      ( ( ! [SY2545: $i] :
            ( ~ ( in @ SY2545 @ SV60 )
            | ~ ( in @ SY2545 @ SV299 )
            | ~ ( in @ SY2545 @ ( symdiff @ SV60 @ SV299 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[815]) ).

thf(1073,plain,
    ! [SV300: $i,SV61: $i] :
      ( ( ! [SY2546: $i,SY2547: $i] :
            ( ~ ( in @ ( kpair @ SY2546 @ SY2547 ) @ ( cartprod @ SV61 @ SV300 ) )
            | ( in @ SY2546 @ SV61 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[816]) ).

thf(1074,plain,
    ! [SV301: $i,SV62: $i] :
      ( ( ! [SY2548: $i] :
            ( ~ ( in @ SY2548 @ SV62 )
            | ! [SY2549: $i] :
                ( ~ ( in @ SY2549 @ SV301 )
                | ( ( kpair @ SY2548 @ SY2549 )
                  = ( kpair @ SY2548 @ SY2549 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[817]) ).

thf(1075,plain,
    ! [SV302: $i,SV63: $i] :
      ( ( ! [SY2550: $i] :
            ( ~ ( subset @ SY2550 @ ( cartprod @ SV63 @ SV302 ) )
            | ! [SY2551: $i > $o] :
                ( ~ ! [SY2552: $i] :
                      ( ~ ( in @ SY2552 @ SV63 )
                      | ! [SY2553: $i] :
                          ( ~ ( in @ SY2553 @ SV302 )
                          | ~ ( in @ ( kpair @ SY2552 @ SY2553 ) @ SY2550 )
                          | ( SY2551 @ ( kpair @ SY2552 @ SY2553 ) ) ) )
                | ! [SX4: $i] :
                    ( ~ ( in @ SX4 @ SY2550 )
                    | ( SY2551 @ SX4 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[818]) ).

thf(1076,plain,
    ! [SV64: $i] :
      ( ( ( ~ ( singleton @ SV64 ) )
        = $true )
      | ( ( in @ ( setunion @ SV64 ) @ SV64 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[819]) ).

thf(1077,plain,
    ! [SV303: $i > $o,SV65: $i] :
      ( ( ! [SY2555: $i] :
            ( ~ ( in @ SY2555 @ SV65 )
            | ~ ( SV303 @ SY2555 )
            | ( ( dsetconstr @ SV65
                @ ^ [SY2556: $i] : ( SV303 @ SY2556 ) )
             != emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[820]) ).

thf(1078,plain,
    ! [SV304: $i,SV66: $i] :
      ( ( ( SV66 != SV304 )
        | ( ( setadjoin @ ( setadjoin @ SV66 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV66 @ ( setadjoin @ SV304 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ SV66 @ emptyset ) @ emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[821]) ).

thf(1079,plain,
    ! [SV305: $o,SV67: $i] :
      ( ( ! [SY2557: $i] :
            ( ~ ( in @ SY2557 @ SV67 )
            | ! [SY2558: $i] :
                ( ~ ( in @ SY2558 @ SV67 )
                | ~ SV305
                | ( in @ SY2557
                  @ ( dsetconstr @ SV67
                    @ ^ [SY2559: $i] :
                        ( ~ ( ~ SV305
                            | ( SY2559 != SY2557 ) )
                        | ~ ( ~ ~ SV305
                            | ( SY2559 != SY2558 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[822]) ).

thf(1080,plain,
    ! [SV67: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV67 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV67 )
                | ~ $true
                | ( in @ SX0
                  @ ( dsetconstr @ SV67
                    @ ^ [SX2: $i] :
                        ( ~ ( ~ $true
                            | ( SX2 != SX0 ) )
                        | ~ ( ~ ~ $true
                            | ( SX2 != SX1 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[822]) ).

thf(1081,plain,
    ! [SV67: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV67 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV67 )
                | ~ $false
                | ( in @ SX0
                  @ ( dsetconstr @ SV67
                    @ ^ [SX2: $i] :
                        ( ~ ( ~ $false
                            | ( SX2 != SX0 ) )
                        | ~ ( ~ ~ $false
                            | ( SX2 != SX1 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[822]) ).

thf(1082,plain,
    ! [SV306: $i,SV68: $i] :
      ( ( ! [SY2560: $i] :
            ( ~ ( func @ SV68 @ SV306 @ SY2560 )
            | ! [SY2561: $i] :
                ( ~ ( in @ SY2561 @ SV68 )
                | ( in
                  @ ( setunion
                    @ ( dsetconstr @ SV306
                      @ ^ [SX4: $i] : ( in @ ( kpair @ SY2561 @ SX4 ) @ SY2560 ) ) )
                  @ SV306 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[823]) ).

thf(1083,plain,
    ! [SV69: $i,SV307: $i] :
      ( ( ~ ( subset @ SV307 @ SV69 )
        | ( ( binintersect @ SV69 @ SV307 )
          = SV307 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[824]) ).

thf(1084,plain,
    ! [SV70: $i,SV308: $i] :
      ( ( ~ ( in @ SV308 @ ( powerset @ SV70 ) )
        | ( subset @ ( setminus @ SV70 @ ( setminus @ SV70 @ SV308 ) ) @ SV308 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[825]) ).

thf(1085,plain,
    ! [SV309: $i,SV71: $i] :
      ( ( ~ ( subset @ SV71 @ SV309 )
        | ( ( binintersect @ SV71 @ SV309 )
          = SV71 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[826]) ).

thf(1086,plain,
    ! [SV72: $i,SV310: $i] :
      ( ( ~ ( in @ SV310 @ ( powerset @ SV72 ) )
        | ! [SY2563: $i] :
            ( ~ ( in @ SY2563 @ ( powerset @ SV72 ) )
            | ~ ( subset @ SV310 @ ( setminus @ SV72 @ SY2563 ) )
            | ( subset @ SY2563 @ ( setminus @ SV72 @ SV310 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[827]) ).

thf(1087,plain,
    ! [SV311: $i,SV73: $i] :
      ( ( ! [SY2564: $i] :
            ( ~ ( in @ SY2564 @ ( funcSet @ SV73 @ SV311 ) )
            | ! [SY2565: $i] :
                ( ~ ( in @ SY2565 @ ( funcSet @ SV73 @ SV311 ) )
                | ~ ! [SY2566: $i] :
                      ( ~ ( in @ SY2566 @ SV73 )
                      | ( ( ap @ SV73 @ SV311 @ SY2564 @ SY2566 )
                        = ( ap @ SV73 @ SV311 @ SY2565 @ SY2566 ) ) )
                | ( SY2564 = SY2565 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[828]) ).

thf(1088,plain,
    ! [SV312: $i,SV74: $i] :
      ( ( ! [SY2567: $i] :
            ( ~ ~ ( in @ SY2567 @ ( setminus @ SV74 @ SV312 ) )
            | ~ ~ ( in @ SY2567 @ SV312 )
            | ~ ( in @ SY2567 @ SV74 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[829]) ).

thf(1089,plain,
    ! [SV313: $i,SV75: $i] :
      ( ( ! [SY2568: $i] :
            ~ ( ~ ( ~ ( in @ SY2568 @ ( setadjoin @ SV75 @ SV313 ) )
                  | ( SY2568 = SV75 )
                  | ( in @ SY2568 @ SV313 ) )
              | ~ ( ~ ( ( SY2568 = SV75 )
                      | ( in @ SY2568 @ SV313 ) )
                  | ( in @ SY2568 @ ( setadjoin @ SV75 @ SV313 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[830]) ).

thf(1090,plain,
    ! [SV76: $i,SV314: $i] :
      ( ( ~ ( in @ SV314 @ ( powerset @ SV76 ) )
        | ! [SY2569: $i] :
            ( ~ ( in @ SY2569 @ ( powerset @ SV76 ) )
            | ! [SY2570: $i] :
                ( ~ ( in @ SY2570 @ ( powerset @ SV76 ) )
                | ! [SY2571: $i] :
                    ( ~ ( in @ SY2571 @ SV76 )
                    | ~ ( in @ SY2571 @ ( binintersect @ SV314 @ SY2569 ) )
                    | ( in @ SY2571 @ ( binintersect @ ( binunion @ SV314 @ SY2570 ) @ ( binunion @ SY2569 @ SY2570 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[831]) ).

thf(1091,plain,
    ! [SV315: $i > $o,SV77: $i > $o] :
      ( ( ~ ! [SY2572: $i,SY2573: $i] :
              ( ( SY2572 != SY2573 )
              | ~ ( ~ ( ~ ( SV77 @ SY2572 )
                      | ( SV315 @ SY2573 ) )
                  | ~ ( ~ ( SV315 @ SY2573 )
                      | ( SV77 @ SY2572 ) ) ) )
        | ~ ~ ! [SY2001: $i] :
                ~ ~ ( ~ ( SV77 @ SY2001 )
                    | ~ ! [SY2002: $i] :
                          ( ~ ( SV77 @ SY2002 )
                          | ( SY2001 = SY2002 ) ) )
        | ~ ~ ! [SY2576: $i] :
                ~ ~ ( ~ ( SV315 @ SY2576 )
                    | ~ ! [SY2577: $i] :
                          ( ~ ( SV315 @ SY2577 )
                          | ( SY2576 = SY2577 ) ) )
        | ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[832]) ).

thf(1092,plain,
    ! [SV316: $i > $o,SV78: $i] :
      ( ( ! [SY2580: $i] :
            ( ~ ( in @ SY2580 @ SV78 )
            | ~ ( SV316 @ SY2580 )
            | ( in @ SY2580
              @ ( dsetconstr @ SV78
                @ ^ [SY2581: $i] : ( SV316 @ SY2581 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[833]) ).

thf(1093,plain,
    ! [SV79: $i,SV317: $i] :
      ( ( ~ ( subset @ SV317 @ SV79 )
        | ( in @ SV317 @ ( powerset @ SV79 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[834]) ).

thf(1094,plain,
    ! [SV80: $i,SV318: $i] :
      ( ( ~ ( in @ SV318 @ ( powerset @ SV80 ) )
        | ! [SY2582: $i] :
            ( ~ ( in @ SY2582 @ ( powerset @ SV80 ) )
            | ~ ! [SY2583: $i] :
                  ( ~ ( in @ SY2583 @ SV80 )
                  | ~ ( in @ SY2583 @ SV318 )
                  | ( in @ SY2583 @ SY2582 ) )
            | ~ ! [SY2584: $i] :
                  ( ~ ( in @ SY2584 @ SV80 )
                  | ~ ( in @ SY2584 @ SY2582 )
                  | ( in @ SY2584 @ SV318 ) )
            | ( SV318 = SY2582 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[835]) ).

thf(1095,plain,
    ! [SV319: $i,SV81: $i] :
      ( ( ~ ! [SY2585: $i] :
              ( ~ ( in @ SY2585 @ SV81 )
              | ( in @ SY2585 @ SV319 ) )
        | ~ ! [SY2586: $i] :
              ( ~ ( in @ SY2586 @ SV319 )
              | ( in @ SY2586 @ SV81 ) )
        | ( SV81 = SV319 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[836]) ).

thf(1096,plain,
    ! [SV320: $i,SV82: $i] :
      ( ( ! [SY2587: $i > $i > $o,SY2588: $i] :
            ( ~ ( in @ SY2588 @ SV82 )
            | ! [SY2589: $i] :
                ( ~ ( in @ SY2589 @ SV320 )
                | ~ ( in @ ( kpair @ SY2588 @ SY2589 )
                    @ ( dpsetconstr @ SV82 @ SV320
                      @ ^ [SX5: $i,SX6: $i] : ( SY2587 @ SX5 @ SX6 ) ) )
                | ( SY2587 @ SY2588 @ SY2589 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[837]) ).

thf(1097,plain,
    ! [SV83: $i] :
      ( ( ( ~ ! [SY2024: $i] :
                ~ ( in @ SY2024 @ SV83 ) )
        = $true )
      | ( ( SV83 = emptyset )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[838]) ).

thf(1098,plain,
    ! [SV321: $i > $o,SV84: $i] :
      ( ( ~ ~ ! [SY2592: $i] :
                ( ~ ( in @ SY2592 @ SV84 )
                | ( SV321 @ SY2592 ) )
        | ~ ! [SY2593: $i] :
              ~ ~ ( ~ ( in @ SY2593 @ SV84 )
                  | ~ ~ ( SV321 @ SY2593 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[839]) ).

thf(1099,plain,
    ! [SV322: $i,SV85: $i] :
      ( ( ! [SY2594: $i,SY2595: $o] :
            ( ~ ( in @ SY2594 @ ( binunion @ SV85 @ SV322 ) )
            | ~ ( ~ ( in @ SY2594 @ SV85 )
                | SY2595 )
            | ~ ( ~ ( in @ SY2594 @ SV322 )
                | SY2595 )
            | SY2595 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[840]) ).

thf(1100,plain,
    ! [SV86: $i,SV323: $i] :
      ( ( ! [SY2596: $i] :
            ( ~ ( in @ SV323 @ SY2596 )
            | ~ ( in @ SY2596 @ SV86 )
            | ( in @ SV323 @ ( setunion @ SV86 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[841]) ).

thf(1101,plain,
    ! [SV87: $i] :
      ( ( ( ~ ~ ( ~ ( in @ emptyset @ SV87 )
                | ~ ! [SY2033: $i] :
                      ( ~ ~ ( ~ ( in @ SY2033 @ omega )
                            | ~ ( in @ SY2033 @ SV87 ) )
                      | ( in @ ( setadjoin @ SY2033 @ SY2033 ) @ SV87 ) ) ) )
        = $true )
      | ( ( ! [SY2034: $i] :
              ( ~ ( in @ SY2034 @ omega )
              | ( in @ SY2034 @ SV87 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[842]) ).

thf(1102,plain,
    ( ( ! [SY2597: $i] :
          ( ~ ( in @ SY2597 @ ( powerset @ sK1_SX0 ) )
          | ! [SY2598: $i] :
              ( ~ ( in @ SY2598 @ ( powerset @ sK1_SX0 ) )
              | ! [SY2599: $i] :
                  ( ~ ( in @ SY2599 @ sK1_SX0 )
                  | ~ ( in @ SY2599 @ ( setminus @ sK1_SX0 @ ( binunion @ SY2597 @ SY2598 ) ) )
                  | ( in @ SY2599 @ ( setminus @ sK1_SX0 @ SY2597 ) ) ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[843]) ).

thf(1103,plain,
    ! [SV88: $i,SV324: $i] :
      ( ( ~ ( in @ SV324 @ ( powerset @ SV88 ) )
        | ! [SY2600: $i] :
            ( ~ ( in @ SY2600 @ ( powerset @ SV88 ) )
            | ~ ( subset @ SV324 @ ( setminus @ SV88 @ SY2600 ) )
            | ! [SY2601: $i] :
                ( ~ ( in @ SY2601 @ SV88 )
                | ~ ( in @ SY2601 @ SY2600 )
                | ( in @ SY2601 @ ( setminus @ SV88 @ SV324 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[844]) ).

thf(1104,plain,
    ! [SV325: $i > $o,SV89: $i] :
      ( ( ~ ~ ! [SY2602: $i] :
                ~ ~ ( ~ ( in @ SY2602 @ SV89 )
                    | ~ ( SV325 @ SY2602 ) )
        | ( ( dsetconstr @ SV89
            @ ^ [SY2603: $i] : ( SV325 @ SY2603 ) )
         != emptyset )
        | $false )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[845]) ).

thf(1105,plain,
    ! [SV326: $i,SV90: $i] :
      ( ( ~ ! [SY2604: $i] :
              ( ~ ( in @ SY2604 @ SV90 )
              | ( in @ SY2604 @ SV326 ) )
        | ( subset @ SV90 @ SV326 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[846]) ).

thf(1106,plain,
    ! [SV91: $i,SV327: $i] :
      ( ( ~ ( in @ SV327 @ ( powerset @ SV91 ) )
        | ! [SY2605: $i] :
            ( ~ ( in @ SY2605 @ ( powerset @ SV91 ) )
            | ( in @ ( binintersect @ SV327 @ SY2605 ) @ ( powerset @ SV91 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[847]) ).

thf(1107,plain,
    ! [SV328: $i,SV92: $i] :
      ( ( ( SV92 != SV328 )
        | ! [SY2606: $i,SY2607: $i] :
            ( ( SY2606 != SY2607 )
            | ~ ( in @ SY2606 @ SV92 )
            | ( in @ SY2607 @ SV328 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[848]) ).

thf(1108,plain,
    ! [SV329: $i,SV93: $i] :
      ( ( ! [SY2608: $i > $i > $o,SY2609: $i,SY2610: $i] :
            ( ~ ( in @ ( kpair @ SY2609 @ SY2610 )
                @ ( dpsetconstr @ SV93 @ SV329
                  @ ^ [SX5: $i,SX6: $i] : ( SY2608 @ SX5 @ SX6 ) ) )
            | ( SY2608 @ SY2609 @ SY2610 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[849]) ).

thf(1109,plain,
    ! [SV330: $i,SV94: $i] :
      ( ( ! [SY2613: $i,SY2614: $i] :
            ( ( ( kpair @ SV94 @ SV330 )
             != ( kpair @ SY2613 @ SY2614 ) )
            | ( SV94 = SY2613 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[850]) ).

thf(1110,plain,
    ! [SV331: $i,SV95: $i] :
      ( ( ! [SY2615: $i] :
            ( ~ ( subset @ SV95 @ SV331 )
            | ~ ( in @ SY2615 @ SV95 )
            | ( in @ SY2615 @ SV331 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[851]) ).

thf(1111,plain,
    ! [SV332: $i,SV96: $i] :
      ( ( ! [SY2616: $i] :
            ( ~ ( func @ SV96 @ SV332 @ SY2616 )
            | ! [SY2617: $i] :
                ( ~ ( func @ SV96 @ SV332 @ SY2617 )
                | ~ ! [SY2618: $i] :
                      ( ~ ( in @ SY2618 @ SV96 )
                      | ( ( ap @ SV96 @ SV332 @ SY2616 @ SY2618 )
                        = ( ap @ SV96 @ SV332 @ SY2617 @ SY2618 ) ) )
                | ! [SY2619: $i] :
                    ( ~ ( in @ SY2619 @ SV96 )
                    | ! [SY2620: $i] :
                        ( ~ ( in @ SY2620 @ SV332 )
                        | ~ ( in @ ( kpair @ SY2619 @ SY2620 ) @ SY2617 )
                        | ( in @ ( kpair @ SY2619 @ SY2620 ) @ SY2616 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[852]) ).

thf(1112,plain,
    ! [SV97: $i] :
      ( ( ( ~ ( iskpair @ SV97 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ ( setunion @ SV97 )
            @ ^ [SY2065: $i] : ( in @ ( setadjoin @ SY2065 @ emptyset ) @ SV97 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[853]) ).

thf(1113,plain,
    ! [SV333: $i,SV98: $i] :
      ( ( ! [SY2621: $i] :
            ( ~ ( in @ SY2621 @ ( cartprod @ SV98 @ SV333 ) )
            | ~ ! [SY2622: $i] :
                  ~ ~ ( ~ ( in @ SY2622 @ SV98 )
                      | ~ ~ ! [SY2623: $i] :
                              ~ ~ ( ~ ( in @ SY2623 @ SV333 )
                                  | ( SY2621
                                   != ( kpair @ SY2622 @ SY2623 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[854]) ).

thf(1114,plain,
    ! [SV99: $i,SV334: $i] :
      ( ( ~ ( in @ SV334 @ ( powerset @ SV99 ) )
        | ! [SY2624: $i] :
            ( ~ ( in @ SY2624 @ ( powerset @ SV99 ) )
            | ! [SY2625: $i] :
                ( ~ ( in @ SY2625 @ SV99 )
                | ~ ( in @ SV334 @ ( powerset @ SY2624 ) )
                | ~ ( in @ SY2625 @ SV334 )
                | ( in @ SY2625 @ SY2624 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[855]) ).

thf(1115,plain,
    ! [SV100: $i] :
      ( ( ( ~ ! [SY2073: $i] :
                ~ ( in @ SY2073 @ SV100 ) )
        = $true )
      | ( ( SV100 = emptyset )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[856]) ).

thf(1116,plain,
    ! [SV335: $i,SV101: $i] :
      ( ( ! [SY2626: $i] :
            ( ~ ( in @ SY2626 @ ( setadjoin @ SV101 @ SV335 ) )
            | ( SY2626 = SV101 )
            | ( in @ SY2626 @ SV335 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[857]) ).

thf(1117,plain,
    ! [SV336: $i > $o,SV102: $i] :
      ( ( ~ ! [SY2627: $i] :
              ( ~ ( in @ SY2627 @ SV102 )
              | ! [SY2628: $i] :
                  ( ~ ( in @ SY2628 @ SV102 )
                  | ~ ( SV336 @ SY2627 )
                  | ~ ( SV336 @ SY2628 )
                  | ( SY2627 = SY2628 ) ) )
        | ~ ~ ! [SY2629: $i] :
                ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                    | ~ ( SV336 @ SY2629 ) )
        | ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[858]) ).

thf(1118,plain,
    ! [SV337: $i,SV103: $i] :
      ( ( ! [SY2631: $i > $i > $o,SY2632: $i,SY2633: $i] :
            ( ~ ( in @ ( kpair @ SY2632 @ SY2633 )
                @ ( dpsetconstr @ SV103 @ SV337
                  @ ^ [SX5: $i,SX6: $i] : ( SY2631 @ SX5 @ SX6 ) ) )
            | ( in @ SY2632 @ SV103 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[859]) ).

thf(1119,plain,
    ! [SV338: $i,SV104: $i] :
      ( ( ~ ( ( SV104 != SV338 ) )
        | ~ ( in @ SV338 @ ( setadjoin @ SV104 @ emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[860]) ).

thf(1120,plain,
    ! [SV339: $i,SV105: $i] :
      ( ( ! [SY2636: $i > $i] :
            ( ~ ! [SY2637: $i] :
                  ( ~ ( in @ SY2637 @ SV105 )
                  | ( in @ ( SY2636 @ SY2637 ) @ SV339 ) )
            | ( ( lam @ SV105 @ SV339
                @ ^ [SX3: $i] : ( SY2636 @ SX3 ) )
              = ( lam @ SV105 @ SV339
                @ ^ [SX3: $i] : ( SY2636 @ SX3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[861]) ).

thf(1121,plain,
    ! [SV340: $i,SV106: $i] :
      ( ( ! [SY2640: $i] :
            ( ~ ( in @ SY2640 @ SV106 )
            | ( in @ ( setadjoin @ SY2640 @ emptyset ) @ ( powerset @ ( binunion @ SV106 @ SV340 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[862]) ).

thf(1122,plain,
    ! [SV341: $i,SV107: $i] :
      ( ( ! [SY2641: $i > $i] :
            ( ~ ! [SY2642: $i] :
                  ( ~ ( in @ SY2642 @ SV107 )
                  | ( in @ ( SY2641 @ SY2642 ) @ SV341 ) )
            | ( in
              @ ( lam @ SV107 @ SV341
                @ ^ [SX3: $i] : ( SY2641 @ SX3 ) )
              @ ( funcSet @ SV107 @ SV341 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[863]) ).

thf(1123,plain,
    ! [SV342: $i,SV108: $i] :
      ( ( ( SV108 != SV342 )
        | ( ( setunion @ SV108 )
          = ( setunion @ SV342 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[864]) ).

thf(1124,plain,
    ! [SV109: $i] :
      ( ( ! [SY2100: $i] :
            ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY2101: $i] :
                                  ( ~ ( in @ SY2101 @ SY2100 )
                                  | ! [SY2102: $i] :
                                      ( ~ ( in @ SY2102 @ SY2101 )
                                      | ( in @ SY2102 @ SV109 ) ) )
                            | ~ ! [SY2103: $i,SY2104: $i] :
                                  ( ~ ~ ( ~ ( in @ SY2103 @ SV109 )
                                        | ~ ( in @ SY2104 @ SV109 ) )
                                  | ~ ! [SX4: $i] :
                                        ( ~ ( in @ SX4 @ SY2100 )
                                        | ~ ( ~ ( ~ ( in @ SY2103 @ SX4 )
                                                | ( in @ SY2104 @ SX4 ) )
                                            | ~ ( ~ ( in @ SY2104 @ SX4 )
                                                | ( in @ SY2103 @ SX4 ) ) ) )
                                  | ( SY2103 = SY2104 ) ) )
                      | ~ ! [SX2: $i,SX3: $i] :
                            ( ~ ~ ( ~ ( in @ SX2 @ SY2100 )
                                  | ~ ( in @ SX3 @ SY2100 ) )
                            | ! [SX4: $i] :
                                ( ~ ( in @ SX4 @ SX2 )
                                | ( in @ SX4 @ SX3 ) )
                            | ! [SX4: $i] :
                                ( ~ ( in @ SX4 @ SX3 )
                                | ( in @ SX4 @ SX2 ) ) ) )
                | ~ ! [SY2110: $i] :
                      ( ~ ~ ( ~ ! [SY2111: $i] :
                                  ( ~ ( in @ SY2111 @ SY2110 )
                                  | ( in @ SY2111 @ SV109 ) )
                            | ~ ~ ! [SX3: $i] :
                                    ~ ( in @ SX3 @ SY2110 ) )
                      | ~ ! [SX3: $i] :
                            ~ ~ ! [SX4: $i] :
                                  ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY2100 )
                                                  | ~ ( in @ SX4 @ SY2110 ) )
                                            | ~ ~ ~ ! [SX5: $i] :
                                                      ~ ~ ( ~ ( in @ SX5 @ SX3 )
                                                          | ~ ( in @ SX5 @ SY2110 ) ) )
                                      | ~ ! [SX5: $i] :
                                            ( ~ ( in @ SX5 @ SY2100 )
                                            | ! [SX6: $i] :
                                                ( ~ ( in @ SX6 @ SX5 )
                                                | ( in @ SX6 @ SX3 ) )
                                            | ( in @ SX4 @ SX5 ) ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[865]) ).

thf(1125,plain,
    ! [SV110: $i] :
      ( ( ( ~ ~ ! [SY2118: $i] :
                  ~ ( in @ SY2118 @ SV110 ) )
        = $true )
      | ( ( ~ ! [SY2119: $i] :
                ~ ~ ( ~ ( in @ SY2119 @ SV110 )
                    | ~ ~ ~ ! [SY2120: $i] :
                              ~ ~ ( ~ ( in @ SY2120 @ SY2119 )
                                  | ~ ( in @ SY2120 @ SV110 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[866]) ).

thf(1126,plain,
    ! [SV343: $i,SV111: $i] :
      ( ( ! [SY2644: $i] :
            ( ~ ( in @ SY2644 @ ( binintersect @ SV111 @ SV343 ) )
            | ( in @ SY2644 @ SV111 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[867]) ).

thf(1127,plain,
    ! [SV112: $i > $o] :
      ( ( ( ~ ~ ! [SY2123: $i] :
                  ~ ~ ( ~ ( SV112 @ SY2123 )
                      | ~ ! [SY2124: $i] :
                            ( ~ ( SV112 @ SY2124 )
                            | ( SY2123 = SY2124 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2125: $i] :
                ~ ( SV112 @ SY2125 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[868]) ).

thf(1128,plain,
    ! [SV344: $i,SV113: $i] :
      ( ( ~ ~ ~ ! [SY2645: $i] :
                  ~ ~ ( ~ ( in @ SY2645 @ SV113 )
                      | ~ ( in @ SY2645 @ SV344 ) )
        | ( ( binintersect @ SV113 @ SV344 )
          = emptyset ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[869]) ).

thf(1129,plain,
    ! [SV345: $i,SV114: $i] :
      ( ( ~ ( subset @ SV114 @ SV345 )
        | ( ( setminus @ SV114 @ SV345 )
          = emptyset ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[870]) ).

thf(1130,plain,
    ! [SV115: $i] :
      ( ( ( ~ ( in @ SV115 @ emptyset ) )
        = $true )
      | ( $false = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[871]) ).

thf(1131,plain,
    ! [SV116: $i,SV346: $i] :
      ( ( ~ ( in @ SV346 @ ( powerset @ SV116 ) )
        | ! [SY2646: $i] :
            ( ~ ( in @ SY2646 @ ( powerset @ SV116 ) )
            | ! [SY2647: $i] :
                ( ~ ( in @ SY2647 @ SV116 )
                | ~ ~ ( in @ SY2647 @ ( binunion @ SV346 @ SY2646 ) )
                | ~ ( in @ SY2647 @ SV346 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[872]) ).

thf(1132,plain,
    ! [SV117: $i] :
      ( ( ( ~ ( iskpair @ SV117 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ ( setunion @ SV117 )
            @ ^ [SY2132: $i] :
                ( SV117
                = ( kpair @ ( kfst @ SV117 ) @ SY2132 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[873]) ).

thf(1133,plain,
    ! [SV347: $o,SV118: $i] :
      ( ( ! [SY2648: $i] :
            ( ~ ( in @ SY2648 @ SV118 )
            | ! [SY2649: $i] :
                ( ~ ( in @ SY2649 @ SV118 )
                | ~ ~ SV347
                | ( ( if @ SV118 @ SV347 @ SY2648 @ SY2649 )
                  = SY2649 ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[874]) ).

thf(1134,plain,
    ! [SV118: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV118 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV118 )
                | ~ ~ $true
                | ( ( if @ SV118 @ $true @ SX0 @ SX1 )
                  = SX1 ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[874]) ).

thf(1135,plain,
    ! [SV118: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV118 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV118 )
                | ~ ~ $false
                | ( ( if @ SV118 @ $false @ SX0 @ SX1 )
                  = SX1 ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[874]) ).

thf(1136,plain,
    ! [SV119: $i > $o,SV348: $i] :
      ( ( ~ ( in @ SV348 @ emptyset )
        | ( SV119 @ SV348 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[875]) ).

thf(1137,plain,
    ! [SV120: $o] :
      ( ( ( ~ SV120 ) = $true )
      | ( ( set2prop @ ( prop2set @ SV120 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[876]) ).

thf(1138,plain,
    ( ( ( ~ $true ) = $true )
    | ( ( set2prop @ ( prop2set @ $true ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[877]) ).

thf(1139,plain,
    ( ( ( ~ $false ) = $true )
    | ( ( set2prop @ ( prop2set @ $false ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[878]) ).

thf(1140,plain,
    ! [SV121: $i,SV349: $i] :
      ( ( ~ ( in @ SV349 @ ( powerset @ SV121 ) )
        | ! [SY2650: $i] :
            ( ~ ( in @ SY2650 @ SV121 )
            | ~ ~ ( in @ SY2650 @ ( setminus @ SV121 @ SV349 ) )
            | ( in @ SY2650 @ SV349 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[879]) ).

thf(1141,plain,
    ! [SV122: $i,SV350: $i] :
      ( ( ~ ( in @ SV350 @ ( powerset @ SV122 ) )
        | ! [SY2651: $i] :
            ( ~ ( in @ SY2651 @ ( powerset @ SV122 ) )
            | ( subset @ ( setminus @ SV122 @ SV350 ) @ ( setminus @ SV122 @ ( binintersect @ SV350 @ SY2651 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[880]) ).

thf(1142,plain,
    ! [SV351: $i,SV123: $i] :
      ( ( ! [SY2652: $i] :
            ( ~ ( subset @ SV123 @ SV351 )
            | ~ ~ ( in @ SY2652 @ SV351 )
            | ~ ( in @ SY2652 @ SV123 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[881]) ).

thf(1143,plain,
    ! [SV352: $i,SV124: $i] :
      ( ( ! [SY2653: $i > $i] :
            ( ~ ! [SY2654: $i] :
                  ( ~ ( in @ SY2654 @ SV124 )
                  | ( in @ ( SY2653 @ SY2654 ) @ SV352 ) )
            | ( func @ SV124 @ SV352
              @ ( dpsetconstr @ SV124 @ SV352
                @ ^ [SX3: $i,SX4: $i] :
                    ( ( SY2653 @ SX3 )
                    = SX4 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[882]) ).

thf(1144,plain,
    ! [SV353: $i > $o,SV125: $i] :
      ( ( ~ ! [SY2657: $i] :
              ( ~ ( in @ SY2657 @ SV125 )
              | ! [SY2658: $i] :
                  ( ~ ( in @ SY2658 @ SV125 )
                  | ~ ( SV353 @ SY2657 )
                  | ~ ( SV353 @ SY2658 )
                  | ( SY2657 = SY2658 ) ) )
        | ~ ~ ! [SY2659: $i] :
                ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                    | ~ ( SV353 @ SY2659 ) )
        | ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[883]) ).

thf(1145,plain,
    ! [SV354: $i,SV126: $i] :
      ( ( ! [SY2661: $i] :
            ( ~ ~ ( in @ SY2661 @ SV126 )
            | ~ ( in @ SY2661 @ SV354 )
            | ( in @ SY2661 @ ( symdiff @ SV126 @ SV354 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[884]) ).

thf(1146,plain,
    ! [SV355: $i,SV127: $i] :
      ( ( ! [SY2662: $i] :
            ( ~ ( in @ SY2662 @ ( setadjoin @ SV127 @ ( setadjoin @ SV355 @ emptyset ) ) )
            | ( SY2662 = SV127 )
            | ( SY2662 = SV355 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[885]) ).

thf(1147,plain,
    ! [SV128: $i,SV356: $i] :
      ( ( ~ ( in @ SV356 @ ( powerset @ SV128 ) )
        | ! [SY2663: $i] :
            ( ~ ( in @ SY2663 @ ( powerset @ SV128 ) )
            | ( in @ ( setminus @ SV128 @ SV356 ) @ ( powerset @ ( setminus @ SV128 @ ( binintersect @ SV356 @ SY2663 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[886]) ).

thf(1148,plain,
    ! [SV129: $i,SV357: $i] :
      ( ( ~ ( in @ SV357 @ ( powerset @ SV129 ) )
        | ! [SY2664: $i] :
            ( ~ ( in @ SY2664 @ SV129 )
            | ~ ( in @ SY2664 @ SV357 )
            | ~ ( in @ SY2664 @ ( setminus @ SV129 @ SV357 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[887]) ).

thf(1149,plain,
    ! [SV130: $i,SV358: $i] :
      ( ( ~ ( in @ SV358 @ ( powerset @ SV130 ) )
        | ( SV358
          = ( setminus @ SV130 @ ( setminus @ SV130 @ SV358 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[888]) ).

thf(1150,plain,
    ! [SV359: $i,SV131: $i] :
      ( ( ( SV131 != SV359 )
        | ( ( powerset @ SV131 )
          = ( powerset @ SV359 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[889]) ).

thf(1151,plain,
    ! [SV132: $i,SV360: $i] :
      ( ( ~ ( in @ SV360 @ ( powerset @ SV132 ) )
        | ! [SY2665: $i] :
            ( ~ ( in @ SY2665 @ ( powerset @ SV132 ) )
            | ~ ( subset @ SV360 @ SY2665 )
            | ( subset @ ( setminus @ SV132 @ SY2665 ) @ ( setminus @ SV132 @ SV360 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[890]) ).

thf(1152,plain,
    ! [SV361: $i,SV133: $i] :
      ( ( ! [SY2666: $i] :
            ( ~ ( func @ SV133 @ SV361 @ SY2666 )
            | ! [SY2667: $i] :
                ( ~ ( in @ SY2667 @ SV133 )
                | ( ( ap @ SV133 @ SV361 @ SY2666 @ SY2667 )
                  = ( ap @ SV133 @ SV361 @ SY2666 @ SY2667 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[891]) ).

thf(1153,plain,
    ! [SV362: $i,SV134: $i] :
      ( ( ! [SY2668: $i] :
            ( ~ ( in @ SY2668 @ ( setadjoin @ SV134 @ ( setadjoin @ SV362 @ emptyset ) ) )
            | ( SY2668 = SV134 )
            | ( SY2668 = SV362 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[892]) ).

thf(1154,plain,
    ! [SV363: $i,SV135: $i] :
      ( ( ! [SY2669: $i] :
            ( ~ ( subset @ SY2669 @ ( cartprod @ SV135 @ SV363 ) )
            | ! [SY2670: $i > $o] :
                ( ~ ! [SY2671: $i] :
                      ( ~ ( in @ SY2671 @ SV135 )
                      | ! [SY2672: $i] :
                          ( ~ ( in @ SY2672 @ SV363 )
                          | ~ ( in @ ( kpair @ SY2671 @ SY2672 ) @ SY2669 )
                          | ( SY2670 @ ( kpair @ SY2671 @ SY2672 ) ) ) )
                | ! [SX4: $i] :
                    ( ~ ( in @ SX4 @ SY2669 )
                    | ( SY2670 @ SX4 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[893]) ).

thf(1155,plain,
    ! [SV136: $i,SV364: $i] :
      ( ( ! [SY2674: $i] :
            ( ~ ( in @ SV364 @ ( powerset @ SV136 ) )
            | ~ ( in @ SY2674 @ SV364 )
            | ( in @ SY2674 @ SV136 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[894]) ).

thf(1156,plain,
    ! [SV137: $i,SV365: $i] :
      ( ( ~ ( in @ SV365 @ ( powerset @ SV137 ) )
        | ! [SY2675: $i] :
            ( ~ ( in @ SY2675 @ ( powerset @ SV137 ) )
            | ! [SY2676: $i] :
                ( ~ ( in @ SY2676 @ SV137 )
                | ~ ~ ( in @ SY2676 @ SY2675 )
                | ~ ( in @ SY2676 @ ( binintersect @ SV365 @ SY2675 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[895]) ).

thf(1157,plain,
    ! [SV138: $i,SV366: $i] :
      ( ( ~ ( in @ SV366 @ SV138 )
        | ( in @ ( setadjoin @ SV366 @ emptyset ) @ ( powerset @ SV138 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[896]) ).

thf(1158,plain,
    ! [SV139: $o,SV367: $i] :
      ( ( ~ ( in @ SV367 @ ( prop2set @ SV139 ) )
        | SV139 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[897]) ).

thf(1159,plain,
    ! [SV368: $i] :
      ( ( ~ ( in @ SV368 @ ( prop2set @ $true ) )
        | $true )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[898]) ).

thf(1160,plain,
    ! [SV369: $i] :
      ( ( ~ ( in @ SV369 @ ( prop2set @ $false ) )
        | $false )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[899]) ).

thf(1161,plain,
    ! [SV370: $i,SV140: $i] :
      ( ( ! [SY2677: $i] :
            ( ~ ( in @ SY2677 @ SV140 )
            | ! [SY2678: $i] :
                ( ~ ( in @ SY2678 @ SV370 )
                | ( in @ ( kpair @ SY2677 @ SY2678 ) @ ( cartprod @ SV140 @ SV370 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[900]) ).

thf(1162,plain,
    ! [SV371: $i,SV141: $i] :
      ( ( ! [SY2679: $i] :
            ( ~ ( in @ SY2679 @ ( cartprod @ SV141 @ SV371 ) )
            | ( in @ ( ksnd @ SY2679 ) @ SV371 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[901]) ).

thf(1163,plain,
    ! [SV372: $i > $o,SV142: $i] :
      ( ( ~ ( singleton
            @ ( dsetconstr @ SV142
              @ ^ [SY2680: $i] : ( SV372 @ SY2680 ) ) )
        | ! [SY2681: $i] :
            ( ~ ( in @ SY2681 @ SV142 )
            | ! [SY2682: $i] :
                ( ~ ( in @ SY2682 @ SV142 )
                | ~ ( SV372 @ SY2681 )
                | ~ ( SV372 @ SY2682 )
                | ( SY2681 = SY2682 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[902]) ).

thf(1164,plain,
    ! [SV143: $i,SV373: $i] :
      ( ( ~ ( in @ SV373 @ ( powerset @ SV143 ) )
        | ( subset @ SV373 @ SV143 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[903]) ).

thf(1165,plain,
    ! [SV374: $i,SV144: $i] :
      ( ( ! [SY2683: $i] :
            ( ~ ( in @ SY2683 @ SV144 )
            | ! [SY2684: $i] :
                ( ~ ( in @ SY2684 @ SV374 )
                | ( ( kfst @ ( kpair @ SY2683 @ SY2684 ) )
                  = SY2683 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[904]) ).

thf(1166,plain,
    ! [SV145: $i,SV375: $i] :
      ( ( ~ ( in @ SV375 @ ( powerset @ SV145 ) )
        | ( in @ ( setminus @ SV145 @ SV375 ) @ ( powerset @ SV145 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[905]) ).

thf(1167,plain,
    ! [SV376: $i,SV146: $i] :
      ( ( ! [SY2685: $i,SY2686: $i] :
            ( ( ( kpair @ SV146 @ SV376 )
             != ( kpair @ SY2685 @ SY2686 ) )
            | ( SV376 = SY2686 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[906]) ).

thf(1168,plain,
    ! [SV147: $i > $i > $o,SV377: $i] :
      ( ( ~ ! [SY2687: $i] :
              ( ~ ( in @ SY2687 @ SV377 )
              | ~ ! [SY2202: $i] :
                    ~ ~ ( ~ ( SV147 @ SY2687 @ SY2202 )
                        | ~ ! [SY2203: $i] :
                              ( ~ ( SV147 @ SY2687 @ SY2203 )
                              | ( SY2202 = SY2203 ) ) ) )
        | ~ ! [SY2690: $i] :
              ~ ! [SY2691: $i] :
                  ~ ( ~ ( ~ ( in @ SY2691 @ SY2690 )
                        | ~ ! [SY2692: $i] :
                              ~ ~ ( ~ ( in @ SY2692 @ SV377 )
                                  | ~ ( SV147 @ SY2692 @ SY2691 ) ) )
                    | ~ ( ~ ~ ! [SY2693: $i] :
                                ~ ~ ( ~ ( in @ SY2693 @ SV377 )
                                    | ~ ( SV147 @ SY2693 @ SY2691 ) )
                        | ( in @ SY2691 @ SY2690 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[907]) ).

thf(1169,plain,
    ! [SV378: $i,SV148: $i] :
      ( ( ~ ! [SY2694: $i] :
              ( ~ ( in @ SY2694 @ SV148 )
              | ( in @ SY2694 @ SV378 ) )
        | ( subset @ SV148 @ SV378 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[908]) ).

thf(1170,plain,
    ! [SV379: $i,SV149: $i] :
      ( ( ~ ( subset @ SV149 @ SV379 )
        | ~ ( subset @ SV379 @ SV149 )
        | ( SV149 = SV379 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[909]) ).

thf(1171,plain,
    ! [SV380: $i,SV150: $i] :
      ( ( ! [SY2695: $i] :
            ( ~ ( in @ SY2695 @ SV150 )
            | ( in @ SY2695 @ ( binunion @ SV150 @ SV380 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[910]) ).

thf(1172,plain,
    ! [SV151: $i,SV381: $i] :
      ( ( ~ ( in @ SV381 @ ( powerset @ SV151 ) )
        | ! [SY2696: $i] :
            ( ~ ( in @ SY2696 @ ( powerset @ SV151 ) )
            | ! [SY2697: $i] :
                ( ~ ( in @ SY2697 @ SV151 )
                | ~ ~ ( in @ SY2697 @ ( binunion @ SV381 @ SY2696 ) )
                | ~ ( in @ SY2697 @ SY2696 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[911]) ).

thf(1173,plain,
    ! [SV382: $i,SV152: $i] :
      ( ( ( SV152 != SV382 )
        | ! [SY2698: $i,SY2699: $i] :
            ( ( SY2698 != SY2699 )
            | ( ( setadjoin @ SV152 @ SY2698 )
              = ( setadjoin @ SV382 @ SY2699 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[912]) ).

thf(1174,plain,
    ! [SV153: $i] :
      ( ( ( ~ ( iskpair @ SV153 ) )
        = $true )
      | ( ( ( kpair @ ( kfst @ SV153 ) @ ( ksnd @ SV153 ) )
          = SV153 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[913]) ).

thf(1175,plain,
    ! [SV154: $i,SV383: $i] :
      ( ( ! [SY2700: $i] :
            ( ~ ( in @ SY2700 @ SV383 )
            | ( in @ SY2700 @ ( binunion @ SV154 @ SV383 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[914]) ).

thf(1176,plain,
    ! [SV384: $i,SV155: $i] :
      ( ( ( SV155 != SV384 )
        | ( subset @ SV384 @ SV155 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[915]) ).

thf(1177,plain,
    ! [SV156: $i,SV385: $i] :
      ( ( ~ ( in @ SV385 @ ( powerset @ SV156 ) )
        | ! [SY2701: $i] :
            ( ~ ( in @ SY2701 @ ( powerset @ SV156 ) )
            | ! [SY2702: $i] :
                ( ~ ( in @ SY2702 @ SV156 )
                | ~ ~ ( in @ SY2702 @ SV385 )
                | ~ ( in @ SY2702 @ ( binintersect @ SV385 @ SY2701 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[916]) ).

thf(1178,plain,
    ! [SV157: $i > $o] :
      ( ( ( ~ ~ ! [SY2225: $i] :
                  ~ ~ ( ~ ( SV157 @ SY2225 )
                      | ~ ! [SY2226: $i] :
                            ( ~ ( SV157 @ SY2226 )
                            | ( SY2225 = SY2226 ) ) ) )
        = $true )
      | ( ( SV157
          @ ( descr
            @ ^ [SY2227: $i] : ( SV157 @ SY2227 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[917]) ).

thf(1179,plain,
    ! [SV386: $i,SV158: $i] :
      ( ( ! [SY2703: $i] :
            ( ~ ( in @ SY2703 @ ( setminus @ SV158 @ SV386 ) )
            | ~ ( in @ SY2703 @ SV386 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[918]) ).

thf(1180,plain,
    ! [SV159: $i,SV387: $i] :
      ( ( ~ ( in @ SV387 @ ( powerset @ SV159 ) )
        | ( subset @ SV387 @ ( setminus @ SV159 @ ( setminus @ SV159 @ SV387 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[919]) ).

thf(1181,plain,
    ! [SV388: $i > $o,SV160: $i] :
      ( ( ~ ~ ! [SY2704: $i] :
                ( ~ ( in @ SY2704 @ SV160 )
                | ( SV388 @ SY2704 ) )
        | ~ ! [SY2705: $i] :
              ~ ~ ( ~ ( in @ SY2705 @ SV160 )
                  | ~ ~ ( SV388 @ SY2705 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[920]) ).

thf(1182,plain,
    ! [SV161: $i,SV389: $i] :
      ( ( ~ ( in @ SV389 @ ( powerset @ SV161 ) )
        | ! [SY2706: $i] :
            ( ~ ( in @ SY2706 @ ( powerset @ SV161 ) )
            | ! [SY2707: $i] :
                ( ~ ( in @ SY2707 @ SV161 )
                | ~ ( in @ SY2707 @ ( setminus @ SV161 @ SV389 ) )
                | ( in @ SY2707 @ ( setminus @ SV161 @ ( binintersect @ SV389 @ SY2706 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[921]) ).

thf(1183,plain,
    ! [SV162: $i,SV390: $i] :
      ( ( ~ ( in @ SV390 @ ( powerset @ SV162 ) )
        | ! [SY2708: $i] :
            ( ~ ( in @ SY2708 @ ( powerset @ SV162 ) )
            | ( in @ ( binunion @ SV390 @ SY2708 ) @ ( powerset @ SV162 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[922]) ).

thf(1184,plain,
    ! [SV391: $i,SV163: $i] :
      ( ( ~ ( subset @ SV163 @ SV391 )
        | ( in @ SV163 @ ( powerset @ SV391 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[923]) ).

thf(1185,plain,
    ! [SV392: $i,SV164: $i] :
      ( ( ( ( setminus @ SV164 @ SV392 )
         != emptyset )
        | ( subset @ SV164 @ SV392 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[924]) ).

thf(1186,plain,
    ! [SV165: $i > $o] :
      ( ( ( ~ ~ ! [SY2241: $i] :
                  ~ ( SV165 @ SY2241 ) )
        = $true )
      | ( ( ~ ! [SY2242: $i,SY2243: $i] :
                ( ~ ( SV165 @ SY2242 )
                | ~ ( SV165 @ SY2243 )
                | ( SY2242 = SY2243 ) )
          | ~ ! [SY2244: $i] :
                ~ ~ ( ~ ( SV165 @ SY2244 )
                    | ~ ! [SY2245: $i] :
                          ( ~ ( SV165 @ SY2245 )
                          | ( SY2244 = SY2245 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[925]) ).

thf(1187,plain,
    ! [SV393: $i,SV166: $i] :
      ( ( ! [SY2709: $i] :
            ( ~ ( in @ SY2709 @ SV166 )
            | ~ ~ ( in @ SY2709 @ SV393 )
            | ~ ( subset @ SV166 @ SV393 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[926]) ).

thf(1188,plain,
    ! [SV167: $i,SV394: $i] :
      ( ( ~ ( in @ SV394 @ ( powerset @ SV167 ) )
        | ! [SY2710: $i] :
            ( ~ ( in @ SY2710 @ ( powerset @ SV167 ) )
            | ! [SY2711: $i] :
                ( ~ ( in @ SY2711 @ ( powerset @ SV167 ) )
                | ( in @ ( binintersect @ SV394 @ SY2710 ) @ ( powerset @ ( binintersect @ ( binunion @ SV394 @ SY2711 ) @ ( binunion @ SY2710 @ SY2711 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[927]) ).

thf(1189,plain,
    ! [SV395: $i,SV168: $i] :
      ( ( ! [SY2712: $i] :
            ( ~ ( subset @ SY2712 @ ( cartprod @ SV168 @ SV395 ) )
            | ! [SY2713: $i] :
                ( ~ ( subset @ SY2713 @ ( cartprod @ SV168 @ SV395 ) )
                | ~ ! [SY2714: $i] :
                      ( ~ ( in @ SY2714 @ SV168 )
                      | ! [SY2715: $i] :
                          ( ~ ( in @ SY2715 @ SV395 )
                          | ~ ( in @ ( kpair @ SY2714 @ SY2715 ) @ SY2712 )
                          | ( in @ ( kpair @ SY2714 @ SY2715 ) @ SY2713 ) ) )
                | ( subset @ SY2712 @ SY2713 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[928]) ).

thf(1190,plain,
    ! [SV396: $o,SV169: $i] :
      ( ( ! [SY2716: $i] :
            ( ~ ( in @ SY2716 @ SV169 )
            | ! [SY2717: $i] :
                ( ~ ( in @ SY2717 @ SV169 )
                | ~ SV396
                | ( ( if @ SV169 @ SV396 @ SY2716 @ SY2717 )
                  = SY2716 ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[929]) ).

thf(1191,plain,
    ! [SV169: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV169 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV169 )
                | ~ $true
                | ( ( if @ SV169 @ $true @ SX0 @ SX1 )
                  = SX0 ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[929]) ).

thf(1192,plain,
    ! [SV169: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV169 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV169 )
                | ~ $false
                | ( ( if @ SV169 @ $false @ SX0 @ SX1 )
                  = SX0 ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[929]) ).

thf(1193,plain,
    ! [SV397: $i,SV170: $i] :
      ( ( ! [SY2718: $i > $i] :
            ( ~ ! [SY2719: $i] :
                  ( ~ ( in @ SY2719 @ SV170 )
                  | ( in @ ( SY2718 @ SY2719 ) @ SV397 ) )
            | ! [SY2720: $i] :
                ( ~ ( in @ SY2720 @ SV170 )
                | ( ( ap @ SV170 @ SV397
                    @ ( lam @ SV170 @ SV397
                      @ ^ [SX4: $i] : ( SY2718 @ SX4 ) )
                    @ SY2720 )
                  = ( SY2718 @ SY2720 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[930]) ).

thf(1194,plain,
    ! [SV171: $i] :
      ( ( ( ~ ~ ! [SY2264: $i] :
                  ~ ( in @ SY2264 @ SV171 ) )
        = $true )
      | ( ( SV171 != emptyset )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[931]) ).

thf(1195,plain,
    ! [SV398: $i,SV172: $i] :
      ( ( ! [SY2722: $i] :
            ( ~ ( in @ SY2722 @ ( cartprod @ SV172 @ SV398 ) )
            | ( ( kpair @ ( kfst @ SY2722 ) @ ( ksnd @ SY2722 ) )
              = SY2722 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[932]) ).

thf(1196,plain,
    ! [SV399: $i,SV173: $i] :
      ( ( ! [SY2723: $i] :
            ( ~ ( in @ SY2723 @ ( funcSet @ SV173 @ SV399 ) )
            | ( ( lam @ SV173 @ SV399
                @ ^ [SY2724: $i] : ( ap @ SV173 @ SV399 @ SY2723 @ SY2724 ) )
              = SY2723 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[933]) ).

thf(1197,plain,
    ! [SV400: $i,SV174: $i] :
      ( ( ! [SY2725: $i,SY2726: $i] :
            ( ( ( setadjoin @ ( setadjoin @ SV174 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV174 @ ( setadjoin @ SV400 @ emptyset ) ) @ emptyset ) )
             != ( setadjoin @ ( setadjoin @ SY2725 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2725 @ ( setadjoin @ SY2726 @ emptyset ) ) @ emptyset ) ) )
            | ( SY2725 != SY2726 )
            | ( SV400 = SY2726 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[934]) ).

thf(1198,plain,
    ! [SV401: $i,SV175: $i] :
      ( ( ! [SY2727: $i,SY2728: $i] :
            ( ~ ( in @ ( kpair @ SY2727 @ SY2728 ) @ ( cartprod @ SV175 @ SV401 ) )
            | ( in @ SY2728 @ SV401 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[935]) ).

thf(1199,plain,
    ! [SV402: $i,SV176: $i] :
      ( ( ! [SY2729: $i] :
            ( ~ ( func @ SV176 @ SV402 @ SY2729 )
            | ! [SY2730: $i] :
                ( ~ ( in @ SY2730 @ SV176 )
                | ( in @ ( ap @ SV176 @ SV402 @ SY2729 @ SY2730 ) @ SV402 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[936]) ).

thf(1200,plain,
    ! [SV177: $i,SV403: $i] :
      ( ( ~ ( in @ SV403 @ ( powerset @ SV177 ) )
        | ! [SY2731: $i] :
            ( ~ ( in @ SY2731 @ ( powerset @ SV177 ) )
            | ! [SY2732: $i] :
                ( ~ ( in @ SY2732 @ SV177 )
                | ~ ( subset @ SV403 @ ( setminus @ SV177 @ SY2731 ) )
                | ~ ( in @ SY2732 @ SY2731 )
                | ~ ( in @ SY2732 @ SV403 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[937]) ).

thf(1201,plain,
    ! [SV404: $i,SV178: $i] :
      ( ( ! [SY2733: $i > $i > $o,SY2734: $i] :
            ( ~ ( in @ SY2734 @ SV178 )
            | ! [SY2735: $i] :
                ( ~ ( in @ SY2735 @ SV404 )
                | ~ ( SY2733 @ SY2734 @ SY2735 )
                | ( in @ ( kpair @ SY2734 @ SY2735 )
                  @ ( dpsetconstr @ SV178 @ SV404
                    @ ^ [SX5: $i,SX6: $i] : ( SY2733 @ SX5 @ SX6 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[938]) ).

thf(1202,plain,
    ! [SV405: $i,SV179: $i] :
      ( ( ! [SY2738: $i] :
            ( ~ ( in @ SY2738 @ SV179 )
            | ~ ~ ( in @ SY2738 @ SV405 )
            | ( SV179 != SV405 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[939]) ).

thf(1203,plain,
    ! [SV406: $i,SV180: $i] :
      ( ( ! [SY2739: $i] :
            ( ~ ( in @ SY2739 @ SV180 )
            | ~ ( in @ SY2739 @ SV406 )
            | ( in @ SY2739 @ ( binintersect @ SV180 @ SV406 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[940]) ).

thf(1204,plain,
    ! [SV181: $i,SV407: $i] :
      ( ( ~ ! [SY2740: $i] :
              ( ~ ( in @ SY2740 @ SV407 )
              | ( in @ SY2740 @ SV181 ) )
        | ( in @ SV407 @ ( powerset @ SV181 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[941]) ).

thf(1205,plain,
    ! [SV182: $i,SV408: $i] :
      ( ( ~ ( in @ SV408 @ ( powerset @ SV182 ) )
        | ! [SY2741: $i] :
            ( ~ ( in @ SY2741 @ SV182 )
            | ~ ( in @ SY2741 @ SV408 )
            | ( in @ SY2741 @ ( setminus @ SV182 @ ( setminus @ SV182 @ SV408 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[942]) ).

thf(1206,plain,
    ! [SV409: $i,SV183: $i] :
      ( ( ! [SY2742: $i] :
            ( ~ ( in @ SY2742 @ ( setminus @ SV183 @ SV409 ) )
            | ( in @ SY2742 @ SV183 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[943]) ).

thf(1207,plain,
    ! [SV410: $i,SV184: $i] :
      ( ( ! [SY2743: $i] :
            ( ~ ( in @ SY2743 @ ( cartprod @ SV184 @ SV410 ) )
            | ( iskpair @ SY2743 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[944]) ).

thf(1208,plain,
    ! [SV411: $i,SV185: $i] :
      ( ( ! [SY2744: $i] :
            ( ~ ( func @ SV185 @ SV411 @ SY2744 )
            | ! [SY2745: $i] :
                ( ~ ( in @ SY2745 @ SV185 )
                | ! [SY2746: $i] :
                    ( ~ ( in @ SY2746 @ SV411 )
                    | ~ ( in @ ( kpair @ SY2745 @ SY2746 ) @ SY2744 )
                    | ( ( ap @ SV185 @ SV411 @ SY2744 @ SY2745 )
                      = SY2746 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[945]) ).

thf(1209,plain,
    ! [SV186: $i,SV412: $i] :
      ( ( ~ ( in @ SV412 @ ( powerset @ SV186 ) )
        | ! [SY2747: $i] :
            ( ~ ( in @ SY2747 @ ( powerset @ SV186 ) )
            | ( in @ ( setminus @ SV412 @ SY2747 ) @ ( powerset @ SV186 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[946]) ).

thf(1210,plain,
    ! [SV413: $i > $o,SV187: $i] :
      ( ( ! [SY2748: $i] :
            ( ~ ( in @ SY2748
                @ ( dsetconstr @ SV187
                  @ ^ [SY2749: $i] : ( SV413 @ SY2749 ) ) )
            | ( in @ SY2748 @ SV187 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[947]) ).

thf(1211,plain,
    ! [SV414: $i > $o,SV188: $i] :
      ( ( ! [SY2750: $i] :
            ( ~ ( in @ SY2750 @ SV188 )
            | ~ ( ~ ( ~ ( in @ SY2750
                        @ ( dsetconstr @ SV188
                          @ ^ [SY2751: $i] : ( SV414 @ SY2751 ) ) )
                    | ( SV414 @ SY2750 ) )
                | ~ ( ~ ( SV414 @ SY2750 )
                    | ( in @ SY2750
                      @ ( dsetconstr @ SV188
                        @ ^ [SY2752: $i] : ( SV414 @ SY2752 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[948]) ).

thf(1212,plain,
    ! [SV189: $i,SV415: $i] :
      ( ( ! [SY2753: $i] :
            ( ~ ( in @ SY2753 @ SV415 )
            | ( in @ SY2753 @ ( setadjoin @ SV189 @ SV415 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[949]) ).

thf(1213,plain,
    ! [SV416: $i,SV190: $i] :
      ( ( ! [SY2754: $i] :
            ( ~ ( func @ SV190 @ SV416 @ SY2754 )
            | ! [SY2755: $i] :
                ( ~ ( func @ SV190 @ SV416 @ SY2755 )
                | ~ ! [SY2756: $i] :
                      ( ~ ( in @ SY2756 @ SV190 )
                      | ( ( ap @ SV190 @ SV416 @ SY2754 @ SY2756 )
                        = ( ap @ SV190 @ SV416 @ SY2755 @ SY2756 ) ) )
                | ( SY2754 = SY2755 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[950]) ).

thf(1214,plain,
    ! [SV191: $i,SV417: $i] :
      ( ( ~ ( in @ SV417 @ ( powerset @ SV191 ) )
        | ! [SY2757: $i] :
            ( ~ ( in @ SY2757 @ ( powerset @ SV191 ) )
            | ! [SY2758: $i] :
                ( ~ ( in @ SY2758 @ ( powerset @ SV191 ) )
                | ! [SY2759: $i] :
                    ( ~ ( in @ SY2759 @ SV191 )
                    | ~ ( in @ SY2759 @ ( binintersect @ SV417 @ SY2757 ) )
                    | ( in @ SY2759 @ ( binunion @ SV417 @ SY2758 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[951]) ).

thf(1215,plain,
    ! [SV418: $i > $o,SV192: $i] :
      ( ( ! [SY2760: $i] :
            ( ~ ( in @ SY2760
                @ ( dsetconstr @ SV192
                  @ ^ [SY2761: $i] : ( SV418 @ SY2761 ) ) )
            | ( SV418 @ SY2760 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[952]) ).

thf(1216,plain,
    ! [SV419: $i,SV193: $i] :
      ( ( ( SV193 != SV419 )
        | ! [SY2762: $i,SY2763: $i] :
            ( ( SY2762 != SY2763 )
            | ~ ( ~ ( ~ ( in @ SY2762 @ SV193 )
                    | ( in @ SY2763 @ SV419 ) )
                | ~ ( ~ ( in @ SY2763 @ SV419 )
                    | ( in @ SY2762 @ SV193 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[953]) ).

thf(1217,plain,
    ! [SV420: $o,SV194: $i] :
      ( ( ! [SY2764: $i] :
            ( ~ ( in @ SY2764 @ SV194 )
            | ! [SY2765: $i] :
                ( ~ ( in @ SY2765 @ SV194 )
                | ( singleton
                  @ ( dsetconstr @ SV194
                    @ ^ [SY2766: $i] :
                        ( ~ ( ~ SV420
                            | ( SY2766 != SY2764 ) )
                        | ~ ( ~ ~ SV420
                            | ( SY2766 != SY2765 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[954]) ).

thf(1218,plain,
    ! [SV194: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV194 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV194 )
                | ( singleton
                  @ ( dsetconstr @ SV194
                    @ ^ [SX2: $i] :
                        ( ~ ( ~ $true
                            | ( SX2 != SX0 ) )
                        | ~ ( ~ ~ $true
                            | ( SX2 != SX1 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[954]) ).

thf(1219,plain,
    ! [SV194: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV194 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV194 )
                | ( singleton
                  @ ( dsetconstr @ SV194
                    @ ^ [SX2: $i] :
                        ( ~ ( ~ $false
                            | ( SX2 != SX0 ) )
                        | ~ ( ~ ~ $false
                            | ( SX2 != SX1 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[954]) ).

thf(1220,plain,
    ! [SV421: $i,SV195: $i] :
      ( ( ( ( binintersect @ SV195 @ SV421 )
         != SV195 )
        | ( subset @ SV195 @ SV421 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[955]) ).

thf(1221,plain,
    ! [SV422: $i,SV196: $i] :
      ( ( ! [SY2767: $i] :
            ( ~ ( in @ SY2767 @ SV196 )
            | ! [SY2768: $i] :
                ( ~ ( in @ SY2768 @ SV422 )
                | ( in @ ( kpair @ SY2767 @ SY2768 ) @ ( powerset @ ( powerset @ ( binunion @ SV196 @ SV422 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[956]) ).

thf(1222,plain,
    ! [SV423: $o,SV197: $i] :
      ( ( ! [SY2769: $i] :
            ( ~ ( in @ SY2769 @ SV197 )
            | ! [SY2770: $i] :
                ( ~ ( in @ SY2770 @ SV197 )
                | ( in @ ( if @ SV197 @ SV423 @ SY2769 @ SY2770 ) @ SV197 ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[957]) ).

thf(1223,plain,
    ! [SV197: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV197 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV197 )
                | ( in @ ( if @ SV197 @ $true @ SX0 @ SX1 ) @ SV197 ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[957]) ).

thf(1224,plain,
    ! [SV197: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV197 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV197 )
                | ( in @ ( if @ SV197 @ $false @ SX0 @ SX1 ) @ SV197 ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[957]) ).

thf(1225,plain,
    ! [SV424: $i,SV198: $i] :
      ( ( ! [SY2771: $i] :
            ( ~ ( in @ SY2771 @ ( funcSet @ SV198 @ SV424 ) )
            | ! [SY2772: $i] :
                ( ~ ( in @ SY2772 @ SV198 )
                | ! [SY2773: $i] :
                    ( ~ ( in @ SY2773 @ SV424 )
                    | ~ ( in @ ( kpair @ SY2772 @ SY2773 ) @ SY2771 )
                    | ( ( ap @ SV198 @ SV424 @ SY2771 @ SY2772 )
                      = SY2773 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[958]) ).

thf(1226,plain,
    ! [SV425: $i,SV199: $i] :
      ( ( ! [SY2774: $i > $i] :
            ( ~ ! [SY2775: $i] :
                  ( ~ ( in @ SY2775 @ SV199 )
                  | ( in @ ( SY2774 @ SY2775 ) @ SV425 ) )
            | ( func @ SV199 @ SV425
              @ ( lam @ SV199 @ SV425
                @ ^ [SX3: $i] : ( SY2774 @ SX3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[959]) ).

thf(1227,plain,
    ! [SV426: $i > $o,SV200: $i] :
      ( ( ~ ! [SY2777: $i] :
              ( ~ ( in @ SY2777 @ SV200 )
              | ~ ( SV426 @ SY2777 ) )
        | ~ ~ ! [SY2778: $i] :
                ~ ~ ( ~ ( in @ SY2778 @ SV200 )
                    | ~ ( SV426 @ SY2778 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[960]) ).

thf(1228,plain,
    ! [SV427: $i,SV201: $i] :
      ( ( ( ( setadjoin @ SV201 @ emptyset )
         != ( setadjoin @ SV427 @ emptyset ) )
        | ( SV201 = SV427 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[961]) ).

thf(1229,plain,
    ! [SV428: $i,SV202: $i] :
      ( ( ! [SY2779: $i] :
            ( ~ ( in @ SY2779 @ ( funcSet @ SV202 @ SV428 ) )
            | ! [SY2780: $i] :
                ( ~ ( in @ SY2780 @ SV202 )
                | ( in @ ( ap @ SV202 @ SV428 @ SY2779 @ SY2780 ) @ SV428 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[962]) ).

thf(1230,plain,
    ! [SV203: $i] :
      ( ( ( ~ ( ( SV203 != emptyset ) ) )
        = $true )
      | ( ( ~ ! [SY2355: $i] :
                ~ ( in @ SY2355 @ SV203 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[963]) ).

thf(1231,plain,
    ! [SV429: $i,SV204: $i] :
      ( ( ~ ( in @ SV204 @ ( setadjoin @ SV429 @ emptyset ) )
        | ( in @ SV429 @ ( setadjoin @ SV204 @ emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[964]) ).

thf(1232,plain,
    ! [SV205: $i,SV430: $i] :
      ( ( ~ ( ~ ( ~ ( in @ SV430 @ ( setunion @ SV205 ) )
                | ~ ! [SY2781: $i] :
                      ~ ~ ( ~ ( in @ SV430 @ SY2781 )
                          | ~ ( in @ SY2781 @ SV205 ) ) )
            | ~ ( ~ ~ ! [SY2782: $i] :
                        ~ ~ ( ~ ( in @ SV430 @ SY2782 )
                            | ~ ( in @ SY2782 @ SV205 ) )
                | ( in @ SV430 @ ( setunion @ SV205 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[965]) ).

thf(1233,plain,
    ! [SV431: $i,SV206: $i] :
      ( ( ! [SY2783: $i] :
            ( ~ ( in @ SY2783 @ ( symdiff @ SV206 @ SV431 ) )
            | ! [SY2784: $o] :
                ( ~ ( ~ ( in @ SY2783 @ SV206 )
                    | ~ ~ ( in @ SY2783 @ SV431 )
                    | SY2784 )
                | ~ ( ~ ~ ( in @ SY2783 @ SV206 )
                    | ~ ( in @ SY2783 @ SV431 )
                    | SY2784 )
                | SY2784 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[966]) ).

thf(1234,plain,
    ! [SV432: $i,SV207: $i] :
      ( ( ~ ~ ( subset @ SV207 @ SV432 )
        | ( SV207 != SV432 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[967]) ).

thf(1235,plain,
    ! [SV208: $i,SV433: $i] :
      ( ( ~ ( in @ SV433 @ ( setunion @ SV208 ) )
        | ~ ! [SY2785: $i] :
              ~ ~ ( ~ ( in @ SY2785 @ SV208 )
                  | ~ ( in @ SV433 @ SY2785 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[968]) ).

thf(1236,plain,
    ! [SV434: $i,SV209: $i] :
      ( ( ( SV209 != SV434 )
        | ! [SY2786: $i > $o,SY2787: $i > $o] :
            ( ~ ! [SY2788: $i] :
                  ( ~ ( in @ SY2788 @ SV209 )
                  | ! [SY2789: $i] :
                      ( ~ ( in @ SY2789 @ SV434 )
                      | ( SY2788 != SY2789 )
                      | ~ ( ~ ( ~ ( SY2786 @ SY2788 )
                              | ( SY2787 @ SY2789 ) )
                          | ~ ( ~ ( SY2787 @ SY2789 )
                              | ( SY2786 @ SY2788 ) ) ) ) )
            | ( ( dsetconstr @ SV209
                @ ^ [SX4: $i] : ( SY2786 @ SX4 ) )
              = ( dsetconstr @ SV434
                @ ^ [SX4: $i] : ( SY2787 @ SX4 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[969]) ).

thf(1237,plain,
    ! [SV435: $i,SV210: $i] :
      ( ( ! [SY2792: $i] :
            ( ~ ( in @ SY2792 @ ( setadjoin @ SV210 @ SV435 ) )
            | ! [SY2793: $o] :
                ( ~ ( ( SY2792 != SV210 )
                    | SY2793 )
                | ~ ( ~ ( in @ SY2792 @ SV435 )
                    | SY2793 )
                | SY2793 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[970]) ).

thf(1238,plain,
    ! [SV211: $i > $o] :
      ( ( ( ~ ~ ! [SY2376: $i] :
                  ~ ~ ( ~ ( SV211 @ SY2376 )
                      | ~ ! [SY2377: $i] :
                            ( ~ ( SV211 @ SY2377 )
                            | ( SY2376 = SY2377 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2378: $i] :
                ~ ~ ( ~ ( SV211 @ SY2378 )
                    | ~ ! [SY2379: $i] :
                          ( ~ ( SV211 @ SY2379 )
                          | ( SY2378 = SY2379 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[971]) ).

thf(1239,plain,
    ! [SV436: $i,SV212: $i] :
      ( ( ! [SY2794: $i] :
            ( ~ ( in @ SY2794 @ ( funcSet @ SV212 @ SV436 ) )
            | ! [SY2795: $i] :
                ( ~ ( in @ SY2795 @ SV212 )
                | ( ( ap @ SV212 @ SV436 @ SY2794 @ SY2795 )
                  = ( ap @ SV212 @ SV436 @ SY2794 @ SY2795 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[972]) ).

thf(1240,plain,
    ! [SV213: $i,SV437: $i] :
      ( ( ~ ( in @ SV437 @ ( powerset @ SV213 ) )
        | ! [SY2796: $i] :
            ( ~ ( in @ SY2796 @ SV213 )
            | ~ ( in @ SY2796 @ ( setminus @ SV213 @ ( setminus @ SV213 @ SV437 ) ) )
            | ( in @ SY2796 @ SV437 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[973]) ).

thf(1241,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ~ ! [SY2797: $i,SY2798: $i] :
              ( ( SY2797 != SY2798 )
              | ~ ( ~ ( ~ ( SV214 @ SY2797 )
                      | ( SV438 @ SY2798 ) )
                  | ~ ( ~ ( SV438 @ SY2798 )
                      | ( SV214 @ SY2797 ) ) ) )
        | ~ ( ~ ( ~ ~ ! [SY2388: $i] :
                        ~ ~ ( ~ ( SV214 @ SY2388 )
                            | ~ ! [SY2389: $i] :
                                  ( ~ ( SV214 @ SY2389 )
                                  | ( SY2388 = SY2389 ) ) )
                | ~ ! [SY2801: $i] :
                      ~ ~ ( ~ ( SV438 @ SY2801 )
                          | ~ ! [SY2802: $i] :
                                ( ~ ( SV438 @ SY2802 )
                                | ( SY2801 = SY2802 ) ) ) )
            | ~ ( ~ ~ ! [SY2803: $i] :
                        ~ ~ ( ~ ( SV438 @ SY2803 )
                            | ~ ! [SY2804: $i] :
                                  ( ~ ( SV438 @ SY2804 )
                                  | ( SY2803 = SY2804 ) ) )
                | ~ ! [SY2394: $i] :
                      ~ ~ ( ~ ( SV214 @ SY2394 )
                          | ~ ! [SY2395: $i] :
                                ( ~ ( SV214 @ SY2395 )
                                | ( SY2394 = SY2395 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[974]) ).

thf(1242,plain,
    ! [SV439: $i > $o,SV215: $i] :
      ( ( ~ ( singleton
            @ ( dsetconstr @ SV215
              @ ^ [SY2807: $i] : ( SV439 @ SY2807 ) ) )
        | ~ ! [SY2808: $i] :
              ~ ~ ( ~ ( in @ SY2808 @ SV215 )
                  | ~ ( SV439 @ SY2808 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[975]) ).

thf(1243,plain,
    ! [SV440: $i > $o,SV216: $i] :
      ( ( ! [SY2809: $i] :
            ( ~ ( in @ SY2809 @ SV216 )
            | ~ ( SV440 @ SY2809 )
            | ~ ! [SY2810: $i] :
                  ( ~ ( in @ SY2810 @ SV216 )
                  | ~ ( SV440 @ SY2810 )
                  | ( SY2810 = SY2809 ) )
            | ( singleton
              @ ( dsetconstr @ SV216
                @ ^ [SY2811: $i] : ( SV440 @ SY2811 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[976]) ).

thf(1244,plain,
    ! [SV441: $i,SV217: $i] :
      ( ( ( SV217 != SV441 )
        | ( ( setadjoin @ SV217 @ ( setadjoin @ SV441 @ emptyset ) )
          = ( setadjoin @ SV217 @ emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[977]) ).

thf(1245,plain,
    ! [SV442: $i,SV218: $i] :
      ( ( ! [SY2812: $i] :
            ( ~ ( in @ SY2812 @ SV218 )
            | ! [SY2813: $i] :
                ( ~ ( in @ SY2813 @ SV442 )
                | ( subset @ ( setadjoin @ ( setadjoin @ SY2812 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2812 @ ( setadjoin @ SY2813 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV218 @ SV442 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[978]) ).

thf(1246,plain,
    ! [SV443: $i,SV219: $i] :
      ( ( ! [SY2814: $i] :
            ( ~ ( in @ SY2814 @ SV219 )
            | ! [SY2815: $i] :
                ( ~ ( in @ SY2815 @ SV443 )
                | ( ( ksnd @ ( kpair @ SY2814 @ SY2815 ) )
                  = SY2815 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[979]) ).

thf(1247,plain,
    ! [SV444: $o,SV220: $i] :
      ( ( ! [SY2816: $i] :
            ( ~ ( in @ SY2816 @ SV220 )
            | ! [SY2817: $i] :
                ( ~ ( in @ SY2817 @ SV220 )
                | ~ SV444
                | ( ( dsetconstr @ SV220
                    @ ^ [SY2818: $i] :
                        ( ~ ( ~ SV444
                            | ( SY2818 != SY2816 ) )
                        | ~ ( ~ ~ SV444
                            | ( SY2818 != SY2817 ) ) ) )
                  = ( setadjoin @ SY2816 @ emptyset ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[980]) ).

thf(1248,plain,
    ! [SV220: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV220 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV220 )
                | ~ $true
                | ( ( dsetconstr @ SV220
                    @ ^ [SX2: $i] :
                        ( ~ ( ~ $true
                            | ( SX2 != SX0 ) )
                        | ~ ( ~ ~ $true
                            | ( SX2 != SX1 ) ) ) )
                  = ( setadjoin @ SX0 @ emptyset ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[980]) ).

thf(1249,plain,
    ! [SV220: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV220 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV220 )
                | ~ $false
                | ( ( dsetconstr @ SV220
                    @ ^ [SX2: $i] :
                        ( ~ ( ~ $false
                            | ( SX2 != SX0 ) )
                        | ~ ( ~ ~ $false
                            | ( SX2 != SX1 ) ) ) )
                  = ( setadjoin @ SX0 @ emptyset ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[980]) ).

thf(1250,plain,
    ! [SV445: $i,SV221: $i] :
      ( ( ! [SY2819: $i] :
            ( ~ ( subset @ SY2819 @ ( cartprod @ SV221 @ SV445 ) )
            | ! [SY2820: $i] :
                ( ~ ( subset @ SY2820 @ ( cartprod @ SV221 @ SV445 ) )
                | ~ ! [SY2821: $i] :
                      ( ~ ( in @ SY2821 @ SV221 )
                      | ! [SY2822: $i] :
                          ( ~ ( in @ SY2822 @ SV445 )
                          | ~ ( in @ ( kpair @ SY2821 @ SY2822 ) @ SY2819 )
                          | ( in @ ( kpair @ SY2821 @ SY2822 ) @ SY2820 ) ) )
                | ~ ! [SY2823: $i] :
                      ( ~ ( in @ SY2823 @ SV221 )
                      | ! [SY2824: $i] :
                          ( ~ ( in @ SY2824 @ SV445 )
                          | ~ ( in @ ( kpair @ SY2823 @ SY2824 ) @ SY2820 )
                          | ( in @ ( kpair @ SY2823 @ SY2824 ) @ SY2819 ) ) )
                | ( SY2819 = SY2820 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[981]) ).

thf(1251,plain,
    ! [SV446: $i,SV222: $i] :
      ( ( ! [SY2825: $i] :
            ( ~ ( func @ SV222 @ SV446 @ SY2825 )
            | ! [SY2826: $i] :
                ( ~ ( in @ SY2826 @ SV222 )
                | ( singleton
                  @ ( dsetconstr @ SV446
                    @ ^ [SX4: $i] : ( in @ ( kpair @ SY2826 @ SX4 ) @ SY2825 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[982]) ).

thf(1252,plain,
    ! [SV223: $i,SV447: $i] :
      ( ( ~ ( in @ SV447 @ SV223 )
        | ( subset @ ( setadjoin @ SV447 @ emptyset ) @ SV223 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[983]) ).

thf(1253,plain,
    ! [SV224: $i] :
      ( ( ( ~ ( ( SV224 != emptyset ) ) )
        = $true )
      | ( ( ~ ! [SY2426: $i] :
                ~ ~ ( ~ ( in @ SY2426 @ SV224 )
                    | ~ $true ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[984]) ).

thf(1254,plain,
    ! [SV448: $i,SV225: $i] :
      ( ( ! [SY2828: $i] :
            ( ~ ( subset @ SY2828 @ SV225 )
            | ~ ( subset @ SY2828 @ SV448 )
            | ( subset @ SY2828 @ ( binintersect @ SV225 @ SV448 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[985]) ).

thf(1255,plain,
    ! [SV449: $i,SV226: $i] :
      ( ( ! [SY2829: $i] :
            ( ~ ( in @ SY2829 @ SV226 )
            | ~ ~ ( in @ SY2829 @ SV449 )
            | ( in @ SY2829 @ ( symdiff @ SV226 @ SV449 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[986]) ).

thf(1256,plain,
    ! [SV227: $i,SV450: $i] :
      ( ( ~ ( in @ SV450 @ ( powerset @ SV227 ) )
        | ! [SY2830: $i] :
            ( ~ ( in @ SY2830 @ ( powerset @ SV227 ) )
            | ~ ( subset @ ( setminus @ SV227 @ SY2830 ) @ ( setminus @ SV227 @ SV450 ) )
            | ( subset @ SV450 @ SY2830 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[987]) ).

thf(1257,plain,
    ! [SV228: $i,SV451: $i] :
      ( ( ~ ( in @ SV451 @ ( powerset @ SV228 ) )
        | ! [SY2831: $i] :
            ( ~ ( in @ SY2831 @ ( powerset @ SV228 ) )
            | ! [SY2832: $i] :
                ( ~ ( in @ SY2832 @ ( powerset @ SV228 ) )
                | ! [SY2833: $i] :
                    ( ~ ( in @ SY2833 @ SV228 )
                    | ~ ( in @ SY2833 @ ( binintersect @ SV451 @ SY2831 ) )
                    | ( in @ SY2833 @ ( binunion @ SY2831 @ SY2832 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[988]) ).

thf(1258,plain,
    ! [SV229: $i,SV452: $i] :
      ( ( ~ ( in @ SV452 @ SV229 )
        | ( in @ SV452 @ ( powerset @ ( setunion @ SV229 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[989]) ).

thf(1259,plain,
    ! [SV453: $o,SV230: $i] :
      ( ( ! [SY2834: $i] :
            ( ~ ( in @ SY2834 @ SV230 )
            | ! [SY2835: $i] :
                ( ~ ( in @ SY2835 @ SV230 )
                | ~ ~ SV453
                | ( ( dsetconstr @ SV230
                    @ ^ [SY2836: $i] :
                        ( ~ ( ~ SV453
                            | ( SY2836 != SY2834 ) )
                        | ~ ( ~ ~ SV453
                            | ( SY2836 != SY2835 ) ) ) )
                  = ( setadjoin @ SY2835 @ emptyset ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[990]) ).

thf(1260,plain,
    ! [SV230: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV230 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV230 )
                | ~ ~ $true
                | ( ( dsetconstr @ SV230
                    @ ^ [SX2: $i] :
                        ( ~ ( ~ $true
                            | ( SX2 != SX0 ) )
                        | ~ ( ~ ~ $true
                            | ( SX2 != SX1 ) ) ) )
                  = ( setadjoin @ SX1 @ emptyset ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[990]) ).

thf(1261,plain,
    ! [SV230: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV230 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV230 )
                | ~ ~ $false
                | ( ( dsetconstr @ SV230
                    @ ^ [SX2: $i] :
                        ( ~ ( ~ $false
                            | ( SX2 != SX0 ) )
                        | ~ ( ~ ~ $false
                            | ( SX2 != SX1 ) ) ) )
                  = ( setadjoin @ SX1 @ emptyset ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[990]) ).

thf(1262,plain,
    ! [SV231: $i,SV454: $i] :
      ( ( ~ ( in @ SV454 @ ( powerset @ SV231 ) )
        | ! [SY2837: $i] :
            ( ~ ( in @ SY2837 @ ( powerset @ SV231 ) )
            | ~ ! [SY2838: $i] :
                  ( ~ ( in @ SY2838 @ SV231 )
                  | ~ ( in @ SY2838 @ SV454 )
                  | ( in @ SY2838 @ SY2837 ) )
            | ( in @ SV454 @ ( powerset @ SY2837 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[991]) ).

thf(1263,plain,
    ! [SV455: $i,SV232: $i] :
      ( ( ! [SY2839: $i] :
            ( ~ ( func @ SV232 @ SV455 @ SY2839 )
            | ( ( lam @ SV232 @ SV455
                @ ^ [SY2840: $i] : ( ap @ SV232 @ SV455 @ SY2839 @ SY2840 ) )
              = SY2839 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[992]) ).

thf(1264,plain,
    ! [SV456: $i,SV233: $i] :
      ( ( ( ( binintersect @ SV233 @ SV456 )
         != SV456 )
        | ( subset @ SV456 @ SV233 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[993]) ).

thf(1265,plain,
    ! [SV457: $i,SV234: $i] :
      ( ( ! [SY2841: $i] :
            ( ~ ( in @ SY2841 @ ( cartprod @ SV234 @ SV457 ) )
            | ( in @ ( kfst @ SY2841 ) @ SV234 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[994]) ).

thf(1266,plain,
    ! [SV458: $i,SV235: $i] :
      ( ( ( SV235 != SV458 )
        | ( in @ SV235 @ ( setadjoin @ SV458 @ emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[995]) ).

thf(1267,plain,
    ! [SV459: $i,SV236: $i] :
      ( ( ! [SY2842: $i] :
            ( ~ ( subset @ SV236 @ SV459 )
            | ~ ( subset @ SV459 @ SY2842 )
            | ( subset @ SV236 @ SY2842 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[996]) ).

thf(1268,plain,
    ! [SV460: $i,SV237: $i] :
      ( ( ! [SY2843: $i] :
            ( ( ( setadjoin @ SV237 @ ( setadjoin @ SV460 @ emptyset ) )
             != ( setadjoin @ SY2843 @ emptyset ) )
            | ( SV237 = SV460 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[997]) ).

thf(1269,plain,
    ! [SV461: $i,SV238: $i] :
      ( ( ~ ( subset @ SV238 @ SV461 )
        | ( subset @ ( powerset @ SV238 ) @ ( powerset @ SV461 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[998]) ).

thf(1270,plain,
    ! [SV462: $i,SV239: $i] :
      ( ( ! [SY2844: $i,SY2845: $i] :
            ( ( ( setadjoin @ ( setadjoin @ SV239 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV239 @ ( setadjoin @ SV462 @ emptyset ) ) @ emptyset ) )
             != ( setadjoin @ ( setadjoin @ SY2844 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2844 @ ( setadjoin @ SY2845 @ emptyset ) ) @ emptyset ) ) )
            | ( SV239 = SY2844 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[999]) ).

thf(1271,plain,
    ! [SV463: $i,SV240: $i] :
      ( ( ! [SY2846: $i] :
            ( ~ ( func @ SV240 @ SV463 @ SY2846 )
            | ( in @ SY2846 @ ( funcSet @ SV240 @ SV463 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1000]) ).

thf(1272,plain,
    ! [SV464: $i,SV241: $i] :
      ( ( ! [SY2847: $i] :
            ( ~ ( in @ SY2847 @ ( binintersect @ SV241 @ SV464 ) )
            | ( in @ SY2847 @ SV464 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1001]) ).

thf(1273,plain,
    ! [SV465: $i,SV242: $i] :
      ( ( ! [SY2848: $i] :
            ( ~ ~ ( in @ SY2848 @ SV242 )
            | ~ ( in @ SY2848 @ ( setminus @ SV242 @ SV465 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1002]) ).

thf(1274,plain,
    ! [SV243: $i,SV466: $i] :
      ( ( ~ ( in @ SV466 @ ( powerset @ SV243 ) )
        | ! [SY2849: $i] :
            ( ~ ( in @ SY2849 @ ( powerset @ SV243 ) )
            | ~ ! [SY2850: $i] :
                  ( ~ ( in @ SY2850 @ SV243 )
                  | ~ ( in @ SY2850 @ SV466 )
                  | ( in @ SY2850 @ SY2849 ) )
            | ( subset @ SV466 @ SY2849 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1003]) ).

thf(1275,plain,
    ! [SV467: $i,SV244: $i] :
      ( ( ! [SY2851: $i > $i] :
            ( ~ ! [SY2852: $i] :
                  ( ~ ( in @ SY2852 @ SV244 )
                  | ( in @ ( SY2851 @ SY2852 ) @ SV467 ) )
            | ! [SY2853: $i] :
                ( ~ ( in @ SY2853 @ SV244 )
                | ( ( ap @ SV244 @ SV467
                    @ ( lam @ SV244 @ SV467
                      @ ^ [SX4: $i] : ( SY2851 @ SX4 ) )
                    @ SY2853 )
                  = ( SY2851 @ SY2853 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1004]) ).

thf(1276,plain,
    ! [SV468: $i,SV245: $i] :
      ( ( ! [SY2855: $i] :
            ( ~ ( in @ SY2855 @ ( funcSet @ SV245 @ SV468 ) )
            | ! [SY2856: $i] :
                ( ~ ( in @ SY2856 @ SV245 )
                | ( in @ ( kpair @ SY2856 @ ( ap @ SV245 @ SV468 @ SY2855 @ SY2856 ) ) @ SY2855 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1005]) ).

thf(1277,plain,
    ! [SV246: $i,SV469: $i] :
      ( ( ~ ( in @ SV469 @ ( powerset @ SV246 ) )
        | ! [SY2857: $i] :
            ( ~ ( in @ SY2857 @ ( powerset @ SV246 ) )
            | ! [SY2858: $i] :
                ( ~ ( in @ SY2858 @ SV246 )
                | ~ ( in @ SY2858 @ ( setminus @ SV246 @ SV469 ) )
                | ~ ( in @ SY2858 @ ( binintersect @ SV469 @ SY2857 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1006]) ).

thf(1278,plain,
    ! [SV247: $i] :
      ( ( ( ~ ( in @ SV247 @ omega ) )
        = $true )
      | ( ( in @ ( setadjoin @ SV247 @ SV247 ) @ omega )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1007]) ).

thf(1279,plain,
    ! [SV470: $i,SV248: $i] :
      ( ( ~ ( in @ SV248 @ ( setadjoin @ SV470 @ emptyset ) )
        | ( SV248 = SV470 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1008]) ).

thf(1280,plain,
    ! [SV249: $i,SV471: $i] :
      ( ( ! [SY2859: $i] :
            ( ~ ( in @ SY2859 @ SV471 )
            | ~ ( in @ SY2859 @ ( setminus @ SV249 @ SV471 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1009]) ).

thf(1281,plain,
    ! [SV250: $i] :
      ( ( ( ~ ( singleton @ SV250 ) )
        = $true )
      | ( ( ! [SY2483: $i] :
              ( ~ ( in @ SY2483 @ SV250 )
              | ( ( setunion @ SV250 )
                = SY2483 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1010]) ).

thf(1282,plain,
    ! [SV472: $i,SV251: $i] :
      ( ( ! [SY2860: $i] :
            ( ~ ( in @ SY2860 @ SV251 )
            | ! [SY2861: $i] :
                ( ~ ( in @ SY2861 @ SV472 )
                | ( in @ ( setadjoin @ SY2860 @ ( setadjoin @ SY2861 @ emptyset ) ) @ ( powerset @ ( binunion @ SV251 @ SV472 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1011]) ).

thf(1283,plain,
    ! [SV473: $i,SV252: $i] :
      ( ( ! [SY2862: $i] :
            ( ~ ( in @ SY2862 @ ( binunion @ SV252 @ SV473 ) )
            | ( in @ SY2862 @ SV252 )
            | ( in @ SY2862 @ SV473 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1012]) ).

thf(1284,plain,
    ! [SV253: $i > $o] :
      ( ( ( ~ ~ ! [SY2489: $i] :
                  ~ ! [SY2490: $i] :
                      ~ ( ~ ( ~ ( SV253 @ SY2490 )
                            | ( SY2490 = SY2489 ) )
                        | ~ ( ( SY2490 != SY2489 )
                            | ( SV253 @ SY2490 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2491: $i] :
                ~ ~ ( ~ ( SV253 @ SY2491 )
                    | ~ ! [SY2492: $i] :
                          ( ~ ( SV253 @ SY2492 )
                          | ( SY2491 = SY2492 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1013]) ).

thf(1285,plain,
    ! [SV474: $i,SV254: $i] :
      ( ( ! [SY2863: $i] :
            ( ~ ( subset @ SV254 @ SY2863 )
            | ( subset @ SV254 @ ( setadjoin @ SV474 @ SY2863 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1014]) ).

thf(1286,plain,
    ! [SV255: $i,SV475: $i] :
      ( ( ~ ( in @ SV475 @ ( setunion @ SV255 ) )
        | ! [SY2864: $o] :
            ( ~ ! [SY2865: $i] :
                  ( ~ ( in @ SV475 @ SY2865 )
                  | ~ ( in @ SY2865 @ SV255 )
                  | SY2864 )
            | SY2864 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1015]) ).

thf(1287,plain,
    ! [SV476: $o,SV256: $i] :
      ( ( ! [SY2866: $i] :
            ( ~ ( in @ SY2866 @ SV256 )
            | ! [SY2867: $i] :
                ( ~ ( in @ SY2867 @ SV256 )
                | ( in @ ( if @ SV256 @ SV476 @ SY2866 @ SY2867 ) @ ( setadjoin @ SY2866 @ ( setadjoin @ SY2867 @ emptyset ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[1016]) ).

thf(1288,plain,
    ! [SV256: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV256 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV256 )
                | ( in @ ( if @ SV256 @ $true @ SX0 @ SX1 ) @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[1016]) ).

thf(1289,plain,
    ! [SV256: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV256 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV256 )
                | ( in @ ( if @ SV256 @ $false @ SX0 @ SX1 ) @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[1016]) ).

thf(1290,plain,
    ! [SV477: $i,SV257: $i] :
      ( ( ! [SY2868: $i] :
            ( ~ ( in @ SY2868 @ SV257 )
            | ! [SY2869: $i] :
                ( ~ ( in @ SY2869 @ SV477 )
                | ( subset @ ( setadjoin @ SY2868 @ ( setadjoin @ SY2869 @ emptyset ) ) @ ( binunion @ SV257 @ SV477 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1017]) ).

thf(1291,plain,
    ! [SV478: $i > $i > $o,SV258: $i,SV1: $i] :
      ( ( subset
        @ ( dpsetconstr @ SV1 @ SV258
          @ ^ [SY2870: $i,SY2871: $i] : ( SV478 @ SY2870 @ SY2871 ) )
        @ ( cartprod @ SV1 @ SV258 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1018]) ).

thf(1292,plain,
    ! [SV479: $i > $i > $o,SV259: $i,SV2: $i] :
      ( ( subset
        @ ( dpsetconstr @ SV2 @ SV259
          @ ^ [SY2872: $i,SY2873: $i] : ( SV479 @ SY2872 @ SY2873 ) )
        @ ( cartprod @ SV2 @ SV259 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1019]) ).

thf(1293,plain,
    ! [SV480: $i,SV268: $i,SV14: $i] :
      ( ( ( binintersect @ SV14 @ ( binunion @ SV268 @ SV480 ) )
        = ( binunion @ ( binintersect @ SV14 @ SV268 ) @ ( binintersect @ SV14 @ SV480 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1028]) ).

thf(1294,plain,
    ! [SV280: $i,SV34: $i,SV481: $i] :
      ( ( ~ ( in @ SV481 @ ( funcSet @ SV34 @ SV280 ) )
        | ( func @ SV34 @ SV280 @ SV481 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1042]) ).

thf(1295,plain,
    ! [SV281: $i > $o,SV35: $i] :
      ( ( ( ~ ~ ~ ! [SY2514: $i] :
                    ~ ~ ( ~ ( in @ SY2514 @ SV35 )
                        | ~ ( SV281 @ SY2514 ) ) )
        = $true )
      | ( ( ! [SY2515: $i] :
              ( ~ ( in @ SY2515 @ SV35 )
              | ~ ( SV281 @ SY2515 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1043]) ).

thf(1296,plain,
    ! [SV36: $i,SV282: $i] :
      ( ( ( ~ ( in @ SV282 @ ( powerset @ SV36 ) ) )
        = $true )
      | ( ( ! [SY2516: $i] :
              ( ~ ( in @ SY2516 @ ( powerset @ SV36 ) )
              | ! [SY2517: $i] :
                  ( ~ ( in @ SY2517 @ SV36 )
                  | ~ ( subset @ SV282 @ SY2516 )
                  | ~ ~ ( in @ SY2517 @ SY2516 )
                  | ~ ( in @ SY2517 @ SV282 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1044]) ).

thf(1297,plain,
    ! [SV37: $i > $o] :
      ( ( ( ~ ! [SY1895: $i] :
                ~ ~ ( ~ ( SV37 @ SY1895 )
                    | ~ ! [SY1896: $i] :
                          ( ~ ( SV37 @ SY1896 )
                          | ( SY1895 = SY1896 ) ) ) )
        = $false )
      | ( ( ~ ! [SY1897: $i] :
                ~ ! [SY1898: $i] :
                    ~ ( ~ ( ~ ( SV37 @ SY1898 )
                          | ( SY1898 = SY1897 ) )
                      | ~ ( ( SY1898 != SY1897 )
                          | ( SV37 @ SY1898 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1045]) ).

thf(1298,plain,
    ! [SV482: $i,SV283: $i,SV38: $i] :
      ( ( ~ ( func @ SV38 @ SV283 @ SV482 )
        | ! [SY2874: $i] :
            ( ~ ( in @ SY2874 @ SV38 )
            | ( in @ ( kpair @ SY2874 @ ( ap @ SV38 @ SV283 @ SV482 @ SY2874 ) ) @ SV482 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1046]) ).

thf(1299,plain,
    ! [SV39: $i] :
      ( ( ( in @ SV39 @ emptyset )
        = $false )
      | ( ( ! [SX1: $o] : SX1 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1047]) ).

thf(1300,plain,
    ! [SV284: $o,SV40: $i,SV483: $i] :
      ( ( ~ ( in @ SV483 @ SV40 )
        | ! [SY2875: $i] :
            ( ~ ( in @ SY2875 @ SV40 )
            | ~ ~ SV284
            | ( in @ SY2875
              @ ( dsetconstr @ SV40
                @ ^ [SY2876: $i] :
                    ( ~ ( ~ SV284
                        | ( SY2876 != SV483 ) )
                    | ~ ( ~ ~ SV284
                        | ( SY2876 != SY2875 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1048]) ).

thf(1301,plain,
    ! [SV40: $i,SV484: $i] :
      ( ( ~ ( in @ SV484 @ SV40 )
        | ! [SY2877: $i] :
            ( ~ ( in @ SY2877 @ SV40 )
            | ~ ~ $true
            | ( in @ SY2877
              @ ( dsetconstr @ SV40
                @ ^ [SY2878: $i] :
                    ( ~ ( ~ $true
                        | ( SY2878 != SV484 ) )
                    | ~ ( ~ ~ $true
                        | ( SY2878 != SY2877 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1049]) ).

thf(1302,plain,
    ! [SV40: $i,SV485: $i] :
      ( ( ~ ( in @ SV485 @ SV40 )
        | ! [SY2879: $i] :
            ( ~ ( in @ SY2879 @ SV40 )
            | ~ ~ $false
            | ( in @ SY2879
              @ ( dsetconstr @ SV40
                @ ^ [SY2880: $i] :
                    ( ~ ( ~ $false
                        | ( SY2880 != SV485 ) )
                    | ~ ( ~ ~ $false
                        | ( SY2880 != SY2879 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1050]) ).

thf(1303,plain,
    ! [SV41: $i > $o] :
      ( ( ( ~ ! [SY1907: $i] :
                ~ ~ ( ~ ( SV41 @ SY1907 )
                    | ~ ! [SY1908: $i] :
                          ( ~ ( SV41 @ SY1908 )
                          | ( SY1907 = SY1908 ) ) ) )
        = $false )
      | ( ( ! [SY1909: $i,SY1910: $i] :
              ( ~ ( SV41 @ SY1909 )
              | ~ ( SV41 @ SY1910 )
              | ( SY1909 = SY1910 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1051]) ).

thf(1304,plain,
    ! [SV42: $i,SV285: $i] :
      ( ( ~ ( ~ ( in @ SV285 @ ( powerset @ SV42 ) )
            | ! [SY2523: $i] :
                ( ~ ( in @ SY2523 @ SV285 )
                | ( in @ SY2523 @ SV42 ) ) )
        | ~ ( ~ ! [SY2524: $i] :
                  ( ~ ( in @ SY2524 @ SV285 )
                  | ( in @ SY2524 @ SV42 ) )
            | ( in @ SV285 @ ( powerset @ SV42 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1052]) ).

thf(1305,plain,
    ! [SV43: $i > $o] :
      ( ( ( ~ ! [SY1914: $i] :
                ~ ~ ( ~ ( SV43 @ SY1914 )
                    | ~ ! [SY1915: $i] :
                          ( ~ ( SV43 @ SY1915 )
                          | ( SY1914 = SY1915 ) ) ) )
        = $false )
      | ( ( ! [SY1916: $i,SY1917: $i] :
              ( ~ ( SV43 @ SY1916 )
              | ~ ( SV43 @ SY1917 )
              | ( SY1916 = SY1917 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1053]) ).

thf(1306,plain,
    ! [SV44: $i,SV286: $i] :
      ( ( ( ~ ( in @ SV286 @ ( powerset @ SV44 ) ) )
        = $true )
      | ( ( ! [SY2525: $i] :
              ( ~ ( in @ SY2525 @ ( powerset @ SV44 ) )
              | ! [SY2526: $i] :
                  ( ~ ( in @ SY2526 @ SV44 )
                  | ~ ( in @ SY2526 @ ( setminus @ SV44 @ ( binunion @ SV286 @ SY2525 ) ) )
                  | ~ ( in @ SY2526 @ SV286 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1054]) ).

thf(1307,plain,
    ! [SV45: $o] :
      ( ( SV45 = $false )
      | ( ( in @ emptyset @ ( prop2set @ SV45 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1055]) ).

thf(1308,plain,
    ( ( $true = $false )
    | ( ( in @ emptyset @ ( prop2set @ $true ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1056]) ).

thf(1309,plain,
    ( ( $false = $false )
    | ( ( in @ emptyset @ ( prop2set @ $false ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1057]) ).

thf(1310,plain,
    ! [SV287: $i > $o,SV46: $i] :
      ( ( ( ~ ~ ! [SY2527: $i] :
                  ~ ~ ( ~ ( in @ SY2527 @ SV46 )
                      | ~ ~ ( SV287 @ SY2527 ) ) )
        = $true )
      | ( ( ~ ! [SY2528: $i] :
                ( ~ ( in @ SY2528 @ SV46 )
                | ( SV287 @ SY2528 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1058]) ).

thf(1311,plain,
    ! [SV288: $i,SV47: $i,SV486: $i] :
      ( ( ~ ~ ( in @ SV486 @ ( setminus @ SV47 @ SV288 ) )
        | ~ ( in @ SV486 @ SV47 )
        | ( in @ SV486 @ SV288 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1059]) ).

thf(1312,plain,
    ! [SV48: $i > $o] :
      ( ( ( ~ ! [SY1926: $i] :
                ~ ~ ( ~ ( SV48 @ SY1926 )
                    | ~ ! [SY1927: $i] :
                          ( ~ ( SV48 @ SY1927 )
                          | ( SY1926 = SY1927 ) ) ) )
        = $false )
      | ( ( ~ ! [SY1928: $i] :
                ~ ~ ( ~ ( SV48 @ SY1928 )
                    | ~ ! [SY1929: $i] :
                          ( ~ ( SV48 @ SY1929 )
                          | ( SY1928 = SY1929 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1060]) ).

thf(1313,plain,
    ! [SV289: $i,SV49: $i,SV487: $i] :
      ( ( ~ ( in @ SV487 @ SV49 )
        | ~ ~ ( in @ SV487 @ SV289 )
        | ( in @ SV487 @ ( setminus @ SV49 @ SV289 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1061]) ).

thf(1314,plain,
    ! [SV290: $i,SV50: $i,SV488: $i] :
      ( ( ~ ( in @ SV488 @ SV50 )
        | ! [SY2881: $i] :
            ( ~ ( in @ SY2881 @ SV290 )
            | ( in @ ( setadjoin @ ( setadjoin @ SV488 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV488 @ ( setadjoin @ SY2881 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV50 @ SV290 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1062]) ).

thf(1315,plain,
    ! [SV291: $i,SV51: $i] :
      ( ( ( ~ ! [SY2533: $i] :
                ~ ( ~ ( ~ ( in @ SY2533 @ SV51 )
                      | ( in @ SY2533 @ SV291 ) )
                  | ~ ( ~ ( in @ SY2533 @ SV291 )
                      | ( in @ SY2533 @ SV51 ) ) ) )
        = $true )
      | ( ( SV51 = SV291 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1063]) ).

thf(1316,plain,
    ! [SV292: $i > $o,SV52: $i] :
      ( ( ( ~ ~ ~ ! [SY2534: $i] :
                    ~ ~ ( ~ ( in @ SY2534 @ SV52 )
                        | ~ ( SV292 @ SY2534 ) ) )
        = $true )
      | ( ( ! [SY2535: $i] :
              ( ~ ( in @ SY2535 @ SV52 )
              | ~ ( SV292 @ SY2535 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1064]) ).

thf(1317,plain,
    ! [SV293: $i,SV53: $i] :
      ( ( ( SV53 != SV293 )
        = $true )
      | ( ( subset @ SV53 @ SV293 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1065]) ).

thf(1318,plain,
    ! [SV54: $i,SV294: $i] :
      ( ( ( ~ ( in @ SV294 @ ( powerset @ SV54 ) ) )
        = $true )
      | ( ( in @ ( powerset @ SV294 ) @ ( powerset @ ( powerset @ SV54 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1066]) ).

thf(1319,plain,
    ! [SV295: $i,SV55: $i,SV489: $i] :
      ( ( ~ ~ ( in @ SV489 @ SV55 )
        | ~ ~ ( in @ SV489 @ SV295 )
        | ~ ( in @ SV489 @ ( symdiff @ SV55 @ SV295 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1067]) ).

thf(1320,plain,
    ! [SV490: $i > $i > $o,SV296: $i,SV56: $i] :
      ( ( ! [SY2882: $i,SY2883: $i] :
            ( ~ ( in @ ( kpair @ SY2882 @ SY2883 )
                @ ( dpsetconstr @ SV56 @ SV296
                  @ ^ [SY2884: $i,SY2885: $i] : ( SV490 @ SY2884 @ SY2885 ) ) )
            | ( in @ SY2883 @ SV296 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1068]) ).

thf(1321,plain,
    ! [SV57: $i] :
      ( ( ( subset @ SV57 @ emptyset )
        = $false )
      | ( ( SV57 = emptyset )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1069]) ).

thf(1322,plain,
    ! [SV297: $i,SV58: $i,SV491: $i] :
      ( ( ~ ( in @ ( setadjoin @ SV491 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV58 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV58 @ ( setadjoin @ SV297 @ emptyset ) ) @ emptyset ) ) )
        | ( SV58 = SV491 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1070]) ).

thf(1323,plain,
    ! [SV492: $i,SV298: $i,SV59: $i] :
      ( ( ! [SY2886: $i] :
            ( ( ( setadjoin @ ( setadjoin @ SV59 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV59 @ ( setadjoin @ SV298 @ emptyset ) ) @ emptyset ) )
             != ( setadjoin @ ( setadjoin @ SV492 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV492 @ ( setadjoin @ SY2886 @ emptyset ) ) @ emptyset ) ) )
            | ( SV298 = SY2886 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1071]) ).

thf(1324,plain,
    ! [SV299: $i,SV60: $i,SV493: $i] :
      ( ( ~ ( in @ SV493 @ SV60 )
        | ~ ( in @ SV493 @ SV299 )
        | ~ ( in @ SV493 @ ( symdiff @ SV60 @ SV299 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1072]) ).

thf(1325,plain,
    ! [SV300: $i,SV61: $i,SV494: $i] :
      ( ( ! [SY2887: $i] :
            ( ~ ( in @ ( kpair @ SV494 @ SY2887 ) @ ( cartprod @ SV61 @ SV300 ) )
            | ( in @ SV494 @ SV61 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1073]) ).

thf(1326,plain,
    ! [SV301: $i,SV62: $i,SV495: $i] :
      ( ( ~ ( in @ SV495 @ SV62 )
        | ! [SY2888: $i] :
            ( ~ ( in @ SY2888 @ SV301 )
            | ( ( kpair @ SV495 @ SY2888 )
              = ( kpair @ SV495 @ SY2888 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1074]) ).

thf(1327,plain,
    ! [SV302: $i,SV63: $i,SV496: $i] :
      ( ( ~ ( subset @ SV496 @ ( cartprod @ SV63 @ SV302 ) )
        | ! [SY2889: $i > $o] :
            ( ~ ! [SY2890: $i] :
                  ( ~ ( in @ SY2890 @ SV63 )
                  | ! [SY2891: $i] :
                      ( ~ ( in @ SY2891 @ SV302 )
                      | ~ ( in @ ( kpair @ SY2890 @ SY2891 ) @ SV496 )
                      | ( SY2889 @ ( kpair @ SY2890 @ SY2891 ) ) ) )
            | ! [SY2892: $i] :
                ( ~ ( in @ SY2892 @ SV496 )
                | ( SY2889 @ SY2892 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1075]) ).

thf(1328,plain,
    ! [SV64: $i] :
      ( ( ( singleton @ SV64 )
        = $false )
      | ( ( in @ ( setunion @ SV64 ) @ SV64 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1076]) ).

thf(1329,plain,
    ! [SV303: $i > $o,SV65: $i,SV497: $i] :
      ( ( ~ ( in @ SV497 @ SV65 )
        | ~ ( SV303 @ SV497 )
        | ( ( dsetconstr @ SV65
            @ ^ [SY2556: $i] : ( SV303 @ SY2556 ) )
         != emptyset ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1077]) ).

thf(1330,plain,
    ! [SV304: $i,SV66: $i] :
      ( ( ( SV66 != SV304 )
        = $true )
      | ( ( ( setadjoin @ ( setadjoin @ SV66 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV66 @ ( setadjoin @ SV304 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ SV66 @ emptyset ) @ emptyset ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1078]) ).

thf(1331,plain,
    ! [SV305: $o,SV67: $i,SV498: $i] :
      ( ( ~ ( in @ SV498 @ SV67 )
        | ! [SY2894: $i] :
            ( ~ ( in @ SY2894 @ SV67 )
            | ~ SV305
            | ( in @ SV498
              @ ( dsetconstr @ SV67
                @ ^ [SY2895: $i] :
                    ( ~ ( ~ SV305
                        | ( SY2895 != SV498 ) )
                    | ~ ( ~ ~ SV305
                        | ( SY2895 != SY2894 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1079]) ).

thf(1332,plain,
    ! [SV67: $i,SV499: $i] :
      ( ( ~ ( in @ SV499 @ SV67 )
        | ! [SY2896: $i] :
            ( ~ ( in @ SY2896 @ SV67 )
            | ~ $true
            | ( in @ SV499
              @ ( dsetconstr @ SV67
                @ ^ [SY2897: $i] :
                    ( ~ ( ~ $true
                        | ( SY2897 != SV499 ) )
                    | ~ ( ~ ~ $true
                        | ( SY2897 != SY2896 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1080]) ).

thf(1333,plain,
    ! [SV67: $i,SV500: $i] :
      ( ( ~ ( in @ SV500 @ SV67 )
        | ! [SY2898: $i] :
            ( ~ ( in @ SY2898 @ SV67 )
            | ~ $false
            | ( in @ SV500
              @ ( dsetconstr @ SV67
                @ ^ [SY2899: $i] :
                    ( ~ ( ~ $false
                        | ( SY2899 != SV500 ) )
                    | ~ ( ~ ~ $false
                        | ( SY2899 != SY2898 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1081]) ).

thf(1334,plain,
    ! [SV501: $i,SV306: $i,SV68: $i] :
      ( ( ~ ( func @ SV68 @ SV306 @ SV501 )
        | ! [SY2900: $i] :
            ( ~ ( in @ SY2900 @ SV68 )
            | ( in
              @ ( setunion
                @ ( dsetconstr @ SV306
                  @ ^ [SY2901: $i] : ( in @ ( kpair @ SY2900 @ SY2901 ) @ SV501 ) ) )
              @ SV306 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1082]) ).

thf(1335,plain,
    ! [SV69: $i,SV307: $i] :
      ( ( ( ~ ( subset @ SV307 @ SV69 ) )
        = $true )
      | ( ( ( binintersect @ SV69 @ SV307 )
          = SV307 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1083]) ).

thf(1336,plain,
    ! [SV70: $i,SV308: $i] :
      ( ( ( ~ ( in @ SV308 @ ( powerset @ SV70 ) ) )
        = $true )
      | ( ( subset @ ( setminus @ SV70 @ ( setminus @ SV70 @ SV308 ) ) @ SV308 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1084]) ).

thf(1337,plain,
    ! [SV309: $i,SV71: $i] :
      ( ( ( ~ ( subset @ SV71 @ SV309 ) )
        = $true )
      | ( ( ( binintersect @ SV71 @ SV309 )
          = SV71 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1085]) ).

thf(1338,plain,
    ! [SV72: $i,SV310: $i] :
      ( ( ( ~ ( in @ SV310 @ ( powerset @ SV72 ) ) )
        = $true )
      | ( ( ! [SY2563: $i] :
              ( ~ ( in @ SY2563 @ ( powerset @ SV72 ) )
              | ~ ( subset @ SV310 @ ( setminus @ SV72 @ SY2563 ) )
              | ( subset @ SY2563 @ ( setminus @ SV72 @ SV310 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1086]) ).

thf(1339,plain,
    ! [SV311: $i,SV73: $i,SV502: $i] :
      ( ( ~ ( in @ SV502 @ ( funcSet @ SV73 @ SV311 ) )
        | ! [SY2902: $i] :
            ( ~ ( in @ SY2902 @ ( funcSet @ SV73 @ SV311 ) )
            | ~ ! [SY2903: $i] :
                  ( ~ ( in @ SY2903 @ SV73 )
                  | ( ( ap @ SV73 @ SV311 @ SV502 @ SY2903 )
                    = ( ap @ SV73 @ SV311 @ SY2902 @ SY2903 ) ) )
            | ( SV502 = SY2902 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1087]) ).

thf(1340,plain,
    ! [SV312: $i,SV74: $i,SV503: $i] :
      ( ( ~ ~ ( in @ SV503 @ ( setminus @ SV74 @ SV312 ) )
        | ~ ~ ( in @ SV503 @ SV312 )
        | ~ ( in @ SV503 @ SV74 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1088]) ).

thf(1341,plain,
    ! [SV313: $i,SV75: $i,SV504: $i] :
      ( ( ~ ( ~ ( ~ ( in @ SV504 @ ( setadjoin @ SV75 @ SV313 ) )
                | ( SV504 = SV75 )
                | ( in @ SV504 @ SV313 ) )
            | ~ ( ~ ( ( SV504 = SV75 )
                    | ( in @ SV504 @ SV313 ) )
                | ( in @ SV504 @ ( setadjoin @ SV75 @ SV313 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1089]) ).

thf(1342,plain,
    ! [SV76: $i,SV314: $i] :
      ( ( ( ~ ( in @ SV314 @ ( powerset @ SV76 ) ) )
        = $true )
      | ( ( ! [SY2569: $i] :
              ( ~ ( in @ SY2569 @ ( powerset @ SV76 ) )
              | ! [SY2570: $i] :
                  ( ~ ( in @ SY2570 @ ( powerset @ SV76 ) )
                  | ! [SY2571: $i] :
                      ( ~ ( in @ SY2571 @ SV76 )
                      | ~ ( in @ SY2571 @ ( binintersect @ SV314 @ SY2569 ) )
                      | ( in @ SY2571 @ ( binintersect @ ( binunion @ SV314 @ SY2570 ) @ ( binunion @ SY2569 @ SY2570 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1090]) ).

thf(1343,plain,
    ! [SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ~ ! [SY2572: $i,SY2573: $i] :
                ( ( SY2572 != SY2573 )
                | ~ ( ~ ( ~ ( SV77 @ SY2572 )
                        | ( SV315 @ SY2573 ) )
                    | ~ ( ~ ( SV315 @ SY2573 )
                        | ( SV77 @ SY2572 ) ) ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2001: $i] :
                  ~ ~ ( ~ ( SV77 @ SY2001 )
                      | ~ ! [SY2002: $i] :
                            ( ~ ( SV77 @ SY2002 )
                            | ( SY2001 = SY2002 ) ) )
          | ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1091]) ).

thf(1344,plain,
    ! [SV316: $i > $o,SV78: $i,SV505: $i] :
      ( ( ~ ( in @ SV505 @ SV78 )
        | ~ ( SV316 @ SV505 )
        | ( in @ SV505
          @ ( dsetconstr @ SV78
            @ ^ [SY2581: $i] : ( SV316 @ SY2581 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1092]) ).

thf(1345,plain,
    ! [SV79: $i,SV317: $i] :
      ( ( ( ~ ( subset @ SV317 @ SV79 ) )
        = $true )
      | ( ( in @ SV317 @ ( powerset @ SV79 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1093]) ).

thf(1346,plain,
    ! [SV80: $i,SV318: $i] :
      ( ( ( ~ ( in @ SV318 @ ( powerset @ SV80 ) ) )
        = $true )
      | ( ( ! [SY2582: $i] :
              ( ~ ( in @ SY2582 @ ( powerset @ SV80 ) )
              | ~ ! [SY2583: $i] :
                    ( ~ ( in @ SY2583 @ SV80 )
                    | ~ ( in @ SY2583 @ SV318 )
                    | ( in @ SY2583 @ SY2582 ) )
              | ~ ! [SY2584: $i] :
                    ( ~ ( in @ SY2584 @ SV80 )
                    | ~ ( in @ SY2584 @ SY2582 )
                    | ( in @ SY2584 @ SV318 ) )
              | ( SV318 = SY2582 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1094]) ).

thf(1347,plain,
    ! [SV319: $i,SV81: $i] :
      ( ( ( ~ ! [SY2585: $i] :
                ( ~ ( in @ SY2585 @ SV81 )
                | ( in @ SY2585 @ SV319 ) ) )
        = $true )
      | ( ( ~ ! [SY2586: $i] :
                ( ~ ( in @ SY2586 @ SV319 )
                | ( in @ SY2586 @ SV81 ) )
          | ( SV81 = SV319 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1095]) ).

thf(1348,plain,
    ! [SV506: $i > $i > $o,SV320: $i,SV82: $i] :
      ( ( ! [SY2905: $i] :
            ( ~ ( in @ SY2905 @ SV82 )
            | ! [SY2906: $i] :
                ( ~ ( in @ SY2906 @ SV320 )
                | ~ ( in @ ( kpair @ SY2905 @ SY2906 )
                    @ ( dpsetconstr @ SV82 @ SV320
                      @ ^ [SY2907: $i,SY2908: $i] : ( SV506 @ SY2907 @ SY2908 ) ) )
                | ( SV506 @ SY2905 @ SY2906 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1096]) ).

thf(1349,plain,
    ! [SV83: $i] :
      ( ( ( ! [SY2024: $i] :
              ~ ( in @ SY2024 @ SV83 ) )
        = $false )
      | ( ( SV83 = emptyset )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1097]) ).

thf(1350,plain,
    ! [SV321: $i > $o,SV84: $i] :
      ( ( ( ~ ~ ! [SY2592: $i] :
                  ( ~ ( in @ SY2592 @ SV84 )
                  | ( SV321 @ SY2592 ) ) )
        = $true )
      | ( ( ~ ! [SY2593: $i] :
                ~ ~ ( ~ ( in @ SY2593 @ SV84 )
                    | ~ ~ ( SV321 @ SY2593 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1098]) ).

thf(1351,plain,
    ! [SV322: $i,SV85: $i,SV507: $i] :
      ( ( ! [SY2909: $o] :
            ( ~ ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
            | ~ ( ~ ( in @ SV507 @ SV85 )
                | SY2909 )
            | ~ ( ~ ( in @ SV507 @ SV322 )
                | SY2909 )
            | SY2909 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1099]) ).

thf(1352,plain,
    ! [SV86: $i,SV508: $i,SV323: $i] :
      ( ( ~ ( in @ SV323 @ SV508 )
        | ~ ( in @ SV508 @ SV86 )
        | ( in @ SV323 @ ( setunion @ SV86 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1100]) ).

thf(1353,plain,
    ! [SV87: $i] :
      ( ( ( ~ ( ~ ( in @ emptyset @ SV87 )
              | ~ ! [SY2033: $i] :
                    ( ~ ~ ( ~ ( in @ SY2033 @ omega )
                          | ~ ( in @ SY2033 @ SV87 ) )
                    | ( in @ ( setadjoin @ SY2033 @ SY2033 ) @ SV87 ) ) ) )
        = $false )
      | ( ( ! [SY2034: $i] :
              ( ~ ( in @ SY2034 @ omega )
              | ( in @ SY2034 @ SV87 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1101]) ).

thf(1354,plain,
    ( ( ~ ( in @ sK2_SY2597 @ ( powerset @ sK1_SX0 ) )
      | ! [SY2910: $i] :
          ( ~ ( in @ SY2910 @ ( powerset @ sK1_SX0 ) )
          | ! [SY2911: $i] :
              ( ~ ( in @ SY2911 @ sK1_SX0 )
              | ~ ( in @ SY2911 @ ( setminus @ sK1_SX0 @ ( binunion @ sK2_SY2597 @ SY2910 ) ) )
              | ( in @ SY2911 @ ( setminus @ sK1_SX0 @ sK2_SY2597 ) ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[1102]) ).

thf(1355,plain,
    ! [SV88: $i,SV324: $i] :
      ( ( ( ~ ( in @ SV324 @ ( powerset @ SV88 ) ) )
        = $true )
      | ( ( ! [SY2600: $i] :
              ( ~ ( in @ SY2600 @ ( powerset @ SV88 ) )
              | ~ ( subset @ SV324 @ ( setminus @ SV88 @ SY2600 ) )
              | ! [SY2601: $i] :
                  ( ~ ( in @ SY2601 @ SV88 )
                  | ~ ( in @ SY2601 @ SY2600 )
                  | ( in @ SY2601 @ ( setminus @ SV88 @ SV324 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1103]) ).

thf(1356,plain,
    ! [SV325: $i > $o,SV89: $i] :
      ( ( ( ~ ~ ! [SY2602: $i] :
                  ~ ~ ( ~ ( in @ SY2602 @ SV89 )
                      | ~ ( SV325 @ SY2602 ) ) )
        = $true )
      | ( ( ( ( dsetconstr @ SV89
              @ ^ [SY2603: $i] : ( SV325 @ SY2603 ) )
           != emptyset )
          | $false )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1104]) ).

thf(1357,plain,
    ! [SV326: $i,SV90: $i] :
      ( ( ( ~ ! [SY2604: $i] :
                ( ~ ( in @ SY2604 @ SV90 )
                | ( in @ SY2604 @ SV326 ) ) )
        = $true )
      | ( ( subset @ SV90 @ SV326 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1105]) ).

thf(1358,plain,
    ! [SV91: $i,SV327: $i] :
      ( ( ( ~ ( in @ SV327 @ ( powerset @ SV91 ) ) )
        = $true )
      | ( ( ! [SY2605: $i] :
              ( ~ ( in @ SY2605 @ ( powerset @ SV91 ) )
              | ( in @ ( binintersect @ SV327 @ SY2605 ) @ ( powerset @ SV91 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1106]) ).

thf(1359,plain,
    ! [SV328: $i,SV92: $i] :
      ( ( ( SV92 != SV328 )
        = $true )
      | ( ( ! [SY2606: $i,SY2607: $i] :
              ( ( SY2606 != SY2607 )
              | ~ ( in @ SY2606 @ SV92 )
              | ( in @ SY2607 @ SV328 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1107]) ).

thf(1360,plain,
    ! [SV509: $i > $i > $o,SV329: $i,SV93: $i] :
      ( ( ! [SY2912: $i,SY2913: $i] :
            ( ~ ( in @ ( kpair @ SY2912 @ SY2913 )
                @ ( dpsetconstr @ SV93 @ SV329
                  @ ^ [SY2914: $i,SY2915: $i] : ( SV509 @ SY2914 @ SY2915 ) ) )
            | ( SV509 @ SY2912 @ SY2913 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1108]) ).

thf(1361,plain,
    ! [SV510: $i,SV330: $i,SV94: $i] :
      ( ( ! [SY2916: $i] :
            ( ( ( kpair @ SV94 @ SV330 )
             != ( kpair @ SV510 @ SY2916 ) )
            | ( SV94 = SV510 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1109]) ).

thf(1362,plain,
    ! [SV511: $i,SV331: $i,SV95: $i] :
      ( ( ~ ( subset @ SV95 @ SV331 )
        | ~ ( in @ SV511 @ SV95 )
        | ( in @ SV511 @ SV331 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1110]) ).

thf(1363,plain,
    ! [SV512: $i,SV332: $i,SV96: $i] :
      ( ( ~ ( func @ SV96 @ SV332 @ SV512 )
        | ! [SY2917: $i] :
            ( ~ ( func @ SV96 @ SV332 @ SY2917 )
            | ~ ! [SY2918: $i] :
                  ( ~ ( in @ SY2918 @ SV96 )
                  | ( ( ap @ SV96 @ SV332 @ SV512 @ SY2918 )
                    = ( ap @ SV96 @ SV332 @ SY2917 @ SY2918 ) ) )
            | ! [SY2919: $i] :
                ( ~ ( in @ SY2919 @ SV96 )
                | ! [SY2920: $i] :
                    ( ~ ( in @ SY2920 @ SV332 )
                    | ~ ( in @ ( kpair @ SY2919 @ SY2920 ) @ SY2917 )
                    | ( in @ ( kpair @ SY2919 @ SY2920 ) @ SV512 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1111]) ).

thf(1364,plain,
    ! [SV97: $i] :
      ( ( ( iskpair @ SV97 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ ( setunion @ SV97 )
            @ ^ [SY2065: $i] : ( in @ ( setadjoin @ SY2065 @ emptyset ) @ SV97 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1112]) ).

thf(1365,plain,
    ! [SV333: $i,SV98: $i,SV513: $i] :
      ( ( ~ ( in @ SV513 @ ( cartprod @ SV98 @ SV333 ) )
        | ~ ! [SY2921: $i] :
              ~ ~ ( ~ ( in @ SY2921 @ SV98 )
                  | ~ ~ ! [SY2922: $i] :
                          ~ ~ ( ~ ( in @ SY2922 @ SV333 )
                              | ( SV513
                               != ( kpair @ SY2921 @ SY2922 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1113]) ).

thf(1366,plain,
    ! [SV99: $i,SV334: $i] :
      ( ( ( ~ ( in @ SV334 @ ( powerset @ SV99 ) ) )
        = $true )
      | ( ( ! [SY2624: $i] :
              ( ~ ( in @ SY2624 @ ( powerset @ SV99 ) )
              | ! [SY2625: $i] :
                  ( ~ ( in @ SY2625 @ SV99 )
                  | ~ ( in @ SV334 @ ( powerset @ SY2624 ) )
                  | ~ ( in @ SY2625 @ SV334 )
                  | ( in @ SY2625 @ SY2624 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1114]) ).

thf(1367,plain,
    ! [SV100: $i] :
      ( ( ( ! [SY2073: $i] :
              ~ ( in @ SY2073 @ SV100 ) )
        = $false )
      | ( ( SV100 = emptyset )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1115]) ).

thf(1368,plain,
    ! [SV335: $i,SV101: $i,SV514: $i] :
      ( ( ~ ( in @ SV514 @ ( setadjoin @ SV101 @ SV335 ) )
        | ( SV514 = SV101 )
        | ( in @ SV514 @ SV335 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1116]) ).

thf(1369,plain,
    ! [SV336: $i > $o,SV102: $i] :
      ( ( ( ~ ! [SY2627: $i] :
                ( ~ ( in @ SY2627 @ SV102 )
                | ! [SY2628: $i] :
                    ( ~ ( in @ SY2628 @ SV102 )
                    | ~ ( SV336 @ SY2627 )
                    | ~ ( SV336 @ SY2628 )
                    | ( SY2627 = SY2628 ) ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2629: $i] :
                  ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                      | ~ ( SV336 @ SY2629 ) )
          | ( singleton
            @ ( dsetconstr @ SV102
              @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1117]) ).

thf(1370,plain,
    ! [SV515: $i > $i > $o,SV337: $i,SV103: $i] :
      ( ( ! [SY2923: $i,SY2924: $i] :
            ( ~ ( in @ ( kpair @ SY2923 @ SY2924 )
                @ ( dpsetconstr @ SV103 @ SV337
                  @ ^ [SY2925: $i,SY2926: $i] : ( SV515 @ SY2925 @ SY2926 ) ) )
            | ( in @ SY2923 @ SV103 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1118]) ).

thf(1371,plain,
    ! [SV338: $i,SV104: $i] :
      ( ( ( ~ ( ( SV104 != SV338 ) ) )
        = $true )
      | ( ( ~ ( in @ SV338 @ ( setadjoin @ SV104 @ emptyset ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1119]) ).

thf(1372,plain,
    ! [SV339: $i,SV516: $i > $i,SV105: $i] :
      ( ( ~ ! [SY2927: $i] :
              ( ~ ( in @ SY2927 @ SV105 )
              | ( in @ ( SV516 @ SY2927 ) @ SV339 ) )
        | ( ( lam @ SV105 @ SV339
            @ ^ [SY2928: $i] : ( SV516 @ SY2928 ) )
          = ( lam @ SV105 @ SV339
            @ ^ [SY2929: $i] : ( SV516 @ SY2929 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1120]) ).

thf(1373,plain,
    ! [SV340: $i,SV106: $i,SV517: $i] :
      ( ( ~ ( in @ SV517 @ SV106 )
        | ( in @ ( setadjoin @ SV517 @ emptyset ) @ ( powerset @ ( binunion @ SV106 @ SV340 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1121]) ).

thf(1374,plain,
    ! [SV341: $i,SV518: $i > $i,SV107: $i] :
      ( ( ~ ! [SY2930: $i] :
              ( ~ ( in @ SY2930 @ SV107 )
              | ( in @ ( SV518 @ SY2930 ) @ SV341 ) )
        | ( in
          @ ( lam @ SV107 @ SV341
            @ ^ [SY2931: $i] : ( SV518 @ SY2931 ) )
          @ ( funcSet @ SV107 @ SV341 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1122]) ).

thf(1375,plain,
    ! [SV342: $i,SV108: $i] :
      ( ( ( SV108 != SV342 )
        = $true )
      | ( ( ( setunion @ SV108 )
          = ( setunion @ SV342 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1123]) ).

thf(1376,plain,
    ! [SV109: $i] :
      ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY2932: $i] :
                                ( ~ ( in @ SY2932 @ ( sK3_SY2100 @ SV109 ) )
                                | ! [SY2102: $i] :
                                    ( ~ ( in @ SY2102 @ SY2932 )
                                    | ( in @ SY2102 @ SV109 ) ) )
                          | ~ ! [SY2934: $i,SY2935: $i] :
                                ( ~ ~ ( ~ ( in @ SY2934 @ SV109 )
                                      | ~ ( in @ SY2935 @ SV109 ) )
                                | ~ ! [SY2936: $i] :
                                      ( ~ ( in @ SY2936 @ ( sK3_SY2100 @ SV109 ) )
                                      | ~ ( ~ ( ~ ( in @ SY2934 @ SY2936 )
                                              | ( in @ SY2935 @ SY2936 ) )
                                          | ~ ( ~ ( in @ SY2935 @ SY2936 )
                                              | ( in @ SY2934 @ SY2936 ) ) ) )
                                | ( SY2934 = SY2935 ) ) )
                    | ~ ! [SY2937: $i,SY2938: $i] :
                          ( ~ ~ ( ~ ( in @ SY2937 @ ( sK3_SY2100 @ SV109 ) )
                                | ~ ( in @ SY2938 @ ( sK3_SY2100 @ SV109 ) ) )
                          | ! [SX4: $i] :
                              ( ~ ( in @ SX4 @ SY2937 )
                              | ( in @ SX4 @ SY2938 ) )
                          | ! [SX4: $i] :
                              ( ~ ( in @ SX4 @ SY2938 )
                              | ( in @ SX4 @ SY2937 ) ) ) )
              | ~ ! [SY2941: $i] :
                    ( ~ ~ ( ~ ! [SY2111: $i] :
                                ( ~ ( in @ SY2111 @ SY2941 )
                                | ( in @ SY2111 @ SV109 ) )
                          | ~ ~ ! [SX3: $i] :
                                  ~ ( in @ SX3 @ SY2941 ) )
                    | ~ ! [SY2944: $i] :
                          ~ ~ ! [SY2945: $i] :
                                ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY2944 @ ( sK3_SY2100 @ SV109 ) )
                                                | ~ ( in @ SY2945 @ SY2941 ) )
                                          | ~ ~ ~ ! [SX5: $i] :
                                                    ~ ~ ( ~ ( in @ SX5 @ SY2944 )
                                                        | ~ ( in @ SX5 @ SY2941 ) ) )
                                    | ~ ! [SY2947: $i] :
                                          ( ~ ( in @ SY2947 @ ( sK3_SY2100 @ SV109 ) )
                                          | ! [SX6: $i] :
                                              ( ~ ( in @ SX6 @ SY2947 )
                                              | ( in @ SX6 @ SY2944 ) )
                                          | ( in @ SY2945 @ SY2947 ) ) ) ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[1124]) ).

thf(1377,plain,
    ! [SV110: $i] :
      ( ( ( ~ ! [SY2118: $i] :
                ~ ( in @ SY2118 @ SV110 ) )
        = $false )
      | ( ( ~ ! [SY2119: $i] :
                ~ ~ ( ~ ( in @ SY2119 @ SV110 )
                    | ~ ~ ~ ! [SY2120: $i] :
                              ~ ~ ( ~ ( in @ SY2120 @ SY2119 )
                                  | ~ ( in @ SY2120 @ SV110 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1125]) ).

thf(1378,plain,
    ! [SV343: $i,SV111: $i,SV519: $i] :
      ( ( ~ ( in @ SV519 @ ( binintersect @ SV111 @ SV343 ) )
        | ( in @ SV519 @ SV111 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1126]) ).

thf(1379,plain,
    ! [SV112: $i > $o] :
      ( ( ( ~ ! [SY2123: $i] :
                ~ ~ ( ~ ( SV112 @ SY2123 )
                    | ~ ! [SY2124: $i] :
                          ( ~ ( SV112 @ SY2124 )
                          | ( SY2123 = SY2124 ) ) ) )
        = $false )
      | ( ( ~ ! [SY2125: $i] :
                ~ ( SV112 @ SY2125 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1127]) ).

thf(1380,plain,
    ! [SV344: $i,SV113: $i] :
      ( ( ( ~ ~ ~ ! [SY2645: $i] :
                    ~ ~ ( ~ ( in @ SY2645 @ SV113 )
                        | ~ ( in @ SY2645 @ SV344 ) ) )
        = $true )
      | ( ( ( binintersect @ SV113 @ SV344 )
          = emptyset )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1128]) ).

thf(1381,plain,
    ! [SV345: $i,SV114: $i] :
      ( ( ( ~ ( subset @ SV114 @ SV345 ) )
        = $true )
      | ( ( ( setminus @ SV114 @ SV345 )
          = emptyset )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1129]) ).

thf(1382,plain,
    ! [SV115: $i] :
      ( ( ( in @ SV115 @ emptyset )
        = $false )
      | ( $false = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1130]) ).

thf(1383,plain,
    ! [SV116: $i,SV346: $i] :
      ( ( ( ~ ( in @ SV346 @ ( powerset @ SV116 ) ) )
        = $true )
      | ( ( ! [SY2646: $i] :
              ( ~ ( in @ SY2646 @ ( powerset @ SV116 ) )
              | ! [SY2647: $i] :
                  ( ~ ( in @ SY2647 @ SV116 )
                  | ~ ~ ( in @ SY2647 @ ( binunion @ SV346 @ SY2646 ) )
                  | ~ ( in @ SY2647 @ SV346 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1131]) ).

thf(1384,plain,
    ! [SV117: $i] :
      ( ( ( iskpair @ SV117 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ ( setunion @ SV117 )
            @ ^ [SY2132: $i] :
                ( SV117
                = ( kpair @ ( kfst @ SV117 ) @ SY2132 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1132]) ).

thf(1385,plain,
    ! [SV347: $o,SV118: $i,SV520: $i] :
      ( ( ~ ( in @ SV520 @ SV118 )
        | ! [SY2949: $i] :
            ( ~ ( in @ SY2949 @ SV118 )
            | ~ ~ SV347
            | ( ( if @ SV118 @ SV347 @ SV520 @ SY2949 )
              = SY2949 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1133]) ).

thf(1386,plain,
    ! [SV118: $i,SV521: $i] :
      ( ( ~ ( in @ SV521 @ SV118 )
        | ! [SY2950: $i] :
            ( ~ ( in @ SY2950 @ SV118 )
            | ~ ~ $true
            | ( ( if @ SV118 @ $true @ SV521 @ SY2950 )
              = SY2950 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1134]) ).

thf(1387,plain,
    ! [SV118: $i,SV522: $i] :
      ( ( ~ ( in @ SV522 @ SV118 )
        | ! [SY2951: $i] :
            ( ~ ( in @ SY2951 @ SV118 )
            | ~ ~ $false
            | ( ( if @ SV118 @ $false @ SV522 @ SY2951 )
              = SY2951 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1135]) ).

thf(1388,plain,
    ! [SV119: $i > $o,SV348: $i] :
      ( ( ( ~ ( in @ SV348 @ emptyset ) )
        = $true )
      | ( ( SV119 @ SV348 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1136]) ).

thf(1389,plain,
    ! [SV120: $o] :
      ( ( SV120 = $false )
      | ( ( set2prop @ ( prop2set @ SV120 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1137]) ).

thf(1390,plain,
    ( ( $true = $false )
    | ( ( set2prop @ ( prop2set @ $true ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1138]) ).

thf(1391,plain,
    ( ( $false = $false )
    | ( ( set2prop @ ( prop2set @ $false ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1139]) ).

thf(1392,plain,
    ! [SV121: $i,SV349: $i] :
      ( ( ( ~ ( in @ SV349 @ ( powerset @ SV121 ) ) )
        = $true )
      | ( ( ! [SY2650: $i] :
              ( ~ ( in @ SY2650 @ SV121 )
              | ~ ~ ( in @ SY2650 @ ( setminus @ SV121 @ SV349 ) )
              | ( in @ SY2650 @ SV349 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1140]) ).

thf(1393,plain,
    ! [SV122: $i,SV350: $i] :
      ( ( ( ~ ( in @ SV350 @ ( powerset @ SV122 ) ) )
        = $true )
      | ( ( ! [SY2651: $i] :
              ( ~ ( in @ SY2651 @ ( powerset @ SV122 ) )
              | ( subset @ ( setminus @ SV122 @ SV350 ) @ ( setminus @ SV122 @ ( binintersect @ SV350 @ SY2651 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1141]) ).

thf(1394,plain,
    ! [SV523: $i,SV351: $i,SV123: $i] :
      ( ( ~ ( subset @ SV123 @ SV351 )
        | ~ ~ ( in @ SV523 @ SV351 )
        | ~ ( in @ SV523 @ SV123 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1142]) ).

thf(1395,plain,
    ! [SV352: $i,SV524: $i > $i,SV124: $i] :
      ( ( ~ ! [SY2952: $i] :
              ( ~ ( in @ SY2952 @ SV124 )
              | ( in @ ( SV524 @ SY2952 ) @ SV352 ) )
        | ( func @ SV124 @ SV352
          @ ( dpsetconstr @ SV124 @ SV352
            @ ^ [SY2953: $i,SY2954: $i] :
                ( ( SV524 @ SY2953 )
                = SY2954 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1143]) ).

thf(1396,plain,
    ! [SV353: $i > $o,SV125: $i] :
      ( ( ( ~ ! [SY2657: $i] :
                ( ~ ( in @ SY2657 @ SV125 )
                | ! [SY2658: $i] :
                    ( ~ ( in @ SY2658 @ SV125 )
                    | ~ ( SV353 @ SY2657 )
                    | ~ ( SV353 @ SY2658 )
                    | ( SY2657 = SY2658 ) ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2659: $i] :
                  ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                      | ~ ( SV353 @ SY2659 ) )
          | ( singleton
            @ ( dsetconstr @ SV125
              @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1144]) ).

thf(1397,plain,
    ! [SV354: $i,SV126: $i,SV525: $i] :
      ( ( ~ ~ ( in @ SV525 @ SV126 )
        | ~ ( in @ SV525 @ SV354 )
        | ( in @ SV525 @ ( symdiff @ SV126 @ SV354 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1145]) ).

thf(1398,plain,
    ! [SV355: $i,SV127: $i,SV526: $i] :
      ( ( ~ ( in @ SV526 @ ( setadjoin @ SV127 @ ( setadjoin @ SV355 @ emptyset ) ) )
        | ( SV526 = SV127 )
        | ( SV526 = SV355 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1146]) ).

thf(1399,plain,
    ! [SV128: $i,SV356: $i] :
      ( ( ( ~ ( in @ SV356 @ ( powerset @ SV128 ) ) )
        = $true )
      | ( ( ! [SY2663: $i] :
              ( ~ ( in @ SY2663 @ ( powerset @ SV128 ) )
              | ( in @ ( setminus @ SV128 @ SV356 ) @ ( powerset @ ( setminus @ SV128 @ ( binintersect @ SV356 @ SY2663 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1147]) ).

thf(1400,plain,
    ! [SV129: $i,SV357: $i] :
      ( ( ( ~ ( in @ SV357 @ ( powerset @ SV129 ) ) )
        = $true )
      | ( ( ! [SY2664: $i] :
              ( ~ ( in @ SY2664 @ SV129 )
              | ~ ( in @ SY2664 @ SV357 )
              | ~ ( in @ SY2664 @ ( setminus @ SV129 @ SV357 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1148]) ).

thf(1401,plain,
    ! [SV130: $i,SV358: $i] :
      ( ( ( ~ ( in @ SV358 @ ( powerset @ SV130 ) ) )
        = $true )
      | ( ( SV358
          = ( setminus @ SV130 @ ( setminus @ SV130 @ SV358 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1149]) ).

thf(1402,plain,
    ! [SV359: $i,SV131: $i] :
      ( ( ( SV131 != SV359 )
        = $true )
      | ( ( ( powerset @ SV131 )
          = ( powerset @ SV359 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1150]) ).

thf(1403,plain,
    ! [SV132: $i,SV360: $i] :
      ( ( ( ~ ( in @ SV360 @ ( powerset @ SV132 ) ) )
        = $true )
      | ( ( ! [SY2665: $i] :
              ( ~ ( in @ SY2665 @ ( powerset @ SV132 ) )
              | ~ ( subset @ SV360 @ SY2665 )
              | ( subset @ ( setminus @ SV132 @ SY2665 ) @ ( setminus @ SV132 @ SV360 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1151]) ).

thf(1404,plain,
    ! [SV527: $i,SV361: $i,SV133: $i] :
      ( ( ~ ( func @ SV133 @ SV361 @ SV527 )
        | ! [SY2955: $i] :
            ( ~ ( in @ SY2955 @ SV133 )
            | ( ( ap @ SV133 @ SV361 @ SV527 @ SY2955 )
              = ( ap @ SV133 @ SV361 @ SV527 @ SY2955 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1152]) ).

thf(1405,plain,
    ! [SV362: $i,SV134: $i,SV528: $i] :
      ( ( ~ ( in @ SV528 @ ( setadjoin @ SV134 @ ( setadjoin @ SV362 @ emptyset ) ) )
        | ( SV528 = SV134 )
        | ( SV528 = SV362 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1153]) ).

thf(1406,plain,
    ! [SV363: $i,SV135: $i,SV529: $i] :
      ( ( ~ ( subset @ SV529 @ ( cartprod @ SV135 @ SV363 ) )
        | ! [SY2956: $i > $o] :
            ( ~ ! [SY2957: $i] :
                  ( ~ ( in @ SY2957 @ SV135 )
                  | ! [SY2958: $i] :
                      ( ~ ( in @ SY2958 @ SV363 )
                      | ~ ( in @ ( kpair @ SY2957 @ SY2958 ) @ SV529 )
                      | ( SY2956 @ ( kpair @ SY2957 @ SY2958 ) ) ) )
            | ! [SY2959: $i] :
                ( ~ ( in @ SY2959 @ SV529 )
                | ( SY2956 @ SY2959 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1154]) ).

thf(1407,plain,
    ! [SV530: $i,SV136: $i,SV364: $i] :
      ( ( ~ ( in @ SV364 @ ( powerset @ SV136 ) )
        | ~ ( in @ SV530 @ SV364 )
        | ( in @ SV530 @ SV136 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1155]) ).

thf(1408,plain,
    ! [SV137: $i,SV365: $i] :
      ( ( ( ~ ( in @ SV365 @ ( powerset @ SV137 ) ) )
        = $true )
      | ( ( ! [SY2675: $i] :
              ( ~ ( in @ SY2675 @ ( powerset @ SV137 ) )
              | ! [SY2676: $i] :
                  ( ~ ( in @ SY2676 @ SV137 )
                  | ~ ~ ( in @ SY2676 @ SY2675 )
                  | ~ ( in @ SY2676 @ ( binintersect @ SV365 @ SY2675 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1156]) ).

thf(1409,plain,
    ! [SV138: $i,SV366: $i] :
      ( ( ( ~ ( in @ SV366 @ SV138 ) )
        = $true )
      | ( ( in @ ( setadjoin @ SV366 @ emptyset ) @ ( powerset @ SV138 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1157]) ).

thf(1410,plain,
    ! [SV139: $o,SV367: $i] :
      ( ( ( ~ ( in @ SV367 @ ( prop2set @ SV139 ) ) )
        = $true )
      | ( SV139 = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1158]) ).

thf(1411,plain,
    ! [SV368: $i] :
      ( ( ( ~ ( in @ SV368 @ ( prop2set @ $true ) ) )
        = $true )
      | ( $true = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1159]) ).

thf(1412,plain,
    ! [SV369: $i] :
      ( ( ( ~ ( in @ SV369 @ ( prop2set @ $false ) ) )
        = $true )
      | ( $false = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1160]) ).

thf(1413,plain,
    ! [SV370: $i,SV140: $i,SV531: $i] :
      ( ( ~ ( in @ SV531 @ SV140 )
        | ! [SY2960: $i] :
            ( ~ ( in @ SY2960 @ SV370 )
            | ( in @ ( kpair @ SV531 @ SY2960 ) @ ( cartprod @ SV140 @ SV370 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1161]) ).

thf(1414,plain,
    ! [SV371: $i,SV141: $i,SV532: $i] :
      ( ( ~ ( in @ SV532 @ ( cartprod @ SV141 @ SV371 ) )
        | ( in @ ( ksnd @ SV532 ) @ SV371 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1162]) ).

thf(1415,plain,
    ! [SV372: $i > $o,SV142: $i] :
      ( ( ( ~ ( singleton
              @ ( dsetconstr @ SV142
                @ ^ [SY2680: $i] : ( SV372 @ SY2680 ) ) ) )
        = $true )
      | ( ( ! [SY2681: $i] :
              ( ~ ( in @ SY2681 @ SV142 )
              | ! [SY2682: $i] :
                  ( ~ ( in @ SY2682 @ SV142 )
                  | ~ ( SV372 @ SY2681 )
                  | ~ ( SV372 @ SY2682 )
                  | ( SY2681 = SY2682 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1163]) ).

thf(1416,plain,
    ! [SV143: $i,SV373: $i] :
      ( ( ( ~ ( in @ SV373 @ ( powerset @ SV143 ) ) )
        = $true )
      | ( ( subset @ SV373 @ SV143 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1164]) ).

thf(1417,plain,
    ! [SV374: $i,SV144: $i,SV533: $i] :
      ( ( ~ ( in @ SV533 @ SV144 )
        | ! [SY2961: $i] :
            ( ~ ( in @ SY2961 @ SV374 )
            | ( ( kfst @ ( kpair @ SV533 @ SY2961 ) )
              = SV533 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1165]) ).

thf(1418,plain,
    ! [SV145: $i,SV375: $i] :
      ( ( ( ~ ( in @ SV375 @ ( powerset @ SV145 ) ) )
        = $true )
      | ( ( in @ ( setminus @ SV145 @ SV375 ) @ ( powerset @ SV145 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1166]) ).

thf(1419,plain,
    ! [SV534: $i,SV376: $i,SV146: $i] :
      ( ( ! [SY2962: $i] :
            ( ( ( kpair @ SV146 @ SV376 )
             != ( kpair @ SV534 @ SY2962 ) )
            | ( SV376 = SY2962 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1167]) ).

thf(1420,plain,
    ! [SV147: $i > $i > $o,SV377: $i] :
      ( ( ( ~ ! [SY2687: $i] :
                ( ~ ( in @ SY2687 @ SV377 )
                | ~ ! [SY2202: $i] :
                      ~ ~ ( ~ ( SV147 @ SY2687 @ SY2202 )
                          | ~ ! [SY2203: $i] :
                                ( ~ ( SV147 @ SY2687 @ SY2203 )
                                | ( SY2202 = SY2203 ) ) ) ) )
        = $true )
      | ( ( ~ ! [SY2690: $i] :
                ~ ! [SY2691: $i] :
                    ~ ( ~ ( ~ ( in @ SY2691 @ SY2690 )
                          | ~ ! [SY2692: $i] :
                                ~ ~ ( ~ ( in @ SY2692 @ SV377 )
                                    | ~ ( SV147 @ SY2692 @ SY2691 ) ) )
                      | ~ ( ~ ~ ! [SY2693: $i] :
                                  ~ ~ ( ~ ( in @ SY2693 @ SV377 )
                                      | ~ ( SV147 @ SY2693 @ SY2691 ) )
                          | ( in @ SY2691 @ SY2690 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1168]) ).

thf(1421,plain,
    ! [SV378: $i,SV148: $i] :
      ( ( ( ~ ! [SY2694: $i] :
                ( ~ ( in @ SY2694 @ SV148 )
                | ( in @ SY2694 @ SV378 ) ) )
        = $true )
      | ( ( subset @ SV148 @ SV378 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1169]) ).

thf(1422,plain,
    ! [SV379: $i,SV149: $i] :
      ( ( ( ~ ( subset @ SV149 @ SV379 ) )
        = $true )
      | ( ( ~ ( subset @ SV379 @ SV149 )
          | ( SV149 = SV379 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1170]) ).

thf(1423,plain,
    ! [SV380: $i,SV150: $i,SV535: $i] :
      ( ( ~ ( in @ SV535 @ SV150 )
        | ( in @ SV535 @ ( binunion @ SV150 @ SV380 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1171]) ).

thf(1424,plain,
    ! [SV151: $i,SV381: $i] :
      ( ( ( ~ ( in @ SV381 @ ( powerset @ SV151 ) ) )
        = $true )
      | ( ( ! [SY2696: $i] :
              ( ~ ( in @ SY2696 @ ( powerset @ SV151 ) )
              | ! [SY2697: $i] :
                  ( ~ ( in @ SY2697 @ SV151 )
                  | ~ ~ ( in @ SY2697 @ ( binunion @ SV381 @ SY2696 ) )
                  | ~ ( in @ SY2697 @ SY2696 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1172]) ).

thf(1425,plain,
    ! [SV382: $i,SV152: $i] :
      ( ( ( SV152 != SV382 )
        = $true )
      | ( ( ! [SY2698: $i,SY2699: $i] :
              ( ( SY2698 != SY2699 )
              | ( ( setadjoin @ SV152 @ SY2698 )
                = ( setadjoin @ SV382 @ SY2699 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1173]) ).

thf(1426,plain,
    ! [SV153: $i] :
      ( ( ( iskpair @ SV153 )
        = $false )
      | ( ( ( kpair @ ( kfst @ SV153 ) @ ( ksnd @ SV153 ) )
          = SV153 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1174]) ).

thf(1427,plain,
    ! [SV154: $i,SV383: $i,SV536: $i] :
      ( ( ~ ( in @ SV536 @ SV383 )
        | ( in @ SV536 @ ( binunion @ SV154 @ SV383 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1175]) ).

thf(1428,plain,
    ! [SV384: $i,SV155: $i] :
      ( ( ( SV155 != SV384 )
        = $true )
      | ( ( subset @ SV384 @ SV155 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1176]) ).

thf(1429,plain,
    ! [SV156: $i,SV385: $i] :
      ( ( ( ~ ( in @ SV385 @ ( powerset @ SV156 ) ) )
        = $true )
      | ( ( ! [SY2701: $i] :
              ( ~ ( in @ SY2701 @ ( powerset @ SV156 ) )
              | ! [SY2702: $i] :
                  ( ~ ( in @ SY2702 @ SV156 )
                  | ~ ~ ( in @ SY2702 @ SV385 )
                  | ~ ( in @ SY2702 @ ( binintersect @ SV385 @ SY2701 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1177]) ).

thf(1430,plain,
    ! [SV157: $i > $o] :
      ( ( ( ~ ! [SY2225: $i] :
                ~ ~ ( ~ ( SV157 @ SY2225 )
                    | ~ ! [SY2226: $i] :
                          ( ~ ( SV157 @ SY2226 )
                          | ( SY2225 = SY2226 ) ) ) )
        = $false )
      | ( ( SV157
          @ ( descr
            @ ^ [SY2227: $i] : ( SV157 @ SY2227 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1178]) ).

thf(1431,plain,
    ! [SV386: $i,SV158: $i,SV537: $i] :
      ( ( ~ ( in @ SV537 @ ( setminus @ SV158 @ SV386 ) )
        | ~ ( in @ SV537 @ SV386 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1179]) ).

thf(1432,plain,
    ! [SV159: $i,SV387: $i] :
      ( ( ( ~ ( in @ SV387 @ ( powerset @ SV159 ) ) )
        = $true )
      | ( ( subset @ SV387 @ ( setminus @ SV159 @ ( setminus @ SV159 @ SV387 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1180]) ).

thf(1433,plain,
    ! [SV388: $i > $o,SV160: $i] :
      ( ( ( ~ ~ ! [SY2704: $i] :
                  ( ~ ( in @ SY2704 @ SV160 )
                  | ( SV388 @ SY2704 ) ) )
        = $true )
      | ( ( ~ ! [SY2705: $i] :
                ~ ~ ( ~ ( in @ SY2705 @ SV160 )
                    | ~ ~ ( SV388 @ SY2705 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1181]) ).

thf(1434,plain,
    ! [SV161: $i,SV389: $i] :
      ( ( ( ~ ( in @ SV389 @ ( powerset @ SV161 ) ) )
        = $true )
      | ( ( ! [SY2706: $i] :
              ( ~ ( in @ SY2706 @ ( powerset @ SV161 ) )
              | ! [SY2707: $i] :
                  ( ~ ( in @ SY2707 @ SV161 )
                  | ~ ( in @ SY2707 @ ( setminus @ SV161 @ SV389 ) )
                  | ( in @ SY2707 @ ( setminus @ SV161 @ ( binintersect @ SV389 @ SY2706 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1182]) ).

thf(1435,plain,
    ! [SV162: $i,SV390: $i] :
      ( ( ( ~ ( in @ SV390 @ ( powerset @ SV162 ) ) )
        = $true )
      | ( ( ! [SY2708: $i] :
              ( ~ ( in @ SY2708 @ ( powerset @ SV162 ) )
              | ( in @ ( binunion @ SV390 @ SY2708 ) @ ( powerset @ SV162 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1183]) ).

thf(1436,plain,
    ! [SV391: $i,SV163: $i] :
      ( ( ( ~ ( subset @ SV163 @ SV391 ) )
        = $true )
      | ( ( in @ SV163 @ ( powerset @ SV391 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1184]) ).

thf(1437,plain,
    ! [SV392: $i,SV164: $i] :
      ( ( ( ( setminus @ SV164 @ SV392 )
         != emptyset )
        = $true )
      | ( ( subset @ SV164 @ SV392 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1185]) ).

thf(1438,plain,
    ! [SV165: $i > $o] :
      ( ( ( ~ ! [SY2241: $i] :
                ~ ( SV165 @ SY2241 ) )
        = $false )
      | ( ( ~ ! [SY2242: $i,SY2243: $i] :
                ( ~ ( SV165 @ SY2242 )
                | ~ ( SV165 @ SY2243 )
                | ( SY2242 = SY2243 ) )
          | ~ ! [SY2244: $i] :
                ~ ~ ( ~ ( SV165 @ SY2244 )
                    | ~ ! [SY2245: $i] :
                          ( ~ ( SV165 @ SY2245 )
                          | ( SY2244 = SY2245 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1186]) ).

thf(1439,plain,
    ! [SV393: $i,SV166: $i,SV538: $i] :
      ( ( ~ ( in @ SV538 @ SV166 )
        | ~ ~ ( in @ SV538 @ SV393 )
        | ~ ( subset @ SV166 @ SV393 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1187]) ).

thf(1440,plain,
    ! [SV167: $i,SV394: $i] :
      ( ( ( ~ ( in @ SV394 @ ( powerset @ SV167 ) ) )
        = $true )
      | ( ( ! [SY2710: $i] :
              ( ~ ( in @ SY2710 @ ( powerset @ SV167 ) )
              | ! [SY2711: $i] :
                  ( ~ ( in @ SY2711 @ ( powerset @ SV167 ) )
                  | ( in @ ( binintersect @ SV394 @ SY2710 ) @ ( powerset @ ( binintersect @ ( binunion @ SV394 @ SY2711 ) @ ( binunion @ SY2710 @ SY2711 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1188]) ).

thf(1441,plain,
    ! [SV395: $i,SV168: $i,SV539: $i] :
      ( ( ~ ( subset @ SV539 @ ( cartprod @ SV168 @ SV395 ) )
        | ! [SY2963: $i] :
            ( ~ ( subset @ SY2963 @ ( cartprod @ SV168 @ SV395 ) )
            | ~ ! [SY2964: $i] :
                  ( ~ ( in @ SY2964 @ SV168 )
                  | ! [SY2965: $i] :
                      ( ~ ( in @ SY2965 @ SV395 )
                      | ~ ( in @ ( kpair @ SY2964 @ SY2965 ) @ SV539 )
                      | ( in @ ( kpair @ SY2964 @ SY2965 ) @ SY2963 ) ) )
            | ( subset @ SV539 @ SY2963 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1189]) ).

thf(1442,plain,
    ! [SV396: $o,SV169: $i,SV540: $i] :
      ( ( ~ ( in @ SV540 @ SV169 )
        | ! [SY2966: $i] :
            ( ~ ( in @ SY2966 @ SV169 )
            | ~ SV396
            | ( ( if @ SV169 @ SV396 @ SV540 @ SY2966 )
              = SV540 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1190]) ).

thf(1443,plain,
    ! [SV169: $i,SV541: $i] :
      ( ( ~ ( in @ SV541 @ SV169 )
        | ! [SY2967: $i] :
            ( ~ ( in @ SY2967 @ SV169 )
            | ~ $true
            | ( ( if @ SV169 @ $true @ SV541 @ SY2967 )
              = SV541 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1191]) ).

thf(1444,plain,
    ! [SV169: $i,SV542: $i] :
      ( ( ~ ( in @ SV542 @ SV169 )
        | ! [SY2968: $i] :
            ( ~ ( in @ SY2968 @ SV169 )
            | ~ $false
            | ( ( if @ SV169 @ $false @ SV542 @ SY2968 )
              = SV542 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1192]) ).

thf(1445,plain,
    ! [SV397: $i,SV543: $i > $i,SV170: $i] :
      ( ( ~ ! [SY2969: $i] :
              ( ~ ( in @ SY2969 @ SV170 )
              | ( in @ ( SV543 @ SY2969 ) @ SV397 ) )
        | ! [SY2970: $i] :
            ( ~ ( in @ SY2970 @ SV170 )
            | ( ( ap @ SV170 @ SV397
                @ ( lam @ SV170 @ SV397
                  @ ^ [SY2971: $i] : ( SV543 @ SY2971 ) )
                @ SY2970 )
              = ( SV543 @ SY2970 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1193]) ).

thf(1446,plain,
    ! [SV171: $i] :
      ( ( ( ~ ! [SY2264: $i] :
                ~ ( in @ SY2264 @ SV171 ) )
        = $false )
      | ( ( SV171 != emptyset )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1194]) ).

thf(1447,plain,
    ! [SV398: $i,SV172: $i,SV544: $i] :
      ( ( ~ ( in @ SV544 @ ( cartprod @ SV172 @ SV398 ) )
        | ( ( kpair @ ( kfst @ SV544 ) @ ( ksnd @ SV544 ) )
          = SV544 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1195]) ).

thf(1448,plain,
    ! [SV399: $i,SV173: $i,SV545: $i] :
      ( ( ~ ( in @ SV545 @ ( funcSet @ SV173 @ SV399 ) )
        | ( ( lam @ SV173 @ SV399
            @ ^ [SY2972: $i] : ( ap @ SV173 @ SV399 @ SV545 @ SY2972 ) )
          = SV545 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1196]) ).

thf(1449,plain,
    ! [SV546: $i,SV400: $i,SV174: $i] :
      ( ( ! [SY2973: $i] :
            ( ( ( setadjoin @ ( setadjoin @ SV174 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV174 @ ( setadjoin @ SV400 @ emptyset ) ) @ emptyset ) )
             != ( setadjoin @ ( setadjoin @ SV546 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV546 @ ( setadjoin @ SY2973 @ emptyset ) ) @ emptyset ) ) )
            | ( SV546 != SY2973 )
            | ( SV400 = SY2973 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1197]) ).

thf(1450,plain,
    ! [SV401: $i,SV175: $i,SV547: $i] :
      ( ( ! [SY2974: $i] :
            ( ~ ( in @ ( kpair @ SV547 @ SY2974 ) @ ( cartprod @ SV175 @ SV401 ) )
            | ( in @ SY2974 @ SV401 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1198]) ).

thf(1451,plain,
    ! [SV548: $i,SV402: $i,SV176: $i] :
      ( ( ~ ( func @ SV176 @ SV402 @ SV548 )
        | ! [SY2975: $i] :
            ( ~ ( in @ SY2975 @ SV176 )
            | ( in @ ( ap @ SV176 @ SV402 @ SV548 @ SY2975 ) @ SV402 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1199]) ).

thf(1452,plain,
    ! [SV177: $i,SV403: $i] :
      ( ( ( ~ ( in @ SV403 @ ( powerset @ SV177 ) ) )
        = $true )
      | ( ( ! [SY2731: $i] :
              ( ~ ( in @ SY2731 @ ( powerset @ SV177 ) )
              | ! [SY2732: $i] :
                  ( ~ ( in @ SY2732 @ SV177 )
                  | ~ ( subset @ SV403 @ ( setminus @ SV177 @ SY2731 ) )
                  | ~ ( in @ SY2732 @ SY2731 )
                  | ~ ( in @ SY2732 @ SV403 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1200]) ).

thf(1453,plain,
    ! [SV549: $i > $i > $o,SV404: $i,SV178: $i] :
      ( ( ! [SY2976: $i] :
            ( ~ ( in @ SY2976 @ SV178 )
            | ! [SY2977: $i] :
                ( ~ ( in @ SY2977 @ SV404 )
                | ~ ( SV549 @ SY2976 @ SY2977 )
                | ( in @ ( kpair @ SY2976 @ SY2977 )
                  @ ( dpsetconstr @ SV178 @ SV404
                    @ ^ [SY2978: $i,SY2979: $i] : ( SV549 @ SY2978 @ SY2979 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1201]) ).

thf(1454,plain,
    ! [SV405: $i,SV179: $i,SV550: $i] :
      ( ( ~ ( in @ SV550 @ SV179 )
        | ~ ~ ( in @ SV550 @ SV405 )
        | ( SV179 != SV405 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1202]) ).

thf(1455,plain,
    ! [SV406: $i,SV180: $i,SV551: $i] :
      ( ( ~ ( in @ SV551 @ SV180 )
        | ~ ( in @ SV551 @ SV406 )
        | ( in @ SV551 @ ( binintersect @ SV180 @ SV406 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1203]) ).

thf(1456,plain,
    ! [SV181: $i,SV407: $i] :
      ( ( ( ~ ! [SY2740: $i] :
                ( ~ ( in @ SY2740 @ SV407 )
                | ( in @ SY2740 @ SV181 ) ) )
        = $true )
      | ( ( in @ SV407 @ ( powerset @ SV181 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1204]) ).

thf(1457,plain,
    ! [SV182: $i,SV408: $i] :
      ( ( ( ~ ( in @ SV408 @ ( powerset @ SV182 ) ) )
        = $true )
      | ( ( ! [SY2741: $i] :
              ( ~ ( in @ SY2741 @ SV182 )
              | ~ ( in @ SY2741 @ SV408 )
              | ( in @ SY2741 @ ( setminus @ SV182 @ ( setminus @ SV182 @ SV408 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1205]) ).

thf(1458,plain,
    ! [SV409: $i,SV183: $i,SV552: $i] :
      ( ( ~ ( in @ SV552 @ ( setminus @ SV183 @ SV409 ) )
        | ( in @ SV552 @ SV183 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1206]) ).

thf(1459,plain,
    ! [SV410: $i,SV184: $i,SV553: $i] :
      ( ( ~ ( in @ SV553 @ ( cartprod @ SV184 @ SV410 ) )
        | ( iskpair @ SV553 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1207]) ).

thf(1460,plain,
    ! [SV554: $i,SV411: $i,SV185: $i] :
      ( ( ~ ( func @ SV185 @ SV411 @ SV554 )
        | ! [SY2980: $i] :
            ( ~ ( in @ SY2980 @ SV185 )
            | ! [SY2981: $i] :
                ( ~ ( in @ SY2981 @ SV411 )
                | ~ ( in @ ( kpair @ SY2980 @ SY2981 ) @ SV554 )
                | ( ( ap @ SV185 @ SV411 @ SV554 @ SY2980 )
                  = SY2981 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1208]) ).

thf(1461,plain,
    ! [SV186: $i,SV412: $i] :
      ( ( ( ~ ( in @ SV412 @ ( powerset @ SV186 ) ) )
        = $true )
      | ( ( ! [SY2747: $i] :
              ( ~ ( in @ SY2747 @ ( powerset @ SV186 ) )
              | ( in @ ( setminus @ SV412 @ SY2747 ) @ ( powerset @ SV186 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1209]) ).

thf(1462,plain,
    ! [SV413: $i > $o,SV187: $i,SV555: $i] :
      ( ( ~ ( in @ SV555
            @ ( dsetconstr @ SV187
              @ ^ [SY2749: $i] : ( SV413 @ SY2749 ) ) )
        | ( in @ SV555 @ SV187 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1210]) ).

thf(1463,plain,
    ! [SV414: $i > $o,SV188: $i,SV556: $i] :
      ( ( ~ ( in @ SV556 @ SV188 )
        | ~ ( ~ ( ~ ( in @ SV556
                    @ ( dsetconstr @ SV188
                      @ ^ [SY2751: $i] : ( SV414 @ SY2751 ) ) )
                | ( SV414 @ SV556 ) )
            | ~ ( ~ ( SV414 @ SV556 )
                | ( in @ SV556
                  @ ( dsetconstr @ SV188
                    @ ^ [SY2752: $i] : ( SV414 @ SY2752 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1211]) ).

thf(1464,plain,
    ! [SV189: $i,SV415: $i,SV557: $i] :
      ( ( ~ ( in @ SV557 @ SV415 )
        | ( in @ SV557 @ ( setadjoin @ SV189 @ SV415 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1212]) ).

thf(1465,plain,
    ! [SV558: $i,SV416: $i,SV190: $i] :
      ( ( ~ ( func @ SV190 @ SV416 @ SV558 )
        | ! [SY2985: $i] :
            ( ~ ( func @ SV190 @ SV416 @ SY2985 )
            | ~ ! [SY2986: $i] :
                  ( ~ ( in @ SY2986 @ SV190 )
                  | ( ( ap @ SV190 @ SV416 @ SV558 @ SY2986 )
                    = ( ap @ SV190 @ SV416 @ SY2985 @ SY2986 ) ) )
            | ( SV558 = SY2985 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1213]) ).

thf(1466,plain,
    ! [SV191: $i,SV417: $i] :
      ( ( ( ~ ( in @ SV417 @ ( powerset @ SV191 ) ) )
        = $true )
      | ( ( ! [SY2757: $i] :
              ( ~ ( in @ SY2757 @ ( powerset @ SV191 ) )
              | ! [SY2758: $i] :
                  ( ~ ( in @ SY2758 @ ( powerset @ SV191 ) )
                  | ! [SY2759: $i] :
                      ( ~ ( in @ SY2759 @ SV191 )
                      | ~ ( in @ SY2759 @ ( binintersect @ SV417 @ SY2757 ) )
                      | ( in @ SY2759 @ ( binunion @ SV417 @ SY2758 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1214]) ).

thf(1467,plain,
    ! [SV418: $i > $o,SV192: $i,SV559: $i] :
      ( ( ~ ( in @ SV559
            @ ( dsetconstr @ SV192
              @ ^ [SY2761: $i] : ( SV418 @ SY2761 ) ) )
        | ( SV418 @ SV559 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1215]) ).

thf(1468,plain,
    ! [SV419: $i,SV193: $i] :
      ( ( ( SV193 != SV419 )
        = $true )
      | ( ( ! [SY2762: $i,SY2763: $i] :
              ( ( SY2762 != SY2763 )
              | ~ ( ~ ( ~ ( in @ SY2762 @ SV193 )
                      | ( in @ SY2763 @ SV419 ) )
                  | ~ ( ~ ( in @ SY2763 @ SV419 )
                      | ( in @ SY2762 @ SV193 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1216]) ).

thf(1469,plain,
    ! [SV420: $o,SV194: $i,SV560: $i] :
      ( ( ~ ( in @ SV560 @ SV194 )
        | ! [SY2988: $i] :
            ( ~ ( in @ SY2988 @ SV194 )
            | ( singleton
              @ ( dsetconstr @ SV194
                @ ^ [SY2989: $i] :
                    ( ~ ( ~ SV420
                        | ( SY2989 != SV560 ) )
                    | ~ ( ~ ~ SV420
                        | ( SY2989 != SY2988 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1217]) ).

thf(1470,plain,
    ! [SV194: $i,SV561: $i] :
      ( ( ~ ( in @ SV561 @ SV194 )
        | ! [SY2990: $i] :
            ( ~ ( in @ SY2990 @ SV194 )
            | ( singleton
              @ ( dsetconstr @ SV194
                @ ^ [SY2991: $i] :
                    ( ~ ( ~ $true
                        | ( SY2991 != SV561 ) )
                    | ~ ( ~ ~ $true
                        | ( SY2991 != SY2990 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1218]) ).

thf(1471,plain,
    ! [SV194: $i,SV562: $i] :
      ( ( ~ ( in @ SV562 @ SV194 )
        | ! [SY2992: $i] :
            ( ~ ( in @ SY2992 @ SV194 )
            | ( singleton
              @ ( dsetconstr @ SV194
                @ ^ [SY2993: $i] :
                    ( ~ ( ~ $false
                        | ( SY2993 != SV562 ) )
                    | ~ ( ~ ~ $false
                        | ( SY2993 != SY2992 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1219]) ).

thf(1472,plain,
    ! [SV421: $i,SV195: $i] :
      ( ( ( ( binintersect @ SV195 @ SV421 )
         != SV195 )
        = $true )
      | ( ( subset @ SV195 @ SV421 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1220]) ).

thf(1473,plain,
    ! [SV422: $i,SV196: $i,SV563: $i] :
      ( ( ~ ( in @ SV563 @ SV196 )
        | ! [SY2994: $i] :
            ( ~ ( in @ SY2994 @ SV422 )
            | ( in @ ( kpair @ SV563 @ SY2994 ) @ ( powerset @ ( powerset @ ( binunion @ SV196 @ SV422 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1221]) ).

thf(1474,plain,
    ! [SV423: $o,SV197: $i,SV564: $i] :
      ( ( ~ ( in @ SV564 @ SV197 )
        | ! [SY2995: $i] :
            ( ~ ( in @ SY2995 @ SV197 )
            | ( in @ ( if @ SV197 @ SV423 @ SV564 @ SY2995 ) @ SV197 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1222]) ).

thf(1475,plain,
    ! [SV197: $i,SV565: $i] :
      ( ( ~ ( in @ SV565 @ SV197 )
        | ! [SY2996: $i] :
            ( ~ ( in @ SY2996 @ SV197 )
            | ( in @ ( if @ SV197 @ $true @ SV565 @ SY2996 ) @ SV197 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1223]) ).

thf(1476,plain,
    ! [SV197: $i,SV566: $i] :
      ( ( ~ ( in @ SV566 @ SV197 )
        | ! [SY2997: $i] :
            ( ~ ( in @ SY2997 @ SV197 )
            | ( in @ ( if @ SV197 @ $false @ SV566 @ SY2997 ) @ SV197 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1224]) ).

thf(1477,plain,
    ! [SV424: $i,SV198: $i,SV567: $i] :
      ( ( ~ ( in @ SV567 @ ( funcSet @ SV198 @ SV424 ) )
        | ! [SY2998: $i] :
            ( ~ ( in @ SY2998 @ SV198 )
            | ! [SY2999: $i] :
                ( ~ ( in @ SY2999 @ SV424 )
                | ~ ( in @ ( kpair @ SY2998 @ SY2999 ) @ SV567 )
                | ( ( ap @ SV198 @ SV424 @ SV567 @ SY2998 )
                  = SY2999 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1225]) ).

thf(1478,plain,
    ! [SV425: $i,SV568: $i > $i,SV199: $i] :
      ( ( ~ ! [SY3000: $i] :
              ( ~ ( in @ SY3000 @ SV199 )
              | ( in @ ( SV568 @ SY3000 ) @ SV425 ) )
        | ( func @ SV199 @ SV425
          @ ( lam @ SV199 @ SV425
            @ ^ [SY3001: $i] : ( SV568 @ SY3001 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1226]) ).

thf(1479,plain,
    ! [SV426: $i > $o,SV200: $i] :
      ( ( ( ~ ! [SY2777: $i] :
                ( ~ ( in @ SY2777 @ SV200 )
                | ~ ( SV426 @ SY2777 ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2778: $i] :
                  ~ ~ ( ~ ( in @ SY2778 @ SV200 )
                      | ~ ( SV426 @ SY2778 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1227]) ).

thf(1480,plain,
    ! [SV427: $i,SV201: $i] :
      ( ( ( ( setadjoin @ SV201 @ emptyset )
         != ( setadjoin @ SV427 @ emptyset ) )
        = $true )
      | ( ( SV201 = SV427 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1228]) ).

thf(1481,plain,
    ! [SV428: $i,SV202: $i,SV569: $i] :
      ( ( ~ ( in @ SV569 @ ( funcSet @ SV202 @ SV428 ) )
        | ! [SY3002: $i] :
            ( ~ ( in @ SY3002 @ SV202 )
            | ( in @ ( ap @ SV202 @ SV428 @ SV569 @ SY3002 ) @ SV428 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1229]) ).

thf(1482,plain,
    ! [SV203: $i] :
      ( ( ( SV203 != emptyset )
        = $false )
      | ( ( ~ ! [SY2355: $i] :
                ~ ( in @ SY2355 @ SV203 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1230]) ).

thf(1483,plain,
    ! [SV429: $i,SV204: $i] :
      ( ( ( ~ ( in @ SV204 @ ( setadjoin @ SV429 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV429 @ ( setadjoin @ SV204 @ emptyset ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1231]) ).

thf(1484,plain,
    ! [SV205: $i,SV430: $i] :
      ( ( ~ ( ~ ( in @ SV430 @ ( setunion @ SV205 ) )
            | ~ ! [SY2781: $i] :
                  ~ ~ ( ~ ( in @ SV430 @ SY2781 )
                      | ~ ( in @ SY2781 @ SV205 ) ) )
        | ~ ( ~ ~ ! [SY2782: $i] :
                    ~ ~ ( ~ ( in @ SV430 @ SY2782 )
                        | ~ ( in @ SY2782 @ SV205 ) )
            | ( in @ SV430 @ ( setunion @ SV205 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1232]) ).

thf(1485,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ~ ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        | ! [SY3003: $o] :
            ( ~ ( ~ ( in @ SV570 @ SV206 )
                | ~ ~ ( in @ SV570 @ SV431 )
                | SY3003 )
            | ~ ( ~ ~ ( in @ SV570 @ SV206 )
                | ~ ( in @ SV570 @ SV431 )
                | SY3003 )
            | SY3003 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1233]) ).

thf(1486,plain,
    ! [SV432: $i,SV207: $i] :
      ( ( ( ~ ~ ( subset @ SV207 @ SV432 ) )
        = $true )
      | ( ( SV207 != SV432 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1234]) ).

thf(1487,plain,
    ! [SV208: $i,SV433: $i] :
      ( ( ( ~ ( in @ SV433 @ ( setunion @ SV208 ) ) )
        = $true )
      | ( ( ~ ! [SY2785: $i] :
                ~ ~ ( ~ ( in @ SY2785 @ SV208 )
                    | ~ ( in @ SV433 @ SY2785 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1235]) ).

thf(1488,plain,
    ! [SV434: $i,SV209: $i] :
      ( ( ( SV209 != SV434 )
        = $true )
      | ( ( ! [SY2786: $i > $o,SY2787: $i > $o] :
              ( ~ ! [SY2788: $i] :
                    ( ~ ( in @ SY2788 @ SV209 )
                    | ! [SY2789: $i] :
                        ( ~ ( in @ SY2789 @ SV434 )
                        | ( SY2788 != SY2789 )
                        | ~ ( ~ ( ~ ( SY2786 @ SY2788 )
                                | ( SY2787 @ SY2789 ) )
                            | ~ ( ~ ( SY2787 @ SY2789 )
                                | ( SY2786 @ SY2788 ) ) ) ) )
              | ( ( dsetconstr @ SV209
                  @ ^ [SX4: $i] : ( SY2786 @ SX4 ) )
                = ( dsetconstr @ SV434
                  @ ^ [SX4: $i] : ( SY2787 @ SX4 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1236]) ).

thf(1489,plain,
    ! [SV435: $i,SV210: $i,SV571: $i] :
      ( ( ~ ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        | ! [SY3004: $o] :
            ( ~ ( ( SV571 != SV210 )
                | SY3004 )
            | ~ ( ~ ( in @ SV571 @ SV435 )
                | SY3004 )
            | SY3004 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1237]) ).

thf(1490,plain,
    ! [SV211: $i > $o] :
      ( ( ( ~ ! [SY2376: $i] :
                ~ ~ ( ~ ( SV211 @ SY2376 )
                    | ~ ! [SY2377: $i] :
                          ( ~ ( SV211 @ SY2377 )
                          | ( SY2376 = SY2377 ) ) ) )
        = $false )
      | ( ( ~ ! [SY2378: $i] :
                ~ ~ ( ~ ( SV211 @ SY2378 )
                    | ~ ! [SY2379: $i] :
                          ( ~ ( SV211 @ SY2379 )
                          | ( SY2378 = SY2379 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1238]) ).

thf(1491,plain,
    ! [SV436: $i,SV212: $i,SV572: $i] :
      ( ( ~ ( in @ SV572 @ ( funcSet @ SV212 @ SV436 ) )
        | ! [SY3005: $i] :
            ( ~ ( in @ SY3005 @ SV212 )
            | ( ( ap @ SV212 @ SV436 @ SV572 @ SY3005 )
              = ( ap @ SV212 @ SV436 @ SV572 @ SY3005 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1239]) ).

thf(1492,plain,
    ! [SV213: $i,SV437: $i] :
      ( ( ( ~ ( in @ SV437 @ ( powerset @ SV213 ) ) )
        = $true )
      | ( ( ! [SY2796: $i] :
              ( ~ ( in @ SY2796 @ SV213 )
              | ~ ( in @ SY2796 @ ( setminus @ SV213 @ ( setminus @ SV213 @ SV437 ) ) )
              | ( in @ SY2796 @ SV437 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1240]) ).

thf(1493,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ! [SY2797: $i,SY2798: $i] :
                ( ( SY2797 != SY2798 )
                | ~ ( ~ ( ~ ( SV214 @ SY2797 )
                        | ( SV438 @ SY2798 ) )
                    | ~ ( ~ ( SV438 @ SY2798 )
                        | ( SV214 @ SY2797 ) ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ~ ! [SY2388: $i] :
                          ~ ~ ( ~ ( SV214 @ SY2388 )
                              | ~ ! [SY2389: $i] :
                                    ( ~ ( SV214 @ SY2389 )
                                    | ( SY2388 = SY2389 ) ) )
                  | ~ ! [SY2801: $i] :
                        ~ ~ ( ~ ( SV438 @ SY2801 )
                            | ~ ! [SY2802: $i] :
                                  ( ~ ( SV438 @ SY2802 )
                                  | ( SY2801 = SY2802 ) ) ) )
              | ~ ( ~ ~ ! [SY2803: $i] :
                          ~ ~ ( ~ ( SV438 @ SY2803 )
                              | ~ ! [SY2804: $i] :
                                    ( ~ ( SV438 @ SY2804 )
                                    | ( SY2803 = SY2804 ) ) )
                  | ~ ! [SY2394: $i] :
                        ~ ~ ( ~ ( SV214 @ SY2394 )
                            | ~ ! [SY2395: $i] :
                                  ( ~ ( SV214 @ SY2395 )
                                  | ( SY2394 = SY2395 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1241]) ).

thf(1494,plain,
    ! [SV439: $i > $o,SV215: $i] :
      ( ( ( ~ ( singleton
              @ ( dsetconstr @ SV215
                @ ^ [SY2807: $i] : ( SV439 @ SY2807 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2808: $i] :
                ~ ~ ( ~ ( in @ SY2808 @ SV215 )
                    | ~ ( SV439 @ SY2808 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1242]) ).

thf(1495,plain,
    ! [SV440: $i > $o,SV216: $i,SV573: $i] :
      ( ( ~ ( in @ SV573 @ SV216 )
        | ~ ( SV440 @ SV573 )
        | ~ ! [SY3006: $i] :
              ( ~ ( in @ SY3006 @ SV216 )
              | ~ ( SV440 @ SY3006 )
              | ( SY3006 = SV573 ) )
        | ( singleton
          @ ( dsetconstr @ SV216
            @ ^ [SY2811: $i] : ( SV440 @ SY2811 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1243]) ).

thf(1496,plain,
    ! [SV441: $i,SV217: $i] :
      ( ( ( SV217 != SV441 )
        = $true )
      | ( ( ( setadjoin @ SV217 @ ( setadjoin @ SV441 @ emptyset ) )
          = ( setadjoin @ SV217 @ emptyset ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1244]) ).

thf(1497,plain,
    ! [SV442: $i,SV218: $i,SV574: $i] :
      ( ( ~ ( in @ SV574 @ SV218 )
        | ! [SY3008: $i] :
            ( ~ ( in @ SY3008 @ SV442 )
            | ( subset @ ( setadjoin @ ( setadjoin @ SV574 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV574 @ ( setadjoin @ SY3008 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV218 @ SV442 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1245]) ).

thf(1498,plain,
    ! [SV443: $i,SV219: $i,SV575: $i] :
      ( ( ~ ( in @ SV575 @ SV219 )
        | ! [SY3009: $i] :
            ( ~ ( in @ SY3009 @ SV443 )
            | ( ( ksnd @ ( kpair @ SV575 @ SY3009 ) )
              = SY3009 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1246]) ).

thf(1499,plain,
    ! [SV444: $o,SV220: $i,SV576: $i] :
      ( ( ~ ( in @ SV576 @ SV220 )
        | ! [SY3010: $i] :
            ( ~ ( in @ SY3010 @ SV220 )
            | ~ SV444
            | ( ( dsetconstr @ SV220
                @ ^ [SY3011: $i] :
                    ( ~ ( ~ SV444
                        | ( SY3011 != SV576 ) )
                    | ~ ( ~ ~ SV444
                        | ( SY3011 != SY3010 ) ) ) )
              = ( setadjoin @ SV576 @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1247]) ).

thf(1500,plain,
    ! [SV220: $i,SV577: $i] :
      ( ( ~ ( in @ SV577 @ SV220 )
        | ! [SY3012: $i] :
            ( ~ ( in @ SY3012 @ SV220 )
            | ~ $true
            | ( ( dsetconstr @ SV220
                @ ^ [SY3013: $i] :
                    ( ~ ( ~ $true
                        | ( SY3013 != SV577 ) )
                    | ~ ( ~ ~ $true
                        | ( SY3013 != SY3012 ) ) ) )
              = ( setadjoin @ SV577 @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1248]) ).

thf(1501,plain,
    ! [SV220: $i,SV578: $i] :
      ( ( ~ ( in @ SV578 @ SV220 )
        | ! [SY3014: $i] :
            ( ~ ( in @ SY3014 @ SV220 )
            | ~ $false
            | ( ( dsetconstr @ SV220
                @ ^ [SY3015: $i] :
                    ( ~ ( ~ $false
                        | ( SY3015 != SV578 ) )
                    | ~ ( ~ ~ $false
                        | ( SY3015 != SY3014 ) ) ) )
              = ( setadjoin @ SV578 @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1249]) ).

thf(1502,plain,
    ! [SV445: $i,SV221: $i,SV579: $i] :
      ( ( ~ ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        | ! [SY3016: $i] :
            ( ~ ( subset @ SY3016 @ ( cartprod @ SV221 @ SV445 ) )
            | ~ ! [SY3017: $i] :
                  ( ~ ( in @ SY3017 @ SV221 )
                  | ! [SY3018: $i] :
                      ( ~ ( in @ SY3018 @ SV445 )
                      | ~ ( in @ ( kpair @ SY3017 @ SY3018 ) @ SV579 )
                      | ( in @ ( kpair @ SY3017 @ SY3018 ) @ SY3016 ) ) )
            | ~ ! [SY3019: $i] :
                  ( ~ ( in @ SY3019 @ SV221 )
                  | ! [SY3020: $i] :
                      ( ~ ( in @ SY3020 @ SV445 )
                      | ~ ( in @ ( kpair @ SY3019 @ SY3020 ) @ SY3016 )
                      | ( in @ ( kpair @ SY3019 @ SY3020 ) @ SV579 ) ) )
            | ( SV579 = SY3016 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1250]) ).

thf(1503,plain,
    ! [SV580: $i,SV446: $i,SV222: $i] :
      ( ( ~ ( func @ SV222 @ SV446 @ SV580 )
        | ! [SY3021: $i] :
            ( ~ ( in @ SY3021 @ SV222 )
            | ( singleton
              @ ( dsetconstr @ SV446
                @ ^ [SY3022: $i] : ( in @ ( kpair @ SY3021 @ SY3022 ) @ SV580 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1251]) ).

thf(1504,plain,
    ! [SV223: $i,SV447: $i] :
      ( ( ( ~ ( in @ SV447 @ SV223 ) )
        = $true )
      | ( ( subset @ ( setadjoin @ SV447 @ emptyset ) @ SV223 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1252]) ).

thf(1505,plain,
    ! [SV224: $i] :
      ( ( ( SV224 != emptyset )
        = $false )
      | ( ( ~ ! [SY2426: $i] :
                ~ ~ ( ~ ( in @ SY2426 @ SV224 )
                    | ~ $true ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1253]) ).

thf(1506,plain,
    ! [SV448: $i,SV225: $i,SV581: $i] :
      ( ( ~ ( subset @ SV581 @ SV225 )
        | ~ ( subset @ SV581 @ SV448 )
        | ( subset @ SV581 @ ( binintersect @ SV225 @ SV448 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1254]) ).

thf(1507,plain,
    ! [SV449: $i,SV226: $i,SV582: $i] :
      ( ( ~ ( in @ SV582 @ SV226 )
        | ~ ~ ( in @ SV582 @ SV449 )
        | ( in @ SV582 @ ( symdiff @ SV226 @ SV449 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1255]) ).

thf(1508,plain,
    ! [SV227: $i,SV450: $i] :
      ( ( ( ~ ( in @ SV450 @ ( powerset @ SV227 ) ) )
        = $true )
      | ( ( ! [SY2830: $i] :
              ( ~ ( in @ SY2830 @ ( powerset @ SV227 ) )
              | ~ ( subset @ ( setminus @ SV227 @ SY2830 ) @ ( setminus @ SV227 @ SV450 ) )
              | ( subset @ SV450 @ SY2830 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1256]) ).

thf(1509,plain,
    ! [SV228: $i,SV451: $i] :
      ( ( ( ~ ( in @ SV451 @ ( powerset @ SV228 ) ) )
        = $true )
      | ( ( ! [SY2831: $i] :
              ( ~ ( in @ SY2831 @ ( powerset @ SV228 ) )
              | ! [SY2832: $i] :
                  ( ~ ( in @ SY2832 @ ( powerset @ SV228 ) )
                  | ! [SY2833: $i] :
                      ( ~ ( in @ SY2833 @ SV228 )
                      | ~ ( in @ SY2833 @ ( binintersect @ SV451 @ SY2831 ) )
                      | ( in @ SY2833 @ ( binunion @ SY2831 @ SY2832 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1257]) ).

thf(1510,plain,
    ! [SV229: $i,SV452: $i] :
      ( ( ( ~ ( in @ SV452 @ SV229 ) )
        = $true )
      | ( ( in @ SV452 @ ( powerset @ ( setunion @ SV229 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1258]) ).

thf(1511,plain,
    ! [SV453: $o,SV230: $i,SV583: $i] :
      ( ( ~ ( in @ SV583 @ SV230 )
        | ! [SY3023: $i] :
            ( ~ ( in @ SY3023 @ SV230 )
            | ~ ~ SV453
            | ( ( dsetconstr @ SV230
                @ ^ [SY3024: $i] :
                    ( ~ ( ~ SV453
                        | ( SY3024 != SV583 ) )
                    | ~ ( ~ ~ SV453
                        | ( SY3024 != SY3023 ) ) ) )
              = ( setadjoin @ SY3023 @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1259]) ).

thf(1512,plain,
    ! [SV230: $i,SV584: $i] :
      ( ( ~ ( in @ SV584 @ SV230 )
        | ! [SY3025: $i] :
            ( ~ ( in @ SY3025 @ SV230 )
            | ~ ~ $true
            | ( ( dsetconstr @ SV230
                @ ^ [SY3026: $i] :
                    ( ~ ( ~ $true
                        | ( SY3026 != SV584 ) )
                    | ~ ( ~ ~ $true
                        | ( SY3026 != SY3025 ) ) ) )
              = ( setadjoin @ SY3025 @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1260]) ).

thf(1513,plain,
    ! [SV230: $i,SV585: $i] :
      ( ( ~ ( in @ SV585 @ SV230 )
        | ! [SY3027: $i] :
            ( ~ ( in @ SY3027 @ SV230 )
            | ~ ~ $false
            | ( ( dsetconstr @ SV230
                @ ^ [SY3028: $i] :
                    ( ~ ( ~ $false
                        | ( SY3028 != SV585 ) )
                    | ~ ( ~ ~ $false
                        | ( SY3028 != SY3027 ) ) ) )
              = ( setadjoin @ SY3027 @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1261]) ).

thf(1514,plain,
    ! [SV231: $i,SV454: $i] :
      ( ( ( ~ ( in @ SV454 @ ( powerset @ SV231 ) ) )
        = $true )
      | ( ( ! [SY2837: $i] :
              ( ~ ( in @ SY2837 @ ( powerset @ SV231 ) )
              | ~ ! [SY2838: $i] :
                    ( ~ ( in @ SY2838 @ SV231 )
                    | ~ ( in @ SY2838 @ SV454 )
                    | ( in @ SY2838 @ SY2837 ) )
              | ( in @ SV454 @ ( powerset @ SY2837 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1262]) ).

thf(1515,plain,
    ! [SV586: $i,SV455: $i,SV232: $i] :
      ( ( ~ ( func @ SV232 @ SV455 @ SV586 )
        | ( ( lam @ SV232 @ SV455
            @ ^ [SY3029: $i] : ( ap @ SV232 @ SV455 @ SV586 @ SY3029 ) )
          = SV586 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1263]) ).

thf(1516,plain,
    ! [SV456: $i,SV233: $i] :
      ( ( ( ( binintersect @ SV233 @ SV456 )
         != SV456 )
        = $true )
      | ( ( subset @ SV456 @ SV233 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1264]) ).

thf(1517,plain,
    ! [SV457: $i,SV234: $i,SV587: $i] :
      ( ( ~ ( in @ SV587 @ ( cartprod @ SV234 @ SV457 ) )
        | ( in @ ( kfst @ SV587 ) @ SV234 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1265]) ).

thf(1518,plain,
    ! [SV458: $i,SV235: $i] :
      ( ( ( SV235 != SV458 )
        = $true )
      | ( ( in @ SV235 @ ( setadjoin @ SV458 @ emptyset ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1266]) ).

thf(1519,plain,
    ! [SV588: $i,SV459: $i,SV236: $i] :
      ( ( ~ ( subset @ SV236 @ SV459 )
        | ~ ( subset @ SV459 @ SV588 )
        | ( subset @ SV236 @ SV588 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1267]) ).

thf(1520,plain,
    ! [SV589: $i,SV460: $i,SV237: $i] :
      ( ( ( ( setadjoin @ SV237 @ ( setadjoin @ SV460 @ emptyset ) )
         != ( setadjoin @ SV589 @ emptyset ) )
        | ( SV237 = SV460 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1268]) ).

thf(1521,plain,
    ! [SV461: $i,SV238: $i] :
      ( ( ( ~ ( subset @ SV238 @ SV461 ) )
        = $true )
      | ( ( subset @ ( powerset @ SV238 ) @ ( powerset @ SV461 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1269]) ).

thf(1522,plain,
    ! [SV590: $i,SV462: $i,SV239: $i] :
      ( ( ! [SY3030: $i] :
            ( ( ( setadjoin @ ( setadjoin @ SV239 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV239 @ ( setadjoin @ SV462 @ emptyset ) ) @ emptyset ) )
             != ( setadjoin @ ( setadjoin @ SV590 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV590 @ ( setadjoin @ SY3030 @ emptyset ) ) @ emptyset ) ) )
            | ( SV239 = SV590 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1270]) ).

thf(1523,plain,
    ! [SV591: $i,SV463: $i,SV240: $i] :
      ( ( ~ ( func @ SV240 @ SV463 @ SV591 )
        | ( in @ SV591 @ ( funcSet @ SV240 @ SV463 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1271]) ).

thf(1524,plain,
    ! [SV464: $i,SV241: $i,SV592: $i] :
      ( ( ~ ( in @ SV592 @ ( binintersect @ SV241 @ SV464 ) )
        | ( in @ SV592 @ SV464 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1272]) ).

thf(1525,plain,
    ! [SV465: $i,SV242: $i,SV593: $i] :
      ( ( ~ ~ ( in @ SV593 @ SV242 )
        | ~ ( in @ SV593 @ ( setminus @ SV242 @ SV465 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1273]) ).

thf(1526,plain,
    ! [SV243: $i,SV466: $i] :
      ( ( ( ~ ( in @ SV466 @ ( powerset @ SV243 ) ) )
        = $true )
      | ( ( ! [SY2849: $i] :
              ( ~ ( in @ SY2849 @ ( powerset @ SV243 ) )
              | ~ ! [SY2850: $i] :
                    ( ~ ( in @ SY2850 @ SV243 )
                    | ~ ( in @ SY2850 @ SV466 )
                    | ( in @ SY2850 @ SY2849 ) )
              | ( subset @ SV466 @ SY2849 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1274]) ).

thf(1527,plain,
    ! [SV467: $i,SV594: $i > $i,SV244: $i] :
      ( ( ~ ! [SY3031: $i] :
              ( ~ ( in @ SY3031 @ SV244 )
              | ( in @ ( SV594 @ SY3031 ) @ SV467 ) )
        | ! [SY3032: $i] :
            ( ~ ( in @ SY3032 @ SV244 )
            | ( ( ap @ SV244 @ SV467
                @ ( lam @ SV244 @ SV467
                  @ ^ [SY3033: $i] : ( SV594 @ SY3033 ) )
                @ SY3032 )
              = ( SV594 @ SY3032 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1275]) ).

thf(1528,plain,
    ! [SV468: $i,SV245: $i,SV595: $i] :
      ( ( ~ ( in @ SV595 @ ( funcSet @ SV245 @ SV468 ) )
        | ! [SY3034: $i] :
            ( ~ ( in @ SY3034 @ SV245 )
            | ( in @ ( kpair @ SY3034 @ ( ap @ SV245 @ SV468 @ SV595 @ SY3034 ) ) @ SV595 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1276]) ).

thf(1529,plain,
    ! [SV246: $i,SV469: $i] :
      ( ( ( ~ ( in @ SV469 @ ( powerset @ SV246 ) ) )
        = $true )
      | ( ( ! [SY2857: $i] :
              ( ~ ( in @ SY2857 @ ( powerset @ SV246 ) )
              | ! [SY2858: $i] :
                  ( ~ ( in @ SY2858 @ SV246 )
                  | ~ ( in @ SY2858 @ ( setminus @ SV246 @ SV469 ) )
                  | ~ ( in @ SY2858 @ ( binintersect @ SV469 @ SY2857 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1277]) ).

thf(1530,plain,
    ! [SV247: $i] :
      ( ( ( in @ SV247 @ omega )
        = $false )
      | ( ( in @ ( setadjoin @ SV247 @ SV247 ) @ omega )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1278]) ).

thf(1531,plain,
    ! [SV470: $i,SV248: $i] :
      ( ( ( ~ ( in @ SV248 @ ( setadjoin @ SV470 @ emptyset ) ) )
        = $true )
      | ( ( SV248 = SV470 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1279]) ).

thf(1532,plain,
    ! [SV249: $i,SV471: $i,SV596: $i] :
      ( ( ~ ( in @ SV596 @ SV471 )
        | ~ ( in @ SV596 @ ( setminus @ SV249 @ SV471 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1280]) ).

thf(1533,plain,
    ! [SV250: $i] :
      ( ( ( singleton @ SV250 )
        = $false )
      | ( ( ! [SY2483: $i] :
              ( ~ ( in @ SY2483 @ SV250 )
              | ( ( setunion @ SV250 )
                = SY2483 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1281]) ).

thf(1534,plain,
    ! [SV472: $i,SV251: $i,SV597: $i] :
      ( ( ~ ( in @ SV597 @ SV251 )
        | ! [SY3035: $i] :
            ( ~ ( in @ SY3035 @ SV472 )
            | ( in @ ( setadjoin @ SV597 @ ( setadjoin @ SY3035 @ emptyset ) ) @ ( powerset @ ( binunion @ SV251 @ SV472 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1282]) ).

thf(1535,plain,
    ! [SV473: $i,SV252: $i,SV598: $i] :
      ( ( ~ ( in @ SV598 @ ( binunion @ SV252 @ SV473 ) )
        | ( in @ SV598 @ SV252 )
        | ( in @ SV598 @ SV473 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1283]) ).

thf(1536,plain,
    ! [SV253: $i > $o] :
      ( ( ( ~ ! [SY2489: $i] :
                ~ ! [SY2490: $i] :
                    ~ ( ~ ( ~ ( SV253 @ SY2490 )
                          | ( SY2490 = SY2489 ) )
                      | ~ ( ( SY2490 != SY2489 )
                          | ( SV253 @ SY2490 ) ) ) )
        = $false )
      | ( ( ~ ! [SY2491: $i] :
                ~ ~ ( ~ ( SV253 @ SY2491 )
                    | ~ ! [SY2492: $i] :
                          ( ~ ( SV253 @ SY2492 )
                          | ( SY2491 = SY2492 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1284]) ).

thf(1537,plain,
    ! [SV474: $i,SV599: $i,SV254: $i] :
      ( ( ~ ( subset @ SV254 @ SV599 )
        | ( subset @ SV254 @ ( setadjoin @ SV474 @ SV599 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1285]) ).

thf(1538,plain,
    ! [SV255: $i,SV475: $i] :
      ( ( ( ~ ( in @ SV475 @ ( setunion @ SV255 ) ) )
        = $true )
      | ( ( ! [SY2864: $o] :
              ( ~ ! [SY2865: $i] :
                    ( ~ ( in @ SV475 @ SY2865 )
                    | ~ ( in @ SY2865 @ SV255 )
                    | SY2864 )
              | SY2864 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1286]) ).

thf(1539,plain,
    ! [SV476: $o,SV256: $i,SV600: $i] :
      ( ( ~ ( in @ SV600 @ SV256 )
        | ! [SY3036: $i] :
            ( ~ ( in @ SY3036 @ SV256 )
            | ( in @ ( if @ SV256 @ SV476 @ SV600 @ SY3036 ) @ ( setadjoin @ SV600 @ ( setadjoin @ SY3036 @ emptyset ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1287]) ).

thf(1540,plain,
    ! [SV256: $i,SV601: $i] :
      ( ( ~ ( in @ SV601 @ SV256 )
        | ! [SY3037: $i] :
            ( ~ ( in @ SY3037 @ SV256 )
            | ( in @ ( if @ SV256 @ $true @ SV601 @ SY3037 ) @ ( setadjoin @ SV601 @ ( setadjoin @ SY3037 @ emptyset ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1288]) ).

thf(1541,plain,
    ! [SV256: $i,SV602: $i] :
      ( ( ~ ( in @ SV602 @ SV256 )
        | ! [SY3038: $i] :
            ( ~ ( in @ SY3038 @ SV256 )
            | ( in @ ( if @ SV256 @ $false @ SV602 @ SY3038 ) @ ( setadjoin @ SV602 @ ( setadjoin @ SY3038 @ emptyset ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1289]) ).

thf(1542,plain,
    ! [SV477: $i,SV257: $i,SV603: $i] :
      ( ( ~ ( in @ SV603 @ SV257 )
        | ! [SY3039: $i] :
            ( ~ ( in @ SY3039 @ SV477 )
            | ( subset @ ( setadjoin @ SV603 @ ( setadjoin @ SY3039 @ emptyset ) ) @ ( binunion @ SV257 @ SV477 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1290]) ).

thf(1543,plain,
    ! [SV280: $i,SV34: $i,SV481: $i] :
      ( ( ( ~ ( in @ SV481 @ ( funcSet @ SV34 @ SV280 ) ) )
        = $true )
      | ( ( func @ SV34 @ SV280 @ SV481 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1294]) ).

thf(1544,plain,
    ! [SV281: $i > $o,SV35: $i] :
      ( ( ( ~ ~ ! [SY2514: $i] :
                  ~ ~ ( ~ ( in @ SY2514 @ SV35 )
                      | ~ ( SV281 @ SY2514 ) ) )
        = $false )
      | ( ( ! [SY2515: $i] :
              ( ~ ( in @ SY2515 @ SV35 )
              | ~ ( SV281 @ SY2515 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1295]) ).

thf(1545,plain,
    ! [SV36: $i,SV282: $i] :
      ( ( ( in @ SV282 @ ( powerset @ SV36 ) )
        = $false )
      | ( ( ! [SY2516: $i] :
              ( ~ ( in @ SY2516 @ ( powerset @ SV36 ) )
              | ! [SY2517: $i] :
                  ( ~ ( in @ SY2517 @ SV36 )
                  | ~ ( subset @ SV282 @ SY2516 )
                  | ~ ~ ( in @ SY2517 @ SY2516 )
                  | ~ ( in @ SY2517 @ SV282 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1296]) ).

thf(1546,plain,
    ! [SV37: $i > $o] :
      ( ( ( ! [SY1895: $i] :
              ~ ~ ( ~ ( SV37 @ SY1895 )
                  | ~ ! [SY1896: $i] :
                        ( ~ ( SV37 @ SY1896 )
                        | ( SY1895 = SY1896 ) ) ) )
        = $true )
      | ( ( ~ ! [SY1897: $i] :
                ~ ! [SY1898: $i] :
                    ~ ( ~ ( ~ ( SV37 @ SY1898 )
                          | ( SY1898 = SY1897 ) )
                      | ~ ( ( SY1898 != SY1897 )
                          | ( SV37 @ SY1898 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1297]) ).

thf(1547,plain,
    ! [SV482: $i,SV283: $i,SV38: $i] :
      ( ( ( ~ ( func @ SV38 @ SV283 @ SV482 ) )
        = $true )
      | ( ( ! [SY2874: $i] :
              ( ~ ( in @ SY2874 @ SV38 )
              | ( in @ ( kpair @ SY2874 @ ( ap @ SV38 @ SV283 @ SV482 @ SY2874 ) ) @ SV482 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1298]) ).

thf(1548,plain,
    ! [SV39: $i,SV604: $o] :
      ( ( SV604 = $true )
      | ( ( in @ SV39 @ emptyset )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[1299]) ).

thf(1549,plain,
    ! [SV39: $i] :
      ( ( $true = $true )
      | ( ( in @ SV39 @ emptyset )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[1299]) ).

thf(1550,plain,
    ! [SV39: $i] :
      ( ( $false = $true )
      | ( ( in @ SV39 @ emptyset )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[1299]) ).

thf(1551,plain,
    ! [SV284: $o,SV40: $i,SV483: $i] :
      ( ( ( ~ ( in @ SV483 @ SV40 ) )
        = $true )
      | ( ( ! [SY2875: $i] :
              ( ~ ( in @ SY2875 @ SV40 )
              | ~ ~ SV284
              | ( in @ SY2875
                @ ( dsetconstr @ SV40
                  @ ^ [SY2876: $i] :
                      ( ~ ( ~ SV284
                          | ( SY2876 != SV483 ) )
                      | ~ ( ~ ~ SV284
                          | ( SY2876 != SY2875 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1300]) ).

thf(1552,plain,
    ! [SV40: $i,SV484: $i] :
      ( ( ( ~ ( in @ SV484 @ SV40 ) )
        = $true )
      | ( ( ! [SY2877: $i] :
              ( ~ ( in @ SY2877 @ SV40 )
              | ~ ~ $true
              | ( in @ SY2877
                @ ( dsetconstr @ SV40
                  @ ^ [SY2878: $i] :
                      ( ~ ( ~ $true
                          | ( SY2878 != SV484 ) )
                      | ~ ( ~ ~ $true
                          | ( SY2878 != SY2877 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1301]) ).

thf(1553,plain,
    ! [SV40: $i,SV485: $i] :
      ( ( ( ~ ( in @ SV485 @ SV40 ) )
        = $true )
      | ( ( ! [SY2879: $i] :
              ( ~ ( in @ SY2879 @ SV40 )
              | ~ ~ $false
              | ( in @ SY2879
                @ ( dsetconstr @ SV40
                  @ ^ [SY2880: $i] :
                      ( ~ ( ~ $false
                          | ( SY2880 != SV485 ) )
                      | ~ ( ~ ~ $false
                          | ( SY2880 != SY2879 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1302]) ).

thf(1554,plain,
    ! [SV41: $i > $o] :
      ( ( ( ! [SY1907: $i] :
              ~ ~ ( ~ ( SV41 @ SY1907 )
                  | ~ ! [SY1908: $i] :
                        ( ~ ( SV41 @ SY1908 )
                        | ( SY1907 = SY1908 ) ) ) )
        = $true )
      | ( ( ! [SY1909: $i,SY1910: $i] :
              ( ~ ( SV41 @ SY1909 )
              | ~ ( SV41 @ SY1910 )
              | ( SY1909 = SY1910 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1303]) ).

thf(1555,plain,
    ! [SV42: $i,SV285: $i] :
      ( ( ~ ( ~ ( in @ SV285 @ ( powerset @ SV42 ) )
            | ! [SY2523: $i] :
                ( ~ ( in @ SY2523 @ SV285 )
                | ( in @ SY2523 @ SV42 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1304]) ).

thf(1556,plain,
    ! [SV42: $i,SV285: $i] :
      ( ( ~ ( ~ ! [SY2524: $i] :
                  ( ~ ( in @ SY2524 @ SV285 )
                  | ( in @ SY2524 @ SV42 ) )
            | ( in @ SV285 @ ( powerset @ SV42 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1304]) ).

thf(1557,plain,
    ! [SV43: $i > $o] :
      ( ( ( ! [SY1914: $i] :
              ~ ~ ( ~ ( SV43 @ SY1914 )
                  | ~ ! [SY1915: $i] :
                        ( ~ ( SV43 @ SY1915 )
                        | ( SY1914 = SY1915 ) ) ) )
        = $true )
      | ( ( ! [SY1916: $i,SY1917: $i] :
              ( ~ ( SV43 @ SY1916 )
              | ~ ( SV43 @ SY1917 )
              | ( SY1916 = SY1917 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1305]) ).

thf(1558,plain,
    ! [SV44: $i,SV286: $i] :
      ( ( ( in @ SV286 @ ( powerset @ SV44 ) )
        = $false )
      | ( ( ! [SY2525: $i] :
              ( ~ ( in @ SY2525 @ ( powerset @ SV44 ) )
              | ! [SY2526: $i] :
                  ( ~ ( in @ SY2526 @ SV44 )
                  | ~ ( in @ SY2526 @ ( setminus @ SV44 @ ( binunion @ SV286 @ SY2525 ) ) )
                  | ~ ( in @ SY2526 @ SV286 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1306]) ).

thf(1559,plain,
    ! [SV287: $i > $o,SV46: $i] :
      ( ( ( ~ ! [SY2527: $i] :
                ~ ~ ( ~ ( in @ SY2527 @ SV46 )
                    | ~ ~ ( SV287 @ SY2527 ) ) )
        = $false )
      | ( ( ~ ! [SY2528: $i] :
                ( ~ ( in @ SY2528 @ SV46 )
                | ( SV287 @ SY2528 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1310]) ).

thf(1560,plain,
    ! [SV288: $i,SV47: $i,SV486: $i] :
      ( ( ( ~ ~ ( in @ SV486 @ ( setminus @ SV47 @ SV288 ) ) )
        = $true )
      | ( ( ~ ( in @ SV486 @ SV47 )
          | ( in @ SV486 @ SV288 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1311]) ).

thf(1561,plain,
    ! [SV48: $i > $o] :
      ( ( ( ! [SY1926: $i] :
              ~ ~ ( ~ ( SV48 @ SY1926 )
                  | ~ ! [SY1927: $i] :
                        ( ~ ( SV48 @ SY1927 )
                        | ( SY1926 = SY1927 ) ) ) )
        = $true )
      | ( ( ~ ! [SY1928: $i] :
                ~ ~ ( ~ ( SV48 @ SY1928 )
                    | ~ ! [SY1929: $i] :
                          ( ~ ( SV48 @ SY1929 )
                          | ( SY1928 = SY1929 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1312]) ).

thf(1562,plain,
    ! [SV289: $i,SV49: $i,SV487: $i] :
      ( ( ( ~ ( in @ SV487 @ SV49 ) )
        = $true )
      | ( ( ~ ~ ( in @ SV487 @ SV289 )
          | ( in @ SV487 @ ( setminus @ SV49 @ SV289 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1313]) ).

thf(1563,plain,
    ! [SV290: $i,SV50: $i,SV488: $i] :
      ( ( ( ~ ( in @ SV488 @ SV50 ) )
        = $true )
      | ( ( ! [SY2881: $i] :
              ( ~ ( in @ SY2881 @ SV290 )
              | ( in @ ( setadjoin @ ( setadjoin @ SV488 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV488 @ ( setadjoin @ SY2881 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV50 @ SV290 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1314]) ).

thf(1564,plain,
    ! [SV291: $i,SV51: $i] :
      ( ( ( ! [SY2533: $i] :
              ~ ( ~ ( ~ ( in @ SY2533 @ SV51 )
                    | ( in @ SY2533 @ SV291 ) )
                | ~ ( ~ ( in @ SY2533 @ SV291 )
                    | ( in @ SY2533 @ SV51 ) ) ) )
        = $false )
      | ( ( SV51 = SV291 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1315]) ).

thf(1565,plain,
    ! [SV292: $i > $o,SV52: $i] :
      ( ( ( ~ ~ ! [SY2534: $i] :
                  ~ ~ ( ~ ( in @ SY2534 @ SV52 )
                      | ~ ( SV292 @ SY2534 ) ) )
        = $false )
      | ( ( ! [SY2535: $i] :
              ( ~ ( in @ SY2535 @ SV52 )
              | ~ ( SV292 @ SY2535 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1316]) ).

thf(1566,plain,
    ! [SV293: $i,SV53: $i] :
      ( ( ( SV53 = SV293 )
        = $false )
      | ( ( subset @ SV53 @ SV293 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1317]) ).

thf(1567,plain,
    ! [SV54: $i,SV294: $i] :
      ( ( ( in @ SV294 @ ( powerset @ SV54 ) )
        = $false )
      | ( ( in @ ( powerset @ SV294 ) @ ( powerset @ ( powerset @ SV54 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1318]) ).

thf(1568,plain,
    ! [SV295: $i,SV55: $i,SV489: $i] :
      ( ( ( ~ ~ ( in @ SV489 @ SV55 ) )
        = $true )
      | ( ( ~ ~ ( in @ SV489 @ SV295 )
          | ~ ( in @ SV489 @ ( symdiff @ SV55 @ SV295 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1319]) ).

thf(1569,plain,
    ! [SV490: $i > $i > $o,SV296: $i,SV56: $i,SV605: $i] :
      ( ( ! [SY3040: $i] :
            ( ~ ( in @ ( kpair @ SV605 @ SY3040 )
                @ ( dpsetconstr @ SV56 @ SV296
                  @ ^ [SY2884: $i,SY2885: $i] : ( SV490 @ SY2884 @ SY2885 ) ) )
            | ( in @ SY3040 @ SV296 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1320]) ).

thf(1570,plain,
    ! [SV297: $i,SV58: $i,SV491: $i] :
      ( ( ( ~ ( in @ ( setadjoin @ SV491 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV58 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV58 @ ( setadjoin @ SV297 @ emptyset ) ) @ emptyset ) ) ) )
        = $true )
      | ( ( SV58 = SV491 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1322]) ).

thf(1571,plain,
    ! [SV606: $i,SV492: $i,SV298: $i,SV59: $i] :
      ( ( ( ( setadjoin @ ( setadjoin @ SV59 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV59 @ ( setadjoin @ SV298 @ emptyset ) ) @ emptyset ) )
         != ( setadjoin @ ( setadjoin @ SV492 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV492 @ ( setadjoin @ SV606 @ emptyset ) ) @ emptyset ) ) )
        | ( SV298 = SV606 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1323]) ).

thf(1572,plain,
    ! [SV299: $i,SV60: $i,SV493: $i] :
      ( ( ( ~ ( in @ SV493 @ SV60 ) )
        = $true )
      | ( ( ~ ( in @ SV493 @ SV299 )
          | ~ ( in @ SV493 @ ( symdiff @ SV60 @ SV299 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1324]) ).

thf(1573,plain,
    ! [SV300: $i,SV61: $i,SV607: $i,SV494: $i] :
      ( ( ~ ( in @ ( kpair @ SV494 @ SV607 ) @ ( cartprod @ SV61 @ SV300 ) )
        | ( in @ SV494 @ SV61 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1325]) ).

thf(1574,plain,
    ! [SV301: $i,SV62: $i,SV495: $i] :
      ( ( ( ~ ( in @ SV495 @ SV62 ) )
        = $true )
      | ( ( ! [SY2888: $i] :
              ( ~ ( in @ SY2888 @ SV301 )
              | ( ( kpair @ SV495 @ SY2888 )
                = ( kpair @ SV495 @ SY2888 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1326]) ).

thf(1575,plain,
    ! [SV302: $i,SV63: $i,SV496: $i] :
      ( ( ( ~ ( subset @ SV496 @ ( cartprod @ SV63 @ SV302 ) ) )
        = $true )
      | ( ( ! [SY2889: $i > $o] :
              ( ~ ! [SY2890: $i] :
                    ( ~ ( in @ SY2890 @ SV63 )
                    | ! [SY2891: $i] :
                        ( ~ ( in @ SY2891 @ SV302 )
                        | ~ ( in @ ( kpair @ SY2890 @ SY2891 ) @ SV496 )
                        | ( SY2889 @ ( kpair @ SY2890 @ SY2891 ) ) ) )
              | ! [SY2892: $i] :
                  ( ~ ( in @ SY2892 @ SV496 )
                  | ( SY2889 @ SY2892 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1327]) ).

thf(1576,plain,
    ! [SV303: $i > $o,SV65: $i,SV497: $i] :
      ( ( ( ~ ( in @ SV497 @ SV65 ) )
        = $true )
      | ( ( ~ ( SV303 @ SV497 )
          | ( ( dsetconstr @ SV65
              @ ^ [SY2556: $i] : ( SV303 @ SY2556 ) )
           != emptyset ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1329]) ).

thf(1577,plain,
    ! [SV304: $i,SV66: $i] :
      ( ( ( SV66 = SV304 )
        = $false )
      | ( ( ( setadjoin @ ( setadjoin @ SV66 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV66 @ ( setadjoin @ SV304 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ SV66 @ emptyset ) @ emptyset ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1330]) ).

thf(1578,plain,
    ! [SV305: $o,SV67: $i,SV498: $i] :
      ( ( ( ~ ( in @ SV498 @ SV67 ) )
        = $true )
      | ( ( ! [SY2894: $i] :
              ( ~ ( in @ SY2894 @ SV67 )
              | ~ SV305
              | ( in @ SV498
                @ ( dsetconstr @ SV67
                  @ ^ [SY2895: $i] :
                      ( ~ ( ~ SV305
                          | ( SY2895 != SV498 ) )
                      | ~ ( ~ ~ SV305
                          | ( SY2895 != SY2894 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1331]) ).

thf(1579,plain,
    ! [SV67: $i,SV499: $i] :
      ( ( ( ~ ( in @ SV499 @ SV67 ) )
        = $true )
      | ( ( ! [SY2896: $i] :
              ( ~ ( in @ SY2896 @ SV67 )
              | ~ $true
              | ( in @ SV499
                @ ( dsetconstr @ SV67
                  @ ^ [SY2897: $i] :
                      ( ~ ( ~ $true
                          | ( SY2897 != SV499 ) )
                      | ~ ( ~ ~ $true
                          | ( SY2897 != SY2896 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1332]) ).

thf(1580,plain,
    ! [SV67: $i,SV500: $i] :
      ( ( ( ~ ( in @ SV500 @ SV67 ) )
        = $true )
      | ( ( ! [SY2898: $i] :
              ( ~ ( in @ SY2898 @ SV67 )
              | ~ $false
              | ( in @ SV500
                @ ( dsetconstr @ SV67
                  @ ^ [SY2899: $i] :
                      ( ~ ( ~ $false
                          | ( SY2899 != SV500 ) )
                      | ~ ( ~ ~ $false
                          | ( SY2899 != SY2898 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1333]) ).

thf(1581,plain,
    ! [SV501: $i,SV306: $i,SV68: $i] :
      ( ( ( ~ ( func @ SV68 @ SV306 @ SV501 ) )
        = $true )
      | ( ( ! [SY2900: $i] :
              ( ~ ( in @ SY2900 @ SV68 )
              | ( in
                @ ( setunion
                  @ ( dsetconstr @ SV306
                    @ ^ [SY2901: $i] : ( in @ ( kpair @ SY2900 @ SY2901 ) @ SV501 ) ) )
                @ SV306 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1334]) ).

thf(1582,plain,
    ! [SV69: $i,SV307: $i] :
      ( ( ( subset @ SV307 @ SV69 )
        = $false )
      | ( ( ( binintersect @ SV69 @ SV307 )
          = SV307 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1335]) ).

thf(1583,plain,
    ! [SV70: $i,SV308: $i] :
      ( ( ( in @ SV308 @ ( powerset @ SV70 ) )
        = $false )
      | ( ( subset @ ( setminus @ SV70 @ ( setminus @ SV70 @ SV308 ) ) @ SV308 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1336]) ).

thf(1584,plain,
    ! [SV309: $i,SV71: $i] :
      ( ( ( subset @ SV71 @ SV309 )
        = $false )
      | ( ( ( binintersect @ SV71 @ SV309 )
          = SV71 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1337]) ).

thf(1585,plain,
    ! [SV72: $i,SV310: $i] :
      ( ( ( in @ SV310 @ ( powerset @ SV72 ) )
        = $false )
      | ( ( ! [SY2563: $i] :
              ( ~ ( in @ SY2563 @ ( powerset @ SV72 ) )
              | ~ ( subset @ SV310 @ ( setminus @ SV72 @ SY2563 ) )
              | ( subset @ SY2563 @ ( setminus @ SV72 @ SV310 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1338]) ).

thf(1586,plain,
    ! [SV311: $i,SV73: $i,SV502: $i] :
      ( ( ( ~ ( in @ SV502 @ ( funcSet @ SV73 @ SV311 ) ) )
        = $true )
      | ( ( ! [SY2902: $i] :
              ( ~ ( in @ SY2902 @ ( funcSet @ SV73 @ SV311 ) )
              | ~ ! [SY2903: $i] :
                    ( ~ ( in @ SY2903 @ SV73 )
                    | ( ( ap @ SV73 @ SV311 @ SV502 @ SY2903 )
                      = ( ap @ SV73 @ SV311 @ SY2902 @ SY2903 ) ) )
              | ( SV502 = SY2902 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1339]) ).

thf(1587,plain,
    ! [SV312: $i,SV74: $i,SV503: $i] :
      ( ( ( ~ ~ ( in @ SV503 @ ( setminus @ SV74 @ SV312 ) ) )
        = $true )
      | ( ( ~ ~ ( in @ SV503 @ SV312 )
          | ~ ( in @ SV503 @ SV74 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1340]) ).

thf(1588,plain,
    ! [SV313: $i,SV75: $i,SV504: $i] :
      ( ( ~ ( ~ ( in @ SV504 @ ( setadjoin @ SV75 @ SV313 ) )
            | ( SV504 = SV75 )
            | ( in @ SV504 @ SV313 ) )
        | ~ ( ~ ( ( SV504 = SV75 )
                | ( in @ SV504 @ SV313 ) )
            | ( in @ SV504 @ ( setadjoin @ SV75 @ SV313 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1341]) ).

thf(1589,plain,
    ! [SV76: $i,SV314: $i] :
      ( ( ( in @ SV314 @ ( powerset @ SV76 ) )
        = $false )
      | ( ( ! [SY2569: $i] :
              ( ~ ( in @ SY2569 @ ( powerset @ SV76 ) )
              | ! [SY2570: $i] :
                  ( ~ ( in @ SY2570 @ ( powerset @ SV76 ) )
                  | ! [SY2571: $i] :
                      ( ~ ( in @ SY2571 @ SV76 )
                      | ~ ( in @ SY2571 @ ( binintersect @ SV314 @ SY2569 ) )
                      | ( in @ SY2571 @ ( binintersect @ ( binunion @ SV314 @ SY2570 ) @ ( binunion @ SY2569 @ SY2570 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1342]) ).

thf(1590,plain,
    ! [SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ! [SY2572: $i,SY2573: $i] :
              ( ( SY2572 != SY2573 )
              | ~ ( ~ ( ~ ( SV77 @ SY2572 )
                      | ( SV315 @ SY2573 ) )
                  | ~ ( ~ ( SV315 @ SY2573 )
                      | ( SV77 @ SY2572 ) ) ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2001: $i] :
                  ~ ~ ( ~ ( SV77 @ SY2001 )
                      | ~ ! [SY2002: $i] :
                            ( ~ ( SV77 @ SY2002 )
                            | ( SY2001 = SY2002 ) ) )
          | ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1343]) ).

thf(1591,plain,
    ! [SV316: $i > $o,SV78: $i,SV505: $i] :
      ( ( ( ~ ( in @ SV505 @ SV78 ) )
        = $true )
      | ( ( ~ ( SV316 @ SV505 )
          | ( in @ SV505
            @ ( dsetconstr @ SV78
              @ ^ [SY2581: $i] : ( SV316 @ SY2581 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1344]) ).

thf(1592,plain,
    ! [SV79: $i,SV317: $i] :
      ( ( ( subset @ SV317 @ SV79 )
        = $false )
      | ( ( in @ SV317 @ ( powerset @ SV79 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1345]) ).

thf(1593,plain,
    ! [SV80: $i,SV318: $i] :
      ( ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( ! [SY2582: $i] :
              ( ~ ( in @ SY2582 @ ( powerset @ SV80 ) )
              | ~ ! [SY2583: $i] :
                    ( ~ ( in @ SY2583 @ SV80 )
                    | ~ ( in @ SY2583 @ SV318 )
                    | ( in @ SY2583 @ SY2582 ) )
              | ~ ! [SY2584: $i] :
                    ( ~ ( in @ SY2584 @ SV80 )
                    | ~ ( in @ SY2584 @ SY2582 )
                    | ( in @ SY2584 @ SV318 ) )
              | ( SV318 = SY2582 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1346]) ).

thf(1594,plain,
    ! [SV319: $i,SV81: $i] :
      ( ( ( ! [SY2585: $i] :
              ( ~ ( in @ SY2585 @ SV81 )
              | ( in @ SY2585 @ SV319 ) ) )
        = $false )
      | ( ( ~ ! [SY2586: $i] :
                ( ~ ( in @ SY2586 @ SV319 )
                | ( in @ SY2586 @ SV81 ) )
          | ( SV81 = SV319 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1347]) ).

thf(1595,plain,
    ! [SV506: $i > $i > $o,SV320: $i,SV82: $i,SV608: $i] :
      ( ( ~ ( in @ SV608 @ SV82 )
        | ! [SY3043: $i] :
            ( ~ ( in @ SY3043 @ SV320 )
            | ~ ( in @ ( kpair @ SV608 @ SY3043 )
                @ ( dpsetconstr @ SV82 @ SV320
                  @ ^ [SY2907: $i,SY2908: $i] : ( SV506 @ SY2907 @ SY2908 ) ) )
            | ( SV506 @ SV608 @ SY3043 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1348]) ).

thf(1596,plain,
    ! [SV83: $i] :
      ( ( ( ~ ( in @ ( sK4_SY2024 @ SV83 ) @ SV83 ) )
        = $false )
      | ( ( SV83 = emptyset )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[1349]) ).

thf(1597,plain,
    ! [SV321: $i > $o,SV84: $i] :
      ( ( ( ~ ! [SY2592: $i] :
                ( ~ ( in @ SY2592 @ SV84 )
                | ( SV321 @ SY2592 ) ) )
        = $false )
      | ( ( ~ ! [SY2593: $i] :
                ~ ~ ( ~ ( in @ SY2593 @ SV84 )
                    | ~ ~ ( SV321 @ SY2593 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1350]) ).

thf(1598,plain,
    ! [SV609: $o,SV322: $i,SV85: $i,SV507: $i] :
      ( ( ~ ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        | ~ ( ~ ( in @ SV507 @ SV85 )
            | SV609 )
        | ~ ( ~ ( in @ SV507 @ SV322 )
            | SV609 )
        | SV609 )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[1351]) ).

thf(1599,plain,
    ! [SV322: $i,SV85: $i,SV507: $i] :
      ( ( ~ ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        | ~ ( ~ ( in @ SV507 @ SV85 )
            | $true )
        | ~ ( ~ ( in @ SV507 @ SV322 )
            | $true )
        | $true )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[1351]) ).

thf(1600,plain,
    ! [SV322: $i,SV85: $i,SV507: $i] :
      ( ( ~ ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        | ~ ( ~ ( in @ SV507 @ SV85 )
            | $false )
        | ~ ( ~ ( in @ SV507 @ SV322 )
            | $false )
        | $false )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[1351]) ).

thf(1601,plain,
    ! [SV86: $i,SV508: $i,SV323: $i] :
      ( ( ( ~ ( in @ SV323 @ SV508 ) )
        = $true )
      | ( ( ~ ( in @ SV508 @ SV86 )
          | ( in @ SV323 @ ( setunion @ SV86 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1352]) ).

thf(1602,plain,
    ! [SV87: $i] :
      ( ( ( ~ ( in @ emptyset @ SV87 )
          | ~ ! [SY2033: $i] :
                ( ~ ~ ( ~ ( in @ SY2033 @ omega )
                      | ~ ( in @ SY2033 @ SV87 ) )
                | ( in @ ( setadjoin @ SY2033 @ SY2033 ) @ SV87 ) ) )
        = $true )
      | ( ( ! [SY2034: $i] :
              ( ~ ( in @ SY2034 @ omega )
              | ( in @ SY2034 @ SV87 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1353]) ).

thf(1603,plain,
    ( ( ~ ( in @ sK2_SY2597 @ ( powerset @ sK1_SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1354]) ).

thf(1604,plain,
    ( ( ! [SY2910: $i] :
          ( ~ ( in @ SY2910 @ ( powerset @ sK1_SX0 ) )
          | ! [SY2911: $i] :
              ( ~ ( in @ SY2911 @ sK1_SX0 )
              | ~ ( in @ SY2911 @ ( setminus @ sK1_SX0 @ ( binunion @ sK2_SY2597 @ SY2910 ) ) )
              | ( in @ SY2911 @ ( setminus @ sK1_SX0 @ sK2_SY2597 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1354]) ).

thf(1605,plain,
    ! [SV88: $i,SV324: $i] :
      ( ( ( in @ SV324 @ ( powerset @ SV88 ) )
        = $false )
      | ( ( ! [SY2600: $i] :
              ( ~ ( in @ SY2600 @ ( powerset @ SV88 ) )
              | ~ ( subset @ SV324 @ ( setminus @ SV88 @ SY2600 ) )
              | ! [SY2601: $i] :
                  ( ~ ( in @ SY2601 @ SV88 )
                  | ~ ( in @ SY2601 @ SY2600 )
                  | ( in @ SY2601 @ ( setminus @ SV88 @ SV324 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1355]) ).

thf(1606,plain,
    ! [SV325: $i > $o,SV89: $i] :
      ( ( ( ~ ! [SY2602: $i] :
                ~ ~ ( ~ ( in @ SY2602 @ SV89 )
                    | ~ ( SV325 @ SY2602 ) ) )
        = $false )
      | ( ( ( ( dsetconstr @ SV89
              @ ^ [SY2603: $i] : ( SV325 @ SY2603 ) )
           != emptyset )
          | $false )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1356]) ).

thf(1607,plain,
    ! [SV326: $i,SV90: $i] :
      ( ( ( ! [SY2604: $i] :
              ( ~ ( in @ SY2604 @ SV90 )
              | ( in @ SY2604 @ SV326 ) ) )
        = $false )
      | ( ( subset @ SV90 @ SV326 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1357]) ).

thf(1608,plain,
    ! [SV91: $i,SV327: $i] :
      ( ( ( in @ SV327 @ ( powerset @ SV91 ) )
        = $false )
      | ( ( ! [SY2605: $i] :
              ( ~ ( in @ SY2605 @ ( powerset @ SV91 ) )
              | ( in @ ( binintersect @ SV327 @ SY2605 ) @ ( powerset @ SV91 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1358]) ).

thf(1609,plain,
    ! [SV328: $i,SV92: $i] :
      ( ( ( SV92 = SV328 )
        = $false )
      | ( ( ! [SY2606: $i,SY2607: $i] :
              ( ( SY2606 != SY2607 )
              | ~ ( in @ SY2606 @ SV92 )
              | ( in @ SY2607 @ SV328 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1359]) ).

thf(1610,plain,
    ! [SV509: $i > $i > $o,SV329: $i,SV93: $i,SV610: $i] :
      ( ( ! [SY3046: $i] :
            ( ~ ( in @ ( kpair @ SV610 @ SY3046 )
                @ ( dpsetconstr @ SV93 @ SV329
                  @ ^ [SY2914: $i,SY2915: $i] : ( SV509 @ SY2914 @ SY2915 ) ) )
            | ( SV509 @ SV610 @ SY3046 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1360]) ).

thf(1611,plain,
    ! [SV611: $i,SV510: $i,SV330: $i,SV94: $i] :
      ( ( ( ( kpair @ SV94 @ SV330 )
         != ( kpair @ SV510 @ SV611 ) )
        | ( SV94 = SV510 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1361]) ).

thf(1612,plain,
    ! [SV511: $i,SV331: $i,SV95: $i] :
      ( ( ( ~ ( subset @ SV95 @ SV331 ) )
        = $true )
      | ( ( ~ ( in @ SV511 @ SV95 )
          | ( in @ SV511 @ SV331 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1362]) ).

thf(1613,plain,
    ! [SV512: $i,SV332: $i,SV96: $i] :
      ( ( ( ~ ( func @ SV96 @ SV332 @ SV512 ) )
        = $true )
      | ( ( ! [SY2917: $i] :
              ( ~ ( func @ SV96 @ SV332 @ SY2917 )
              | ~ ! [SY2918: $i] :
                    ( ~ ( in @ SY2918 @ SV96 )
                    | ( ( ap @ SV96 @ SV332 @ SV512 @ SY2918 )
                      = ( ap @ SV96 @ SV332 @ SY2917 @ SY2918 ) ) )
              | ! [SY2919: $i] :
                  ( ~ ( in @ SY2919 @ SV96 )
                  | ! [SY2920: $i] :
                      ( ~ ( in @ SY2920 @ SV332 )
                      | ~ ( in @ ( kpair @ SY2919 @ SY2920 ) @ SY2917 )
                      | ( in @ ( kpair @ SY2919 @ SY2920 ) @ SV512 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1363]) ).

thf(1614,plain,
    ! [SV333: $i,SV98: $i,SV513: $i] :
      ( ( ( ~ ( in @ SV513 @ ( cartprod @ SV98 @ SV333 ) ) )
        = $true )
      | ( ( ~ ! [SY2921: $i] :
                ~ ~ ( ~ ( in @ SY2921 @ SV98 )
                    | ~ ~ ! [SY2922: $i] :
                            ~ ~ ( ~ ( in @ SY2922 @ SV333 )
                                | ( SV513
                                 != ( kpair @ SY2921 @ SY2922 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1365]) ).

thf(1615,plain,
    ! [SV99: $i,SV334: $i] :
      ( ( ( in @ SV334 @ ( powerset @ SV99 ) )
        = $false )
      | ( ( ! [SY2624: $i] :
              ( ~ ( in @ SY2624 @ ( powerset @ SV99 ) )
              | ! [SY2625: $i] :
                  ( ~ ( in @ SY2625 @ SV99 )
                  | ~ ( in @ SV334 @ ( powerset @ SY2624 ) )
                  | ~ ( in @ SY2625 @ SV334 )
                  | ( in @ SY2625 @ SY2624 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1366]) ).

thf(1616,plain,
    ! [SV100: $i] :
      ( ( ( ~ ( in @ ( sK5_SY2073 @ SV100 ) @ SV100 ) )
        = $false )
      | ( ( SV100 = emptyset )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[1367]) ).

thf(1617,plain,
    ! [SV335: $i,SV101: $i,SV514: $i] :
      ( ( ( ~ ( in @ SV514 @ ( setadjoin @ SV101 @ SV335 ) ) )
        = $true )
      | ( ( ( SV514 = SV101 )
          | ( in @ SV514 @ SV335 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1368]) ).

thf(1618,plain,
    ! [SV336: $i > $o,SV102: $i] :
      ( ( ( ! [SY2627: $i] :
              ( ~ ( in @ SY2627 @ SV102 )
              | ! [SY2628: $i] :
                  ( ~ ( in @ SY2628 @ SV102 )
                  | ~ ( SV336 @ SY2627 )
                  | ~ ( SV336 @ SY2628 )
                  | ( SY2627 = SY2628 ) ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2629: $i] :
                  ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                      | ~ ( SV336 @ SY2629 ) )
          | ( singleton
            @ ( dsetconstr @ SV102
              @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1369]) ).

thf(1619,plain,
    ! [SV515: $i > $i > $o,SV337: $i,SV103: $i,SV612: $i] :
      ( ( ! [SY3049: $i] :
            ( ~ ( in @ ( kpair @ SV612 @ SY3049 )
                @ ( dpsetconstr @ SV103 @ SV337
                  @ ^ [SY2925: $i,SY2926: $i] : ( SV515 @ SY2925 @ SY2926 ) ) )
            | ( in @ SV612 @ SV103 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1370]) ).

thf(1620,plain,
    ! [SV338: $i,SV104: $i] :
      ( ( ( SV104 != SV338 )
        = $false )
      | ( ( ~ ( in @ SV338 @ ( setadjoin @ SV104 @ emptyset ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1371]) ).

thf(1621,plain,
    ! [SV339: $i,SV516: $i > $i,SV105: $i] :
      ( ( ( ~ ! [SY2927: $i] :
                ( ~ ( in @ SY2927 @ SV105 )
                | ( in @ ( SV516 @ SY2927 ) @ SV339 ) ) )
        = $true )
      | ( ( ( lam @ SV105 @ SV339
            @ ^ [SY2928: $i] : ( SV516 @ SY2928 ) )
          = ( lam @ SV105 @ SV339
            @ ^ [SY2929: $i] : ( SV516 @ SY2929 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1372]) ).

thf(1622,plain,
    ! [SV340: $i,SV106: $i,SV517: $i] :
      ( ( ( ~ ( in @ SV517 @ SV106 ) )
        = $true )
      | ( ( in @ ( setadjoin @ SV517 @ emptyset ) @ ( powerset @ ( binunion @ SV106 @ SV340 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1373]) ).

thf(1623,plain,
    ! [SV341: $i,SV518: $i > $i,SV107: $i] :
      ( ( ( ~ ! [SY2930: $i] :
                ( ~ ( in @ SY2930 @ SV107 )
                | ( in @ ( SV518 @ SY2930 ) @ SV341 ) ) )
        = $true )
      | ( ( in
          @ ( lam @ SV107 @ SV341
            @ ^ [SY2931: $i] : ( SV518 @ SY2931 ) )
          @ ( funcSet @ SV107 @ SV341 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1374]) ).

thf(1624,plain,
    ! [SV342: $i,SV108: $i] :
      ( ( ( SV108 = SV342 )
        = $false )
      | ( ( ( setunion @ SV108 )
          = ( setunion @ SV342 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1375]) ).

thf(1625,plain,
    ! [SV109: $i] :
      ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY2932: $i] :
                              ( ~ ( in @ SY2932 @ ( sK3_SY2100 @ SV109 ) )
                              | ! [SY2102: $i] :
                                  ( ~ ( in @ SY2102 @ SY2932 )
                                  | ( in @ SY2102 @ SV109 ) ) )
                        | ~ ! [SY2934: $i,SY2935: $i] :
                              ( ~ ~ ( ~ ( in @ SY2934 @ SV109 )
                                    | ~ ( in @ SY2935 @ SV109 ) )
                              | ~ ! [SY2936: $i] :
                                    ( ~ ( in @ SY2936 @ ( sK3_SY2100 @ SV109 ) )
                                    | ~ ( ~ ( ~ ( in @ SY2934 @ SY2936 )
                                            | ( in @ SY2935 @ SY2936 ) )
                                        | ~ ( ~ ( in @ SY2935 @ SY2936 )
                                            | ( in @ SY2934 @ SY2936 ) ) ) )
                              | ( SY2934 = SY2935 ) ) )
                  | ~ ! [SY2937: $i,SY2938: $i] :
                        ( ~ ~ ( ~ ( in @ SY2937 @ ( sK3_SY2100 @ SV109 ) )
                              | ~ ( in @ SY2938 @ ( sK3_SY2100 @ SV109 ) ) )
                        | ! [SX4: $i] :
                            ( ~ ( in @ SX4 @ SY2937 )
                            | ( in @ SX4 @ SY2938 ) )
                        | ! [SX4: $i] :
                            ( ~ ( in @ SX4 @ SY2938 )
                            | ( in @ SX4 @ SY2937 ) ) ) )
            | ~ ! [SY2941: $i] :
                  ( ~ ~ ( ~ ! [SY2111: $i] :
                              ( ~ ( in @ SY2111 @ SY2941 )
                              | ( in @ SY2111 @ SV109 ) )
                        | ~ ~ ! [SX3: $i] :
                                ~ ( in @ SX3 @ SY2941 ) )
                  | ~ ! [SY2944: $i] :
                        ~ ~ ! [SY2945: $i] :
                              ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY2944 @ ( sK3_SY2100 @ SV109 ) )
                                              | ~ ( in @ SY2945 @ SY2941 ) )
                                        | ~ ~ ~ ! [SX5: $i] :
                                                  ~ ~ ( ~ ( in @ SX5 @ SY2944 )
                                                      | ~ ( in @ SX5 @ SY2941 ) ) )
                                  | ~ ! [SY2947: $i] :
                                        ( ~ ( in @ SY2947 @ ( sK3_SY2100 @ SV109 ) )
                                        | ! [SX6: $i] :
                                            ( ~ ( in @ SX6 @ SY2947 )
                                            | ( in @ SX6 @ SY2944 ) )
                                        | ( in @ SY2945 @ SY2947 ) ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1376]) ).

thf(1626,plain,
    ! [SV110: $i] :
      ( ( ( ! [SY2118: $i] :
              ~ ( in @ SY2118 @ SV110 ) )
        = $true )
      | ( ( ~ ! [SY2119: $i] :
                ~ ~ ( ~ ( in @ SY2119 @ SV110 )
                    | ~ ~ ~ ! [SY2120: $i] :
                              ~ ~ ( ~ ( in @ SY2120 @ SY2119 )
                                  | ~ ( in @ SY2120 @ SV110 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1377]) ).

thf(1627,plain,
    ! [SV343: $i,SV111: $i,SV519: $i] :
      ( ( ( ~ ( in @ SV519 @ ( binintersect @ SV111 @ SV343 ) ) )
        = $true )
      | ( ( in @ SV519 @ SV111 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1378]) ).

thf(1628,plain,
    ! [SV112: $i > $o] :
      ( ( ( ! [SY2123: $i] :
              ~ ~ ( ~ ( SV112 @ SY2123 )
                  | ~ ! [SY2124: $i] :
                        ( ~ ( SV112 @ SY2124 )
                        | ( SY2123 = SY2124 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2125: $i] :
                ~ ( SV112 @ SY2125 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1379]) ).

thf(1629,plain,
    ! [SV344: $i,SV113: $i] :
      ( ( ( ~ ~ ! [SY2645: $i] :
                  ~ ~ ( ~ ( in @ SY2645 @ SV113 )
                      | ~ ( in @ SY2645 @ SV344 ) ) )
        = $false )
      | ( ( ( binintersect @ SV113 @ SV344 )
          = emptyset )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1380]) ).

thf(1630,plain,
    ! [SV345: $i,SV114: $i] :
      ( ( ( subset @ SV114 @ SV345 )
        = $false )
      | ( ( ( setminus @ SV114 @ SV345 )
          = emptyset )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1381]) ).

thf(1631,plain,
    ! [SV116: $i,SV346: $i] :
      ( ( ( in @ SV346 @ ( powerset @ SV116 ) )
        = $false )
      | ( ( ! [SY2646: $i] :
              ( ~ ( in @ SY2646 @ ( powerset @ SV116 ) )
              | ! [SY2647: $i] :
                  ( ~ ( in @ SY2647 @ SV116 )
                  | ~ ~ ( in @ SY2647 @ ( binunion @ SV346 @ SY2646 ) )
                  | ~ ( in @ SY2647 @ SV346 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1383]) ).

thf(1632,plain,
    ! [SV347: $o,SV118: $i,SV520: $i] :
      ( ( ( ~ ( in @ SV520 @ SV118 ) )
        = $true )
      | ( ( ! [SY2949: $i] :
              ( ~ ( in @ SY2949 @ SV118 )
              | ~ ~ SV347
              | ( ( if @ SV118 @ SV347 @ SV520 @ SY2949 )
                = SY2949 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1385]) ).

thf(1633,plain,
    ! [SV118: $i,SV521: $i] :
      ( ( ( ~ ( in @ SV521 @ SV118 ) )
        = $true )
      | ( ( ! [SY2950: $i] :
              ( ~ ( in @ SY2950 @ SV118 )
              | ~ ~ $true
              | ( ( if @ SV118 @ $true @ SV521 @ SY2950 )
                = SY2950 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1386]) ).

thf(1634,plain,
    ! [SV118: $i,SV522: $i] :
      ( ( ( ~ ( in @ SV522 @ SV118 ) )
        = $true )
      | ( ( ! [SY2951: $i] :
              ( ~ ( in @ SY2951 @ SV118 )
              | ~ ~ $false
              | ( ( if @ SV118 @ $false @ SV522 @ SY2951 )
                = SY2951 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1387]) ).

thf(1635,plain,
    ! [SV119: $i > $o,SV348: $i] :
      ( ( ( in @ SV348 @ emptyset )
        = $false )
      | ( ( SV119 @ SV348 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1388]) ).

thf(1636,plain,
    ! [SV121: $i,SV349: $i] :
      ( ( ( in @ SV349 @ ( powerset @ SV121 ) )
        = $false )
      | ( ( ! [SY2650: $i] :
              ( ~ ( in @ SY2650 @ SV121 )
              | ~ ~ ( in @ SY2650 @ ( setminus @ SV121 @ SV349 ) )
              | ( in @ SY2650 @ SV349 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1392]) ).

thf(1637,plain,
    ! [SV122: $i,SV350: $i] :
      ( ( ( in @ SV350 @ ( powerset @ SV122 ) )
        = $false )
      | ( ( ! [SY2651: $i] :
              ( ~ ( in @ SY2651 @ ( powerset @ SV122 ) )
              | ( subset @ ( setminus @ SV122 @ SV350 ) @ ( setminus @ SV122 @ ( binintersect @ SV350 @ SY2651 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1393]) ).

thf(1638,plain,
    ! [SV523: $i,SV351: $i,SV123: $i] :
      ( ( ( ~ ( subset @ SV123 @ SV351 ) )
        = $true )
      | ( ( ~ ~ ( in @ SV523 @ SV351 )
          | ~ ( in @ SV523 @ SV123 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1394]) ).

thf(1639,plain,
    ! [SV352: $i,SV524: $i > $i,SV124: $i] :
      ( ( ( ~ ! [SY2952: $i] :
                ( ~ ( in @ SY2952 @ SV124 )
                | ( in @ ( SV524 @ SY2952 ) @ SV352 ) ) )
        = $true )
      | ( ( func @ SV124 @ SV352
          @ ( dpsetconstr @ SV124 @ SV352
            @ ^ [SY2953: $i,SY2954: $i] :
                ( ( SV524 @ SY2953 )
                = SY2954 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1395]) ).

thf(1640,plain,
    ! [SV353: $i > $o,SV125: $i] :
      ( ( ( ! [SY2657: $i] :
              ( ~ ( in @ SY2657 @ SV125 )
              | ! [SY2658: $i] :
                  ( ~ ( in @ SY2658 @ SV125 )
                  | ~ ( SV353 @ SY2657 )
                  | ~ ( SV353 @ SY2658 )
                  | ( SY2657 = SY2658 ) ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2659: $i] :
                  ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                      | ~ ( SV353 @ SY2659 ) )
          | ( singleton
            @ ( dsetconstr @ SV125
              @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1396]) ).

thf(1641,plain,
    ! [SV354: $i,SV126: $i,SV525: $i] :
      ( ( ( ~ ~ ( in @ SV525 @ SV126 ) )
        = $true )
      | ( ( ~ ( in @ SV525 @ SV354 )
          | ( in @ SV525 @ ( symdiff @ SV126 @ SV354 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1397]) ).

thf(1642,plain,
    ! [SV355: $i,SV127: $i,SV526: $i] :
      ( ( ( ~ ( in @ SV526 @ ( setadjoin @ SV127 @ ( setadjoin @ SV355 @ emptyset ) ) ) )
        = $true )
      | ( ( ( SV526 = SV127 )
          | ( SV526 = SV355 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1398]) ).

thf(1643,plain,
    ! [SV128: $i,SV356: $i] :
      ( ( ( in @ SV356 @ ( powerset @ SV128 ) )
        = $false )
      | ( ( ! [SY2663: $i] :
              ( ~ ( in @ SY2663 @ ( powerset @ SV128 ) )
              | ( in @ ( setminus @ SV128 @ SV356 ) @ ( powerset @ ( setminus @ SV128 @ ( binintersect @ SV356 @ SY2663 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1399]) ).

thf(1644,plain,
    ! [SV129: $i,SV357: $i] :
      ( ( ( in @ SV357 @ ( powerset @ SV129 ) )
        = $false )
      | ( ( ! [SY2664: $i] :
              ( ~ ( in @ SY2664 @ SV129 )
              | ~ ( in @ SY2664 @ SV357 )
              | ~ ( in @ SY2664 @ ( setminus @ SV129 @ SV357 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1400]) ).

thf(1645,plain,
    ! [SV130: $i,SV358: $i] :
      ( ( ( in @ SV358 @ ( powerset @ SV130 ) )
        = $false )
      | ( ( SV358
          = ( setminus @ SV130 @ ( setminus @ SV130 @ SV358 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1401]) ).

thf(1646,plain,
    ! [SV359: $i,SV131: $i] :
      ( ( ( SV131 = SV359 )
        = $false )
      | ( ( ( powerset @ SV131 )
          = ( powerset @ SV359 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1402]) ).

thf(1647,plain,
    ! [SV132: $i,SV360: $i] :
      ( ( ( in @ SV360 @ ( powerset @ SV132 ) )
        = $false )
      | ( ( ! [SY2665: $i] :
              ( ~ ( in @ SY2665 @ ( powerset @ SV132 ) )
              | ~ ( subset @ SV360 @ SY2665 )
              | ( subset @ ( setminus @ SV132 @ SY2665 ) @ ( setminus @ SV132 @ SV360 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1403]) ).

thf(1648,plain,
    ! [SV527: $i,SV361: $i,SV133: $i] :
      ( ( ( ~ ( func @ SV133 @ SV361 @ SV527 ) )
        = $true )
      | ( ( ! [SY2955: $i] :
              ( ~ ( in @ SY2955 @ SV133 )
              | ( ( ap @ SV133 @ SV361 @ SV527 @ SY2955 )
                = ( ap @ SV133 @ SV361 @ SV527 @ SY2955 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1404]) ).

thf(1649,plain,
    ! [SV362: $i,SV134: $i,SV528: $i] :
      ( ( ( ~ ( in @ SV528 @ ( setadjoin @ SV134 @ ( setadjoin @ SV362 @ emptyset ) ) ) )
        = $true )
      | ( ( ( SV528 = SV134 )
          | ( SV528 = SV362 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1405]) ).

thf(1650,plain,
    ! [SV363: $i,SV135: $i,SV529: $i] :
      ( ( ( ~ ( subset @ SV529 @ ( cartprod @ SV135 @ SV363 ) ) )
        = $true )
      | ( ( ! [SY2956: $i > $o] :
              ( ~ ! [SY2957: $i] :
                    ( ~ ( in @ SY2957 @ SV135 )
                    | ! [SY2958: $i] :
                        ( ~ ( in @ SY2958 @ SV363 )
                        | ~ ( in @ ( kpair @ SY2957 @ SY2958 ) @ SV529 )
                        | ( SY2956 @ ( kpair @ SY2957 @ SY2958 ) ) ) )
              | ! [SY2959: $i] :
                  ( ~ ( in @ SY2959 @ SV529 )
                  | ( SY2956 @ SY2959 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1406]) ).

thf(1651,plain,
    ! [SV530: $i,SV136: $i,SV364: $i] :
      ( ( ( ~ ( in @ SV364 @ ( powerset @ SV136 ) ) )
        = $true )
      | ( ( ~ ( in @ SV530 @ SV364 )
          | ( in @ SV530 @ SV136 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1407]) ).

thf(1652,plain,
    ! [SV137: $i,SV365: $i] :
      ( ( ( in @ SV365 @ ( powerset @ SV137 ) )
        = $false )
      | ( ( ! [SY2675: $i] :
              ( ~ ( in @ SY2675 @ ( powerset @ SV137 ) )
              | ! [SY2676: $i] :
                  ( ~ ( in @ SY2676 @ SV137 )
                  | ~ ~ ( in @ SY2676 @ SY2675 )
                  | ~ ( in @ SY2676 @ ( binintersect @ SV365 @ SY2675 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1408]) ).

thf(1653,plain,
    ! [SV138: $i,SV366: $i] :
      ( ( ( in @ SV366 @ SV138 )
        = $false )
      | ( ( in @ ( setadjoin @ SV366 @ emptyset ) @ ( powerset @ SV138 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1409]) ).

thf(1654,plain,
    ! [SV139: $o,SV367: $i] :
      ( ( ( in @ SV367 @ ( prop2set @ SV139 ) )
        = $false )
      | ( SV139 = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1410]) ).

thf(1655,plain,
    ! [SV368: $i] :
      ( ( ( in @ SV368 @ ( prop2set @ $true ) )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1411]) ).

thf(1656,plain,
    ! [SV369: $i] :
      ( ( ( in @ SV369 @ ( prop2set @ $false ) )
        = $false )
      | ( $false = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1412]) ).

thf(1657,plain,
    ! [SV370: $i,SV140: $i,SV531: $i] :
      ( ( ( ~ ( in @ SV531 @ SV140 ) )
        = $true )
      | ( ( ! [SY2960: $i] :
              ( ~ ( in @ SY2960 @ SV370 )
              | ( in @ ( kpair @ SV531 @ SY2960 ) @ ( cartprod @ SV140 @ SV370 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1413]) ).

thf(1658,plain,
    ! [SV371: $i,SV141: $i,SV532: $i] :
      ( ( ( ~ ( in @ SV532 @ ( cartprod @ SV141 @ SV371 ) ) )
        = $true )
      | ( ( in @ ( ksnd @ SV532 ) @ SV371 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1414]) ).

thf(1659,plain,
    ! [SV372: $i > $o,SV142: $i] :
      ( ( ( singleton
          @ ( dsetconstr @ SV142
            @ ^ [SY2680: $i] : ( SV372 @ SY2680 ) ) )
        = $false )
      | ( ( ! [SY2681: $i] :
              ( ~ ( in @ SY2681 @ SV142 )
              | ! [SY2682: $i] :
                  ( ~ ( in @ SY2682 @ SV142 )
                  | ~ ( SV372 @ SY2681 )
                  | ~ ( SV372 @ SY2682 )
                  | ( SY2681 = SY2682 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1415]) ).

thf(1660,plain,
    ! [SV143: $i,SV373: $i] :
      ( ( ( in @ SV373 @ ( powerset @ SV143 ) )
        = $false )
      | ( ( subset @ SV373 @ SV143 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1416]) ).

thf(1661,plain,
    ! [SV374: $i,SV144: $i,SV533: $i] :
      ( ( ( ~ ( in @ SV533 @ SV144 ) )
        = $true )
      | ( ( ! [SY2961: $i] :
              ( ~ ( in @ SY2961 @ SV374 )
              | ( ( kfst @ ( kpair @ SV533 @ SY2961 ) )
                = SV533 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1417]) ).

thf(1662,plain,
    ! [SV145: $i,SV375: $i] :
      ( ( ( in @ SV375 @ ( powerset @ SV145 ) )
        = $false )
      | ( ( in @ ( setminus @ SV145 @ SV375 ) @ ( powerset @ SV145 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1418]) ).

thf(1663,plain,
    ! [SV613: $i,SV534: $i,SV376: $i,SV146: $i] :
      ( ( ( ( kpair @ SV146 @ SV376 )
         != ( kpair @ SV534 @ SV613 ) )
        | ( SV376 = SV613 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1419]) ).

thf(1664,plain,
    ! [SV147: $i > $i > $o,SV377: $i] :
      ( ( ( ! [SY2687: $i] :
              ( ~ ( in @ SY2687 @ SV377 )
              | ~ ! [SY2202: $i] :
                    ~ ~ ( ~ ( SV147 @ SY2687 @ SY2202 )
                        | ~ ! [SY2203: $i] :
                              ( ~ ( SV147 @ SY2687 @ SY2203 )
                              | ( SY2202 = SY2203 ) ) ) ) )
        = $false )
      | ( ( ~ ! [SY2690: $i] :
                ~ ! [SY2691: $i] :
                    ~ ( ~ ( ~ ( in @ SY2691 @ SY2690 )
                          | ~ ! [SY2692: $i] :
                                ~ ~ ( ~ ( in @ SY2692 @ SV377 )
                                    | ~ ( SV147 @ SY2692 @ SY2691 ) ) )
                      | ~ ( ~ ~ ! [SY2693: $i] :
                                  ~ ~ ( ~ ( in @ SY2693 @ SV377 )
                                      | ~ ( SV147 @ SY2693 @ SY2691 ) )
                          | ( in @ SY2691 @ SY2690 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1420]) ).

thf(1665,plain,
    ! [SV378: $i,SV148: $i] :
      ( ( ( ! [SY2694: $i] :
              ( ~ ( in @ SY2694 @ SV148 )
              | ( in @ SY2694 @ SV378 ) ) )
        = $false )
      | ( ( subset @ SV148 @ SV378 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1421]) ).

thf(1666,plain,
    ! [SV379: $i,SV149: $i] :
      ( ( ( subset @ SV149 @ SV379 )
        = $false )
      | ( ( ~ ( subset @ SV379 @ SV149 )
          | ( SV149 = SV379 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1422]) ).

thf(1667,plain,
    ! [SV380: $i,SV150: $i,SV535: $i] :
      ( ( ( ~ ( in @ SV535 @ SV150 ) )
        = $true )
      | ( ( in @ SV535 @ ( binunion @ SV150 @ SV380 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1423]) ).

thf(1668,plain,
    ! [SV151: $i,SV381: $i] :
      ( ( ( in @ SV381 @ ( powerset @ SV151 ) )
        = $false )
      | ( ( ! [SY2696: $i] :
              ( ~ ( in @ SY2696 @ ( powerset @ SV151 ) )
              | ! [SY2697: $i] :
                  ( ~ ( in @ SY2697 @ SV151 )
                  | ~ ~ ( in @ SY2697 @ ( binunion @ SV381 @ SY2696 ) )
                  | ~ ( in @ SY2697 @ SY2696 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1424]) ).

thf(1669,plain,
    ! [SV382: $i,SV152: $i] :
      ( ( ( SV152 = SV382 )
        = $false )
      | ( ( ! [SY2698: $i,SY2699: $i] :
              ( ( SY2698 != SY2699 )
              | ( ( setadjoin @ SV152 @ SY2698 )
                = ( setadjoin @ SV382 @ SY2699 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1425]) ).

thf(1670,plain,
    ! [SV154: $i,SV383: $i,SV536: $i] :
      ( ( ( ~ ( in @ SV536 @ SV383 ) )
        = $true )
      | ( ( in @ SV536 @ ( binunion @ SV154 @ SV383 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1427]) ).

thf(1671,plain,
    ! [SV384: $i,SV155: $i] :
      ( ( ( SV155 = SV384 )
        = $false )
      | ( ( subset @ SV384 @ SV155 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1428]) ).

thf(1672,plain,
    ! [SV156: $i,SV385: $i] :
      ( ( ( in @ SV385 @ ( powerset @ SV156 ) )
        = $false )
      | ( ( ! [SY2701: $i] :
              ( ~ ( in @ SY2701 @ ( powerset @ SV156 ) )
              | ! [SY2702: $i] :
                  ( ~ ( in @ SY2702 @ SV156 )
                  | ~ ~ ( in @ SY2702 @ SV385 )
                  | ~ ( in @ SY2702 @ ( binintersect @ SV385 @ SY2701 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1429]) ).

thf(1673,plain,
    ! [SV157: $i > $o] :
      ( ( ( ! [SY2225: $i] :
              ~ ~ ( ~ ( SV157 @ SY2225 )
                  | ~ ! [SY2226: $i] :
                        ( ~ ( SV157 @ SY2226 )
                        | ( SY2225 = SY2226 ) ) ) )
        = $true )
      | ( ( SV157
          @ ( descr
            @ ^ [SY2227: $i] : ( SV157 @ SY2227 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1430]) ).

thf(1674,plain,
    ! [SV386: $i,SV158: $i,SV537: $i] :
      ( ( ( ~ ( in @ SV537 @ ( setminus @ SV158 @ SV386 ) ) )
        = $true )
      | ( ( ~ ( in @ SV537 @ SV386 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1431]) ).

thf(1675,plain,
    ! [SV159: $i,SV387: $i] :
      ( ( ( in @ SV387 @ ( powerset @ SV159 ) )
        = $false )
      | ( ( subset @ SV387 @ ( setminus @ SV159 @ ( setminus @ SV159 @ SV387 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1432]) ).

thf(1676,plain,
    ! [SV388: $i > $o,SV160: $i] :
      ( ( ( ~ ! [SY2704: $i] :
                ( ~ ( in @ SY2704 @ SV160 )
                | ( SV388 @ SY2704 ) ) )
        = $false )
      | ( ( ~ ! [SY2705: $i] :
                ~ ~ ( ~ ( in @ SY2705 @ SV160 )
                    | ~ ~ ( SV388 @ SY2705 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1433]) ).

thf(1677,plain,
    ! [SV161: $i,SV389: $i] :
      ( ( ( in @ SV389 @ ( powerset @ SV161 ) )
        = $false )
      | ( ( ! [SY2706: $i] :
              ( ~ ( in @ SY2706 @ ( powerset @ SV161 ) )
              | ! [SY2707: $i] :
                  ( ~ ( in @ SY2707 @ SV161 )
                  | ~ ( in @ SY2707 @ ( setminus @ SV161 @ SV389 ) )
                  | ( in @ SY2707 @ ( setminus @ SV161 @ ( binintersect @ SV389 @ SY2706 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1434]) ).

thf(1678,plain,
    ! [SV162: $i,SV390: $i] :
      ( ( ( in @ SV390 @ ( powerset @ SV162 ) )
        = $false )
      | ( ( ! [SY2708: $i] :
              ( ~ ( in @ SY2708 @ ( powerset @ SV162 ) )
              | ( in @ ( binunion @ SV390 @ SY2708 ) @ ( powerset @ SV162 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1435]) ).

thf(1679,plain,
    ! [SV391: $i,SV163: $i] :
      ( ( ( subset @ SV163 @ SV391 )
        = $false )
      | ( ( in @ SV163 @ ( powerset @ SV391 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1436]) ).

thf(1680,plain,
    ! [SV392: $i,SV164: $i] :
      ( ( ( ( setminus @ SV164 @ SV392 )
          = emptyset )
        = $false )
      | ( ( subset @ SV164 @ SV392 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1437]) ).

thf(1681,plain,
    ! [SV165: $i > $o] :
      ( ( ( ! [SY2241: $i] :
              ~ ( SV165 @ SY2241 ) )
        = $true )
      | ( ( ~ ! [SY2242: $i,SY2243: $i] :
                ( ~ ( SV165 @ SY2242 )
                | ~ ( SV165 @ SY2243 )
                | ( SY2242 = SY2243 ) )
          | ~ ! [SY2244: $i] :
                ~ ~ ( ~ ( SV165 @ SY2244 )
                    | ~ ! [SY2245: $i] :
                          ( ~ ( SV165 @ SY2245 )
                          | ( SY2244 = SY2245 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1438]) ).

thf(1682,plain,
    ! [SV393: $i,SV166: $i,SV538: $i] :
      ( ( ( ~ ( in @ SV538 @ SV166 ) )
        = $true )
      | ( ( ~ ~ ( in @ SV538 @ SV393 )
          | ~ ( subset @ SV166 @ SV393 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1439]) ).

thf(1683,plain,
    ! [SV167: $i,SV394: $i] :
      ( ( ( in @ SV394 @ ( powerset @ SV167 ) )
        = $false )
      | ( ( ! [SY2710: $i] :
              ( ~ ( in @ SY2710 @ ( powerset @ SV167 ) )
              | ! [SY2711: $i] :
                  ( ~ ( in @ SY2711 @ ( powerset @ SV167 ) )
                  | ( in @ ( binintersect @ SV394 @ SY2710 ) @ ( powerset @ ( binintersect @ ( binunion @ SV394 @ SY2711 ) @ ( binunion @ SY2710 @ SY2711 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1440]) ).

thf(1684,plain,
    ! [SV395: $i,SV168: $i,SV539: $i] :
      ( ( ( ~ ( subset @ SV539 @ ( cartprod @ SV168 @ SV395 ) ) )
        = $true )
      | ( ( ! [SY2963: $i] :
              ( ~ ( subset @ SY2963 @ ( cartprod @ SV168 @ SV395 ) )
              | ~ ! [SY2964: $i] :
                    ( ~ ( in @ SY2964 @ SV168 )
                    | ! [SY2965: $i] :
                        ( ~ ( in @ SY2965 @ SV395 )
                        | ~ ( in @ ( kpair @ SY2964 @ SY2965 ) @ SV539 )
                        | ( in @ ( kpair @ SY2964 @ SY2965 ) @ SY2963 ) ) )
              | ( subset @ SV539 @ SY2963 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1441]) ).

thf(1685,plain,
    ! [SV396: $o,SV169: $i,SV540: $i] :
      ( ( ( ~ ( in @ SV540 @ SV169 ) )
        = $true )
      | ( ( ! [SY2966: $i] :
              ( ~ ( in @ SY2966 @ SV169 )
              | ~ SV396
              | ( ( if @ SV169 @ SV396 @ SV540 @ SY2966 )
                = SV540 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1442]) ).

thf(1686,plain,
    ! [SV169: $i,SV541: $i] :
      ( ( ( ~ ( in @ SV541 @ SV169 ) )
        = $true )
      | ( ( ! [SY2967: $i] :
              ( ~ ( in @ SY2967 @ SV169 )
              | ~ $true
              | ( ( if @ SV169 @ $true @ SV541 @ SY2967 )
                = SV541 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1443]) ).

thf(1687,plain,
    ! [SV169: $i,SV542: $i] :
      ( ( ( ~ ( in @ SV542 @ SV169 ) )
        = $true )
      | ( ( ! [SY2968: $i] :
              ( ~ ( in @ SY2968 @ SV169 )
              | ~ $false
              | ( ( if @ SV169 @ $false @ SV542 @ SY2968 )
                = SV542 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1444]) ).

thf(1688,plain,
    ! [SV397: $i,SV543: $i > $i,SV170: $i] :
      ( ( ( ~ ! [SY2969: $i] :
                ( ~ ( in @ SY2969 @ SV170 )
                | ( in @ ( SV543 @ SY2969 ) @ SV397 ) ) )
        = $true )
      | ( ( ! [SY2970: $i] :
              ( ~ ( in @ SY2970 @ SV170 )
              | ( ( ap @ SV170 @ SV397
                  @ ( lam @ SV170 @ SV397
                    @ ^ [SY2971: $i] : ( SV543 @ SY2971 ) )
                  @ SY2970 )
                = ( SV543 @ SY2970 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1445]) ).

thf(1689,plain,
    ! [SV171: $i] :
      ( ( ( ! [SY2264: $i] :
              ~ ( in @ SY2264 @ SV171 ) )
        = $true )
      | ( ( SV171 != emptyset )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1446]) ).

thf(1690,plain,
    ! [SV398: $i,SV172: $i,SV544: $i] :
      ( ( ( ~ ( in @ SV544 @ ( cartprod @ SV172 @ SV398 ) ) )
        = $true )
      | ( ( ( kpair @ ( kfst @ SV544 ) @ ( ksnd @ SV544 ) )
          = SV544 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1447]) ).

thf(1691,plain,
    ! [SV399: $i,SV173: $i,SV545: $i] :
      ( ( ( ~ ( in @ SV545 @ ( funcSet @ SV173 @ SV399 ) ) )
        = $true )
      | ( ( ( lam @ SV173 @ SV399
            @ ^ [SY2972: $i] : ( ap @ SV173 @ SV399 @ SV545 @ SY2972 ) )
          = SV545 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1448]) ).

thf(1692,plain,
    ! [SV614: $i,SV546: $i,SV400: $i,SV174: $i] :
      ( ( ( ( setadjoin @ ( setadjoin @ SV174 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV174 @ ( setadjoin @ SV400 @ emptyset ) ) @ emptyset ) )
         != ( setadjoin @ ( setadjoin @ SV546 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV546 @ ( setadjoin @ SV614 @ emptyset ) ) @ emptyset ) ) )
        | ( SV546 != SV614 )
        | ( SV400 = SV614 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1449]) ).

thf(1693,plain,
    ! [SV401: $i,SV175: $i,SV615: $i,SV547: $i] :
      ( ( ~ ( in @ ( kpair @ SV547 @ SV615 ) @ ( cartprod @ SV175 @ SV401 ) )
        | ( in @ SV615 @ SV401 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1450]) ).

thf(1694,plain,
    ! [SV548: $i,SV402: $i,SV176: $i] :
      ( ( ( ~ ( func @ SV176 @ SV402 @ SV548 ) )
        = $true )
      | ( ( ! [SY2975: $i] :
              ( ~ ( in @ SY2975 @ SV176 )
              | ( in @ ( ap @ SV176 @ SV402 @ SV548 @ SY2975 ) @ SV402 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1451]) ).

thf(1695,plain,
    ! [SV177: $i,SV403: $i] :
      ( ( ( in @ SV403 @ ( powerset @ SV177 ) )
        = $false )
      | ( ( ! [SY2731: $i] :
              ( ~ ( in @ SY2731 @ ( powerset @ SV177 ) )
              | ! [SY2732: $i] :
                  ( ~ ( in @ SY2732 @ SV177 )
                  | ~ ( subset @ SV403 @ ( setminus @ SV177 @ SY2731 ) )
                  | ~ ( in @ SY2732 @ SY2731 )
                  | ~ ( in @ SY2732 @ SV403 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1452]) ).

thf(1696,plain,
    ! [SV549: $i > $i > $o,SV404: $i,SV178: $i,SV616: $i] :
      ( ( ~ ( in @ SV616 @ SV178 )
        | ! [SY3052: $i] :
            ( ~ ( in @ SY3052 @ SV404 )
            | ~ ( SV549 @ SV616 @ SY3052 )
            | ( in @ ( kpair @ SV616 @ SY3052 )
              @ ( dpsetconstr @ SV178 @ SV404
                @ ^ [SY2978: $i,SY2979: $i] : ( SV549 @ SY2978 @ SY2979 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1453]) ).

thf(1697,plain,
    ! [SV405: $i,SV179: $i,SV550: $i] :
      ( ( ( ~ ( in @ SV550 @ SV179 ) )
        = $true )
      | ( ( ~ ~ ( in @ SV550 @ SV405 )
          | ( SV179 != SV405 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1454]) ).

thf(1698,plain,
    ! [SV406: $i,SV180: $i,SV551: $i] :
      ( ( ( ~ ( in @ SV551 @ SV180 ) )
        = $true )
      | ( ( ~ ( in @ SV551 @ SV406 )
          | ( in @ SV551 @ ( binintersect @ SV180 @ SV406 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1455]) ).

thf(1699,plain,
    ! [SV181: $i,SV407: $i] :
      ( ( ( ! [SY2740: $i] :
              ( ~ ( in @ SY2740 @ SV407 )
              | ( in @ SY2740 @ SV181 ) ) )
        = $false )
      | ( ( in @ SV407 @ ( powerset @ SV181 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1456]) ).

thf(1700,plain,
    ! [SV182: $i,SV408: $i] :
      ( ( ( in @ SV408 @ ( powerset @ SV182 ) )
        = $false )
      | ( ( ! [SY2741: $i] :
              ( ~ ( in @ SY2741 @ SV182 )
              | ~ ( in @ SY2741 @ SV408 )
              | ( in @ SY2741 @ ( setminus @ SV182 @ ( setminus @ SV182 @ SV408 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1457]) ).

thf(1701,plain,
    ! [SV409: $i,SV183: $i,SV552: $i] :
      ( ( ( ~ ( in @ SV552 @ ( setminus @ SV183 @ SV409 ) ) )
        = $true )
      | ( ( in @ SV552 @ SV183 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1458]) ).

thf(1702,plain,
    ! [SV410: $i,SV184: $i,SV553: $i] :
      ( ( ( ~ ( in @ SV553 @ ( cartprod @ SV184 @ SV410 ) ) )
        = $true )
      | ( ( iskpair @ SV553 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1459]) ).

thf(1703,plain,
    ! [SV554: $i,SV411: $i,SV185: $i] :
      ( ( ( ~ ( func @ SV185 @ SV411 @ SV554 ) )
        = $true )
      | ( ( ! [SY2980: $i] :
              ( ~ ( in @ SY2980 @ SV185 )
              | ! [SY2981: $i] :
                  ( ~ ( in @ SY2981 @ SV411 )
                  | ~ ( in @ ( kpair @ SY2980 @ SY2981 ) @ SV554 )
                  | ( ( ap @ SV185 @ SV411 @ SV554 @ SY2980 )
                    = SY2981 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1460]) ).

thf(1704,plain,
    ! [SV186: $i,SV412: $i] :
      ( ( ( in @ SV412 @ ( powerset @ SV186 ) )
        = $false )
      | ( ( ! [SY2747: $i] :
              ( ~ ( in @ SY2747 @ ( powerset @ SV186 ) )
              | ( in @ ( setminus @ SV412 @ SY2747 ) @ ( powerset @ SV186 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1461]) ).

thf(1705,plain,
    ! [SV413: $i > $o,SV187: $i,SV555: $i] :
      ( ( ( ~ ( in @ SV555
              @ ( dsetconstr @ SV187
                @ ^ [SY2749: $i] : ( SV413 @ SY2749 ) ) ) )
        = $true )
      | ( ( in @ SV555 @ SV187 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1462]) ).

thf(1706,plain,
    ! [SV414: $i > $o,SV188: $i,SV556: $i] :
      ( ( ( ~ ( in @ SV556 @ SV188 ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( in @ SV556
                      @ ( dsetconstr @ SV188
                        @ ^ [SY2751: $i] : ( SV414 @ SY2751 ) ) )
                  | ( SV414 @ SV556 ) )
              | ~ ( ~ ( SV414 @ SV556 )
                  | ( in @ SV556
                    @ ( dsetconstr @ SV188
                      @ ^ [SY2752: $i] : ( SV414 @ SY2752 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1463]) ).

thf(1707,plain,
    ! [SV189: $i,SV415: $i,SV557: $i] :
      ( ( ( ~ ( in @ SV557 @ SV415 ) )
        = $true )
      | ( ( in @ SV557 @ ( setadjoin @ SV189 @ SV415 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1464]) ).

thf(1708,plain,
    ! [SV558: $i,SV416: $i,SV190: $i] :
      ( ( ( ~ ( func @ SV190 @ SV416 @ SV558 ) )
        = $true )
      | ( ( ! [SY2985: $i] :
              ( ~ ( func @ SV190 @ SV416 @ SY2985 )
              | ~ ! [SY2986: $i] :
                    ( ~ ( in @ SY2986 @ SV190 )
                    | ( ( ap @ SV190 @ SV416 @ SV558 @ SY2986 )
                      = ( ap @ SV190 @ SV416 @ SY2985 @ SY2986 ) ) )
              | ( SV558 = SY2985 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1465]) ).

thf(1709,plain,
    ! [SV191: $i,SV417: $i] :
      ( ( ( in @ SV417 @ ( powerset @ SV191 ) )
        = $false )
      | ( ( ! [SY2757: $i] :
              ( ~ ( in @ SY2757 @ ( powerset @ SV191 ) )
              | ! [SY2758: $i] :
                  ( ~ ( in @ SY2758 @ ( powerset @ SV191 ) )
                  | ! [SY2759: $i] :
                      ( ~ ( in @ SY2759 @ SV191 )
                      | ~ ( in @ SY2759 @ ( binintersect @ SV417 @ SY2757 ) )
                      | ( in @ SY2759 @ ( binunion @ SV417 @ SY2758 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1466]) ).

thf(1710,plain,
    ! [SV418: $i > $o,SV192: $i,SV559: $i] :
      ( ( ( ~ ( in @ SV559
              @ ( dsetconstr @ SV192
                @ ^ [SY2761: $i] : ( SV418 @ SY2761 ) ) ) )
        = $true )
      | ( ( SV418 @ SV559 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1467]) ).

thf(1711,plain,
    ! [SV419: $i,SV193: $i] :
      ( ( ( SV193 = SV419 )
        = $false )
      | ( ( ! [SY2762: $i,SY2763: $i] :
              ( ( SY2762 != SY2763 )
              | ~ ( ~ ( ~ ( in @ SY2762 @ SV193 )
                      | ( in @ SY2763 @ SV419 ) )
                  | ~ ( ~ ( in @ SY2763 @ SV419 )
                      | ( in @ SY2762 @ SV193 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1468]) ).

thf(1712,plain,
    ! [SV420: $o,SV194: $i,SV560: $i] :
      ( ( ( ~ ( in @ SV560 @ SV194 ) )
        = $true )
      | ( ( ! [SY2988: $i] :
              ( ~ ( in @ SY2988 @ SV194 )
              | ( singleton
                @ ( dsetconstr @ SV194
                  @ ^ [SY2989: $i] :
                      ( ~ ( ~ SV420
                          | ( SY2989 != SV560 ) )
                      | ~ ( ~ ~ SV420
                          | ( SY2989 != SY2988 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1469]) ).

thf(1713,plain,
    ! [SV194: $i,SV561: $i] :
      ( ( ( ~ ( in @ SV561 @ SV194 ) )
        = $true )
      | ( ( ! [SY2990: $i] :
              ( ~ ( in @ SY2990 @ SV194 )
              | ( singleton
                @ ( dsetconstr @ SV194
                  @ ^ [SY2991: $i] :
                      ( ~ ( ~ $true
                          | ( SY2991 != SV561 ) )
                      | ~ ( ~ ~ $true
                          | ( SY2991 != SY2990 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1470]) ).

thf(1714,plain,
    ! [SV194: $i,SV562: $i] :
      ( ( ( ~ ( in @ SV562 @ SV194 ) )
        = $true )
      | ( ( ! [SY2992: $i] :
              ( ~ ( in @ SY2992 @ SV194 )
              | ( singleton
                @ ( dsetconstr @ SV194
                  @ ^ [SY2993: $i] :
                      ( ~ ( ~ $false
                          | ( SY2993 != SV562 ) )
                      | ~ ( ~ ~ $false
                          | ( SY2993 != SY2992 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1471]) ).

thf(1715,plain,
    ! [SV421: $i,SV195: $i] :
      ( ( ( ( binintersect @ SV195 @ SV421 )
          = SV195 )
        = $false )
      | ( ( subset @ SV195 @ SV421 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1472]) ).

thf(1716,plain,
    ! [SV422: $i,SV196: $i,SV563: $i] :
      ( ( ( ~ ( in @ SV563 @ SV196 ) )
        = $true )
      | ( ( ! [SY2994: $i] :
              ( ~ ( in @ SY2994 @ SV422 )
              | ( in @ ( kpair @ SV563 @ SY2994 ) @ ( powerset @ ( powerset @ ( binunion @ SV196 @ SV422 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1473]) ).

thf(1717,plain,
    ! [SV423: $o,SV197: $i,SV564: $i] :
      ( ( ( ~ ( in @ SV564 @ SV197 ) )
        = $true )
      | ( ( ! [SY2995: $i] :
              ( ~ ( in @ SY2995 @ SV197 )
              | ( in @ ( if @ SV197 @ SV423 @ SV564 @ SY2995 ) @ SV197 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1474]) ).

thf(1718,plain,
    ! [SV197: $i,SV565: $i] :
      ( ( ( ~ ( in @ SV565 @ SV197 ) )
        = $true )
      | ( ( ! [SY2996: $i] :
              ( ~ ( in @ SY2996 @ SV197 )
              | ( in @ ( if @ SV197 @ $true @ SV565 @ SY2996 ) @ SV197 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1475]) ).

thf(1719,plain,
    ! [SV197: $i,SV566: $i] :
      ( ( ( ~ ( in @ SV566 @ SV197 ) )
        = $true )
      | ( ( ! [SY2997: $i] :
              ( ~ ( in @ SY2997 @ SV197 )
              | ( in @ ( if @ SV197 @ $false @ SV566 @ SY2997 ) @ SV197 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1476]) ).

thf(1720,plain,
    ! [SV424: $i,SV198: $i,SV567: $i] :
      ( ( ( ~ ( in @ SV567 @ ( funcSet @ SV198 @ SV424 ) ) )
        = $true )
      | ( ( ! [SY2998: $i] :
              ( ~ ( in @ SY2998 @ SV198 )
              | ! [SY2999: $i] :
                  ( ~ ( in @ SY2999 @ SV424 )
                  | ~ ( in @ ( kpair @ SY2998 @ SY2999 ) @ SV567 )
                  | ( ( ap @ SV198 @ SV424 @ SV567 @ SY2998 )
                    = SY2999 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1477]) ).

thf(1721,plain,
    ! [SV425: $i,SV568: $i > $i,SV199: $i] :
      ( ( ( ~ ! [SY3000: $i] :
                ( ~ ( in @ SY3000 @ SV199 )
                | ( in @ ( SV568 @ SY3000 ) @ SV425 ) ) )
        = $true )
      | ( ( func @ SV199 @ SV425
          @ ( lam @ SV199 @ SV425
            @ ^ [SY3001: $i] : ( SV568 @ SY3001 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1478]) ).

thf(1722,plain,
    ! [SV426: $i > $o,SV200: $i] :
      ( ( ( ! [SY2777: $i] :
              ( ~ ( in @ SY2777 @ SV200 )
              | ~ ( SV426 @ SY2777 ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2778: $i] :
                  ~ ~ ( ~ ( in @ SY2778 @ SV200 )
                      | ~ ( SV426 @ SY2778 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1479]) ).

thf(1723,plain,
    ! [SV427: $i,SV201: $i] :
      ( ( ( ( setadjoin @ SV201 @ emptyset )
          = ( setadjoin @ SV427 @ emptyset ) )
        = $false )
      | ( ( SV201 = SV427 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1480]) ).

thf(1724,plain,
    ! [SV428: $i,SV202: $i,SV569: $i] :
      ( ( ( ~ ( in @ SV569 @ ( funcSet @ SV202 @ SV428 ) ) )
        = $true )
      | ( ( ! [SY3002: $i] :
              ( ~ ( in @ SY3002 @ SV202 )
              | ( in @ ( ap @ SV202 @ SV428 @ SV569 @ SY3002 ) @ SV428 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1481]) ).

thf(1725,plain,
    ! [SV203: $i] :
      ( ( ( SV203 = emptyset )
        = $true )
      | ( ( ~ ! [SY2355: $i] :
                ~ ( in @ SY2355 @ SV203 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1482]) ).

thf(1726,plain,
    ! [SV429: $i,SV204: $i] :
      ( ( ( in @ SV204 @ ( setadjoin @ SV429 @ emptyset ) )
        = $false )
      | ( ( in @ SV429 @ ( setadjoin @ SV204 @ emptyset ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1483]) ).

thf(1727,plain,
    ! [SV205: $i,SV430: $i] :
      ( ( ~ ( ~ ( in @ SV430 @ ( setunion @ SV205 ) )
            | ~ ! [SY2781: $i] :
                  ~ ~ ( ~ ( in @ SV430 @ SY2781 )
                      | ~ ( in @ SY2781 @ SV205 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1484]) ).

thf(1728,plain,
    ! [SV205: $i,SV430: $i] :
      ( ( ~ ( ~ ~ ! [SY2782: $i] :
                    ~ ~ ( ~ ( in @ SV430 @ SY2782 )
                        | ~ ( in @ SY2782 @ SV205 ) )
            | ( in @ SV430 @ ( setunion @ SV205 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1484]) ).

thf(1729,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) ) )
        = $true )
      | ( ( ! [SY3003: $o] :
              ( ~ ( ~ ( in @ SV570 @ SV206 )
                  | ~ ~ ( in @ SV570 @ SV431 )
                  | SY3003 )
              | ~ ( ~ ~ ( in @ SV570 @ SV206 )
                  | ~ ( in @ SV570 @ SV431 )
                  | SY3003 )
              | SY3003 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1485]) ).

thf(1730,plain,
    ! [SV432: $i,SV207: $i] :
      ( ( ( ~ ( subset @ SV207 @ SV432 ) )
        = $false )
      | ( ( SV207 != SV432 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1486]) ).

thf(1731,plain,
    ! [SV208: $i,SV433: $i] :
      ( ( ( in @ SV433 @ ( setunion @ SV208 ) )
        = $false )
      | ( ( ~ ! [SY2785: $i] :
                ~ ~ ( ~ ( in @ SY2785 @ SV208 )
                    | ~ ( in @ SV433 @ SY2785 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1487]) ).

thf(1732,plain,
    ! [SV434: $i,SV209: $i] :
      ( ( ( SV209 = SV434 )
        = $false )
      | ( ( ! [SY2786: $i > $o,SY2787: $i > $o] :
              ( ~ ! [SY2788: $i] :
                    ( ~ ( in @ SY2788 @ SV209 )
                    | ! [SY2789: $i] :
                        ( ~ ( in @ SY2789 @ SV434 )
                        | ( SY2788 != SY2789 )
                        | ~ ( ~ ( ~ ( SY2786 @ SY2788 )
                                | ( SY2787 @ SY2789 ) )
                            | ~ ( ~ ( SY2787 @ SY2789 )
                                | ( SY2786 @ SY2788 ) ) ) ) )
              | ( ( dsetconstr @ SV209
                  @ ^ [SX4: $i] : ( SY2786 @ SX4 ) )
                = ( dsetconstr @ SV434
                  @ ^ [SX4: $i] : ( SY2787 @ SX4 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1488]) ).

thf(1733,plain,
    ! [SV435: $i,SV210: $i,SV571: $i] :
      ( ( ( ~ ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) ) )
        = $true )
      | ( ( ! [SY3004: $o] :
              ( ~ ( ( SV571 != SV210 )
                  | SY3004 )
              | ~ ( ~ ( in @ SV571 @ SV435 )
                  | SY3004 )
              | SY3004 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1489]) ).

thf(1734,plain,
    ! [SV211: $i > $o] :
      ( ( ( ! [SY2376: $i] :
              ~ ~ ( ~ ( SV211 @ SY2376 )
                  | ~ ! [SY2377: $i] :
                        ( ~ ( SV211 @ SY2377 )
                        | ( SY2376 = SY2377 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2378: $i] :
                ~ ~ ( ~ ( SV211 @ SY2378 )
                    | ~ ! [SY2379: $i] :
                          ( ~ ( SV211 @ SY2379 )
                          | ( SY2378 = SY2379 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1490]) ).

thf(1735,plain,
    ! [SV436: $i,SV212: $i,SV572: $i] :
      ( ( ( ~ ( in @ SV572 @ ( funcSet @ SV212 @ SV436 ) ) )
        = $true )
      | ( ( ! [SY3005: $i] :
              ( ~ ( in @ SY3005 @ SV212 )
              | ( ( ap @ SV212 @ SV436 @ SV572 @ SY3005 )
                = ( ap @ SV212 @ SV436 @ SV572 @ SY3005 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1491]) ).

thf(1736,plain,
    ! [SV213: $i,SV437: $i] :
      ( ( ( in @ SV437 @ ( powerset @ SV213 ) )
        = $false )
      | ( ( ! [SY2796: $i] :
              ( ~ ( in @ SY2796 @ SV213 )
              | ~ ( in @ SY2796 @ ( setminus @ SV213 @ ( setminus @ SV213 @ SV437 ) ) )
              | ( in @ SY2796 @ SV437 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1492]) ).

thf(1737,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ! [SY2797: $i,SY2798: $i] :
              ( ( SY2797 != SY2798 )
              | ~ ( ~ ( ~ ( SV214 @ SY2797 )
                      | ( SV438 @ SY2798 ) )
                  | ~ ( ~ ( SV438 @ SY2798 )
                      | ( SV214 @ SY2797 ) ) ) ) )
        = $false )
      | ( ( ~ ( ~ ( ~ ~ ! [SY2388: $i] :
                          ~ ~ ( ~ ( SV214 @ SY2388 )
                              | ~ ! [SY2389: $i] :
                                    ( ~ ( SV214 @ SY2389 )
                                    | ( SY2388 = SY2389 ) ) )
                  | ~ ! [SY2801: $i] :
                        ~ ~ ( ~ ( SV438 @ SY2801 )
                            | ~ ! [SY2802: $i] :
                                  ( ~ ( SV438 @ SY2802 )
                                  | ( SY2801 = SY2802 ) ) ) )
              | ~ ( ~ ~ ! [SY2803: $i] :
                          ~ ~ ( ~ ( SV438 @ SY2803 )
                              | ~ ! [SY2804: $i] :
                                    ( ~ ( SV438 @ SY2804 )
                                    | ( SY2803 = SY2804 ) ) )
                  | ~ ! [SY2394: $i] :
                        ~ ~ ( ~ ( SV214 @ SY2394 )
                            | ~ ! [SY2395: $i] :
                                  ( ~ ( SV214 @ SY2395 )
                                  | ( SY2394 = SY2395 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1493]) ).

thf(1738,plain,
    ! [SV439: $i > $o,SV215: $i] :
      ( ( ( singleton
          @ ( dsetconstr @ SV215
            @ ^ [SY2807: $i] : ( SV439 @ SY2807 ) ) )
        = $false )
      | ( ( ~ ! [SY2808: $i] :
                ~ ~ ( ~ ( in @ SY2808 @ SV215 )
                    | ~ ( SV439 @ SY2808 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1494]) ).

thf(1739,plain,
    ! [SV440: $i > $o,SV216: $i,SV573: $i] :
      ( ( ( ~ ( in @ SV573 @ SV216 ) )
        = $true )
      | ( ( ~ ( SV440 @ SV573 )
          | ~ ! [SY3006: $i] :
                ( ~ ( in @ SY3006 @ SV216 )
                | ~ ( SV440 @ SY3006 )
                | ( SY3006 = SV573 ) )
          | ( singleton
            @ ( dsetconstr @ SV216
              @ ^ [SY2811: $i] : ( SV440 @ SY2811 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1495]) ).

thf(1740,plain,
    ! [SV441: $i,SV217: $i] :
      ( ( ( SV217 = SV441 )
        = $false )
      | ( ( ( setadjoin @ SV217 @ ( setadjoin @ SV441 @ emptyset ) )
          = ( setadjoin @ SV217 @ emptyset ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1496]) ).

thf(1741,plain,
    ! [SV442: $i,SV218: $i,SV574: $i] :
      ( ( ( ~ ( in @ SV574 @ SV218 ) )
        = $true )
      | ( ( ! [SY3008: $i] :
              ( ~ ( in @ SY3008 @ SV442 )
              | ( subset @ ( setadjoin @ ( setadjoin @ SV574 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV574 @ ( setadjoin @ SY3008 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV218 @ SV442 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1497]) ).

thf(1742,plain,
    ! [SV443: $i,SV219: $i,SV575: $i] :
      ( ( ( ~ ( in @ SV575 @ SV219 ) )
        = $true )
      | ( ( ! [SY3009: $i] :
              ( ~ ( in @ SY3009 @ SV443 )
              | ( ( ksnd @ ( kpair @ SV575 @ SY3009 ) )
                = SY3009 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1498]) ).

thf(1743,plain,
    ! [SV444: $o,SV220: $i,SV576: $i] :
      ( ( ( ~ ( in @ SV576 @ SV220 ) )
        = $true )
      | ( ( ! [SY3010: $i] :
              ( ~ ( in @ SY3010 @ SV220 )
              | ~ SV444
              | ( ( dsetconstr @ SV220
                  @ ^ [SY3011: $i] :
                      ( ~ ( ~ SV444
                          | ( SY3011 != SV576 ) )
                      | ~ ( ~ ~ SV444
                          | ( SY3011 != SY3010 ) ) ) )
                = ( setadjoin @ SV576 @ emptyset ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1499]) ).

thf(1744,plain,
    ! [SV220: $i,SV577: $i] :
      ( ( ( ~ ( in @ SV577 @ SV220 ) )
        = $true )
      | ( ( ! [SY3012: $i] :
              ( ~ ( in @ SY3012 @ SV220 )
              | ~ $true
              | ( ( dsetconstr @ SV220
                  @ ^ [SY3013: $i] :
                      ( ~ ( ~ $true
                          | ( SY3013 != SV577 ) )
                      | ~ ( ~ ~ $true
                          | ( SY3013 != SY3012 ) ) ) )
                = ( setadjoin @ SV577 @ emptyset ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1500]) ).

thf(1745,plain,
    ! [SV220: $i,SV578: $i] :
      ( ( ( ~ ( in @ SV578 @ SV220 ) )
        = $true )
      | ( ( ! [SY3014: $i] :
              ( ~ ( in @ SY3014 @ SV220 )
              | ~ $false
              | ( ( dsetconstr @ SV220
                  @ ^ [SY3015: $i] :
                      ( ~ ( ~ $false
                          | ( SY3015 != SV578 ) )
                      | ~ ( ~ ~ $false
                          | ( SY3015 != SY3014 ) ) ) )
                = ( setadjoin @ SV578 @ emptyset ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1501]) ).

thf(1746,plain,
    ! [SV445: $i,SV221: $i,SV579: $i] :
      ( ( ( ~ ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) ) )
        = $true )
      | ( ( ! [SY3016: $i] :
              ( ~ ( subset @ SY3016 @ ( cartprod @ SV221 @ SV445 ) )
              | ~ ! [SY3017: $i] :
                    ( ~ ( in @ SY3017 @ SV221 )
                    | ! [SY3018: $i] :
                        ( ~ ( in @ SY3018 @ SV445 )
                        | ~ ( in @ ( kpair @ SY3017 @ SY3018 ) @ SV579 )
                        | ( in @ ( kpair @ SY3017 @ SY3018 ) @ SY3016 ) ) )
              | ~ ! [SY3019: $i] :
                    ( ~ ( in @ SY3019 @ SV221 )
                    | ! [SY3020: $i] :
                        ( ~ ( in @ SY3020 @ SV445 )
                        | ~ ( in @ ( kpair @ SY3019 @ SY3020 ) @ SY3016 )
                        | ( in @ ( kpair @ SY3019 @ SY3020 ) @ SV579 ) ) )
              | ( SV579 = SY3016 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1502]) ).

thf(1747,plain,
    ! [SV580: $i,SV446: $i,SV222: $i] :
      ( ( ( ~ ( func @ SV222 @ SV446 @ SV580 ) )
        = $true )
      | ( ( ! [SY3021: $i] :
              ( ~ ( in @ SY3021 @ SV222 )
              | ( singleton
                @ ( dsetconstr @ SV446
                  @ ^ [SY3022: $i] : ( in @ ( kpair @ SY3021 @ SY3022 ) @ SV580 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1503]) ).

thf(1748,plain,
    ! [SV223: $i,SV447: $i] :
      ( ( ( in @ SV447 @ SV223 )
        = $false )
      | ( ( subset @ ( setadjoin @ SV447 @ emptyset ) @ SV223 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1504]) ).

thf(1749,plain,
    ! [SV224: $i] :
      ( ( ( SV224 = emptyset )
        = $true )
      | ( ( ~ ! [SY2426: $i] :
                ~ ~ ( ~ ( in @ SY2426 @ SV224 )
                    | ~ $true ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1505]) ).

thf(1750,plain,
    ! [SV448: $i,SV225: $i,SV581: $i] :
      ( ( ( ~ ( subset @ SV581 @ SV225 ) )
        = $true )
      | ( ( ~ ( subset @ SV581 @ SV448 )
          | ( subset @ SV581 @ ( binintersect @ SV225 @ SV448 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1506]) ).

thf(1751,plain,
    ! [SV449: $i,SV226: $i,SV582: $i] :
      ( ( ( ~ ( in @ SV582 @ SV226 ) )
        = $true )
      | ( ( ~ ~ ( in @ SV582 @ SV449 )
          | ( in @ SV582 @ ( symdiff @ SV226 @ SV449 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1507]) ).

thf(1752,plain,
    ! [SV227: $i,SV450: $i] :
      ( ( ( in @ SV450 @ ( powerset @ SV227 ) )
        = $false )
      | ( ( ! [SY2830: $i] :
              ( ~ ( in @ SY2830 @ ( powerset @ SV227 ) )
              | ~ ( subset @ ( setminus @ SV227 @ SY2830 ) @ ( setminus @ SV227 @ SV450 ) )
              | ( subset @ SV450 @ SY2830 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1508]) ).

thf(1753,plain,
    ! [SV228: $i,SV451: $i] :
      ( ( ( in @ SV451 @ ( powerset @ SV228 ) )
        = $false )
      | ( ( ! [SY2831: $i] :
              ( ~ ( in @ SY2831 @ ( powerset @ SV228 ) )
              | ! [SY2832: $i] :
                  ( ~ ( in @ SY2832 @ ( powerset @ SV228 ) )
                  | ! [SY2833: $i] :
                      ( ~ ( in @ SY2833 @ SV228 )
                      | ~ ( in @ SY2833 @ ( binintersect @ SV451 @ SY2831 ) )
                      | ( in @ SY2833 @ ( binunion @ SY2831 @ SY2832 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1509]) ).

thf(1754,plain,
    ! [SV229: $i,SV452: $i] :
      ( ( ( in @ SV452 @ SV229 )
        = $false )
      | ( ( in @ SV452 @ ( powerset @ ( setunion @ SV229 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1510]) ).

thf(1755,plain,
    ! [SV453: $o,SV230: $i,SV583: $i] :
      ( ( ( ~ ( in @ SV583 @ SV230 ) )
        = $true )
      | ( ( ! [SY3023: $i] :
              ( ~ ( in @ SY3023 @ SV230 )
              | ~ ~ SV453
              | ( ( dsetconstr @ SV230
                  @ ^ [SY3024: $i] :
                      ( ~ ( ~ SV453
                          | ( SY3024 != SV583 ) )
                      | ~ ( ~ ~ SV453
                          | ( SY3024 != SY3023 ) ) ) )
                = ( setadjoin @ SY3023 @ emptyset ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1511]) ).

thf(1756,plain,
    ! [SV230: $i,SV584: $i] :
      ( ( ( ~ ( in @ SV584 @ SV230 ) )
        = $true )
      | ( ( ! [SY3025: $i] :
              ( ~ ( in @ SY3025 @ SV230 )
              | ~ ~ $true
              | ( ( dsetconstr @ SV230
                  @ ^ [SY3026: $i] :
                      ( ~ ( ~ $true
                          | ( SY3026 != SV584 ) )
                      | ~ ( ~ ~ $true
                          | ( SY3026 != SY3025 ) ) ) )
                = ( setadjoin @ SY3025 @ emptyset ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1512]) ).

thf(1757,plain,
    ! [SV230: $i,SV585: $i] :
      ( ( ( ~ ( in @ SV585 @ SV230 ) )
        = $true )
      | ( ( ! [SY3027: $i] :
              ( ~ ( in @ SY3027 @ SV230 )
              | ~ ~ $false
              | ( ( dsetconstr @ SV230
                  @ ^ [SY3028: $i] :
                      ( ~ ( ~ $false
                          | ( SY3028 != SV585 ) )
                      | ~ ( ~ ~ $false
                          | ( SY3028 != SY3027 ) ) ) )
                = ( setadjoin @ SY3027 @ emptyset ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1513]) ).

thf(1758,plain,
    ! [SV231: $i,SV454: $i] :
      ( ( ( in @ SV454 @ ( powerset @ SV231 ) )
        = $false )
      | ( ( ! [SY2837: $i] :
              ( ~ ( in @ SY2837 @ ( powerset @ SV231 ) )
              | ~ ! [SY2838: $i] :
                    ( ~ ( in @ SY2838 @ SV231 )
                    | ~ ( in @ SY2838 @ SV454 )
                    | ( in @ SY2838 @ SY2837 ) )
              | ( in @ SV454 @ ( powerset @ SY2837 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1514]) ).

thf(1759,plain,
    ! [SV586: $i,SV455: $i,SV232: $i] :
      ( ( ( ~ ( func @ SV232 @ SV455 @ SV586 ) )
        = $true )
      | ( ( ( lam @ SV232 @ SV455
            @ ^ [SY3029: $i] : ( ap @ SV232 @ SV455 @ SV586 @ SY3029 ) )
          = SV586 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1515]) ).

thf(1760,plain,
    ! [SV456: $i,SV233: $i] :
      ( ( ( ( binintersect @ SV233 @ SV456 )
          = SV456 )
        = $false )
      | ( ( subset @ SV456 @ SV233 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1516]) ).

thf(1761,plain,
    ! [SV457: $i,SV234: $i,SV587: $i] :
      ( ( ( ~ ( in @ SV587 @ ( cartprod @ SV234 @ SV457 ) ) )
        = $true )
      | ( ( in @ ( kfst @ SV587 ) @ SV234 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1517]) ).

thf(1762,plain,
    ! [SV458: $i,SV235: $i] :
      ( ( ( SV235 = SV458 )
        = $false )
      | ( ( in @ SV235 @ ( setadjoin @ SV458 @ emptyset ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1518]) ).

thf(1763,plain,
    ! [SV588: $i,SV459: $i,SV236: $i] :
      ( ( ( ~ ( subset @ SV236 @ SV459 ) )
        = $true )
      | ( ( ~ ( subset @ SV459 @ SV588 )
          | ( subset @ SV236 @ SV588 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1519]) ).

thf(1764,plain,
    ! [SV589: $i,SV460: $i,SV237: $i] :
      ( ( ( ( setadjoin @ SV237 @ ( setadjoin @ SV460 @ emptyset ) )
         != ( setadjoin @ SV589 @ emptyset ) )
        = $true )
      | ( ( SV237 = SV460 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1520]) ).

thf(1765,plain,
    ! [SV461: $i,SV238: $i] :
      ( ( ( subset @ SV238 @ SV461 )
        = $false )
      | ( ( subset @ ( powerset @ SV238 ) @ ( powerset @ SV461 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1521]) ).

thf(1766,plain,
    ! [SV617: $i,SV590: $i,SV462: $i,SV239: $i] :
      ( ( ( ( setadjoin @ ( setadjoin @ SV239 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV239 @ ( setadjoin @ SV462 @ emptyset ) ) @ emptyset ) )
         != ( setadjoin @ ( setadjoin @ SV590 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV590 @ ( setadjoin @ SV617 @ emptyset ) ) @ emptyset ) ) )
        | ( SV239 = SV590 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1522]) ).

thf(1767,plain,
    ! [SV591: $i,SV463: $i,SV240: $i] :
      ( ( ( ~ ( func @ SV240 @ SV463 @ SV591 ) )
        = $true )
      | ( ( in @ SV591 @ ( funcSet @ SV240 @ SV463 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1523]) ).

thf(1768,plain,
    ! [SV464: $i,SV241: $i,SV592: $i] :
      ( ( ( ~ ( in @ SV592 @ ( binintersect @ SV241 @ SV464 ) ) )
        = $true )
      | ( ( in @ SV592 @ SV464 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1524]) ).

thf(1769,plain,
    ! [SV465: $i,SV242: $i,SV593: $i] :
      ( ( ( ~ ~ ( in @ SV593 @ SV242 ) )
        = $true )
      | ( ( ~ ( in @ SV593 @ ( setminus @ SV242 @ SV465 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1525]) ).

thf(1770,plain,
    ! [SV243: $i,SV466: $i] :
      ( ( ( in @ SV466 @ ( powerset @ SV243 ) )
        = $false )
      | ( ( ! [SY2849: $i] :
              ( ~ ( in @ SY2849 @ ( powerset @ SV243 ) )
              | ~ ! [SY2850: $i] :
                    ( ~ ( in @ SY2850 @ SV243 )
                    | ~ ( in @ SY2850 @ SV466 )
                    | ( in @ SY2850 @ SY2849 ) )
              | ( subset @ SV466 @ SY2849 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1526]) ).

thf(1771,plain,
    ! [SV467: $i,SV594: $i > $i,SV244: $i] :
      ( ( ( ~ ! [SY3031: $i] :
                ( ~ ( in @ SY3031 @ SV244 )
                | ( in @ ( SV594 @ SY3031 ) @ SV467 ) ) )
        = $true )
      | ( ( ! [SY3032: $i] :
              ( ~ ( in @ SY3032 @ SV244 )
              | ( ( ap @ SV244 @ SV467
                  @ ( lam @ SV244 @ SV467
                    @ ^ [SY3033: $i] : ( SV594 @ SY3033 ) )
                  @ SY3032 )
                = ( SV594 @ SY3032 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1527]) ).

thf(1772,plain,
    ! [SV468: $i,SV245: $i,SV595: $i] :
      ( ( ( ~ ( in @ SV595 @ ( funcSet @ SV245 @ SV468 ) ) )
        = $true )
      | ( ( ! [SY3034: $i] :
              ( ~ ( in @ SY3034 @ SV245 )
              | ( in @ ( kpair @ SY3034 @ ( ap @ SV245 @ SV468 @ SV595 @ SY3034 ) ) @ SV595 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1528]) ).

thf(1773,plain,
    ! [SV246: $i,SV469: $i] :
      ( ( ( in @ SV469 @ ( powerset @ SV246 ) )
        = $false )
      | ( ( ! [SY2857: $i] :
              ( ~ ( in @ SY2857 @ ( powerset @ SV246 ) )
              | ! [SY2858: $i] :
                  ( ~ ( in @ SY2858 @ SV246 )
                  | ~ ( in @ SY2858 @ ( setminus @ SV246 @ SV469 ) )
                  | ~ ( in @ SY2858 @ ( binintersect @ SV469 @ SY2857 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1529]) ).

thf(1774,plain,
    ! [SV470: $i,SV248: $i] :
      ( ( ( in @ SV248 @ ( setadjoin @ SV470 @ emptyset ) )
        = $false )
      | ( ( SV248 = SV470 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1531]) ).

thf(1775,plain,
    ! [SV249: $i,SV471: $i,SV596: $i] :
      ( ( ( ~ ( in @ SV596 @ SV471 ) )
        = $true )
      | ( ( ~ ( in @ SV596 @ ( setminus @ SV249 @ SV471 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1532]) ).

thf(1776,plain,
    ! [SV250: $i,SV618: $i] :
      ( ( ( ~ ( in @ SV618 @ SV250 )
          | ( ( setunion @ SV250 )
            = SV618 ) )
        = $true )
      | ( ( singleton @ SV250 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1533]) ).

thf(1777,plain,
    ! [SV472: $i,SV251: $i,SV597: $i] :
      ( ( ( ~ ( in @ SV597 @ SV251 ) )
        = $true )
      | ( ( ! [SY3035: $i] :
              ( ~ ( in @ SY3035 @ SV472 )
              | ( in @ ( setadjoin @ SV597 @ ( setadjoin @ SY3035 @ emptyset ) ) @ ( powerset @ ( binunion @ SV251 @ SV472 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1534]) ).

thf(1778,plain,
    ! [SV473: $i,SV252: $i,SV598: $i] :
      ( ( ( ~ ( in @ SV598 @ ( binunion @ SV252 @ SV473 ) ) )
        = $true )
      | ( ( ( in @ SV598 @ SV252 )
          | ( in @ SV598 @ SV473 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1535]) ).

thf(1779,plain,
    ! [SV253: $i > $o] :
      ( ( ( ! [SY2489: $i] :
              ~ ! [SY2490: $i] :
                  ~ ( ~ ( ~ ( SV253 @ SY2490 )
                        | ( SY2490 = SY2489 ) )
                    | ~ ( ( SY2490 != SY2489 )
                        | ( SV253 @ SY2490 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2491: $i] :
                ~ ~ ( ~ ( SV253 @ SY2491 )
                    | ~ ! [SY2492: $i] :
                          ( ~ ( SV253 @ SY2492 )
                          | ( SY2491 = SY2492 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1536]) ).

thf(1780,plain,
    ! [SV474: $i,SV599: $i,SV254: $i] :
      ( ( ( ~ ( subset @ SV254 @ SV599 ) )
        = $true )
      | ( ( subset @ SV254 @ ( setadjoin @ SV474 @ SV599 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1537]) ).

thf(1781,plain,
    ! [SV255: $i,SV475: $i] :
      ( ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false )
      | ( ( ! [SY2864: $o] :
              ( ~ ! [SY2865: $i] :
                    ( ~ ( in @ SV475 @ SY2865 )
                    | ~ ( in @ SY2865 @ SV255 )
                    | SY2864 )
              | SY2864 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1538]) ).

thf(1782,plain,
    ! [SV476: $o,SV256: $i,SV600: $i] :
      ( ( ( ~ ( in @ SV600 @ SV256 ) )
        = $true )
      | ( ( ! [SY3036: $i] :
              ( ~ ( in @ SY3036 @ SV256 )
              | ( in @ ( if @ SV256 @ SV476 @ SV600 @ SY3036 ) @ ( setadjoin @ SV600 @ ( setadjoin @ SY3036 @ emptyset ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1539]) ).

thf(1783,plain,
    ! [SV256: $i,SV601: $i] :
      ( ( ( ~ ( in @ SV601 @ SV256 ) )
        = $true )
      | ( ( ! [SY3037: $i] :
              ( ~ ( in @ SY3037 @ SV256 )
              | ( in @ ( if @ SV256 @ $true @ SV601 @ SY3037 ) @ ( setadjoin @ SV601 @ ( setadjoin @ SY3037 @ emptyset ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1540]) ).

thf(1784,plain,
    ! [SV256: $i,SV602: $i] :
      ( ( ( ~ ( in @ SV602 @ SV256 ) )
        = $true )
      | ( ( ! [SY3038: $i] :
              ( ~ ( in @ SY3038 @ SV256 )
              | ( in @ ( if @ SV256 @ $false @ SV602 @ SY3038 ) @ ( setadjoin @ SV602 @ ( setadjoin @ SY3038 @ emptyset ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1541]) ).

thf(1785,plain,
    ! [SV477: $i,SV257: $i,SV603: $i] :
      ( ( ( ~ ( in @ SV603 @ SV257 ) )
        = $true )
      | ( ( ! [SY3039: $i] :
              ( ~ ( in @ SY3039 @ SV477 )
              | ( subset @ ( setadjoin @ SV603 @ ( setadjoin @ SY3039 @ emptyset ) ) @ ( binunion @ SV257 @ SV477 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1542]) ).

thf(1786,plain,
    ! [SV280: $i,SV34: $i,SV481: $i] :
      ( ( ( in @ SV481 @ ( funcSet @ SV34 @ SV280 ) )
        = $false )
      | ( ( func @ SV34 @ SV280 @ SV481 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1543]) ).

thf(1787,plain,
    ! [SV281: $i > $o,SV35: $i] :
      ( ( ( ~ ! [SY2514: $i] :
                ~ ~ ( ~ ( in @ SY2514 @ SV35 )
                    | ~ ( SV281 @ SY2514 ) ) )
        = $true )
      | ( ( ! [SY2515: $i] :
              ( ~ ( in @ SY2515 @ SV35 )
              | ~ ( SV281 @ SY2515 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1544]) ).

thf(1788,plain,
    ! [SV282: $i,SV36: $i,SV619: $i] :
      ( ( ( ~ ( in @ SV619 @ ( powerset @ SV36 ) )
          | ! [SY3055: $i] :
              ( ~ ( in @ SY3055 @ SV36 )
              | ~ ( subset @ SV282 @ SV619 )
              | ~ ~ ( in @ SY3055 @ SV619 )
              | ~ ( in @ SY3055 @ SV282 ) ) )
        = $true )
      | ( ( in @ SV282 @ ( powerset @ SV36 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1545]) ).

thf(1789,plain,
    ! [SV620: $i,SV37: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV37 @ SV620 )
                | ~ ! [SY3056: $i] :
                      ( ~ ( SV37 @ SY3056 )
                      | ( SV620 = SY3056 ) ) ) )
        = $true )
      | ( ( ~ ! [SY1897: $i] :
                ~ ! [SY1898: $i] :
                    ~ ( ~ ( ~ ( SV37 @ SY1898 )
                          | ( SY1898 = SY1897 ) )
                      | ~ ( ( SY1898 != SY1897 )
                          | ( SV37 @ SY1898 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1546]) ).

thf(1790,plain,
    ! [SV482: $i,SV283: $i,SV38: $i] :
      ( ( ( func @ SV38 @ SV283 @ SV482 )
        = $false )
      | ( ( ! [SY2874: $i] :
              ( ~ ( in @ SY2874 @ SV38 )
              | ( in @ ( kpair @ SY2874 @ ( ap @ SV38 @ SV283 @ SV482 @ SY2874 ) ) @ SV482 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1547]) ).

thf(1791,plain,
    ! [SV284: $o,SV40: $i,SV483: $i] :
      ( ( ( in @ SV483 @ SV40 )
        = $false )
      | ( ( ! [SY2875: $i] :
              ( ~ ( in @ SY2875 @ SV40 )
              | ~ ~ SV284
              | ( in @ SY2875
                @ ( dsetconstr @ SV40
                  @ ^ [SY2876: $i] :
                      ( ~ ( ~ SV284
                          | ( SY2876 != SV483 ) )
                      | ~ ( ~ ~ SV284
                          | ( SY2876 != SY2875 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1551]) ).

thf(1792,plain,
    ! [SV40: $i,SV484: $i] :
      ( ( ( in @ SV484 @ SV40 )
        = $false )
      | ( ( ! [SY2877: $i] :
              ( ~ ( in @ SY2877 @ SV40 )
              | ~ ~ $true
              | ( in @ SY2877
                @ ( dsetconstr @ SV40
                  @ ^ [SY2878: $i] :
                      ( ~ ( ~ $true
                          | ( SY2878 != SV484 ) )
                      | ~ ( ~ ~ $true
                          | ( SY2878 != SY2877 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1552]) ).

thf(1793,plain,
    ! [SV40: $i,SV485: $i] :
      ( ( ( in @ SV485 @ SV40 )
        = $false )
      | ( ( ! [SY2879: $i] :
              ( ~ ( in @ SY2879 @ SV40 )
              | ~ ~ $false
              | ( in @ SY2879
                @ ( dsetconstr @ SV40
                  @ ^ [SY2880: $i] :
                      ( ~ ( ~ $false
                          | ( SY2880 != SV485 ) )
                      | ~ ( ~ ~ $false
                          | ( SY2880 != SY2879 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1553]) ).

thf(1794,plain,
    ! [SV621: $i,SV41: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV41 @ SV621 )
                | ~ ! [SY3057: $i] :
                      ( ~ ( SV41 @ SY3057 )
                      | ( SV621 = SY3057 ) ) ) )
        = $true )
      | ( ( ! [SY1909: $i,SY1910: $i] :
              ( ~ ( SV41 @ SY1909 )
              | ~ ( SV41 @ SY1910 )
              | ( SY1909 = SY1910 ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1554]) ).

thf(1795,plain,
    ! [SV42: $i,SV285: $i] :
      ( ( ~ ( in @ SV285 @ ( powerset @ SV42 ) )
        | ! [SY2523: $i] :
            ( ~ ( in @ SY2523 @ SV285 )
            | ( in @ SY2523 @ SV42 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1555]) ).

thf(1796,plain,
    ! [SV42: $i,SV285: $i] :
      ( ( ~ ! [SY2524: $i] :
              ( ~ ( in @ SY2524 @ SV285 )
              | ( in @ SY2524 @ SV42 ) )
        | ( in @ SV285 @ ( powerset @ SV42 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1556]) ).

thf(1797,plain,
    ! [SV622: $i,SV43: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV43 @ SV622 )
                | ~ ! [SY3058: $i] :
                      ( ~ ( SV43 @ SY3058 )
                      | ( SV622 = SY3058 ) ) ) )
        = $true )
      | ( ( ! [SY1916: $i,SY1917: $i] :
              ( ~ ( SV43 @ SY1916 )
              | ~ ( SV43 @ SY1917 )
              | ( SY1916 = SY1917 ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1557]) ).

thf(1798,plain,
    ! [SV286: $i,SV44: $i,SV623: $i] :
      ( ( ( ~ ( in @ SV623 @ ( powerset @ SV44 ) )
          | ! [SY3059: $i] :
              ( ~ ( in @ SY3059 @ SV44 )
              | ~ ( in @ SY3059 @ ( setminus @ SV44 @ ( binunion @ SV286 @ SV623 ) ) )
              | ~ ( in @ SY3059 @ SV286 ) ) )
        = $true )
      | ( ( in @ SV286 @ ( powerset @ SV44 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1558]) ).

thf(1799,plain,
    ! [SV287: $i > $o,SV46: $i] :
      ( ( ( ! [SY2527: $i] :
              ~ ~ ( ~ ( in @ SY2527 @ SV46 )
                  | ~ ~ ( SV287 @ SY2527 ) ) )
        = $true )
      | ( ( ~ ! [SY2528: $i] :
                ( ~ ( in @ SY2528 @ SV46 )
                | ( SV287 @ SY2528 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1559]) ).

thf(1800,plain,
    ! [SV288: $i,SV47: $i,SV486: $i] :
      ( ( ( ~ ( in @ SV486 @ ( setminus @ SV47 @ SV288 ) ) )
        = $false )
      | ( ( ~ ( in @ SV486 @ SV47 )
          | ( in @ SV486 @ SV288 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1560]) ).

thf(1801,plain,
    ! [SV624: $i,SV48: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV48 @ SV624 )
                | ~ ! [SY3060: $i] :
                      ( ~ ( SV48 @ SY3060 )
                      | ( SV624 = SY3060 ) ) ) )
        = $true )
      | ( ( ~ ! [SY1928: $i] :
                ~ ~ ( ~ ( SV48 @ SY1928 )
                    | ~ ! [SY1929: $i] :
                          ( ~ ( SV48 @ SY1929 )
                          | ( SY1928 = SY1929 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1561]) ).

thf(1802,plain,
    ! [SV289: $i,SV49: $i,SV487: $i] :
      ( ( ( in @ SV487 @ SV49 )
        = $false )
      | ( ( ~ ~ ( in @ SV487 @ SV289 )
          | ( in @ SV487 @ ( setminus @ SV49 @ SV289 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1562]) ).

thf(1803,plain,
    ! [SV290: $i,SV50: $i,SV488: $i] :
      ( ( ( in @ SV488 @ SV50 )
        = $false )
      | ( ( ! [SY2881: $i] :
              ( ~ ( in @ SY2881 @ SV290 )
              | ( in @ ( setadjoin @ ( setadjoin @ SV488 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV488 @ ( setadjoin @ SY2881 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV50 @ SV290 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1563]) ).

thf(1804,plain,
    ! [SV51: $i,SV291: $i] :
      ( ( ( ~ ( ~ ( ~ ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV51 )
                  | ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV291 ) )
              | ~ ( ~ ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV291 )
                  | ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV51 ) ) ) )
        = $false )
      | ( ( SV51 = SV291 )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[1564]) ).

thf(1805,plain,
    ! [SV292: $i > $o,SV52: $i] :
      ( ( ( ~ ! [SY2534: $i] :
                ~ ~ ( ~ ( in @ SY2534 @ SV52 )
                    | ~ ( SV292 @ SY2534 ) ) )
        = $true )
      | ( ( ! [SY2535: $i] :
              ( ~ ( in @ SY2535 @ SV52 )
              | ~ ( SV292 @ SY2535 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1565]) ).

thf(1806,plain,
    ! [SV295: $i,SV55: $i,SV489: $i] :
      ( ( ( ~ ( in @ SV489 @ SV55 ) )
        = $false )
      | ( ( ~ ~ ( in @ SV489 @ SV295 )
          | ~ ( in @ SV489 @ ( symdiff @ SV55 @ SV295 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1568]) ).

thf(1807,plain,
    ! [SV490: $i > $i > $o,SV296: $i,SV56: $i,SV625: $i,SV605: $i] :
      ( ( ~ ( in @ ( kpair @ SV605 @ SV625 )
            @ ( dpsetconstr @ SV56 @ SV296
              @ ^ [SY2884: $i,SY2885: $i] : ( SV490 @ SY2884 @ SY2885 ) ) )
        | ( in @ SV625 @ SV296 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1569]) ).

thf(1808,plain,
    ! [SV297: $i,SV58: $i,SV491: $i] :
      ( ( ( in @ ( setadjoin @ SV491 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV58 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV58 @ ( setadjoin @ SV297 @ emptyset ) ) @ emptyset ) ) )
        = $false )
      | ( ( SV58 = SV491 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1570]) ).

thf(1809,plain,
    ! [SV606: $i,SV492: $i,SV298: $i,SV59: $i] :
      ( ( ( ( setadjoin @ ( setadjoin @ SV59 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV59 @ ( setadjoin @ SV298 @ emptyset ) ) @ emptyset ) )
         != ( setadjoin @ ( setadjoin @ SV492 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV492 @ ( setadjoin @ SV606 @ emptyset ) ) @ emptyset ) ) )
        = $true )
      | ( ( SV298 = SV606 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1571]) ).

thf(1810,plain,
    ! [SV299: $i,SV60: $i,SV493: $i] :
      ( ( ( in @ SV493 @ SV60 )
        = $false )
      | ( ( ~ ( in @ SV493 @ SV299 )
          | ~ ( in @ SV493 @ ( symdiff @ SV60 @ SV299 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1572]) ).

thf(1811,plain,
    ! [SV300: $i,SV61: $i,SV607: $i,SV494: $i] :
      ( ( ( ~ ( in @ ( kpair @ SV494 @ SV607 ) @ ( cartprod @ SV61 @ SV300 ) ) )
        = $true )
      | ( ( in @ SV494 @ SV61 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1573]) ).

thf(1812,plain,
    ! [SV301: $i,SV62: $i,SV495: $i] :
      ( ( ( in @ SV495 @ SV62 )
        = $false )
      | ( ( ! [SY2888: $i] :
              ( ~ ( in @ SY2888 @ SV301 )
              | ( ( kpair @ SV495 @ SY2888 )
                = ( kpair @ SV495 @ SY2888 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1574]) ).

thf(1813,plain,
    ! [SV302: $i,SV63: $i,SV496: $i] :
      ( ( ( subset @ SV496 @ ( cartprod @ SV63 @ SV302 ) )
        = $false )
      | ( ( ! [SY2889: $i > $o] :
              ( ~ ! [SY2890: $i] :
                    ( ~ ( in @ SY2890 @ SV63 )
                    | ! [SY2891: $i] :
                        ( ~ ( in @ SY2891 @ SV302 )
                        | ~ ( in @ ( kpair @ SY2890 @ SY2891 ) @ SV496 )
                        | ( SY2889 @ ( kpair @ SY2890 @ SY2891 ) ) ) )
              | ! [SY2892: $i] :
                  ( ~ ( in @ SY2892 @ SV496 )
                  | ( SY2889 @ SY2892 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1575]) ).

thf(1814,plain,
    ! [SV303: $i > $o,SV65: $i,SV497: $i] :
      ( ( ( in @ SV497 @ SV65 )
        = $false )
      | ( ( ~ ( SV303 @ SV497 )
          | ( ( dsetconstr @ SV65
              @ ^ [SY2556: $i] : ( SV303 @ SY2556 ) )
           != emptyset ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1576]) ).

thf(1815,plain,
    ! [SV305: $o,SV67: $i,SV498: $i] :
      ( ( ( in @ SV498 @ SV67 )
        = $false )
      | ( ( ! [SY2894: $i] :
              ( ~ ( in @ SY2894 @ SV67 )
              | ~ SV305
              | ( in @ SV498
                @ ( dsetconstr @ SV67
                  @ ^ [SY2895: $i] :
                      ( ~ ( ~ SV305
                          | ( SY2895 != SV498 ) )
                      | ~ ( ~ ~ SV305
                          | ( SY2895 != SY2894 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1578]) ).

thf(1816,plain,
    ! [SV67: $i,SV499: $i] :
      ( ( ( in @ SV499 @ SV67 )
        = $false )
      | ( ( ! [SY2896: $i] :
              ( ~ ( in @ SY2896 @ SV67 )
              | ~ $true
              | ( in @ SV499
                @ ( dsetconstr @ SV67
                  @ ^ [SY2897: $i] :
                      ( ~ ( ~ $true
                          | ( SY2897 != SV499 ) )
                      | ~ ( ~ ~ $true
                          | ( SY2897 != SY2896 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1579]) ).

thf(1817,plain,
    ! [SV67: $i,SV500: $i] :
      ( ( ( in @ SV500 @ SV67 )
        = $false )
      | ( ( ! [SY2898: $i] :
              ( ~ ( in @ SY2898 @ SV67 )
              | ~ $false
              | ( in @ SV500
                @ ( dsetconstr @ SV67
                  @ ^ [SY2899: $i] :
                      ( ~ ( ~ $false
                          | ( SY2899 != SV500 ) )
                      | ~ ( ~ ~ $false
                          | ( SY2899 != SY2898 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1580]) ).

thf(1818,plain,
    ! [SV501: $i,SV306: $i,SV68: $i] :
      ( ( ( func @ SV68 @ SV306 @ SV501 )
        = $false )
      | ( ( ! [SY2900: $i] :
              ( ~ ( in @ SY2900 @ SV68 )
              | ( in
                @ ( setunion
                  @ ( dsetconstr @ SV306
                    @ ^ [SY2901: $i] : ( in @ ( kpair @ SY2900 @ SY2901 ) @ SV501 ) ) )
                @ SV306 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1581]) ).

thf(1819,plain,
    ! [SV310: $i,SV72: $i,SV626: $i] :
      ( ( ( ~ ( in @ SV626 @ ( powerset @ SV72 ) )
          | ~ ( subset @ SV310 @ ( setminus @ SV72 @ SV626 ) )
          | ( subset @ SV626 @ ( setminus @ SV72 @ SV310 ) ) )
        = $true )
      | ( ( in @ SV310 @ ( powerset @ SV72 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1585]) ).

thf(1820,plain,
    ! [SV311: $i,SV73: $i,SV502: $i] :
      ( ( ( in @ SV502 @ ( funcSet @ SV73 @ SV311 ) )
        = $false )
      | ( ( ! [SY2902: $i] :
              ( ~ ( in @ SY2902 @ ( funcSet @ SV73 @ SV311 ) )
              | ~ ! [SY2903: $i] :
                    ( ~ ( in @ SY2903 @ SV73 )
                    | ( ( ap @ SV73 @ SV311 @ SV502 @ SY2903 )
                      = ( ap @ SV73 @ SV311 @ SY2902 @ SY2903 ) ) )
              | ( SV502 = SY2902 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1586]) ).

thf(1821,plain,
    ! [SV312: $i,SV74: $i,SV503: $i] :
      ( ( ( ~ ( in @ SV503 @ ( setminus @ SV74 @ SV312 ) ) )
        = $false )
      | ( ( ~ ~ ( in @ SV503 @ SV312 )
          | ~ ( in @ SV503 @ SV74 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1587]) ).

thf(1822,plain,
    ! [SV313: $i,SV75: $i,SV504: $i] :
      ( ( ~ ( ~ ( in @ SV504 @ ( setadjoin @ SV75 @ SV313 ) )
            | ( SV504 = SV75 )
            | ( in @ SV504 @ SV313 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1588]) ).

thf(1823,plain,
    ! [SV313: $i,SV75: $i,SV504: $i] :
      ( ( ~ ( ~ ( ( SV504 = SV75 )
                | ( in @ SV504 @ SV313 ) )
            | ( in @ SV504 @ ( setadjoin @ SV75 @ SV313 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1588]) ).

thf(1824,plain,
    ! [SV314: $i,SV76: $i,SV627: $i] :
      ( ( ( ~ ( in @ SV627 @ ( powerset @ SV76 ) )
          | ! [SY3063: $i] :
              ( ~ ( in @ SY3063 @ ( powerset @ SV76 ) )
              | ! [SY3064: $i] :
                  ( ~ ( in @ SY3064 @ SV76 )
                  | ~ ( in @ SY3064 @ ( binintersect @ SV314 @ SV627 ) )
                  | ( in @ SY3064 @ ( binintersect @ ( binunion @ SV314 @ SY3063 ) @ ( binunion @ SV627 @ SY3063 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV314 @ ( powerset @ SV76 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1589]) ).

thf(1825,plain,
    ! [SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ! [SY3065: $i] :
              ( ( ( sK7_SY2572 @ SV315 @ SV77 )
               != SY3065 )
              | ~ ( ~ ( ~ ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
                      | ( SV315 @ SY3065 ) )
                  | ~ ( ~ ( SV315 @ SY3065 )
                      | ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) ) ) ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2001: $i] :
                  ~ ~ ( ~ ( SV77 @ SY2001 )
                      | ~ ! [SY2002: $i] :
                            ( ~ ( SV77 @ SY2002 )
                            | ( SY2001 = SY2002 ) ) )
          | ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[1590]) ).

thf(1826,plain,
    ! [SV316: $i > $o,SV78: $i,SV505: $i] :
      ( ( ( in @ SV505 @ SV78 )
        = $false )
      | ( ( ~ ( SV316 @ SV505 )
          | ( in @ SV505
            @ ( dsetconstr @ SV78
              @ ^ [SY2581: $i] : ( SV316 @ SY2581 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1591]) ).

thf(1827,plain,
    ! [SV318: $i,SV80: $i,SV628: $i] :
      ( ( ( ~ ( in @ SV628 @ ( powerset @ SV80 ) )
          | ~ ! [SY3066: $i] :
                ( ~ ( in @ SY3066 @ SV80 )
                | ~ ( in @ SY3066 @ SV318 )
                | ( in @ SY3066 @ SV628 ) )
          | ~ ! [SY3067: $i] :
                ( ~ ( in @ SY3067 @ SV80 )
                | ~ ( in @ SY3067 @ SV628 )
                | ( in @ SY3067 @ SV318 ) )
          | ( SV318 = SV628 ) )
        = $true )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1593]) ).

thf(1828,plain,
    ! [SV81: $i,SV319: $i] :
      ( ( ( ~ ( in @ ( sK8_SY2585 @ SV319 @ SV81 ) @ SV81 )
          | ( in @ ( sK8_SY2585 @ SV319 @ SV81 ) @ SV319 ) )
        = $false )
      | ( ( ~ ! [SY2586: $i] :
                ( ~ ( in @ SY2586 @ SV319 )
                | ( in @ SY2586 @ SV81 ) )
          | ( SV81 = SV319 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[1594]) ).

thf(1829,plain,
    ! [SV506: $i > $i > $o,SV320: $i,SV82: $i,SV608: $i] :
      ( ( ( ~ ( in @ SV608 @ SV82 ) )
        = $true )
      | ( ( ! [SY3043: $i] :
              ( ~ ( in @ SY3043 @ SV320 )
              | ~ ( in @ ( kpair @ SV608 @ SY3043 )
                  @ ( dpsetconstr @ SV82 @ SV320
                    @ ^ [SY2907: $i,SY2908: $i] : ( SV506 @ SY2907 @ SY2908 ) ) )
              | ( SV506 @ SV608 @ SY3043 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1595]) ).

thf(1830,plain,
    ! [SV83: $i] :
      ( ( ( in @ ( sK4_SY2024 @ SV83 ) @ SV83 )
        = $true )
      | ( ( SV83 = emptyset )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1596]) ).

thf(1831,plain,
    ! [SV321: $i > $o,SV84: $i] :
      ( ( ( ! [SY2592: $i] :
              ( ~ ( in @ SY2592 @ SV84 )
              | ( SV321 @ SY2592 ) ) )
        = $true )
      | ( ( ~ ! [SY2593: $i] :
                ~ ~ ( ~ ( in @ SY2593 @ SV84 )
                    | ~ ~ ( SV321 @ SY2593 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1597]) ).

thf(1832,plain,
    ! [SV609: $o,SV322: $i,SV85: $i,SV507: $i] :
      ( ( ( ~ ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) ) )
        = $true )
      | ( ( ~ ( ~ ( in @ SV507 @ SV85 )
              | SV609 )
          | ~ ( ~ ( in @ SV507 @ SV322 )
              | SV609 )
          | SV609 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1598]) ).

thf(1833,plain,
    ! [SV322: $i,SV85: $i,SV507: $i] :
      ( ( ( ~ ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) ) )
        = $true )
      | ( ( ~ ( ~ ( in @ SV507 @ SV85 )
              | $true )
          | ~ ( ~ ( in @ SV507 @ SV322 )
              | $true )
          | $true )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1599]) ).

thf(1834,plain,
    ! [SV322: $i,SV85: $i,SV507: $i] :
      ( ( ( ~ ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) ) )
        = $true )
      | ( ( ~ ( ~ ( in @ SV507 @ SV85 )
              | $false )
          | ~ ( ~ ( in @ SV507 @ SV322 )
              | $false )
          | $false )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1600]) ).

thf(1835,plain,
    ! [SV86: $i,SV508: $i,SV323: $i] :
      ( ( ( in @ SV323 @ SV508 )
        = $false )
      | ( ( ~ ( in @ SV508 @ SV86 )
          | ( in @ SV323 @ ( setunion @ SV86 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1601]) ).

thf(1836,plain,
    ! [SV87: $i] :
      ( ( ( ~ ( in @ emptyset @ SV87 ) )
        = $true )
      | ( ( ~ ! [SY2033: $i] :
                ( ~ ~ ( ~ ( in @ SY2033 @ omega )
                      | ~ ( in @ SY2033 @ SV87 ) )
                | ( in @ ( setadjoin @ SY2033 @ SY2033 ) @ SV87 ) ) )
        = $true )
      | ( ( ! [SY2034: $i] :
              ( ~ ( in @ SY2034 @ omega )
              | ( in @ SY2034 @ SV87 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1602]) ).

thf(1837,plain,
    ( ( in @ sK2_SY2597 @ ( powerset @ sK1_SX0 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1603]) ).

thf(1838,plain,
    ( ( ~ ( in @ sK9_SY2910 @ ( powerset @ sK1_SX0 ) )
      | ! [SY3068: $i] :
          ( ~ ( in @ SY3068 @ sK1_SX0 )
          | ~ ( in @ SY3068 @ ( setminus @ sK1_SX0 @ ( binunion @ sK2_SY2597 @ sK9_SY2910 ) ) )
          | ( in @ SY3068 @ ( setminus @ sK1_SX0 @ sK2_SY2597 ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[1604]) ).

thf(1839,plain,
    ! [SV324: $i,SV88: $i,SV629: $i] :
      ( ( ( ~ ( in @ SV629 @ ( powerset @ SV88 ) )
          | ~ ( subset @ SV324 @ ( setminus @ SV88 @ SV629 ) )
          | ! [SY3069: $i] :
              ( ~ ( in @ SY3069 @ SV88 )
              | ~ ( in @ SY3069 @ SV629 )
              | ( in @ SY3069 @ ( setminus @ SV88 @ SV324 ) ) ) )
        = $true )
      | ( ( in @ SV324 @ ( powerset @ SV88 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1605]) ).

thf(1840,plain,
    ! [SV325: $i > $o,SV89: $i] :
      ( ( ( ! [SY2602: $i] :
              ~ ~ ( ~ ( in @ SY2602 @ SV89 )
                  | ~ ( SV325 @ SY2602 ) ) )
        = $true )
      | ( ( ( ( dsetconstr @ SV89
              @ ^ [SY2603: $i] : ( SV325 @ SY2603 ) )
           != emptyset )
          | $false )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1606]) ).

thf(1841,plain,
    ! [SV90: $i,SV326: $i] :
      ( ( ( ~ ( in @ ( sK10_SY2604 @ SV326 @ SV90 ) @ SV90 )
          | ( in @ ( sK10_SY2604 @ SV326 @ SV90 ) @ SV326 ) )
        = $false )
      | ( ( subset @ SV90 @ SV326 )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[1607]) ).

thf(1842,plain,
    ! [SV327: $i,SV91: $i,SV630: $i] :
      ( ( ( ~ ( in @ SV630 @ ( powerset @ SV91 ) )
          | ( in @ ( binintersect @ SV327 @ SV630 ) @ ( powerset @ SV91 ) ) )
        = $true )
      | ( ( in @ SV327 @ ( powerset @ SV91 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1608]) ).

thf(1843,plain,
    ! [SV328: $i,SV92: $i,SV631: $i] :
      ( ( ( ! [SY3070: $i] :
              ( ( SV631 != SY3070 )
              | ~ ( in @ SV631 @ SV92 )
              | ( in @ SY3070 @ SV328 ) ) )
        = $true )
      | ( ( SV92 = SV328 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1609]) ).

thf(1844,plain,
    ! [SV509: $i > $i > $o,SV329: $i,SV93: $i,SV632: $i,SV610: $i] :
      ( ( ~ ( in @ ( kpair @ SV610 @ SV632 )
            @ ( dpsetconstr @ SV93 @ SV329
              @ ^ [SY2914: $i,SY2915: $i] : ( SV509 @ SY2914 @ SY2915 ) ) )
        | ( SV509 @ SV610 @ SV632 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1610]) ).

thf(1845,plain,
    ! [SV611: $i,SV510: $i,SV330: $i,SV94: $i] :
      ( ( ( ( kpair @ SV94 @ SV330 )
         != ( kpair @ SV510 @ SV611 ) )
        = $true )
      | ( ( SV94 = SV510 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1611]) ).

thf(1846,plain,
    ! [SV511: $i,SV331: $i,SV95: $i] :
      ( ( ( subset @ SV95 @ SV331 )
        = $false )
      | ( ( ~ ( in @ SV511 @ SV95 )
          | ( in @ SV511 @ SV331 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1612]) ).

thf(1847,plain,
    ! [SV512: $i,SV332: $i,SV96: $i] :
      ( ( ( func @ SV96 @ SV332 @ SV512 )
        = $false )
      | ( ( ! [SY2917: $i] :
              ( ~ ( func @ SV96 @ SV332 @ SY2917 )
              | ~ ! [SY2918: $i] :
                    ( ~ ( in @ SY2918 @ SV96 )
                    | ( ( ap @ SV96 @ SV332 @ SV512 @ SY2918 )
                      = ( ap @ SV96 @ SV332 @ SY2917 @ SY2918 ) ) )
              | ! [SY2919: $i] :
                  ( ~ ( in @ SY2919 @ SV96 )
                  | ! [SY2920: $i] :
                      ( ~ ( in @ SY2920 @ SV332 )
                      | ~ ( in @ ( kpair @ SY2919 @ SY2920 ) @ SY2917 )
                      | ( in @ ( kpair @ SY2919 @ SY2920 ) @ SV512 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1613]) ).

thf(1848,plain,
    ! [SV333: $i,SV98: $i,SV513: $i] :
      ( ( ( in @ SV513 @ ( cartprod @ SV98 @ SV333 ) )
        = $false )
      | ( ( ~ ! [SY2921: $i] :
                ~ ~ ( ~ ( in @ SY2921 @ SV98 )
                    | ~ ~ ! [SY2922: $i] :
                            ~ ~ ( ~ ( in @ SY2922 @ SV333 )
                                | ( SV513
                                 != ( kpair @ SY2921 @ SY2922 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1614]) ).

thf(1849,plain,
    ! [SV334: $i,SV99: $i,SV633: $i] :
      ( ( ( ~ ( in @ SV633 @ ( powerset @ SV99 ) )
          | ! [SY3073: $i] :
              ( ~ ( in @ SY3073 @ SV99 )
              | ~ ( in @ SV334 @ ( powerset @ SV633 ) )
              | ~ ( in @ SY3073 @ SV334 )
              | ( in @ SY3073 @ SV633 ) ) )
        = $true )
      | ( ( in @ SV334 @ ( powerset @ SV99 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1615]) ).

thf(1850,plain,
    ! [SV100: $i] :
      ( ( ( in @ ( sK5_SY2073 @ SV100 ) @ SV100 )
        = $true )
      | ( ( SV100 = emptyset )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1616]) ).

thf(1851,plain,
    ! [SV335: $i,SV101: $i,SV514: $i] :
      ( ( ( in @ SV514 @ ( setadjoin @ SV101 @ SV335 ) )
        = $false )
      | ( ( ( SV514 = SV101 )
          | ( in @ SV514 @ SV335 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1617]) ).

thf(1852,plain,
    ! [SV102: $i,SV336: $i > $o] :
      ( ( ( ~ ( in @ ( sK11_SY2627 @ SV336 @ SV102 ) @ SV102 )
          | ! [SY3074: $i] :
              ( ~ ( in @ SY3074 @ SV102 )
              | ~ ( SV336 @ ( sK11_SY2627 @ SV336 @ SV102 ) )
              | ~ ( SV336 @ SY3074 )
              | ( ( sK11_SY2627 @ SV336 @ SV102 )
                = SY3074 ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2629: $i] :
                  ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                      | ~ ( SV336 @ SY2629 ) )
          | ( singleton
            @ ( dsetconstr @ SV102
              @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[1618]) ).

thf(1853,plain,
    ! [SV515: $i > $i > $o,SV337: $i,SV103: $i,SV634: $i,SV612: $i] :
      ( ( ~ ( in @ ( kpair @ SV612 @ SV634 )
            @ ( dpsetconstr @ SV103 @ SV337
              @ ^ [SY2925: $i,SY2926: $i] : ( SV515 @ SY2925 @ SY2926 ) ) )
        | ( in @ SV612 @ SV103 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1619]) ).

thf(1854,plain,
    ! [SV338: $i,SV104: $i] :
      ( ( ( SV104 = SV338 )
        = $true )
      | ( ( ~ ( in @ SV338 @ ( setadjoin @ SV104 @ emptyset ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1620]) ).

thf(1855,plain,
    ! [SV339: $i,SV516: $i > $i,SV105: $i] :
      ( ( ( ! [SY2927: $i] :
              ( ~ ( in @ SY2927 @ SV105 )
              | ( in @ ( SV516 @ SY2927 ) @ SV339 ) ) )
        = $false )
      | ( ( ( lam @ SV105 @ SV339
            @ ^ [SY2928: $i] : ( SV516 @ SY2928 ) )
          = ( lam @ SV105 @ SV339
            @ ^ [SY2929: $i] : ( SV516 @ SY2929 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1621]) ).

thf(1856,plain,
    ! [SV340: $i,SV106: $i,SV517: $i] :
      ( ( ( in @ SV517 @ SV106 )
        = $false )
      | ( ( in @ ( setadjoin @ SV517 @ emptyset ) @ ( powerset @ ( binunion @ SV106 @ SV340 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1622]) ).

thf(1857,plain,
    ! [SV341: $i,SV518: $i > $i,SV107: $i] :
      ( ( ( ! [SY2930: $i] :
              ( ~ ( in @ SY2930 @ SV107 )
              | ( in @ ( SV518 @ SY2930 ) @ SV341 ) ) )
        = $false )
      | ( ( in
          @ ( lam @ SV107 @ SV341
            @ ^ [SY2931: $i] : ( SV518 @ SY2931 ) )
          @ ( funcSet @ SV107 @ SV341 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1623]) ).

thf(1858,plain,
    ! [SV109: $i] :
      ( ( ~ ~ ( ~ ~ ( ~ ! [SY2932: $i] :
                          ( ~ ( in @ SY2932 @ ( sK3_SY2100 @ SV109 ) )
                          | ! [SY2102: $i] :
                              ( ~ ( in @ SY2102 @ SY2932 )
                              | ( in @ SY2102 @ SV109 ) ) )
                    | ~ ! [SY2934: $i,SY2935: $i] :
                          ( ~ ~ ( ~ ( in @ SY2934 @ SV109 )
                                | ~ ( in @ SY2935 @ SV109 ) )
                          | ~ ! [SY2936: $i] :
                                ( ~ ( in @ SY2936 @ ( sK3_SY2100 @ SV109 ) )
                                | ~ ( ~ ( ~ ( in @ SY2934 @ SY2936 )
                                        | ( in @ SY2935 @ SY2936 ) )
                                    | ~ ( ~ ( in @ SY2935 @ SY2936 )
                                        | ( in @ SY2934 @ SY2936 ) ) ) )
                          | ( SY2934 = SY2935 ) ) )
              | ~ ! [SY2937: $i,SY2938: $i] :
                    ( ~ ~ ( ~ ( in @ SY2937 @ ( sK3_SY2100 @ SV109 ) )
                          | ~ ( in @ SY2938 @ ( sK3_SY2100 @ SV109 ) ) )
                    | ! [SX4: $i] :
                        ( ~ ( in @ SX4 @ SY2937 )
                        | ( in @ SX4 @ SY2938 ) )
                    | ! [SX4: $i] :
                        ( ~ ( in @ SX4 @ SY2938 )
                        | ( in @ SX4 @ SY2937 ) ) ) )
        | ~ ! [SY2941: $i] :
              ( ~ ~ ( ~ ! [SY2111: $i] :
                          ( ~ ( in @ SY2111 @ SY2941 )
                          | ( in @ SY2111 @ SV109 ) )
                    | ~ ~ ! [SX3: $i] :
                            ~ ( in @ SX3 @ SY2941 ) )
              | ~ ! [SY2944: $i] :
                    ~ ~ ! [SY2945: $i] :
                          ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY2944 @ ( sK3_SY2100 @ SV109 ) )
                                          | ~ ( in @ SY2945 @ SY2941 ) )
                                    | ~ ~ ~ ! [SX5: $i] :
                                              ~ ~ ( ~ ( in @ SX5 @ SY2944 )
                                                  | ~ ( in @ SX5 @ SY2941 ) ) )
                              | ~ ! [SY2947: $i] :
                                    ( ~ ( in @ SY2947 @ ( sK3_SY2100 @ SV109 ) )
                                    | ! [SX6: $i] :
                                        ( ~ ( in @ SX6 @ SY2947 )
                                        | ( in @ SX6 @ SY2944 ) )
                                    | ( in @ SY2945 @ SY2947 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1625]) ).

thf(1859,plain,
    ! [SV110: $i,SV635: $i] :
      ( ( ( ~ ( in @ SV635 @ SV110 ) )
        = $true )
      | ( ( ~ ! [SY2119: $i] :
                ~ ~ ( ~ ( in @ SY2119 @ SV110 )
                    | ~ ~ ~ ! [SY2120: $i] :
                              ~ ~ ( ~ ( in @ SY2120 @ SY2119 )
                                  | ~ ( in @ SY2120 @ SV110 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1626]) ).

thf(1860,plain,
    ! [SV343: $i,SV111: $i,SV519: $i] :
      ( ( ( in @ SV519 @ ( binintersect @ SV111 @ SV343 ) )
        = $false )
      | ( ( in @ SV519 @ SV111 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1627]) ).

thf(1861,plain,
    ! [SV636: $i,SV112: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV112 @ SV636 )
                | ~ ! [SY3077: $i] :
                      ( ~ ( SV112 @ SY3077 )
                      | ( SV636 = SY3077 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2125: $i] :
                ~ ( SV112 @ SY2125 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1628]) ).

thf(1862,plain,
    ! [SV344: $i,SV113: $i] :
      ( ( ( ~ ! [SY2645: $i] :
                ~ ~ ( ~ ( in @ SY2645 @ SV113 )
                    | ~ ( in @ SY2645 @ SV344 ) ) )
        = $true )
      | ( ( ( binintersect @ SV113 @ SV344 )
          = emptyset )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1629]) ).

thf(1863,plain,
    ! [SV346: $i,SV116: $i,SV637: $i] :
      ( ( ( ~ ( in @ SV637 @ ( powerset @ SV116 ) )
          | ! [SY3078: $i] :
              ( ~ ( in @ SY3078 @ SV116 )
              | ~ ~ ( in @ SY3078 @ ( binunion @ SV346 @ SV637 ) )
              | ~ ( in @ SY3078 @ SV346 ) ) )
        = $true )
      | ( ( in @ SV346 @ ( powerset @ SV116 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1631]) ).

thf(1864,plain,
    ! [SV347: $o,SV118: $i,SV520: $i] :
      ( ( ( in @ SV520 @ SV118 )
        = $false )
      | ( ( ! [SY2949: $i] :
              ( ~ ( in @ SY2949 @ SV118 )
              | ~ ~ SV347
              | ( ( if @ SV118 @ SV347 @ SV520 @ SY2949 )
                = SY2949 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1632]) ).

thf(1865,plain,
    ! [SV118: $i,SV521: $i] :
      ( ( ( in @ SV521 @ SV118 )
        = $false )
      | ( ( ! [SY2950: $i] :
              ( ~ ( in @ SY2950 @ SV118 )
              | ~ ~ $true
              | ( ( if @ SV118 @ $true @ SV521 @ SY2950 )
                = SY2950 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1633]) ).

thf(1866,plain,
    ! [SV118: $i,SV522: $i] :
      ( ( ( in @ SV522 @ SV118 )
        = $false )
      | ( ( ! [SY2951: $i] :
              ( ~ ( in @ SY2951 @ SV118 )
              | ~ ~ $false
              | ( ( if @ SV118 @ $false @ SV522 @ SY2951 )
                = SY2951 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1634]) ).

thf(1867,plain,
    ! [SV349: $i,SV121: $i,SV638: $i] :
      ( ( ( ~ ( in @ SV638 @ SV121 )
          | ~ ~ ( in @ SV638 @ ( setminus @ SV121 @ SV349 ) )
          | ( in @ SV638 @ SV349 ) )
        = $true )
      | ( ( in @ SV349 @ ( powerset @ SV121 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1636]) ).

thf(1868,plain,
    ! [SV350: $i,SV122: $i,SV639: $i] :
      ( ( ( ~ ( in @ SV639 @ ( powerset @ SV122 ) )
          | ( subset @ ( setminus @ SV122 @ SV350 ) @ ( setminus @ SV122 @ ( binintersect @ SV350 @ SV639 ) ) ) )
        = $true )
      | ( ( in @ SV350 @ ( powerset @ SV122 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1637]) ).

thf(1869,plain,
    ! [SV523: $i,SV351: $i,SV123: $i] :
      ( ( ( subset @ SV123 @ SV351 )
        = $false )
      | ( ( ~ ~ ( in @ SV523 @ SV351 )
          | ~ ( in @ SV523 @ SV123 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1638]) ).

thf(1870,plain,
    ! [SV352: $i,SV524: $i > $i,SV124: $i] :
      ( ( ( ! [SY2952: $i] :
              ( ~ ( in @ SY2952 @ SV124 )
              | ( in @ ( SV524 @ SY2952 ) @ SV352 ) ) )
        = $false )
      | ( ( func @ SV124 @ SV352
          @ ( dpsetconstr @ SV124 @ SV352
            @ ^ [SY2953: $i,SY2954: $i] :
                ( ( SV524 @ SY2953 )
                = SY2954 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1639]) ).

thf(1871,plain,
    ! [SV125: $i,SV353: $i > $o] :
      ( ( ( ~ ( in @ ( sK12_SY2657 @ SV353 @ SV125 ) @ SV125 )
          | ! [SY3079: $i] :
              ( ~ ( in @ SY3079 @ SV125 )
              | ~ ( SV353 @ ( sK12_SY2657 @ SV353 @ SV125 ) )
              | ~ ( SV353 @ SY3079 )
              | ( ( sK12_SY2657 @ SV353 @ SV125 )
                = SY3079 ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2659: $i] :
                  ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                      | ~ ( SV353 @ SY2659 ) )
          | ( singleton
            @ ( dsetconstr @ SV125
              @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[1640]) ).

thf(1872,plain,
    ! [SV354: $i,SV126: $i,SV525: $i] :
      ( ( ( ~ ( in @ SV525 @ SV126 ) )
        = $false )
      | ( ( ~ ( in @ SV525 @ SV354 )
          | ( in @ SV525 @ ( symdiff @ SV126 @ SV354 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1641]) ).

thf(1873,plain,
    ! [SV355: $i,SV127: $i,SV526: $i] :
      ( ( ( in @ SV526 @ ( setadjoin @ SV127 @ ( setadjoin @ SV355 @ emptyset ) ) )
        = $false )
      | ( ( ( SV526 = SV127 )
          | ( SV526 = SV355 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1642]) ).

thf(1874,plain,
    ! [SV356: $i,SV128: $i,SV640: $i] :
      ( ( ( ~ ( in @ SV640 @ ( powerset @ SV128 ) )
          | ( in @ ( setminus @ SV128 @ SV356 ) @ ( powerset @ ( setminus @ SV128 @ ( binintersect @ SV356 @ SV640 ) ) ) ) )
        = $true )
      | ( ( in @ SV356 @ ( powerset @ SV128 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1643]) ).

thf(1875,plain,
    ! [SV357: $i,SV129: $i,SV641: $i] :
      ( ( ( ~ ( in @ SV641 @ SV129 )
          | ~ ( in @ SV641 @ SV357 )
          | ~ ( in @ SV641 @ ( setminus @ SV129 @ SV357 ) ) )
        = $true )
      | ( ( in @ SV357 @ ( powerset @ SV129 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1644]) ).

thf(1876,plain,
    ! [SV360: $i,SV132: $i,SV642: $i] :
      ( ( ( ~ ( in @ SV642 @ ( powerset @ SV132 ) )
          | ~ ( subset @ SV360 @ SV642 )
          | ( subset @ ( setminus @ SV132 @ SV642 ) @ ( setminus @ SV132 @ SV360 ) ) )
        = $true )
      | ( ( in @ SV360 @ ( powerset @ SV132 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1647]) ).

thf(1877,plain,
    ! [SV527: $i,SV361: $i,SV133: $i] :
      ( ( ( func @ SV133 @ SV361 @ SV527 )
        = $false )
      | ( ( ! [SY2955: $i] :
              ( ~ ( in @ SY2955 @ SV133 )
              | ( ( ap @ SV133 @ SV361 @ SV527 @ SY2955 )
                = ( ap @ SV133 @ SV361 @ SV527 @ SY2955 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1648]) ).

thf(1878,plain,
    ! [SV362: $i,SV134: $i,SV528: $i] :
      ( ( ( in @ SV528 @ ( setadjoin @ SV134 @ ( setadjoin @ SV362 @ emptyset ) ) )
        = $false )
      | ( ( ( SV528 = SV134 )
          | ( SV528 = SV362 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1649]) ).

thf(1879,plain,
    ! [SV363: $i,SV135: $i,SV529: $i] :
      ( ( ( subset @ SV529 @ ( cartprod @ SV135 @ SV363 ) )
        = $false )
      | ( ( ! [SY2956: $i > $o] :
              ( ~ ! [SY2957: $i] :
                    ( ~ ( in @ SY2957 @ SV135 )
                    | ! [SY2958: $i] :
                        ( ~ ( in @ SY2958 @ SV363 )
                        | ~ ( in @ ( kpair @ SY2957 @ SY2958 ) @ SV529 )
                        | ( SY2956 @ ( kpair @ SY2957 @ SY2958 ) ) ) )
              | ! [SY2959: $i] :
                  ( ~ ( in @ SY2959 @ SV529 )
                  | ( SY2956 @ SY2959 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1650]) ).

thf(1880,plain,
    ! [SV530: $i,SV136: $i,SV364: $i] :
      ( ( ( in @ SV364 @ ( powerset @ SV136 ) )
        = $false )
      | ( ( ~ ( in @ SV530 @ SV364 )
          | ( in @ SV530 @ SV136 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1651]) ).

thf(1881,plain,
    ! [SV365: $i,SV137: $i,SV643: $i] :
      ( ( ( ~ ( in @ SV643 @ ( powerset @ SV137 ) )
          | ! [SY3080: $i] :
              ( ~ ( in @ SY3080 @ SV137 )
              | ~ ~ ( in @ SY3080 @ SV643 )
              | ~ ( in @ SY3080 @ ( binintersect @ SV365 @ SV643 ) ) ) )
        = $true )
      | ( ( in @ SV365 @ ( powerset @ SV137 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1652]) ).

thf(1882,plain,
    ! [SV370: $i,SV140: $i,SV531: $i] :
      ( ( ( in @ SV531 @ SV140 )
        = $false )
      | ( ( ! [SY2960: $i] :
              ( ~ ( in @ SY2960 @ SV370 )
              | ( in @ ( kpair @ SV531 @ SY2960 ) @ ( cartprod @ SV140 @ SV370 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1657]) ).

thf(1883,plain,
    ! [SV371: $i,SV141: $i,SV532: $i] :
      ( ( ( in @ SV532 @ ( cartprod @ SV141 @ SV371 ) )
        = $false )
      | ( ( in @ ( ksnd @ SV532 ) @ SV371 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1658]) ).

thf(1884,plain,
    ! [SV372: $i > $o,SV142: $i,SV644: $i] :
      ( ( ( ~ ( in @ SV644 @ SV142 )
          | ! [SY3081: $i] :
              ( ~ ( in @ SY3081 @ SV142 )
              | ~ ( SV372 @ SV644 )
              | ~ ( SV372 @ SY3081 )
              | ( SV644 = SY3081 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV142
            @ ^ [SY2680: $i] : ( SV372 @ SY2680 ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1659]) ).

thf(1885,plain,
    ! [SV374: $i,SV144: $i,SV533: $i] :
      ( ( ( in @ SV533 @ SV144 )
        = $false )
      | ( ( ! [SY2961: $i] :
              ( ~ ( in @ SY2961 @ SV374 )
              | ( ( kfst @ ( kpair @ SV533 @ SY2961 ) )
                = SV533 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1661]) ).

thf(1886,plain,
    ! [SV613: $i,SV534: $i,SV376: $i,SV146: $i] :
      ( ( ( ( kpair @ SV146 @ SV376 )
         != ( kpair @ SV534 @ SV613 ) )
        = $true )
      | ( ( SV376 = SV613 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1663]) ).

thf(1887,plain,
    ! [SV377: $i,SV147: $i > $i > $o] :
      ( ( ( ~ ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
          | ~ ! [SY3082: $i] :
                ~ ~ ( ~ ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SY3082 )
                    | ~ ! [SY3083: $i] :
                          ( ~ ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SY3083 )
                          | ( SY3082 = SY3083 ) ) ) )
        = $false )
      | ( ( ~ ! [SY2690: $i] :
                ~ ! [SY2691: $i] :
                    ~ ( ~ ( ~ ( in @ SY2691 @ SY2690 )
                          | ~ ! [SY2692: $i] :
                                ~ ~ ( ~ ( in @ SY2692 @ SV377 )
                                    | ~ ( SV147 @ SY2692 @ SY2691 ) ) )
                      | ~ ( ~ ~ ! [SY2693: $i] :
                                  ~ ~ ( ~ ( in @ SY2693 @ SV377 )
                                      | ~ ( SV147 @ SY2693 @ SY2691 ) )
                          | ( in @ SY2691 @ SY2690 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[1664]) ).

thf(1888,plain,
    ! [SV148: $i,SV378: $i] :
      ( ( ( ~ ( in @ ( sK14_SY2694 @ SV378 @ SV148 ) @ SV148 )
          | ( in @ ( sK14_SY2694 @ SV378 @ SV148 ) @ SV378 ) )
        = $false )
      | ( ( subset @ SV148 @ SV378 )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[1665]) ).

thf(1889,plain,
    ! [SV149: $i,SV379: $i] :
      ( ( ( ~ ( subset @ SV379 @ SV149 ) )
        = $true )
      | ( ( SV149 = SV379 )
        = $true )
      | ( ( subset @ SV149 @ SV379 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1666]) ).

thf(1890,plain,
    ! [SV380: $i,SV150: $i,SV535: $i] :
      ( ( ( in @ SV535 @ SV150 )
        = $false )
      | ( ( in @ SV535 @ ( binunion @ SV150 @ SV380 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1667]) ).

thf(1891,plain,
    ! [SV381: $i,SV151: $i,SV645: $i] :
      ( ( ( ~ ( in @ SV645 @ ( powerset @ SV151 ) )
          | ! [SY3084: $i] :
              ( ~ ( in @ SY3084 @ SV151 )
              | ~ ~ ( in @ SY3084 @ ( binunion @ SV381 @ SV645 ) )
              | ~ ( in @ SY3084 @ SV645 ) ) )
        = $true )
      | ( ( in @ SV381 @ ( powerset @ SV151 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1668]) ).

thf(1892,plain,
    ! [SV382: $i,SV152: $i,SV646: $i] :
      ( ( ( ! [SY3085: $i] :
              ( ( SV646 != SY3085 )
              | ( ( setadjoin @ SV152 @ SV646 )
                = ( setadjoin @ SV382 @ SY3085 ) ) ) )
        = $true )
      | ( ( SV152 = SV382 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1669]) ).

thf(1893,plain,
    ! [SV154: $i,SV383: $i,SV536: $i] :
      ( ( ( in @ SV536 @ SV383 )
        = $false )
      | ( ( in @ SV536 @ ( binunion @ SV154 @ SV383 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1670]) ).

thf(1894,plain,
    ! [SV385: $i,SV156: $i,SV647: $i] :
      ( ( ( ~ ( in @ SV647 @ ( powerset @ SV156 ) )
          | ! [SY3086: $i] :
              ( ~ ( in @ SY3086 @ SV156 )
              | ~ ~ ( in @ SY3086 @ SV385 )
              | ~ ( in @ SY3086 @ ( binintersect @ SV385 @ SV647 ) ) ) )
        = $true )
      | ( ( in @ SV385 @ ( powerset @ SV156 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1672]) ).

thf(1895,plain,
    ! [SV648: $i,SV157: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV157 @ SV648 )
                | ~ ! [SY3087: $i] :
                      ( ~ ( SV157 @ SY3087 )
                      | ( SV648 = SY3087 ) ) ) )
        = $true )
      | ( ( SV157
          @ ( descr
            @ ^ [SY2227: $i] : ( SV157 @ SY2227 ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1673]) ).

thf(1896,plain,
    ! [SV386: $i,SV158: $i,SV537: $i] :
      ( ( ( in @ SV537 @ ( setminus @ SV158 @ SV386 ) )
        = $false )
      | ( ( ~ ( in @ SV537 @ SV386 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1674]) ).

thf(1897,plain,
    ! [SV388: $i > $o,SV160: $i] :
      ( ( ( ! [SY2704: $i] :
              ( ~ ( in @ SY2704 @ SV160 )
              | ( SV388 @ SY2704 ) ) )
        = $true )
      | ( ( ~ ! [SY2705: $i] :
                ~ ~ ( ~ ( in @ SY2705 @ SV160 )
                    | ~ ~ ( SV388 @ SY2705 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1676]) ).

thf(1898,plain,
    ! [SV389: $i,SV161: $i,SV649: $i] :
      ( ( ( ~ ( in @ SV649 @ ( powerset @ SV161 ) )
          | ! [SY3088: $i] :
              ( ~ ( in @ SY3088 @ SV161 )
              | ~ ( in @ SY3088 @ ( setminus @ SV161 @ SV389 ) )
              | ( in @ SY3088 @ ( setminus @ SV161 @ ( binintersect @ SV389 @ SV649 ) ) ) ) )
        = $true )
      | ( ( in @ SV389 @ ( powerset @ SV161 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1677]) ).

thf(1899,plain,
    ! [SV390: $i,SV162: $i,SV650: $i] :
      ( ( ( ~ ( in @ SV650 @ ( powerset @ SV162 ) )
          | ( in @ ( binunion @ SV390 @ SV650 ) @ ( powerset @ SV162 ) ) )
        = $true )
      | ( ( in @ SV390 @ ( powerset @ SV162 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1678]) ).

thf(1900,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( ~ ( SV165 @ SV651 ) )
        = $true )
      | ( ( ~ ! [SY2242: $i,SY2243: $i] :
                ( ~ ( SV165 @ SY2242 )
                | ~ ( SV165 @ SY2243 )
                | ( SY2242 = SY2243 ) )
          | ~ ! [SY2244: $i] :
                ~ ~ ( ~ ( SV165 @ SY2244 )
                    | ~ ! [SY2245: $i] :
                          ( ~ ( SV165 @ SY2245 )
                          | ( SY2244 = SY2245 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1681]) ).

thf(1901,plain,
    ! [SV393: $i,SV166: $i,SV538: $i] :
      ( ( ( in @ SV538 @ SV166 )
        = $false )
      | ( ( ~ ~ ( in @ SV538 @ SV393 )
          | ~ ( subset @ SV166 @ SV393 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1682]) ).

thf(1902,plain,
    ! [SV394: $i,SV167: $i,SV652: $i] :
      ( ( ( ~ ( in @ SV652 @ ( powerset @ SV167 ) )
          | ! [SY3089: $i] :
              ( ~ ( in @ SY3089 @ ( powerset @ SV167 ) )
              | ( in @ ( binintersect @ SV394 @ SV652 ) @ ( powerset @ ( binintersect @ ( binunion @ SV394 @ SY3089 ) @ ( binunion @ SV652 @ SY3089 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV394 @ ( powerset @ SV167 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1683]) ).

thf(1903,plain,
    ! [SV395: $i,SV168: $i,SV539: $i] :
      ( ( ( subset @ SV539 @ ( cartprod @ SV168 @ SV395 ) )
        = $false )
      | ( ( ! [SY2963: $i] :
              ( ~ ( subset @ SY2963 @ ( cartprod @ SV168 @ SV395 ) )
              | ~ ! [SY2964: $i] :
                    ( ~ ( in @ SY2964 @ SV168 )
                    | ! [SY2965: $i] :
                        ( ~ ( in @ SY2965 @ SV395 )
                        | ~ ( in @ ( kpair @ SY2964 @ SY2965 ) @ SV539 )
                        | ( in @ ( kpair @ SY2964 @ SY2965 ) @ SY2963 ) ) )
              | ( subset @ SV539 @ SY2963 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1684]) ).

thf(1904,plain,
    ! [SV396: $o,SV169: $i,SV540: $i] :
      ( ( ( in @ SV540 @ SV169 )
        = $false )
      | ( ( ! [SY2966: $i] :
              ( ~ ( in @ SY2966 @ SV169 )
              | ~ SV396
              | ( ( if @ SV169 @ SV396 @ SV540 @ SY2966 )
                = SV540 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1685]) ).

thf(1905,plain,
    ! [SV169: $i,SV541: $i] :
      ( ( ( in @ SV541 @ SV169 )
        = $false )
      | ( ( ! [SY2967: $i] :
              ( ~ ( in @ SY2967 @ SV169 )
              | ~ $true
              | ( ( if @ SV169 @ $true @ SV541 @ SY2967 )
                = SV541 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1686]) ).

thf(1906,plain,
    ! [SV169: $i,SV542: $i] :
      ( ( ( in @ SV542 @ SV169 )
        = $false )
      | ( ( ! [SY2968: $i] :
              ( ~ ( in @ SY2968 @ SV169 )
              | ~ $false
              | ( ( if @ SV169 @ $false @ SV542 @ SY2968 )
                = SV542 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1687]) ).

thf(1907,plain,
    ! [SV397: $i,SV543: $i > $i,SV170: $i] :
      ( ( ( ! [SY2969: $i] :
              ( ~ ( in @ SY2969 @ SV170 )
              | ( in @ ( SV543 @ SY2969 ) @ SV397 ) ) )
        = $false )
      | ( ( ! [SY2970: $i] :
              ( ~ ( in @ SY2970 @ SV170 )
              | ( ( ap @ SV170 @ SV397
                  @ ( lam @ SV170 @ SV397
                    @ ^ [SY2971: $i] : ( SV543 @ SY2971 ) )
                  @ SY2970 )
                = ( SV543 @ SY2970 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1688]) ).

thf(1908,plain,
    ! [SV171: $i,SV653: $i] :
      ( ( ( ~ ( in @ SV653 @ SV171 ) )
        = $true )
      | ( ( SV171 != emptyset )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1689]) ).

thf(1909,plain,
    ! [SV398: $i,SV172: $i,SV544: $i] :
      ( ( ( in @ SV544 @ ( cartprod @ SV172 @ SV398 ) )
        = $false )
      | ( ( ( kpair @ ( kfst @ SV544 ) @ ( ksnd @ SV544 ) )
          = SV544 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1690]) ).

thf(1910,plain,
    ! [SV399: $i,SV173: $i,SV545: $i] :
      ( ( ( in @ SV545 @ ( funcSet @ SV173 @ SV399 ) )
        = $false )
      | ( ( ( lam @ SV173 @ SV399
            @ ^ [SY2972: $i] : ( ap @ SV173 @ SV399 @ SV545 @ SY2972 ) )
          = SV545 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1691]) ).

thf(1911,plain,
    ! [SV614: $i,SV546: $i,SV400: $i,SV174: $i] :
      ( ( ( ( setadjoin @ ( setadjoin @ SV174 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV174 @ ( setadjoin @ SV400 @ emptyset ) ) @ emptyset ) )
         != ( setadjoin @ ( setadjoin @ SV546 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV546 @ ( setadjoin @ SV614 @ emptyset ) ) @ emptyset ) ) )
        = $true )
      | ( ( ( SV546 != SV614 )
          | ( SV400 = SV614 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1692]) ).

thf(1912,plain,
    ! [SV401: $i,SV175: $i,SV615: $i,SV547: $i] :
      ( ( ( ~ ( in @ ( kpair @ SV547 @ SV615 ) @ ( cartprod @ SV175 @ SV401 ) ) )
        = $true )
      | ( ( in @ SV615 @ SV401 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1693]) ).

thf(1913,plain,
    ! [SV548: $i,SV402: $i,SV176: $i] :
      ( ( ( func @ SV176 @ SV402 @ SV548 )
        = $false )
      | ( ( ! [SY2975: $i] :
              ( ~ ( in @ SY2975 @ SV176 )
              | ( in @ ( ap @ SV176 @ SV402 @ SV548 @ SY2975 ) @ SV402 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1694]) ).

thf(1914,plain,
    ! [SV403: $i,SV177: $i,SV654: $i] :
      ( ( ( ~ ( in @ SV654 @ ( powerset @ SV177 ) )
          | ! [SY3090: $i] :
              ( ~ ( in @ SY3090 @ SV177 )
              | ~ ( subset @ SV403 @ ( setminus @ SV177 @ SV654 ) )
              | ~ ( in @ SY3090 @ SV654 )
              | ~ ( in @ SY3090 @ SV403 ) ) )
        = $true )
      | ( ( in @ SV403 @ ( powerset @ SV177 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1695]) ).

thf(1915,plain,
    ! [SV549: $i > $i > $o,SV404: $i,SV178: $i,SV616: $i] :
      ( ( ( ~ ( in @ SV616 @ SV178 ) )
        = $true )
      | ( ( ! [SY3052: $i] :
              ( ~ ( in @ SY3052 @ SV404 )
              | ~ ( SV549 @ SV616 @ SY3052 )
              | ( in @ ( kpair @ SV616 @ SY3052 )
                @ ( dpsetconstr @ SV178 @ SV404
                  @ ^ [SY2978: $i,SY2979: $i] : ( SV549 @ SY2978 @ SY2979 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1696]) ).

thf(1916,plain,
    ! [SV405: $i,SV179: $i,SV550: $i] :
      ( ( ( in @ SV550 @ SV179 )
        = $false )
      | ( ( ~ ~ ( in @ SV550 @ SV405 )
          | ( SV179 != SV405 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1697]) ).

thf(1917,plain,
    ! [SV406: $i,SV180: $i,SV551: $i] :
      ( ( ( in @ SV551 @ SV180 )
        = $false )
      | ( ( ~ ( in @ SV551 @ SV406 )
          | ( in @ SV551 @ ( binintersect @ SV180 @ SV406 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1698]) ).

thf(1918,plain,
    ! [SV407: $i,SV181: $i] :
      ( ( ( ~ ( in @ ( sK15_SY2740 @ SV181 @ SV407 ) @ SV407 )
          | ( in @ ( sK15_SY2740 @ SV181 @ SV407 ) @ SV181 ) )
        = $false )
      | ( ( in @ SV407 @ ( powerset @ SV181 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[1699]) ).

thf(1919,plain,
    ! [SV408: $i,SV182: $i,SV655: $i] :
      ( ( ( ~ ( in @ SV655 @ SV182 )
          | ~ ( in @ SV655 @ SV408 )
          | ( in @ SV655 @ ( setminus @ SV182 @ ( setminus @ SV182 @ SV408 ) ) ) )
        = $true )
      | ( ( in @ SV408 @ ( powerset @ SV182 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1700]) ).

thf(1920,plain,
    ! [SV409: $i,SV183: $i,SV552: $i] :
      ( ( ( in @ SV552 @ ( setminus @ SV183 @ SV409 ) )
        = $false )
      | ( ( in @ SV552 @ SV183 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1701]) ).

thf(1921,plain,
    ! [SV410: $i,SV184: $i,SV553: $i] :
      ( ( ( in @ SV553 @ ( cartprod @ SV184 @ SV410 ) )
        = $false )
      | ( ( iskpair @ SV553 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1702]) ).

thf(1922,plain,
    ! [SV554: $i,SV411: $i,SV185: $i] :
      ( ( ( func @ SV185 @ SV411 @ SV554 )
        = $false )
      | ( ( ! [SY2980: $i] :
              ( ~ ( in @ SY2980 @ SV185 )
              | ! [SY2981: $i] :
                  ( ~ ( in @ SY2981 @ SV411 )
                  | ~ ( in @ ( kpair @ SY2980 @ SY2981 ) @ SV554 )
                  | ( ( ap @ SV185 @ SV411 @ SV554 @ SY2980 )
                    = SY2981 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1703]) ).

thf(1923,plain,
    ! [SV412: $i,SV186: $i,SV656: $i] :
      ( ( ( ~ ( in @ SV656 @ ( powerset @ SV186 ) )
          | ( in @ ( setminus @ SV412 @ SV656 ) @ ( powerset @ SV186 ) ) )
        = $true )
      | ( ( in @ SV412 @ ( powerset @ SV186 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1704]) ).

thf(1924,plain,
    ! [SV413: $i > $o,SV187: $i,SV555: $i] :
      ( ( ( in @ SV555
          @ ( dsetconstr @ SV187
            @ ^ [SY2749: $i] : ( SV413 @ SY2749 ) ) )
        = $false )
      | ( ( in @ SV555 @ SV187 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1705]) ).

thf(1925,plain,
    ! [SV414: $i > $o,SV188: $i,SV556: $i] :
      ( ( ( in @ SV556 @ SV188 )
        = $false )
      | ( ( ~ ( ~ ( ~ ( in @ SV556
                      @ ( dsetconstr @ SV188
                        @ ^ [SY2751: $i] : ( SV414 @ SY2751 ) ) )
                  | ( SV414 @ SV556 ) )
              | ~ ( ~ ( SV414 @ SV556 )
                  | ( in @ SV556
                    @ ( dsetconstr @ SV188
                      @ ^ [SY2752: $i] : ( SV414 @ SY2752 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1706]) ).

thf(1926,plain,
    ! [SV189: $i,SV415: $i,SV557: $i] :
      ( ( ( in @ SV557 @ SV415 )
        = $false )
      | ( ( in @ SV557 @ ( setadjoin @ SV189 @ SV415 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1707]) ).

thf(1927,plain,
    ! [SV558: $i,SV416: $i,SV190: $i] :
      ( ( ( func @ SV190 @ SV416 @ SV558 )
        = $false )
      | ( ( ! [SY2985: $i] :
              ( ~ ( func @ SV190 @ SV416 @ SY2985 )
              | ~ ! [SY2986: $i] :
                    ( ~ ( in @ SY2986 @ SV190 )
                    | ( ( ap @ SV190 @ SV416 @ SV558 @ SY2986 )
                      = ( ap @ SV190 @ SV416 @ SY2985 @ SY2986 ) ) )
              | ( SV558 = SY2985 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1708]) ).

thf(1928,plain,
    ! [SV417: $i,SV191: $i,SV657: $i] :
      ( ( ( ~ ( in @ SV657 @ ( powerset @ SV191 ) )
          | ! [SY3091: $i] :
              ( ~ ( in @ SY3091 @ ( powerset @ SV191 ) )
              | ! [SY3092: $i] :
                  ( ~ ( in @ SY3092 @ SV191 )
                  | ~ ( in @ SY3092 @ ( binintersect @ SV417 @ SV657 ) )
                  | ( in @ SY3092 @ ( binunion @ SV417 @ SY3091 ) ) ) ) )
        = $true )
      | ( ( in @ SV417 @ ( powerset @ SV191 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1709]) ).

thf(1929,plain,
    ! [SV418: $i > $o,SV192: $i,SV559: $i] :
      ( ( ( in @ SV559
          @ ( dsetconstr @ SV192
            @ ^ [SY2761: $i] : ( SV418 @ SY2761 ) ) )
        = $false )
      | ( ( SV418 @ SV559 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1710]) ).

thf(1930,plain,
    ! [SV419: $i,SV193: $i,SV658: $i] :
      ( ( ( ! [SY3093: $i] :
              ( ( SV658 != SY3093 )
              | ~ ( ~ ( ~ ( in @ SV658 @ SV193 )
                      | ( in @ SY3093 @ SV419 ) )
                  | ~ ( ~ ( in @ SY3093 @ SV419 )
                      | ( in @ SV658 @ SV193 ) ) ) ) )
        = $true )
      | ( ( SV193 = SV419 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1711]) ).

thf(1931,plain,
    ! [SV420: $o,SV194: $i,SV560: $i] :
      ( ( ( in @ SV560 @ SV194 )
        = $false )
      | ( ( ! [SY2988: $i] :
              ( ~ ( in @ SY2988 @ SV194 )
              | ( singleton
                @ ( dsetconstr @ SV194
                  @ ^ [SY2989: $i] :
                      ( ~ ( ~ SV420
                          | ( SY2989 != SV560 ) )
                      | ~ ( ~ ~ SV420
                          | ( SY2989 != SY2988 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1712]) ).

thf(1932,plain,
    ! [SV194: $i,SV561: $i] :
      ( ( ( in @ SV561 @ SV194 )
        = $false )
      | ( ( ! [SY2990: $i] :
              ( ~ ( in @ SY2990 @ SV194 )
              | ( singleton
                @ ( dsetconstr @ SV194
                  @ ^ [SY2991: $i] :
                      ( ~ ( ~ $true
                          | ( SY2991 != SV561 ) )
                      | ~ ( ~ ~ $true
                          | ( SY2991 != SY2990 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1713]) ).

thf(1933,plain,
    ! [SV194: $i,SV562: $i] :
      ( ( ( in @ SV562 @ SV194 )
        = $false )
      | ( ( ! [SY2992: $i] :
              ( ~ ( in @ SY2992 @ SV194 )
              | ( singleton
                @ ( dsetconstr @ SV194
                  @ ^ [SY2993: $i] :
                      ( ~ ( ~ $false
                          | ( SY2993 != SV562 ) )
                      | ~ ( ~ ~ $false
                          | ( SY2993 != SY2992 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1714]) ).

thf(1934,plain,
    ! [SV422: $i,SV196: $i,SV563: $i] :
      ( ( ( in @ SV563 @ SV196 )
        = $false )
      | ( ( ! [SY2994: $i] :
              ( ~ ( in @ SY2994 @ SV422 )
              | ( in @ ( kpair @ SV563 @ SY2994 ) @ ( powerset @ ( powerset @ ( binunion @ SV196 @ SV422 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1716]) ).

thf(1935,plain,
    ! [SV423: $o,SV197: $i,SV564: $i] :
      ( ( ( in @ SV564 @ SV197 )
        = $false )
      | ( ( ! [SY2995: $i] :
              ( ~ ( in @ SY2995 @ SV197 )
              | ( in @ ( if @ SV197 @ SV423 @ SV564 @ SY2995 ) @ SV197 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1717]) ).

thf(1936,plain,
    ! [SV197: $i,SV565: $i] :
      ( ( ( in @ SV565 @ SV197 )
        = $false )
      | ( ( ! [SY2996: $i] :
              ( ~ ( in @ SY2996 @ SV197 )
              | ( in @ ( if @ SV197 @ $true @ SV565 @ SY2996 ) @ SV197 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1718]) ).

thf(1937,plain,
    ! [SV197: $i,SV566: $i] :
      ( ( ( in @ SV566 @ SV197 )
        = $false )
      | ( ( ! [SY2997: $i] :
              ( ~ ( in @ SY2997 @ SV197 )
              | ( in @ ( if @ SV197 @ $false @ SV566 @ SY2997 ) @ SV197 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1719]) ).

thf(1938,plain,
    ! [SV424: $i,SV198: $i,SV567: $i] :
      ( ( ( in @ SV567 @ ( funcSet @ SV198 @ SV424 ) )
        = $false )
      | ( ( ! [SY2998: $i] :
              ( ~ ( in @ SY2998 @ SV198 )
              | ! [SY2999: $i] :
                  ( ~ ( in @ SY2999 @ SV424 )
                  | ~ ( in @ ( kpair @ SY2998 @ SY2999 ) @ SV567 )
                  | ( ( ap @ SV198 @ SV424 @ SV567 @ SY2998 )
                    = SY2999 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1720]) ).

thf(1939,plain,
    ! [SV425: $i,SV568: $i > $i,SV199: $i] :
      ( ( ( ! [SY3000: $i] :
              ( ~ ( in @ SY3000 @ SV199 )
              | ( in @ ( SV568 @ SY3000 ) @ SV425 ) ) )
        = $false )
      | ( ( func @ SV199 @ SV425
          @ ( lam @ SV199 @ SV425
            @ ^ [SY3001: $i] : ( SV568 @ SY3001 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1721]) ).

thf(1940,plain,
    ! [SV200: $i,SV426: $i > $o] :
      ( ( ( ~ ( in @ ( sK16_SY2777 @ SV426 @ SV200 ) @ SV200 )
          | ~ ( SV426 @ ( sK16_SY2777 @ SV426 @ SV200 ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2778: $i] :
                  ~ ~ ( ~ ( in @ SY2778 @ SV200 )
                      | ~ ( SV426 @ SY2778 ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[1722]) ).

thf(1941,plain,
    ! [SV428: $i,SV202: $i,SV569: $i] :
      ( ( ( in @ SV569 @ ( funcSet @ SV202 @ SV428 ) )
        = $false )
      | ( ( ! [SY3002: $i] :
              ( ~ ( in @ SY3002 @ SV202 )
              | ( in @ ( ap @ SV202 @ SV428 @ SV569 @ SY3002 ) @ SV428 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1724]) ).

thf(1942,plain,
    ! [SV203: $i] :
      ( ( ( ! [SY2355: $i] :
              ~ ( in @ SY2355 @ SV203 ) )
        = $false )
      | ( ( SV203 = emptyset )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1725]) ).

thf(1943,plain,
    ! [SV205: $i,SV430: $i] :
      ( ( ~ ( in @ SV430 @ ( setunion @ SV205 ) )
        | ~ ! [SY2781: $i] :
              ~ ~ ( ~ ( in @ SV430 @ SY2781 )
                  | ~ ( in @ SY2781 @ SV205 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1727]) ).

thf(1944,plain,
    ! [SV205: $i,SV430: $i] :
      ( ( ~ ~ ! [SY2782: $i] :
                ~ ~ ( ~ ( in @ SV430 @ SY2782 )
                    | ~ ( in @ SY2782 @ SV205 ) )
        | ( in @ SV430 @ ( setunion @ SV205 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1728]) ).

thf(1945,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false )
      | ( ( ! [SY3003: $o] :
              ( ~ ( ~ ( in @ SV570 @ SV206 )
                  | ~ ~ ( in @ SV570 @ SV431 )
                  | SY3003 )
              | ~ ( ~ ~ ( in @ SV570 @ SV206 )
                  | ~ ( in @ SV570 @ SV431 )
                  | SY3003 )
              | SY3003 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1729]) ).

thf(1946,plain,
    ! [SV432: $i,SV207: $i] :
      ( ( ( subset @ SV207 @ SV432 )
        = $true )
      | ( ( SV207 != SV432 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1730]) ).

thf(1947,plain,
    ! [SV433: $i,SV208: $i] :
      ( ( ( ! [SY2785: $i] :
              ~ ~ ( ~ ( in @ SY2785 @ SV208 )
                  | ~ ( in @ SV433 @ SY2785 ) ) )
        = $false )
      | ( ( in @ SV433 @ ( setunion @ SV208 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1731]) ).

thf(1948,plain,
    ! [SV659: $i > $o,SV434: $i,SV209: $i] :
      ( ( ( ! [SY3094: $i > $o] :
              ( ~ ! [SY3095: $i] :
                    ( ~ ( in @ SY3095 @ SV209 )
                    | ! [SY3096: $i] :
                        ( ~ ( in @ SY3096 @ SV434 )
                        | ( SY3095 != SY3096 )
                        | ~ ( ~ ( ~ ( SV659 @ SY3095 )
                                | ( SY3094 @ SY3096 ) )
                            | ~ ( ~ ( SY3094 @ SY3096 )
                                | ( SV659 @ SY3095 ) ) ) ) )
              | ( ( dsetconstr @ SV209
                  @ ^ [SY3097: $i] : ( SV659 @ SY3097 ) )
                = ( dsetconstr @ SV434
                  @ ^ [SX4: $i] : ( SY3094 @ SX4 ) ) ) ) )
        = $true )
      | ( ( SV209 = SV434 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1732]) ).

thf(1949,plain,
    ! [SV435: $i,SV210: $i,SV571: $i] :
      ( ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false )
      | ( ( ! [SY3004: $o] :
              ( ~ ( ( SV571 != SV210 )
                  | SY3004 )
              | ~ ( ~ ( in @ SV571 @ SV435 )
                  | SY3004 )
              | SY3004 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1733]) ).

thf(1950,plain,
    ! [SV660: $i,SV211: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV211 @ SV660 )
                | ~ ! [SY3099: $i] :
                      ( ~ ( SV211 @ SY3099 )
                      | ( SV660 = SY3099 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2378: $i] :
                ~ ~ ( ~ ( SV211 @ SY2378 )
                    | ~ ! [SY2379: $i] :
                          ( ~ ( SV211 @ SY2379 )
                          | ( SY2378 = SY2379 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1734]) ).

thf(1951,plain,
    ! [SV436: $i,SV212: $i,SV572: $i] :
      ( ( ( in @ SV572 @ ( funcSet @ SV212 @ SV436 ) )
        = $false )
      | ( ( ! [SY3005: $i] :
              ( ~ ( in @ SY3005 @ SV212 )
              | ( ( ap @ SV212 @ SV436 @ SV572 @ SY3005 )
                = ( ap @ SV212 @ SV436 @ SV572 @ SY3005 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1735]) ).

thf(1952,plain,
    ! [SV437: $i,SV213: $i,SV661: $i] :
      ( ( ( ~ ( in @ SV661 @ SV213 )
          | ~ ( in @ SV661 @ ( setminus @ SV213 @ ( setminus @ SV213 @ SV437 ) ) )
          | ( in @ SV661 @ SV437 ) )
        = $true )
      | ( ( in @ SV437 @ ( powerset @ SV213 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1736]) ).

thf(1953,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ! [SY3100: $i] :
              ( ( ( sK17_SY2797 @ SV438 @ SV214 )
               != SY3100 )
              | ~ ( ~ ( ~ ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
                      | ( SV438 @ SY3100 ) )
                  | ~ ( ~ ( SV438 @ SY3100 )
                      | ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) ) ) ) ) )
        = $false )
      | ( ( ~ ( ~ ( ~ ~ ! [SY2388: $i] :
                          ~ ~ ( ~ ( SV214 @ SY2388 )
                              | ~ ! [SY2389: $i] :
                                    ( ~ ( SV214 @ SY2389 )
                                    | ( SY2388 = SY2389 ) ) )
                  | ~ ! [SY2801: $i] :
                        ~ ~ ( ~ ( SV438 @ SY2801 )
                            | ~ ! [SY2802: $i] :
                                  ( ~ ( SV438 @ SY2802 )
                                  | ( SY2801 = SY2802 ) ) ) )
              | ~ ( ~ ~ ! [SY2803: $i] :
                          ~ ~ ( ~ ( SV438 @ SY2803 )
                              | ~ ! [SY2804: $i] :
                                    ( ~ ( SV438 @ SY2804 )
                                    | ( SY2803 = SY2804 ) ) )
                  | ~ ! [SY2394: $i] :
                        ~ ~ ( ~ ( SV214 @ SY2394 )
                            | ~ ! [SY2395: $i] :
                                  ( ~ ( SV214 @ SY2395 )
                                  | ( SY2394 = SY2395 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[1737]) ).

thf(1954,plain,
    ! [SV439: $i > $o,SV215: $i] :
      ( ( ( ! [SY2808: $i] :
              ~ ~ ( ~ ( in @ SY2808 @ SV215 )
                  | ~ ( SV439 @ SY2808 ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV215
            @ ^ [SY2807: $i] : ( SV439 @ SY2807 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1738]) ).

thf(1955,plain,
    ! [SV440: $i > $o,SV216: $i,SV573: $i] :
      ( ( ( in @ SV573 @ SV216 )
        = $false )
      | ( ( ~ ( SV440 @ SV573 )
          | ~ ! [SY3006: $i] :
                ( ~ ( in @ SY3006 @ SV216 )
                | ~ ( SV440 @ SY3006 )
                | ( SY3006 = SV573 ) )
          | ( singleton
            @ ( dsetconstr @ SV216
              @ ^ [SY2811: $i] : ( SV440 @ SY2811 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1739]) ).

thf(1956,plain,
    ! [SV442: $i,SV218: $i,SV574: $i] :
      ( ( ( in @ SV574 @ SV218 )
        = $false )
      | ( ( ! [SY3008: $i] :
              ( ~ ( in @ SY3008 @ SV442 )
              | ( subset @ ( setadjoin @ ( setadjoin @ SV574 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV574 @ ( setadjoin @ SY3008 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV218 @ SV442 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1741]) ).

thf(1957,plain,
    ! [SV443: $i,SV219: $i,SV575: $i] :
      ( ( ( in @ SV575 @ SV219 )
        = $false )
      | ( ( ! [SY3009: $i] :
              ( ~ ( in @ SY3009 @ SV443 )
              | ( ( ksnd @ ( kpair @ SV575 @ SY3009 ) )
                = SY3009 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1742]) ).

thf(1958,plain,
    ! [SV444: $o,SV220: $i,SV576: $i] :
      ( ( ( in @ SV576 @ SV220 )
        = $false )
      | ( ( ! [SY3010: $i] :
              ( ~ ( in @ SY3010 @ SV220 )
              | ~ SV444
              | ( ( dsetconstr @ SV220
                  @ ^ [SY3011: $i] :
                      ( ~ ( ~ SV444
                          | ( SY3011 != SV576 ) )
                      | ~ ( ~ ~ SV444
                          | ( SY3011 != SY3010 ) ) ) )
                = ( setadjoin @ SV576 @ emptyset ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1743]) ).

thf(1959,plain,
    ! [SV220: $i,SV577: $i] :
      ( ( ( in @ SV577 @ SV220 )
        = $false )
      | ( ( ! [SY3012: $i] :
              ( ~ ( in @ SY3012 @ SV220 )
              | ~ $true
              | ( ( dsetconstr @ SV220
                  @ ^ [SY3013: $i] :
                      ( ~ ( ~ $true
                          | ( SY3013 != SV577 ) )
                      | ~ ( ~ ~ $true
                          | ( SY3013 != SY3012 ) ) ) )
                = ( setadjoin @ SV577 @ emptyset ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1744]) ).

thf(1960,plain,
    ! [SV220: $i,SV578: $i] :
      ( ( ( in @ SV578 @ SV220 )
        = $false )
      | ( ( ! [SY3014: $i] :
              ( ~ ( in @ SY3014 @ SV220 )
              | ~ $false
              | ( ( dsetconstr @ SV220
                  @ ^ [SY3015: $i] :
                      ( ~ ( ~ $false
                          | ( SY3015 != SV578 ) )
                      | ~ ( ~ ~ $false
                          | ( SY3015 != SY3014 ) ) ) )
                = ( setadjoin @ SV578 @ emptyset ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1745]) ).

thf(1961,plain,
    ! [SV445: $i,SV221: $i,SV579: $i] :
      ( ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( ! [SY3016: $i] :
              ( ~ ( subset @ SY3016 @ ( cartprod @ SV221 @ SV445 ) )
              | ~ ! [SY3017: $i] :
                    ( ~ ( in @ SY3017 @ SV221 )
                    | ! [SY3018: $i] :
                        ( ~ ( in @ SY3018 @ SV445 )
                        | ~ ( in @ ( kpair @ SY3017 @ SY3018 ) @ SV579 )
                        | ( in @ ( kpair @ SY3017 @ SY3018 ) @ SY3016 ) ) )
              | ~ ! [SY3019: $i] :
                    ( ~ ( in @ SY3019 @ SV221 )
                    | ! [SY3020: $i] :
                        ( ~ ( in @ SY3020 @ SV445 )
                        | ~ ( in @ ( kpair @ SY3019 @ SY3020 ) @ SY3016 )
                        | ( in @ ( kpair @ SY3019 @ SY3020 ) @ SV579 ) ) )
              | ( SV579 = SY3016 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1746]) ).

thf(1962,plain,
    ! [SV580: $i,SV446: $i,SV222: $i] :
      ( ( ( func @ SV222 @ SV446 @ SV580 )
        = $false )
      | ( ( ! [SY3021: $i] :
              ( ~ ( in @ SY3021 @ SV222 )
              | ( singleton
                @ ( dsetconstr @ SV446
                  @ ^ [SY3022: $i] : ( in @ ( kpair @ SY3021 @ SY3022 ) @ SV580 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1747]) ).

thf(1963,plain,
    ! [SV224: $i] :
      ( ( ( ! [SY2426: $i] :
              ~ ~ ( ~ ( in @ SY2426 @ SV224 )
                  | ~ $true ) )
        = $false )
      | ( ( SV224 = emptyset )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1749]) ).

thf(1964,plain,
    ! [SV448: $i,SV225: $i,SV581: $i] :
      ( ( ( subset @ SV581 @ SV225 )
        = $false )
      | ( ( ~ ( subset @ SV581 @ SV448 )
          | ( subset @ SV581 @ ( binintersect @ SV225 @ SV448 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1750]) ).

thf(1965,plain,
    ! [SV449: $i,SV226: $i,SV582: $i] :
      ( ( ( in @ SV582 @ SV226 )
        = $false )
      | ( ( ~ ~ ( in @ SV582 @ SV449 )
          | ( in @ SV582 @ ( symdiff @ SV226 @ SV449 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1751]) ).

thf(1966,plain,
    ! [SV450: $i,SV227: $i,SV662: $i] :
      ( ( ( ~ ( in @ SV662 @ ( powerset @ SV227 ) )
          | ~ ( subset @ ( setminus @ SV227 @ SV662 ) @ ( setminus @ SV227 @ SV450 ) )
          | ( subset @ SV450 @ SV662 ) )
        = $true )
      | ( ( in @ SV450 @ ( powerset @ SV227 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1752]) ).

thf(1967,plain,
    ! [SV451: $i,SV228: $i,SV663: $i] :
      ( ( ( ~ ( in @ SV663 @ ( powerset @ SV228 ) )
          | ! [SY3101: $i] :
              ( ~ ( in @ SY3101 @ ( powerset @ SV228 ) )
              | ! [SY3102: $i] :
                  ( ~ ( in @ SY3102 @ SV228 )
                  | ~ ( in @ SY3102 @ ( binintersect @ SV451 @ SV663 ) )
                  | ( in @ SY3102 @ ( binunion @ SV663 @ SY3101 ) ) ) ) )
        = $true )
      | ( ( in @ SV451 @ ( powerset @ SV228 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1753]) ).

thf(1968,plain,
    ! [SV453: $o,SV230: $i,SV583: $i] :
      ( ( ( in @ SV583 @ SV230 )
        = $false )
      | ( ( ! [SY3023: $i] :
              ( ~ ( in @ SY3023 @ SV230 )
              | ~ ~ SV453
              | ( ( dsetconstr @ SV230
                  @ ^ [SY3024: $i] :
                      ( ~ ( ~ SV453
                          | ( SY3024 != SV583 ) )
                      | ~ ( ~ ~ SV453
                          | ( SY3024 != SY3023 ) ) ) )
                = ( setadjoin @ SY3023 @ emptyset ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1755]) ).

thf(1969,plain,
    ! [SV230: $i,SV584: $i] :
      ( ( ( in @ SV584 @ SV230 )
        = $false )
      | ( ( ! [SY3025: $i] :
              ( ~ ( in @ SY3025 @ SV230 )
              | ~ ~ $true
              | ( ( dsetconstr @ SV230
                  @ ^ [SY3026: $i] :
                      ( ~ ( ~ $true
                          | ( SY3026 != SV584 ) )
                      | ~ ( ~ ~ $true
                          | ( SY3026 != SY3025 ) ) ) )
                = ( setadjoin @ SY3025 @ emptyset ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1756]) ).

thf(1970,plain,
    ! [SV230: $i,SV585: $i] :
      ( ( ( in @ SV585 @ SV230 )
        = $false )
      | ( ( ! [SY3027: $i] :
              ( ~ ( in @ SY3027 @ SV230 )
              | ~ ~ $false
              | ( ( dsetconstr @ SV230
                  @ ^ [SY3028: $i] :
                      ( ~ ( ~ $false
                          | ( SY3028 != SV585 ) )
                      | ~ ( ~ ~ $false
                          | ( SY3028 != SY3027 ) ) ) )
                = ( setadjoin @ SY3027 @ emptyset ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1757]) ).

thf(1971,plain,
    ! [SV454: $i,SV231: $i,SV664: $i] :
      ( ( ( ~ ( in @ SV664 @ ( powerset @ SV231 ) )
          | ~ ! [SY3103: $i] :
                ( ~ ( in @ SY3103 @ SV231 )
                | ~ ( in @ SY3103 @ SV454 )
                | ( in @ SY3103 @ SV664 ) )
          | ( in @ SV454 @ ( powerset @ SV664 ) ) )
        = $true )
      | ( ( in @ SV454 @ ( powerset @ SV231 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1758]) ).

thf(1972,plain,
    ! [SV586: $i,SV455: $i,SV232: $i] :
      ( ( ( func @ SV232 @ SV455 @ SV586 )
        = $false )
      | ( ( ( lam @ SV232 @ SV455
            @ ^ [SY3029: $i] : ( ap @ SV232 @ SV455 @ SV586 @ SY3029 ) )
          = SV586 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1759]) ).

thf(1973,plain,
    ! [SV457: $i,SV234: $i,SV587: $i] :
      ( ( ( in @ SV587 @ ( cartprod @ SV234 @ SV457 ) )
        = $false )
      | ( ( in @ ( kfst @ SV587 ) @ SV234 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1761]) ).

thf(1974,plain,
    ! [SV588: $i,SV459: $i,SV236: $i] :
      ( ( ( subset @ SV236 @ SV459 )
        = $false )
      | ( ( ~ ( subset @ SV459 @ SV588 )
          | ( subset @ SV236 @ SV588 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1763]) ).

thf(1975,plain,
    ! [SV589: $i,SV460: $i,SV237: $i] :
      ( ( ( ( setadjoin @ SV237 @ ( setadjoin @ SV460 @ emptyset ) )
          = ( setadjoin @ SV589 @ emptyset ) )
        = $false )
      | ( ( SV237 = SV460 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1764]) ).

thf(1976,plain,
    ! [SV617: $i,SV590: $i,SV462: $i,SV239: $i] :
      ( ( ( ( setadjoin @ ( setadjoin @ SV239 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV239 @ ( setadjoin @ SV462 @ emptyset ) ) @ emptyset ) )
         != ( setadjoin @ ( setadjoin @ SV590 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV590 @ ( setadjoin @ SV617 @ emptyset ) ) @ emptyset ) ) )
        = $true )
      | ( ( SV239 = SV590 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1766]) ).

thf(1977,plain,
    ! [SV591: $i,SV463: $i,SV240: $i] :
      ( ( ( func @ SV240 @ SV463 @ SV591 )
        = $false )
      | ( ( in @ SV591 @ ( funcSet @ SV240 @ SV463 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1767]) ).

thf(1978,plain,
    ! [SV464: $i,SV241: $i,SV592: $i] :
      ( ( ( in @ SV592 @ ( binintersect @ SV241 @ SV464 ) )
        = $false )
      | ( ( in @ SV592 @ SV464 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1768]) ).

thf(1979,plain,
    ! [SV465: $i,SV242: $i,SV593: $i] :
      ( ( ( ~ ( in @ SV593 @ SV242 ) )
        = $false )
      | ( ( ~ ( in @ SV593 @ ( setminus @ SV242 @ SV465 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1769]) ).

thf(1980,plain,
    ! [SV466: $i,SV243: $i,SV665: $i] :
      ( ( ( ~ ( in @ SV665 @ ( powerset @ SV243 ) )
          | ~ ! [SY3104: $i] :
                ( ~ ( in @ SY3104 @ SV243 )
                | ~ ( in @ SY3104 @ SV466 )
                | ( in @ SY3104 @ SV665 ) )
          | ( subset @ SV466 @ SV665 ) )
        = $true )
      | ( ( in @ SV466 @ ( powerset @ SV243 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1770]) ).

thf(1981,plain,
    ! [SV467: $i,SV594: $i > $i,SV244: $i] :
      ( ( ( ! [SY3031: $i] :
              ( ~ ( in @ SY3031 @ SV244 )
              | ( in @ ( SV594 @ SY3031 ) @ SV467 ) ) )
        = $false )
      | ( ( ! [SY3032: $i] :
              ( ~ ( in @ SY3032 @ SV244 )
              | ( ( ap @ SV244 @ SV467
                  @ ( lam @ SV244 @ SV467
                    @ ^ [SY3033: $i] : ( SV594 @ SY3033 ) )
                  @ SY3032 )
                = ( SV594 @ SY3032 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1771]) ).

thf(1982,plain,
    ! [SV468: $i,SV245: $i,SV595: $i] :
      ( ( ( in @ SV595 @ ( funcSet @ SV245 @ SV468 ) )
        = $false )
      | ( ( ! [SY3034: $i] :
              ( ~ ( in @ SY3034 @ SV245 )
              | ( in @ ( kpair @ SY3034 @ ( ap @ SV245 @ SV468 @ SV595 @ SY3034 ) ) @ SV595 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1772]) ).

thf(1983,plain,
    ! [SV469: $i,SV246: $i,SV666: $i] :
      ( ( ( ~ ( in @ SV666 @ ( powerset @ SV246 ) )
          | ! [SY3105: $i] :
              ( ~ ( in @ SY3105 @ SV246 )
              | ~ ( in @ SY3105 @ ( setminus @ SV246 @ SV469 ) )
              | ~ ( in @ SY3105 @ ( binintersect @ SV469 @ SV666 ) ) ) )
        = $true )
      | ( ( in @ SV469 @ ( powerset @ SV246 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1773]) ).

thf(1984,plain,
    ! [SV249: $i,SV471: $i,SV596: $i] :
      ( ( ( in @ SV596 @ SV471 )
        = $false )
      | ( ( ~ ( in @ SV596 @ ( setminus @ SV249 @ SV471 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1775]) ).

thf(1985,plain,
    ! [SV250: $i,SV618: $i] :
      ( ( ( ~ ( in @ SV618 @ SV250 ) )
        = $true )
      | ( ( ( setunion @ SV250 )
          = SV618 )
        = $true )
      | ( ( singleton @ SV250 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1776]) ).

thf(1986,plain,
    ! [SV472: $i,SV251: $i,SV597: $i] :
      ( ( ( in @ SV597 @ SV251 )
        = $false )
      | ( ( ! [SY3035: $i] :
              ( ~ ( in @ SY3035 @ SV472 )
              | ( in @ ( setadjoin @ SV597 @ ( setadjoin @ SY3035 @ emptyset ) ) @ ( powerset @ ( binunion @ SV251 @ SV472 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1777]) ).

thf(1987,plain,
    ! [SV473: $i,SV252: $i,SV598: $i] :
      ( ( ( in @ SV598 @ ( binunion @ SV252 @ SV473 ) )
        = $false )
      | ( ( ( in @ SV598 @ SV252 )
          | ( in @ SV598 @ SV473 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1778]) ).

thf(1988,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ~ ! [SY3106: $i] :
                ~ ( ~ ( ~ ( SV253 @ SY3106 )
                      | ( SY3106 = SV667 ) )
                  | ~ ( ( SY3106 != SV667 )
                      | ( SV253 @ SY3106 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2491: $i] :
                ~ ~ ( ~ ( SV253 @ SY2491 )
                    | ~ ! [SY2492: $i] :
                          ( ~ ( SV253 @ SY2492 )
                          | ( SY2491 = SY2492 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1779]) ).

thf(1989,plain,
    ! [SV474: $i,SV599: $i,SV254: $i] :
      ( ( ( subset @ SV254 @ SV599 )
        = $false )
      | ( ( subset @ SV254 @ ( setadjoin @ SV474 @ SV599 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1780]) ).

thf(1990,plain,
    ! [SV668: $o,SV255: $i,SV475: $i] :
      ( ( ( ~ ! [SY3107: $i] :
                ( ~ ( in @ SV475 @ SY3107 )
                | ~ ( in @ SY3107 @ SV255 )
                | SV668 )
          | SV668 )
        = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[1781]) ).

thf(1991,plain,
    ! [SV255: $i,SV475: $i] :
      ( ( ( ~ ! [SX0: $i] :
                ( ~ ( in @ SV475 @ SX0 )
                | ~ ( in @ SX0 @ SV255 )
                | $true )
          | $true )
        = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[1781]) ).

thf(1992,plain,
    ! [SV255: $i,SV475: $i] :
      ( ( ( ~ ! [SX0: $i] :
                ( ~ ( in @ SV475 @ SX0 )
                | ~ ( in @ SX0 @ SV255 )
                | $false )
          | $false )
        = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[1781]) ).

thf(1993,plain,
    ! [SV476: $o,SV256: $i,SV600: $i] :
      ( ( ( in @ SV600 @ SV256 )
        = $false )
      | ( ( ! [SY3036: $i] :
              ( ~ ( in @ SY3036 @ SV256 )
              | ( in @ ( if @ SV256 @ SV476 @ SV600 @ SY3036 ) @ ( setadjoin @ SV600 @ ( setadjoin @ SY3036 @ emptyset ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1782]) ).

thf(1994,plain,
    ! [SV256: $i,SV601: $i] :
      ( ( ( in @ SV601 @ SV256 )
        = $false )
      | ( ( ! [SY3037: $i] :
              ( ~ ( in @ SY3037 @ SV256 )
              | ( in @ ( if @ SV256 @ $true @ SV601 @ SY3037 ) @ ( setadjoin @ SV601 @ ( setadjoin @ SY3037 @ emptyset ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1783]) ).

thf(1995,plain,
    ! [SV256: $i,SV602: $i] :
      ( ( ( in @ SV602 @ SV256 )
        = $false )
      | ( ( ! [SY3038: $i] :
              ( ~ ( in @ SY3038 @ SV256 )
              | ( in @ ( if @ SV256 @ $false @ SV602 @ SY3038 ) @ ( setadjoin @ SV602 @ ( setadjoin @ SY3038 @ emptyset ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1784]) ).

thf(1996,plain,
    ! [SV477: $i,SV257: $i,SV603: $i] :
      ( ( ( in @ SV603 @ SV257 )
        = $false )
      | ( ( ! [SY3039: $i] :
              ( ~ ( in @ SY3039 @ SV477 )
              | ( subset @ ( setadjoin @ SV603 @ ( setadjoin @ SY3039 @ emptyset ) ) @ ( binunion @ SV257 @ SV477 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1785]) ).

thf(1997,plain,
    ! [SV281: $i > $o,SV35: $i] :
      ( ( ( ! [SY2514: $i] :
              ~ ~ ( ~ ( in @ SY2514 @ SV35 )
                  | ~ ( SV281 @ SY2514 ) ) )
        = $false )
      | ( ( ! [SY2515: $i] :
              ( ~ ( in @ SY2515 @ SV35 )
              | ~ ( SV281 @ SY2515 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1787]) ).

thf(1998,plain,
    ! [SV282: $i,SV36: $i,SV619: $i] :
      ( ( ( ~ ( in @ SV619 @ ( powerset @ SV36 ) ) )
        = $true )
      | ( ( ! [SY3055: $i] :
              ( ~ ( in @ SY3055 @ SV36 )
              | ~ ( subset @ SV282 @ SV619 )
              | ~ ~ ( in @ SY3055 @ SV619 )
              | ~ ( in @ SY3055 @ SV282 ) ) )
        = $true )
      | ( ( in @ SV282 @ ( powerset @ SV36 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1788]) ).

thf(1999,plain,
    ! [SV620: $i,SV37: $i > $o] :
      ( ( ( ~ ( ~ ( SV37 @ SV620 )
              | ~ ! [SY3056: $i] :
                    ( ~ ( SV37 @ SY3056 )
                    | ( SV620 = SY3056 ) ) ) )
        = $false )
      | ( ( ~ ! [SY1897: $i] :
                ~ ! [SY1898: $i] :
                    ~ ( ~ ( ~ ( SV37 @ SY1898 )
                          | ( SY1898 = SY1897 ) )
                      | ~ ( ( SY1898 != SY1897 )
                          | ( SV37 @ SY1898 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1789]) ).

thf(2000,plain,
    ! [SV482: $i,SV283: $i,SV38: $i,SV669: $i] :
      ( ( ( ~ ( in @ SV669 @ SV38 )
          | ( in @ ( kpair @ SV669 @ ( ap @ SV38 @ SV283 @ SV482 @ SV669 ) ) @ SV482 ) )
        = $true )
      | ( ( func @ SV38 @ SV283 @ SV482 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1790]) ).

thf(2001,plain,
    ! [SV483: $i,SV284: $o,SV40: $i,SV670: $i] :
      ( ( ( ~ ( in @ SV670 @ SV40 )
          | ~ ~ SV284
          | ( in @ SV670
            @ ( dsetconstr @ SV40
              @ ^ [SY3108: $i] :
                  ( ~ ( ~ SV284
                      | ( SY3108 != SV483 ) )
                  | ~ ( ~ ~ SV284
                      | ( SY3108 != SV670 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV483 @ SV40 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1791]) ).

thf(2002,plain,
    ! [SV484: $i,SV40: $i,SV671: $i] :
      ( ( ( ~ ( in @ SV671 @ SV40 )
          | ~ ~ $true
          | ( in @ SV671
            @ ( dsetconstr @ SV40
              @ ^ [SY3109: $i] :
                  ( ~ ( ~ $true
                      | ( SY3109 != SV484 ) )
                  | ~ ( ~ ~ $true
                      | ( SY3109 != SV671 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV484 @ SV40 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1792]) ).

thf(2003,plain,
    ! [SV485: $i,SV40: $i,SV672: $i] :
      ( ( ( ~ ( in @ SV672 @ SV40 )
          | ~ ~ $false
          | ( in @ SV672
            @ ( dsetconstr @ SV40
              @ ^ [SY3110: $i] :
                  ( ~ ( ~ $false
                      | ( SY3110 != SV485 ) )
                  | ~ ( ~ ~ $false
                      | ( SY3110 != SV672 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV485 @ SV40 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1793]) ).

thf(2004,plain,
    ! [SV621: $i,SV41: $i > $o] :
      ( ( ( ~ ( ~ ( SV41 @ SV621 )
              | ~ ! [SY3057: $i] :
                    ( ~ ( SV41 @ SY3057 )
                    | ( SV621 = SY3057 ) ) ) )
        = $false )
      | ( ( ! [SY1909: $i,SY1910: $i] :
              ( ~ ( SV41 @ SY1909 )
              | ~ ( SV41 @ SY1910 )
              | ( SY1909 = SY1910 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1794]) ).

thf(2005,plain,
    ! [SV42: $i,SV285: $i] :
      ( ( ( ~ ( in @ SV285 @ ( powerset @ SV42 ) ) )
        = $true )
      | ( ( ! [SY2523: $i] :
              ( ~ ( in @ SY2523 @ SV285 )
              | ( in @ SY2523 @ SV42 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1795]) ).

thf(2006,plain,
    ! [SV42: $i,SV285: $i] :
      ( ( ( ~ ! [SY2524: $i] :
                ( ~ ( in @ SY2524 @ SV285 )
                | ( in @ SY2524 @ SV42 ) ) )
        = $true )
      | ( ( in @ SV285 @ ( powerset @ SV42 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1796]) ).

thf(2007,plain,
    ! [SV622: $i,SV43: $i > $o] :
      ( ( ( ~ ( ~ ( SV43 @ SV622 )
              | ~ ! [SY3058: $i] :
                    ( ~ ( SV43 @ SY3058 )
                    | ( SV622 = SY3058 ) ) ) )
        = $false )
      | ( ( ! [SY1916: $i,SY1917: $i] :
              ( ~ ( SV43 @ SY1916 )
              | ~ ( SV43 @ SY1917 )
              | ( SY1916 = SY1917 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1797]) ).

thf(2008,plain,
    ! [SV286: $i,SV44: $i,SV623: $i] :
      ( ( ( ~ ( in @ SV623 @ ( powerset @ SV44 ) ) )
        = $true )
      | ( ( ! [SY3059: $i] :
              ( ~ ( in @ SY3059 @ SV44 )
              | ~ ( in @ SY3059 @ ( setminus @ SV44 @ ( binunion @ SV286 @ SV623 ) ) )
              | ~ ( in @ SY3059 @ SV286 ) ) )
        = $true )
      | ( ( in @ SV286 @ ( powerset @ SV44 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1798]) ).

thf(2009,plain,
    ! [SV287: $i > $o,SV46: $i,SV673: $i] :
      ( ( ( ~ ~ ( ~ ( in @ SV673 @ SV46 )
                | ~ ~ ( SV287 @ SV673 ) ) )
        = $true )
      | ( ( ~ ! [SY2528: $i] :
                ( ~ ( in @ SY2528 @ SV46 )
                | ( SV287 @ SY2528 ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1799]) ).

thf(2010,plain,
    ! [SV288: $i,SV47: $i,SV486: $i] :
      ( ( ( in @ SV486 @ ( setminus @ SV47 @ SV288 ) )
        = $true )
      | ( ( ~ ( in @ SV486 @ SV47 )
          | ( in @ SV486 @ SV288 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1800]) ).

thf(2011,plain,
    ! [SV624: $i,SV48: $i > $o] :
      ( ( ( ~ ( ~ ( SV48 @ SV624 )
              | ~ ! [SY3060: $i] :
                    ( ~ ( SV48 @ SY3060 )
                    | ( SV624 = SY3060 ) ) ) )
        = $false )
      | ( ( ~ ! [SY1928: $i] :
                ~ ~ ( ~ ( SV48 @ SY1928 )
                    | ~ ! [SY1929: $i] :
                          ( ~ ( SV48 @ SY1929 )
                          | ( SY1928 = SY1929 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1801]) ).

thf(2012,plain,
    ! [SV49: $i,SV289: $i,SV487: $i] :
      ( ( ( ~ ~ ( in @ SV487 @ SV289 ) )
        = $true )
      | ( ( in @ SV487 @ ( setminus @ SV49 @ SV289 ) )
        = $true )
      | ( ( in @ SV487 @ SV49 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1802]) ).

thf(2013,plain,
    ! [SV50: $i,SV488: $i,SV290: $i,SV674: $i] :
      ( ( ( ~ ( in @ SV674 @ SV290 )
          | ( in @ ( setadjoin @ ( setadjoin @ SV488 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV488 @ ( setadjoin @ SV674 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV50 @ SV290 ) ) ) ) )
        = $true )
      | ( ( in @ SV488 @ SV50 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1803]) ).

thf(2014,plain,
    ! [SV51: $i,SV291: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV51 )
              | ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV291 ) )
          | ~ ( ~ ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV291 )
              | ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV51 ) ) )
        = $true )
      | ( ( SV51 = SV291 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1804]) ).

thf(2015,plain,
    ! [SV292: $i > $o,SV52: $i] :
      ( ( ( ! [SY2534: $i] :
              ~ ~ ( ~ ( in @ SY2534 @ SV52 )
                  | ~ ( SV292 @ SY2534 ) ) )
        = $false )
      | ( ( ! [SY2535: $i] :
              ( ~ ( in @ SY2535 @ SV52 )
              | ~ ( SV292 @ SY2535 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1805]) ).

thf(2016,plain,
    ! [SV295: $i,SV55: $i,SV489: $i] :
      ( ( ( in @ SV489 @ SV55 )
        = $true )
      | ( ( ~ ~ ( in @ SV489 @ SV295 )
          | ~ ( in @ SV489 @ ( symdiff @ SV55 @ SV295 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1806]) ).

thf(2017,plain,
    ! [SV490: $i > $i > $o,SV296: $i,SV56: $i,SV625: $i,SV605: $i] :
      ( ( ( ~ ( in @ ( kpair @ SV605 @ SV625 )
              @ ( dpsetconstr @ SV56 @ SV296
                @ ^ [SY2884: $i,SY2885: $i] : ( SV490 @ SY2884 @ SY2885 ) ) ) )
        = $true )
      | ( ( in @ SV625 @ SV296 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1807]) ).

thf(2018,plain,
    ! [SV606: $i,SV492: $i,SV298: $i,SV59: $i] :
      ( ( ( ( setadjoin @ ( setadjoin @ SV59 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV59 @ ( setadjoin @ SV298 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ SV492 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV492 @ ( setadjoin @ SV606 @ emptyset ) ) @ emptyset ) ) )
        = $false )
      | ( ( SV298 = SV606 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1809]) ).

thf(2019,plain,
    ! [SV60: $i,SV299: $i,SV493: $i] :
      ( ( ( ~ ( in @ SV493 @ SV299 ) )
        = $true )
      | ( ( ~ ( in @ SV493 @ ( symdiff @ SV60 @ SV299 ) ) )
        = $true )
      | ( ( in @ SV493 @ SV60 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1810]) ).

thf(2020,plain,
    ! [SV300: $i,SV61: $i,SV607: $i,SV494: $i] :
      ( ( ( in @ ( kpair @ SV494 @ SV607 ) @ ( cartprod @ SV61 @ SV300 ) )
        = $false )
      | ( ( in @ SV494 @ SV61 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1811]) ).

thf(2021,plain,
    ! [SV62: $i,SV495: $i,SV301: $i,SV675: $i] :
      ( ( ( ~ ( in @ SV675 @ SV301 )
          | ( ( kpair @ SV495 @ SV675 )
            = ( kpair @ SV495 @ SV675 ) ) )
        = $true )
      | ( ( in @ SV495 @ SV62 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1812]) ).

thf(2022,plain,
    ! [SV676: $i > $o,SV496: $i,SV302: $i,SV63: $i] :
      ( ( ( ~ ! [SY3111: $i] :
                ( ~ ( in @ SY3111 @ SV63 )
                | ! [SY3112: $i] :
                    ( ~ ( in @ SY3112 @ SV302 )
                    | ~ ( in @ ( kpair @ SY3111 @ SY3112 ) @ SV496 )
                    | ( SV676 @ ( kpair @ SY3111 @ SY3112 ) ) ) )
          | ! [SY3113: $i] :
              ( ~ ( in @ SY3113 @ SV496 )
              | ( SV676 @ SY3113 ) ) )
        = $true )
      | ( ( subset @ SV496 @ ( cartprod @ SV63 @ SV302 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1813]) ).

thf(2023,plain,
    ! [SV65: $i,SV497: $i,SV303: $i > $o] :
      ( ( ( ~ ( SV303 @ SV497 ) )
        = $true )
      | ( ( ( dsetconstr @ SV65
            @ ^ [SY2556: $i] : ( SV303 @ SY2556 ) )
         != emptyset )
        = $true )
      | ( ( in @ SV497 @ SV65 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1814]) ).

thf(2024,plain,
    ! [SV498: $i,SV305: $o,SV67: $i,SV677: $i] :
      ( ( ( ~ ( in @ SV677 @ SV67 )
          | ~ SV305
          | ( in @ SV498
            @ ( dsetconstr @ SV67
              @ ^ [SY3114: $i] :
                  ( ~ ( ~ SV305
                      | ( SY3114 != SV498 ) )
                  | ~ ( ~ ~ SV305
                      | ( SY3114 != SV677 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV498 @ SV67 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1815]) ).

thf(2025,plain,
    ! [SV499: $i,SV67: $i,SV678: $i] :
      ( ( ( ~ ( in @ SV678 @ SV67 )
          | ~ $true
          | ( in @ SV499
            @ ( dsetconstr @ SV67
              @ ^ [SY3115: $i] :
                  ( ~ ( ~ $true
                      | ( SY3115 != SV499 ) )
                  | ~ ( ~ ~ $true
                      | ( SY3115 != SV678 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV499 @ SV67 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1816]) ).

thf(2026,plain,
    ! [SV500: $i,SV67: $i,SV679: $i] :
      ( ( ( ~ ( in @ SV679 @ SV67 )
          | ~ $false
          | ( in @ SV500
            @ ( dsetconstr @ SV67
              @ ^ [SY3116: $i] :
                  ( ~ ( ~ $false
                      | ( SY3116 != SV500 ) )
                  | ~ ( ~ ~ $false
                      | ( SY3116 != SV679 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV500 @ SV67 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1817]) ).

thf(2027,plain,
    ! [SV501: $i,SV306: $i,SV68: $i,SV680: $i] :
      ( ( ( ~ ( in @ SV680 @ SV68 )
          | ( in
            @ ( setunion
              @ ( dsetconstr @ SV306
                @ ^ [SY3117: $i] : ( in @ ( kpair @ SV680 @ SY3117 ) @ SV501 ) ) )
            @ SV306 ) )
        = $true )
      | ( ( func @ SV68 @ SV306 @ SV501 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1818]) ).

thf(2028,plain,
    ! [SV310: $i,SV72: $i,SV626: $i] :
      ( ( ( ~ ( in @ SV626 @ ( powerset @ SV72 ) ) )
        = $true )
      | ( ( ~ ( subset @ SV310 @ ( setminus @ SV72 @ SV626 ) )
          | ( subset @ SV626 @ ( setminus @ SV72 @ SV310 ) ) )
        = $true )
      | ( ( in @ SV310 @ ( powerset @ SV72 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1819]) ).

thf(2029,plain,
    ! [SV502: $i,SV311: $i,SV73: $i,SV681: $i] :
      ( ( ( ~ ( in @ SV681 @ ( funcSet @ SV73 @ SV311 ) )
          | ~ ! [SY3118: $i] :
                ( ~ ( in @ SY3118 @ SV73 )
                | ( ( ap @ SV73 @ SV311 @ SV502 @ SY3118 )
                  = ( ap @ SV73 @ SV311 @ SV681 @ SY3118 ) ) )
          | ( SV502 = SV681 ) )
        = $true )
      | ( ( in @ SV502 @ ( funcSet @ SV73 @ SV311 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1820]) ).

thf(2030,plain,
    ! [SV312: $i,SV74: $i,SV503: $i] :
      ( ( ( in @ SV503 @ ( setminus @ SV74 @ SV312 ) )
        = $true )
      | ( ( ~ ~ ( in @ SV503 @ SV312 )
          | ~ ( in @ SV503 @ SV74 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1821]) ).

thf(2031,plain,
    ! [SV313: $i,SV75: $i,SV504: $i] :
      ( ( ~ ( in @ SV504 @ ( setadjoin @ SV75 @ SV313 ) )
        | ( SV504 = SV75 )
        | ( in @ SV504 @ SV313 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1822]) ).

thf(2032,plain,
    ! [SV313: $i,SV75: $i,SV504: $i] :
      ( ( ~ ( ( SV504 = SV75 )
            | ( in @ SV504 @ SV313 ) )
        | ( in @ SV504 @ ( setadjoin @ SV75 @ SV313 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1823]) ).

thf(2033,plain,
    ! [SV314: $i,SV76: $i,SV627: $i] :
      ( ( ( ~ ( in @ SV627 @ ( powerset @ SV76 ) ) )
        = $true )
      | ( ( ! [SY3063: $i] :
              ( ~ ( in @ SY3063 @ ( powerset @ SV76 ) )
              | ! [SY3064: $i] :
                  ( ~ ( in @ SY3064 @ SV76 )
                  | ~ ( in @ SY3064 @ ( binintersect @ SV314 @ SV627 ) )
                  | ( in @ SY3064 @ ( binintersect @ ( binunion @ SV314 @ SY3063 ) @ ( binunion @ SV627 @ SY3063 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV314 @ ( powerset @ SV76 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1824]) ).

thf(2034,plain,
    ! [SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ( ( sK7_SY2572 @ SV315 @ SV77 )
           != ( sK18_SY3065 @ SV77 @ SV315 ) )
          | ~ ( ~ ( ~ ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
                  | ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) ) )
              | ~ ( ~ ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
                  | ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) ) ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2001: $i] :
                  ~ ~ ( ~ ( SV77 @ SY2001 )
                      | ~ ! [SY2002: $i] :
                            ( ~ ( SV77 @ SY2002 )
                            | ( SY2001 = SY2002 ) ) )
          | ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[1825]) ).

thf(2035,plain,
    ! [SV78: $i,SV505: $i,SV316: $i > $o] :
      ( ( ( ~ ( SV316 @ SV505 ) )
        = $true )
      | ( ( in @ SV505
          @ ( dsetconstr @ SV78
            @ ^ [SY2581: $i] : ( SV316 @ SY2581 ) ) )
        = $true )
      | ( ( in @ SV505 @ SV78 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1826]) ).

thf(2036,plain,
    ! [SV318: $i,SV80: $i,SV628: $i] :
      ( ( ( ~ ( in @ SV628 @ ( powerset @ SV80 ) ) )
        = $true )
      | ( ( ~ ! [SY3066: $i] :
                ( ~ ( in @ SY3066 @ SV80 )
                | ~ ( in @ SY3066 @ SV318 )
                | ( in @ SY3066 @ SV628 ) )
          | ~ ! [SY3067: $i] :
                ( ~ ( in @ SY3067 @ SV80 )
                | ~ ( in @ SY3067 @ SV628 )
                | ( in @ SY3067 @ SV318 ) )
          | ( SV318 = SV628 ) )
        = $true )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1827]) ).

thf(2037,plain,
    ! [SV81: $i,SV319: $i] :
      ( ( ( ~ ( in @ ( sK8_SY2585 @ SV319 @ SV81 ) @ SV81 ) )
        = $false )
      | ( ( ~ ! [SY2586: $i] :
                ( ~ ( in @ SY2586 @ SV319 )
                | ( in @ SY2586 @ SV81 ) )
          | ( SV81 = SV319 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1828]) ).

thf(2038,plain,
    ! [SV81: $i,SV319: $i] :
      ( ( ( in @ ( sK8_SY2585 @ SV319 @ SV81 ) @ SV319 )
        = $false )
      | ( ( ~ ! [SY2586: $i] :
                ( ~ ( in @ SY2586 @ SV319 )
                | ( in @ SY2586 @ SV81 ) )
          | ( SV81 = SV319 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1828]) ).

thf(2039,plain,
    ! [SV506: $i > $i > $o,SV320: $i,SV82: $i,SV608: $i] :
      ( ( ( in @ SV608 @ SV82 )
        = $false )
      | ( ( ! [SY3043: $i] :
              ( ~ ( in @ SY3043 @ SV320 )
              | ~ ( in @ ( kpair @ SV608 @ SY3043 )
                  @ ( dpsetconstr @ SV82 @ SV320
                    @ ^ [SY2907: $i,SY2908: $i] : ( SV506 @ SY2907 @ SY2908 ) ) )
              | ( SV506 @ SV608 @ SY3043 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1829]) ).

thf(2040,plain,
    ! [SV321: $i > $o,SV84: $i,SV682: $i] :
      ( ( ( ~ ( in @ SV682 @ SV84 )
          | ( SV321 @ SV682 ) )
        = $true )
      | ( ( ~ ! [SY2593: $i] :
                ~ ~ ( ~ ( in @ SY2593 @ SV84 )
                    | ~ ~ ( SV321 @ SY2593 ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1831]) ).

thf(2041,plain,
    ! [SV609: $o,SV322: $i,SV85: $i,SV507: $i] :
      ( ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false )
      | ( ( ~ ( ~ ( in @ SV507 @ SV85 )
              | SV609 )
          | ~ ( ~ ( in @ SV507 @ SV322 )
              | SV609 )
          | SV609 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1832]) ).

thf(2042,plain,
    ! [SV322: $i,SV85: $i,SV507: $i] :
      ( ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false )
      | ( ( ~ ( ~ ( in @ SV507 @ SV85 )
              | $true )
          | ~ ( ~ ( in @ SV507 @ SV322 )
              | $true )
          | $true )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1833]) ).

thf(2043,plain,
    ! [SV322: $i,SV85: $i,SV507: $i] :
      ( ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false )
      | ( ( ~ ( ~ ( in @ SV507 @ SV85 )
              | $false )
          | ~ ( ~ ( in @ SV507 @ SV322 )
              | $false )
          | $false )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1834]) ).

thf(2044,plain,
    ! [SV323: $i,SV86: $i,SV508: $i] :
      ( ( ( ~ ( in @ SV508 @ SV86 ) )
        = $true )
      | ( ( in @ SV323 @ ( setunion @ SV86 ) )
        = $true )
      | ( ( in @ SV323 @ SV508 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1835]) ).

thf(2045,plain,
    ! [SV87: $i] :
      ( ( ( in @ emptyset @ SV87 )
        = $false )
      | ( ( ~ ! [SY2033: $i] :
                ( ~ ~ ( ~ ( in @ SY2033 @ omega )
                      | ~ ( in @ SY2033 @ SV87 ) )
                | ( in @ ( setadjoin @ SY2033 @ SY2033 ) @ SV87 ) ) )
        = $true )
      | ( ( ! [SY2034: $i] :
              ( ~ ( in @ SY2034 @ omega )
              | ( in @ SY2034 @ SV87 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1836]) ).

thf(2046,plain,
    ( ( ~ ( in @ sK9_SY2910 @ ( powerset @ sK1_SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1838]) ).

thf(2047,plain,
    ( ( ! [SY3068: $i] :
          ( ~ ( in @ SY3068 @ sK1_SX0 )
          | ~ ( in @ SY3068 @ ( setminus @ sK1_SX0 @ ( binunion @ sK2_SY2597 @ sK9_SY2910 ) ) )
          | ( in @ SY3068 @ ( setminus @ sK1_SX0 @ sK2_SY2597 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1838]) ).

thf(2048,plain,
    ! [SV324: $i,SV88: $i,SV629: $i] :
      ( ( ( ~ ( in @ SV629 @ ( powerset @ SV88 ) ) )
        = $true )
      | ( ( ~ ( subset @ SV324 @ ( setminus @ SV88 @ SV629 ) )
          | ! [SY3069: $i] :
              ( ~ ( in @ SY3069 @ SV88 )
              | ~ ( in @ SY3069 @ SV629 )
              | ( in @ SY3069 @ ( setminus @ SV88 @ SV324 ) ) ) )
        = $true )
      | ( ( in @ SV324 @ ( powerset @ SV88 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1839]) ).

thf(2049,plain,
    ! [SV325: $i > $o,SV89: $i,SV683: $i] :
      ( ( ( ~ ~ ( ~ ( in @ SV683 @ SV89 )
                | ~ ( SV325 @ SV683 ) ) )
        = $true )
      | ( ( ( ( dsetconstr @ SV89
              @ ^ [SY2603: $i] : ( SV325 @ SY2603 ) )
           != emptyset )
          | $false )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1840]) ).

thf(2050,plain,
    ! [SV90: $i,SV326: $i] :
      ( ( ( ~ ( in @ ( sK10_SY2604 @ SV326 @ SV90 ) @ SV90 ) )
        = $false )
      | ( ( subset @ SV90 @ SV326 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1841]) ).

thf(2051,plain,
    ! [SV90: $i,SV326: $i] :
      ( ( ( in @ ( sK10_SY2604 @ SV326 @ SV90 ) @ SV326 )
        = $false )
      | ( ( subset @ SV90 @ SV326 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1841]) ).

thf(2052,plain,
    ! [SV327: $i,SV91: $i,SV630: $i] :
      ( ( ( ~ ( in @ SV630 @ ( powerset @ SV91 ) ) )
        = $true )
      | ( ( in @ ( binintersect @ SV327 @ SV630 ) @ ( powerset @ SV91 ) )
        = $true )
      | ( ( in @ SV327 @ ( powerset @ SV91 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1842]) ).

thf(2053,plain,
    ! [SV328: $i,SV92: $i,SV684: $i,SV631: $i] :
      ( ( ( ( SV631 != SV684 )
          | ~ ( in @ SV631 @ SV92 )
          | ( in @ SV684 @ SV328 ) )
        = $true )
      | ( ( SV92 = SV328 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1843]) ).

thf(2054,plain,
    ! [SV509: $i > $i > $o,SV329: $i,SV93: $i,SV632: $i,SV610: $i] :
      ( ( ( ~ ( in @ ( kpair @ SV610 @ SV632 )
              @ ( dpsetconstr @ SV93 @ SV329
                @ ^ [SY2914: $i,SY2915: $i] : ( SV509 @ SY2914 @ SY2915 ) ) ) )
        = $true )
      | ( ( SV509 @ SV610 @ SV632 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1844]) ).

thf(2055,plain,
    ! [SV611: $i,SV510: $i,SV330: $i,SV94: $i] :
      ( ( ( ( kpair @ SV94 @ SV330 )
          = ( kpair @ SV510 @ SV611 ) )
        = $false )
      | ( ( SV94 = SV510 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1845]) ).

thf(2056,plain,
    ! [SV331: $i,SV95: $i,SV511: $i] :
      ( ( ( ~ ( in @ SV511 @ SV95 ) )
        = $true )
      | ( ( in @ SV511 @ SV331 )
        = $true )
      | ( ( subset @ SV95 @ SV331 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1846]) ).

thf(2057,plain,
    ! [SV512: $i,SV685: $i,SV332: $i,SV96: $i] :
      ( ( ( ~ ( func @ SV96 @ SV332 @ SV685 )
          | ~ ! [SY3119: $i] :
                ( ~ ( in @ SY3119 @ SV96 )
                | ( ( ap @ SV96 @ SV332 @ SV512 @ SY3119 )
                  = ( ap @ SV96 @ SV332 @ SV685 @ SY3119 ) ) )
          | ! [SY3120: $i] :
              ( ~ ( in @ SY3120 @ SV96 )
              | ! [SY3121: $i] :
                  ( ~ ( in @ SY3121 @ SV332 )
                  | ~ ( in @ ( kpair @ SY3120 @ SY3121 ) @ SV685 )
                  | ( in @ ( kpair @ SY3120 @ SY3121 ) @ SV512 ) ) ) )
        = $true )
      | ( ( func @ SV96 @ SV332 @ SV512 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1847]) ).

thf(2058,plain,
    ! [SV513: $i,SV333: $i,SV98: $i] :
      ( ( ( ! [SY2921: $i] :
              ~ ~ ( ~ ( in @ SY2921 @ SV98 )
                  | ~ ~ ! [SY2922: $i] :
                          ~ ~ ( ~ ( in @ SY2922 @ SV333 )
                              | ( SV513
                               != ( kpair @ SY2921 @ SY2922 ) ) ) ) )
        = $false )
      | ( ( in @ SV513 @ ( cartprod @ SV98 @ SV333 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1848]) ).

thf(2059,plain,
    ! [SV334: $i,SV99: $i,SV633: $i] :
      ( ( ( ~ ( in @ SV633 @ ( powerset @ SV99 ) ) )
        = $true )
      | ( ( ! [SY3073: $i] :
              ( ~ ( in @ SY3073 @ SV99 )
              | ~ ( in @ SV334 @ ( powerset @ SV633 ) )
              | ~ ( in @ SY3073 @ SV334 )
              | ( in @ SY3073 @ SV633 ) ) )
        = $true )
      | ( ( in @ SV334 @ ( powerset @ SV99 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1849]) ).

thf(2060,plain,
    ! [SV335: $i,SV101: $i,SV514: $i] :
      ( ( ( SV514 = SV101 )
        = $true )
      | ( ( in @ SV514 @ SV335 )
        = $true )
      | ( ( in @ SV514 @ ( setadjoin @ SV101 @ SV335 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1851]) ).

thf(2061,plain,
    ! [SV102: $i,SV336: $i > $o] :
      ( ( ( ~ ( in @ ( sK11_SY2627 @ SV336 @ SV102 ) @ SV102 ) )
        = $false )
      | ( ( ~ ~ ! [SY2629: $i] :
                  ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                      | ~ ( SV336 @ SY2629 ) )
          | ( singleton
            @ ( dsetconstr @ SV102
              @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1852]) ).

thf(2062,plain,
    ! [SV336: $i > $o,SV102: $i] :
      ( ( ( ! [SY3074: $i] :
              ( ~ ( in @ SY3074 @ SV102 )
              | ~ ( SV336 @ ( sK11_SY2627 @ SV336 @ SV102 ) )
              | ~ ( SV336 @ SY3074 )
              | ( ( sK11_SY2627 @ SV336 @ SV102 )
                = SY3074 ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2629: $i] :
                  ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                      | ~ ( SV336 @ SY2629 ) )
          | ( singleton
            @ ( dsetconstr @ SV102
              @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1852]) ).

thf(2063,plain,
    ! [SV515: $i > $i > $o,SV337: $i,SV103: $i,SV634: $i,SV612: $i] :
      ( ( ( ~ ( in @ ( kpair @ SV612 @ SV634 )
              @ ( dpsetconstr @ SV103 @ SV337
                @ ^ [SY2925: $i,SY2926: $i] : ( SV515 @ SY2925 @ SY2926 ) ) ) )
        = $true )
      | ( ( in @ SV612 @ SV103 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1853]) ).

thf(2064,plain,
    ! [SV104: $i,SV338: $i] :
      ( ( ( in @ SV338 @ ( setadjoin @ SV104 @ emptyset ) )
        = $false )
      | ( ( SV104 = SV338 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1854]) ).

thf(2065,plain,
    ! [SV105: $i,SV516: $i > $i,SV339: $i] :
      ( ( ( ~ ( in @ ( sK19_SY2927 @ SV339 @ SV516 @ SV105 ) @ SV105 )
          | ( in @ ( SV516 @ ( sK19_SY2927 @ SV339 @ SV516 @ SV105 ) ) @ SV339 ) )
        = $false )
      | ( ( ( lam @ SV105 @ SV339
            @ ^ [SY2928: $i] : ( SV516 @ SY2928 ) )
          = ( lam @ SV105 @ SV339
            @ ^ [SY2929: $i] : ( SV516 @ SY2929 ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[1855]) ).

thf(2066,plain,
    ! [SV107: $i,SV518: $i > $i,SV341: $i] :
      ( ( ( ~ ( in @ ( sK20_SY2930 @ SV341 @ SV518 @ SV107 ) @ SV107 )
          | ( in @ ( SV518 @ ( sK20_SY2930 @ SV341 @ SV518 @ SV107 ) ) @ SV341 ) )
        = $false )
      | ( ( in
          @ ( lam @ SV107 @ SV341
            @ ^ [SY2931: $i] : ( SV518 @ SY2931 ) )
          @ ( funcSet @ SV107 @ SV341 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[1857]) ).

thf(2067,plain,
    ! [SV109: $i] :
      ( ( ~ ~ ( ~ ~ ( ~ ! [SY2932: $i] :
                          ( ~ ( in @ SY2932 @ ( sK3_SY2100 @ SV109 ) )
                          | ! [SY2102: $i] :
                              ( ~ ( in @ SY2102 @ SY2932 )
                              | ( in @ SY2102 @ SV109 ) ) )
                    | ~ ! [SY2934: $i,SY2935: $i] :
                          ( ~ ~ ( ~ ( in @ SY2934 @ SV109 )
                                | ~ ( in @ SY2935 @ SV109 ) )
                          | ~ ! [SY2936: $i] :
                                ( ~ ( in @ SY2936 @ ( sK3_SY2100 @ SV109 ) )
                                | ~ ( ~ ( ~ ( in @ SY2934 @ SY2936 )
                                        | ( in @ SY2935 @ SY2936 ) )
                                    | ~ ( ~ ( in @ SY2935 @ SY2936 )
                                        | ( in @ SY2934 @ SY2936 ) ) ) )
                          | ( SY2934 = SY2935 ) ) )
              | ~ ! [SY2937: $i,SY2938: $i] :
                    ( ~ ~ ( ~ ( in @ SY2937 @ ( sK3_SY2100 @ SV109 ) )
                          | ~ ( in @ SY2938 @ ( sK3_SY2100 @ SV109 ) ) )
                    | ! [SX4: $i] :
                        ( ~ ( in @ SX4 @ SY2937 )
                        | ( in @ SX4 @ SY2938 ) )
                    | ! [SX4: $i] :
                        ( ~ ( in @ SX4 @ SY2938 )
                        | ( in @ SX4 @ SY2937 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1858]) ).

thf(2068,plain,
    ! [SV109: $i] :
      ( ( ~ ! [SY2941: $i] :
              ( ~ ~ ( ~ ! [SY2111: $i] :
                          ( ~ ( in @ SY2111 @ SY2941 )
                          | ( in @ SY2111 @ SV109 ) )
                    | ~ ~ ! [SX3: $i] :
                            ~ ( in @ SX3 @ SY2941 ) )
              | ~ ! [SY2944: $i] :
                    ~ ~ ! [SY2945: $i] :
                          ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY2944 @ ( sK3_SY2100 @ SV109 ) )
                                          | ~ ( in @ SY2945 @ SY2941 ) )
                                    | ~ ~ ~ ! [SX5: $i] :
                                              ~ ~ ( ~ ( in @ SX5 @ SY2944 )
                                                  | ~ ( in @ SX5 @ SY2941 ) ) )
                              | ~ ! [SY2947: $i] :
                                    ( ~ ( in @ SY2947 @ ( sK3_SY2100 @ SV109 ) )
                                    | ! [SX6: $i] :
                                        ( ~ ( in @ SX6 @ SY2947 )
                                        | ( in @ SX6 @ SY2944 ) )
                                    | ( in @ SY2945 @ SY2947 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1858]) ).

thf(2069,plain,
    ! [SV110: $i,SV635: $i] :
      ( ( ( in @ SV635 @ SV110 )
        = $false )
      | ( ( ~ ! [SY2119: $i] :
                ~ ~ ( ~ ( in @ SY2119 @ SV110 )
                    | ~ ~ ~ ! [SY2120: $i] :
                              ~ ~ ( ~ ( in @ SY2120 @ SY2119 )
                                  | ~ ( in @ SY2120 @ SV110 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1859]) ).

thf(2070,plain,
    ! [SV636: $i,SV112: $i > $o] :
      ( ( ( ~ ( ~ ( SV112 @ SV636 )
              | ~ ! [SY3077: $i] :
                    ( ~ ( SV112 @ SY3077 )
                    | ( SV636 = SY3077 ) ) ) )
        = $false )
      | ( ( ~ ! [SY2125: $i] :
                ~ ( SV112 @ SY2125 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1861]) ).

thf(2071,plain,
    ! [SV344: $i,SV113: $i] :
      ( ( ( ! [SY2645: $i] :
              ~ ~ ( ~ ( in @ SY2645 @ SV113 )
                  | ~ ( in @ SY2645 @ SV344 ) ) )
        = $false )
      | ( ( ( binintersect @ SV113 @ SV344 )
          = emptyset )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1862]) ).

thf(2072,plain,
    ! [SV346: $i,SV116: $i,SV637: $i] :
      ( ( ( ~ ( in @ SV637 @ ( powerset @ SV116 ) ) )
        = $true )
      | ( ( ! [SY3078: $i] :
              ( ~ ( in @ SY3078 @ SV116 )
              | ~ ~ ( in @ SY3078 @ ( binunion @ SV346 @ SV637 ) )
              | ~ ( in @ SY3078 @ SV346 ) ) )
        = $true )
      | ( ( in @ SV346 @ ( powerset @ SV116 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1863]) ).

thf(2073,plain,
    ! [SV520: $i,SV347: $o,SV118: $i,SV686: $i] :
      ( ( ( ~ ( in @ SV686 @ SV118 )
          | ~ ~ SV347
          | ( ( if @ SV118 @ SV347 @ SV520 @ SV686 )
            = SV686 ) )
        = $true )
      | ( ( in @ SV520 @ SV118 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1864]) ).

thf(2074,plain,
    ! [SV521: $i,SV118: $i,SV687: $i] :
      ( ( ( ~ ( in @ SV687 @ SV118 )
          | ~ ~ $true
          | ( ( if @ SV118 @ $true @ SV521 @ SV687 )
            = SV687 ) )
        = $true )
      | ( ( in @ SV521 @ SV118 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1865]) ).

thf(2075,plain,
    ! [SV522: $i,SV118: $i,SV688: $i] :
      ( ( ( ~ ( in @ SV688 @ SV118 )
          | ~ ~ $false
          | ( ( if @ SV118 @ $false @ SV522 @ SV688 )
            = SV688 ) )
        = $true )
      | ( ( in @ SV522 @ SV118 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1866]) ).

thf(2076,plain,
    ! [SV349: $i,SV121: $i,SV638: $i] :
      ( ( ( ~ ( in @ SV638 @ SV121 ) )
        = $true )
      | ( ( ~ ~ ( in @ SV638 @ ( setminus @ SV121 @ SV349 ) )
          | ( in @ SV638 @ SV349 ) )
        = $true )
      | ( ( in @ SV349 @ ( powerset @ SV121 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1867]) ).

thf(2077,plain,
    ! [SV350: $i,SV122: $i,SV639: $i] :
      ( ( ( ~ ( in @ SV639 @ ( powerset @ SV122 ) ) )
        = $true )
      | ( ( subset @ ( setminus @ SV122 @ SV350 ) @ ( setminus @ SV122 @ ( binintersect @ SV350 @ SV639 ) ) )
        = $true )
      | ( ( in @ SV350 @ ( powerset @ SV122 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1868]) ).

thf(2078,plain,
    ! [SV123: $i,SV351: $i,SV523: $i] :
      ( ( ( ~ ~ ( in @ SV523 @ SV351 ) )
        = $true )
      | ( ( ~ ( in @ SV523 @ SV123 ) )
        = $true )
      | ( ( subset @ SV123 @ SV351 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1869]) ).

thf(2079,plain,
    ! [SV124: $i,SV524: $i > $i,SV352: $i] :
      ( ( ( ~ ( in @ ( sK21_SY2952 @ SV352 @ SV524 @ SV124 ) @ SV124 )
          | ( in @ ( SV524 @ ( sK21_SY2952 @ SV352 @ SV524 @ SV124 ) ) @ SV352 ) )
        = $false )
      | ( ( func @ SV124 @ SV352
          @ ( dpsetconstr @ SV124 @ SV352
            @ ^ [SY2953: $i,SY2954: $i] :
                ( ( SV524 @ SY2953 )
                = SY2954 ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[1870]) ).

thf(2080,plain,
    ! [SV125: $i,SV353: $i > $o] :
      ( ( ( ~ ( in @ ( sK12_SY2657 @ SV353 @ SV125 ) @ SV125 ) )
        = $false )
      | ( ( ~ ~ ! [SY2659: $i] :
                  ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                      | ~ ( SV353 @ SY2659 ) )
          | ( singleton
            @ ( dsetconstr @ SV125
              @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1871]) ).

thf(2081,plain,
    ! [SV353: $i > $o,SV125: $i] :
      ( ( ( ! [SY3079: $i] :
              ( ~ ( in @ SY3079 @ SV125 )
              | ~ ( SV353 @ ( sK12_SY2657 @ SV353 @ SV125 ) )
              | ~ ( SV353 @ SY3079 )
              | ( ( sK12_SY2657 @ SV353 @ SV125 )
                = SY3079 ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2659: $i] :
                  ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                      | ~ ( SV353 @ SY2659 ) )
          | ( singleton
            @ ( dsetconstr @ SV125
              @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1871]) ).

thf(2082,plain,
    ! [SV354: $i,SV126: $i,SV525: $i] :
      ( ( ( in @ SV525 @ SV126 )
        = $true )
      | ( ( ~ ( in @ SV525 @ SV354 )
          | ( in @ SV525 @ ( symdiff @ SV126 @ SV354 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1872]) ).

thf(2083,plain,
    ! [SV355: $i,SV127: $i,SV526: $i] :
      ( ( ( SV526 = SV127 )
        = $true )
      | ( ( SV526 = SV355 )
        = $true )
      | ( ( in @ SV526 @ ( setadjoin @ SV127 @ ( setadjoin @ SV355 @ emptyset ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1873]) ).

thf(2084,plain,
    ! [SV356: $i,SV128: $i,SV640: $i] :
      ( ( ( ~ ( in @ SV640 @ ( powerset @ SV128 ) ) )
        = $true )
      | ( ( in @ ( setminus @ SV128 @ SV356 ) @ ( powerset @ ( setminus @ SV128 @ ( binintersect @ SV356 @ SV640 ) ) ) )
        = $true )
      | ( ( in @ SV356 @ ( powerset @ SV128 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1874]) ).

thf(2085,plain,
    ! [SV357: $i,SV129: $i,SV641: $i] :
      ( ( ( ~ ( in @ SV641 @ SV129 ) )
        = $true )
      | ( ( ~ ( in @ SV641 @ SV357 )
          | ~ ( in @ SV641 @ ( setminus @ SV129 @ SV357 ) ) )
        = $true )
      | ( ( in @ SV357 @ ( powerset @ SV129 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1875]) ).

thf(2086,plain,
    ! [SV360: $i,SV132: $i,SV642: $i] :
      ( ( ( ~ ( in @ SV642 @ ( powerset @ SV132 ) ) )
        = $true )
      | ( ( ~ ( subset @ SV360 @ SV642 )
          | ( subset @ ( setminus @ SV132 @ SV642 ) @ ( setminus @ SV132 @ SV360 ) ) )
        = $true )
      | ( ( in @ SV360 @ ( powerset @ SV132 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1876]) ).

thf(2087,plain,
    ! [SV527: $i,SV361: $i,SV133: $i,SV689: $i] :
      ( ( ( ~ ( in @ SV689 @ SV133 )
          | ( ( ap @ SV133 @ SV361 @ SV527 @ SV689 )
            = ( ap @ SV133 @ SV361 @ SV527 @ SV689 ) ) )
        = $true )
      | ( ( func @ SV133 @ SV361 @ SV527 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1877]) ).

thf(2088,plain,
    ! [SV362: $i,SV134: $i,SV528: $i] :
      ( ( ( SV528 = SV134 )
        = $true )
      | ( ( SV528 = SV362 )
        = $true )
      | ( ( in @ SV528 @ ( setadjoin @ SV134 @ ( setadjoin @ SV362 @ emptyset ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1878]) ).

thf(2089,plain,
    ! [SV690: $i > $o,SV529: $i,SV363: $i,SV135: $i] :
      ( ( ( ~ ! [SY3122: $i] :
                ( ~ ( in @ SY3122 @ SV135 )
                | ! [SY3123: $i] :
                    ( ~ ( in @ SY3123 @ SV363 )
                    | ~ ( in @ ( kpair @ SY3122 @ SY3123 ) @ SV529 )
                    | ( SV690 @ ( kpair @ SY3122 @ SY3123 ) ) ) )
          | ! [SY3124: $i] :
              ( ~ ( in @ SY3124 @ SV529 )
              | ( SV690 @ SY3124 ) ) )
        = $true )
      | ( ( subset @ SV529 @ ( cartprod @ SV135 @ SV363 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1879]) ).

thf(2090,plain,
    ! [SV136: $i,SV364: $i,SV530: $i] :
      ( ( ( ~ ( in @ SV530 @ SV364 ) )
        = $true )
      | ( ( in @ SV530 @ SV136 )
        = $true )
      | ( ( in @ SV364 @ ( powerset @ SV136 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1880]) ).

thf(2091,plain,
    ! [SV365: $i,SV137: $i,SV643: $i] :
      ( ( ( ~ ( in @ SV643 @ ( powerset @ SV137 ) ) )
        = $true )
      | ( ( ! [SY3080: $i] :
              ( ~ ( in @ SY3080 @ SV137 )
              | ~ ~ ( in @ SY3080 @ SV643 )
              | ~ ( in @ SY3080 @ ( binintersect @ SV365 @ SV643 ) ) ) )
        = $true )
      | ( ( in @ SV365 @ ( powerset @ SV137 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1881]) ).

thf(2092,plain,
    ! [SV140: $i,SV531: $i,SV370: $i,SV691: $i] :
      ( ( ( ~ ( in @ SV691 @ SV370 )
          | ( in @ ( kpair @ SV531 @ SV691 ) @ ( cartprod @ SV140 @ SV370 ) ) )
        = $true )
      | ( ( in @ SV531 @ SV140 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1882]) ).

thf(2093,plain,
    ! [SV372: $i > $o,SV142: $i,SV644: $i] :
      ( ( ( ~ ( in @ SV644 @ SV142 ) )
        = $true )
      | ( ( ! [SY3081: $i] :
              ( ~ ( in @ SY3081 @ SV142 )
              | ~ ( SV372 @ SV644 )
              | ~ ( SV372 @ SY3081 )
              | ( SV644 = SY3081 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV142
            @ ^ [SY2680: $i] : ( SV372 @ SY2680 ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1884]) ).

thf(2094,plain,
    ! [SV144: $i,SV533: $i,SV374: $i,SV692: $i] :
      ( ( ( ~ ( in @ SV692 @ SV374 )
          | ( ( kfst @ ( kpair @ SV533 @ SV692 ) )
            = SV533 ) )
        = $true )
      | ( ( in @ SV533 @ SV144 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1885]) ).

thf(2095,plain,
    ! [SV613: $i,SV534: $i,SV376: $i,SV146: $i] :
      ( ( ( ( kpair @ SV146 @ SV376 )
          = ( kpair @ SV534 @ SV613 ) )
        = $false )
      | ( ( SV376 = SV613 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1886]) ).

thf(2096,plain,
    ! [SV377: $i,SV147: $i > $i > $o] :
      ( ( ( ~ ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 ) )
        = $false )
      | ( ( ~ ! [SY2690: $i] :
                ~ ! [SY2691: $i] :
                    ~ ( ~ ( ~ ( in @ SY2691 @ SY2690 )
                          | ~ ! [SY2692: $i] :
                                ~ ~ ( ~ ( in @ SY2692 @ SV377 )
                                    | ~ ( SV147 @ SY2692 @ SY2691 ) ) )
                      | ~ ( ~ ~ ! [SY2693: $i] :
                                  ~ ~ ( ~ ( in @ SY2693 @ SV377 )
                                      | ~ ( SV147 @ SY2693 @ SY2691 ) )
                          | ( in @ SY2691 @ SY2690 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1887]) ).

thf(2097,plain,
    ! [SV377: $i,SV147: $i > $i > $o] :
      ( ( ( ~ ! [SY3082: $i] :
                ~ ~ ( ~ ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SY3082 )
                    | ~ ! [SY3083: $i] :
                          ( ~ ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SY3083 )
                          | ( SY3082 = SY3083 ) ) ) )
        = $false )
      | ( ( ~ ! [SY2690: $i] :
                ~ ! [SY2691: $i] :
                    ~ ( ~ ( ~ ( in @ SY2691 @ SY2690 )
                          | ~ ! [SY2692: $i] :
                                ~ ~ ( ~ ( in @ SY2692 @ SV377 )
                                    | ~ ( SV147 @ SY2692 @ SY2691 ) ) )
                      | ~ ( ~ ~ ! [SY2693: $i] :
                                  ~ ~ ( ~ ( in @ SY2693 @ SV377 )
                                      | ~ ( SV147 @ SY2693 @ SY2691 ) )
                          | ( in @ SY2691 @ SY2690 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1887]) ).

thf(2098,plain,
    ! [SV148: $i,SV378: $i] :
      ( ( ( ~ ( in @ ( sK14_SY2694 @ SV378 @ SV148 ) @ SV148 ) )
        = $false )
      | ( ( subset @ SV148 @ SV378 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1888]) ).

thf(2099,plain,
    ! [SV148: $i,SV378: $i] :
      ( ( ( in @ ( sK14_SY2694 @ SV378 @ SV148 ) @ SV378 )
        = $false )
      | ( ( subset @ SV148 @ SV378 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1888]) ).

thf(2100,plain,
    ! [SV149: $i,SV379: $i] :
      ( ( ( subset @ SV379 @ SV149 )
        = $false )
      | ( ( SV149 = SV379 )
        = $true )
      | ( ( subset @ SV149 @ SV379 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1889]) ).

thf(2101,plain,
    ! [SV381: $i,SV151: $i,SV645: $i] :
      ( ( ( ~ ( in @ SV645 @ ( powerset @ SV151 ) ) )
        = $true )
      | ( ( ! [SY3084: $i] :
              ( ~ ( in @ SY3084 @ SV151 )
              | ~ ~ ( in @ SY3084 @ ( binunion @ SV381 @ SV645 ) )
              | ~ ( in @ SY3084 @ SV645 ) ) )
        = $true )
      | ( ( in @ SV381 @ ( powerset @ SV151 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1891]) ).

thf(2102,plain,
    ! [SV382: $i,SV152: $i,SV693: $i,SV646: $i] :
      ( ( ( ( SV646 != SV693 )
          | ( ( setadjoin @ SV152 @ SV646 )
            = ( setadjoin @ SV382 @ SV693 ) ) )
        = $true )
      | ( ( SV152 = SV382 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1892]) ).

thf(2103,plain,
    ! [SV385: $i,SV156: $i,SV647: $i] :
      ( ( ( ~ ( in @ SV647 @ ( powerset @ SV156 ) ) )
        = $true )
      | ( ( ! [SY3086: $i] :
              ( ~ ( in @ SY3086 @ SV156 )
              | ~ ~ ( in @ SY3086 @ SV385 )
              | ~ ( in @ SY3086 @ ( binintersect @ SV385 @ SV647 ) ) ) )
        = $true )
      | ( ( in @ SV385 @ ( powerset @ SV156 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1894]) ).

thf(2104,plain,
    ! [SV648: $i,SV157: $i > $o] :
      ( ( ( ~ ( ~ ( SV157 @ SV648 )
              | ~ ! [SY3087: $i] :
                    ( ~ ( SV157 @ SY3087 )
                    | ( SV648 = SY3087 ) ) ) )
        = $false )
      | ( ( SV157
          @ ( descr
            @ ^ [SY2227: $i] : ( SV157 @ SY2227 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1895]) ).

thf(2105,plain,
    ! [SV158: $i,SV386: $i,SV537: $i] :
      ( ( ( in @ SV537 @ SV386 )
        = $false )
      | ( ( in @ SV537 @ ( setminus @ SV158 @ SV386 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1896]) ).

thf(2106,plain,
    ! [SV388: $i > $o,SV160: $i,SV694: $i] :
      ( ( ( ~ ( in @ SV694 @ SV160 )
          | ( SV388 @ SV694 ) )
        = $true )
      | ( ( ~ ! [SY2705: $i] :
                ~ ~ ( ~ ( in @ SY2705 @ SV160 )
                    | ~ ~ ( SV388 @ SY2705 ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1897]) ).

thf(2107,plain,
    ! [SV389: $i,SV161: $i,SV649: $i] :
      ( ( ( ~ ( in @ SV649 @ ( powerset @ SV161 ) ) )
        = $true )
      | ( ( ! [SY3088: $i] :
              ( ~ ( in @ SY3088 @ SV161 )
              | ~ ( in @ SY3088 @ ( setminus @ SV161 @ SV389 ) )
              | ( in @ SY3088 @ ( setminus @ SV161 @ ( binintersect @ SV389 @ SV649 ) ) ) ) )
        = $true )
      | ( ( in @ SV389 @ ( powerset @ SV161 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1898]) ).

thf(2108,plain,
    ! [SV390: $i,SV162: $i,SV650: $i] :
      ( ( ( ~ ( in @ SV650 @ ( powerset @ SV162 ) ) )
        = $true )
      | ( ( in @ ( binunion @ SV390 @ SV650 ) @ ( powerset @ SV162 ) )
        = $true )
      | ( ( in @ SV390 @ ( powerset @ SV162 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1899]) ).

thf(2109,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( SV165 @ SV651 )
        = $false )
      | ( ( ~ ! [SY2242: $i,SY2243: $i] :
                ( ~ ( SV165 @ SY2242 )
                | ~ ( SV165 @ SY2243 )
                | ( SY2242 = SY2243 ) )
          | ~ ! [SY2244: $i] :
                ~ ~ ( ~ ( SV165 @ SY2244 )
                    | ~ ! [SY2245: $i] :
                          ( ~ ( SV165 @ SY2245 )
                          | ( SY2244 = SY2245 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1900]) ).

thf(2110,plain,
    ! [SV166: $i,SV393: $i,SV538: $i] :
      ( ( ( ~ ~ ( in @ SV538 @ SV393 ) )
        = $true )
      | ( ( ~ ( subset @ SV166 @ SV393 ) )
        = $true )
      | ( ( in @ SV538 @ SV166 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1901]) ).

thf(2111,plain,
    ! [SV394: $i,SV167: $i,SV652: $i] :
      ( ( ( ~ ( in @ SV652 @ ( powerset @ SV167 ) ) )
        = $true )
      | ( ( ! [SY3089: $i] :
              ( ~ ( in @ SY3089 @ ( powerset @ SV167 ) )
              | ( in @ ( binintersect @ SV394 @ SV652 ) @ ( powerset @ ( binintersect @ ( binunion @ SV394 @ SY3089 ) @ ( binunion @ SV652 @ SY3089 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV394 @ ( powerset @ SV167 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1902]) ).

thf(2112,plain,
    ! [SV539: $i,SV395: $i,SV168: $i,SV695: $i] :
      ( ( ( ~ ( subset @ SV695 @ ( cartprod @ SV168 @ SV395 ) )
          | ~ ! [SY3125: $i] :
                ( ~ ( in @ SY3125 @ SV168 )
                | ! [SY3126: $i] :
                    ( ~ ( in @ SY3126 @ SV395 )
                    | ~ ( in @ ( kpair @ SY3125 @ SY3126 ) @ SV539 )
                    | ( in @ ( kpair @ SY3125 @ SY3126 ) @ SV695 ) ) )
          | ( subset @ SV539 @ SV695 ) )
        = $true )
      | ( ( subset @ SV539 @ ( cartprod @ SV168 @ SV395 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1903]) ).

thf(2113,plain,
    ! [SV540: $i,SV396: $o,SV169: $i,SV696: $i] :
      ( ( ( ~ ( in @ SV696 @ SV169 )
          | ~ SV396
          | ( ( if @ SV169 @ SV396 @ SV540 @ SV696 )
            = SV540 ) )
        = $true )
      | ( ( in @ SV540 @ SV169 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1904]) ).

thf(2114,plain,
    ! [SV541: $i,SV169: $i,SV697: $i] :
      ( ( ( ~ ( in @ SV697 @ SV169 )
          | ~ $true
          | ( ( if @ SV169 @ $true @ SV541 @ SV697 )
            = SV541 ) )
        = $true )
      | ( ( in @ SV541 @ SV169 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1905]) ).

thf(2115,plain,
    ! [SV542: $i,SV169: $i,SV698: $i] :
      ( ( ( ~ ( in @ SV698 @ SV169 )
          | ~ $false
          | ( ( if @ SV169 @ $false @ SV542 @ SV698 )
            = SV542 ) )
        = $true )
      | ( ( in @ SV542 @ SV169 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1906]) ).

thf(2116,plain,
    ! [SV170: $i,SV543: $i > $i,SV397: $i] :
      ( ( ( ~ ( in @ ( sK22_SY2969 @ SV397 @ SV543 @ SV170 ) @ SV170 )
          | ( in @ ( SV543 @ ( sK22_SY2969 @ SV397 @ SV543 @ SV170 ) ) @ SV397 ) )
        = $false )
      | ( ( ! [SY2970: $i] :
              ( ~ ( in @ SY2970 @ SV170 )
              | ( ( ap @ SV170 @ SV397
                  @ ( lam @ SV170 @ SV397
                    @ ^ [SY2971: $i] : ( SV543 @ SY2971 ) )
                  @ SY2970 )
                = ( SV543 @ SY2970 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[1907]) ).

thf(2117,plain,
    ! [SV171: $i,SV653: $i] :
      ( ( ( in @ SV653 @ SV171 )
        = $false )
      | ( ( SV171 != emptyset )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1908]) ).

thf(2118,plain,
    ! [SV614: $i,SV546: $i,SV400: $i,SV174: $i] :
      ( ( ( ( setadjoin @ ( setadjoin @ SV174 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV174 @ ( setadjoin @ SV400 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ SV546 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV546 @ ( setadjoin @ SV614 @ emptyset ) ) @ emptyset ) ) )
        = $false )
      | ( ( ( SV546 != SV614 )
          | ( SV400 = SV614 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1911]) ).

thf(2119,plain,
    ! [SV401: $i,SV175: $i,SV615: $i,SV547: $i] :
      ( ( ( in @ ( kpair @ SV547 @ SV615 ) @ ( cartprod @ SV175 @ SV401 ) )
        = $false )
      | ( ( in @ SV615 @ SV401 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1912]) ).

thf(2120,plain,
    ! [SV548: $i,SV402: $i,SV176: $i,SV699: $i] :
      ( ( ( ~ ( in @ SV699 @ SV176 )
          | ( in @ ( ap @ SV176 @ SV402 @ SV548 @ SV699 ) @ SV402 ) )
        = $true )
      | ( ( func @ SV176 @ SV402 @ SV548 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1913]) ).

thf(2121,plain,
    ! [SV403: $i,SV177: $i,SV654: $i] :
      ( ( ( ~ ( in @ SV654 @ ( powerset @ SV177 ) ) )
        = $true )
      | ( ( ! [SY3090: $i] :
              ( ~ ( in @ SY3090 @ SV177 )
              | ~ ( subset @ SV403 @ ( setminus @ SV177 @ SV654 ) )
              | ~ ( in @ SY3090 @ SV654 )
              | ~ ( in @ SY3090 @ SV403 ) ) )
        = $true )
      | ( ( in @ SV403 @ ( powerset @ SV177 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1914]) ).

thf(2122,plain,
    ! [SV549: $i > $i > $o,SV404: $i,SV178: $i,SV616: $i] :
      ( ( ( in @ SV616 @ SV178 )
        = $false )
      | ( ( ! [SY3052: $i] :
              ( ~ ( in @ SY3052 @ SV404 )
              | ~ ( SV549 @ SV616 @ SY3052 )
              | ( in @ ( kpair @ SV616 @ SY3052 )
                @ ( dpsetconstr @ SV178 @ SV404
                  @ ^ [SY2978: $i,SY2979: $i] : ( SV549 @ SY2978 @ SY2979 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1915]) ).

thf(2123,plain,
    ! [SV179: $i,SV405: $i,SV550: $i] :
      ( ( ( ~ ~ ( in @ SV550 @ SV405 ) )
        = $true )
      | ( ( SV179 != SV405 )
        = $true )
      | ( ( in @ SV550 @ SV179 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1916]) ).

thf(2124,plain,
    ! [SV180: $i,SV406: $i,SV551: $i] :
      ( ( ( ~ ( in @ SV551 @ SV406 ) )
        = $true )
      | ( ( in @ SV551 @ ( binintersect @ SV180 @ SV406 ) )
        = $true )
      | ( ( in @ SV551 @ SV180 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1917]) ).

thf(2125,plain,
    ! [SV407: $i,SV181: $i] :
      ( ( ( ~ ( in @ ( sK15_SY2740 @ SV181 @ SV407 ) @ SV407 ) )
        = $false )
      | ( ( in @ SV407 @ ( powerset @ SV181 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1918]) ).

thf(2126,plain,
    ! [SV407: $i,SV181: $i] :
      ( ( ( in @ ( sK15_SY2740 @ SV181 @ SV407 ) @ SV181 )
        = $false )
      | ( ( in @ SV407 @ ( powerset @ SV181 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1918]) ).

thf(2127,plain,
    ! [SV408: $i,SV182: $i,SV655: $i] :
      ( ( ( ~ ( in @ SV655 @ SV182 ) )
        = $true )
      | ( ( ~ ( in @ SV655 @ SV408 )
          | ( in @ SV655 @ ( setminus @ SV182 @ ( setminus @ SV182 @ SV408 ) ) ) )
        = $true )
      | ( ( in @ SV408 @ ( powerset @ SV182 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1919]) ).

thf(2128,plain,
    ! [SV554: $i,SV411: $i,SV185: $i,SV700: $i] :
      ( ( ( ~ ( in @ SV700 @ SV185 )
          | ! [SY3127: $i] :
              ( ~ ( in @ SY3127 @ SV411 )
              | ~ ( in @ ( kpair @ SV700 @ SY3127 ) @ SV554 )
              | ( ( ap @ SV185 @ SV411 @ SV554 @ SV700 )
                = SY3127 ) ) )
        = $true )
      | ( ( func @ SV185 @ SV411 @ SV554 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1922]) ).

thf(2129,plain,
    ! [SV412: $i,SV186: $i,SV656: $i] :
      ( ( ( ~ ( in @ SV656 @ ( powerset @ SV186 ) ) )
        = $true )
      | ( ( in @ ( setminus @ SV412 @ SV656 ) @ ( powerset @ SV186 ) )
        = $true )
      | ( ( in @ SV412 @ ( powerset @ SV186 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1923]) ).

thf(2130,plain,
    ! [SV414: $i > $o,SV188: $i,SV556: $i] :
      ( ( ( ~ ( ~ ( in @ SV556
                  @ ( dsetconstr @ SV188
                    @ ^ [SY2751: $i] : ( SV414 @ SY2751 ) ) )
              | ( SV414 @ SV556 ) )
          | ~ ( ~ ( SV414 @ SV556 )
              | ( in @ SV556
                @ ( dsetconstr @ SV188
                  @ ^ [SY2752: $i] : ( SV414 @ SY2752 ) ) ) ) )
        = $false )
      | ( ( in @ SV556 @ SV188 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1925]) ).

thf(2131,plain,
    ! [SV558: $i,SV701: $i,SV416: $i,SV190: $i] :
      ( ( ( ~ ( func @ SV190 @ SV416 @ SV701 )
          | ~ ! [SY3128: $i] :
                ( ~ ( in @ SY3128 @ SV190 )
                | ( ( ap @ SV190 @ SV416 @ SV558 @ SY3128 )
                  = ( ap @ SV190 @ SV416 @ SV701 @ SY3128 ) ) )
          | ( SV558 = SV701 ) )
        = $true )
      | ( ( func @ SV190 @ SV416 @ SV558 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1927]) ).

thf(2132,plain,
    ! [SV417: $i,SV191: $i,SV657: $i] :
      ( ( ( ~ ( in @ SV657 @ ( powerset @ SV191 ) ) )
        = $true )
      | ( ( ! [SY3091: $i] :
              ( ~ ( in @ SY3091 @ ( powerset @ SV191 ) )
              | ! [SY3092: $i] :
                  ( ~ ( in @ SY3092 @ SV191 )
                  | ~ ( in @ SY3092 @ ( binintersect @ SV417 @ SV657 ) )
                  | ( in @ SY3092 @ ( binunion @ SV417 @ SY3091 ) ) ) ) )
        = $true )
      | ( ( in @ SV417 @ ( powerset @ SV191 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1928]) ).

thf(2133,plain,
    ! [SV419: $i,SV193: $i,SV702: $i,SV658: $i] :
      ( ( ( ( SV658 != SV702 )
          | ~ ( ~ ( ~ ( in @ SV658 @ SV193 )
                  | ( in @ SV702 @ SV419 ) )
              | ~ ( ~ ( in @ SV702 @ SV419 )
                  | ( in @ SV658 @ SV193 ) ) ) )
        = $true )
      | ( ( SV193 = SV419 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1930]) ).

thf(2134,plain,
    ! [SV560: $i,SV420: $o,SV194: $i,SV703: $i] :
      ( ( ( ~ ( in @ SV703 @ SV194 )
          | ( singleton
            @ ( dsetconstr @ SV194
              @ ^ [SY3129: $i] :
                  ( ~ ( ~ SV420
                      | ( SY3129 != SV560 ) )
                  | ~ ( ~ ~ SV420
                      | ( SY3129 != SV703 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV560 @ SV194 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1931]) ).

thf(2135,plain,
    ! [SV561: $i,SV194: $i,SV704: $i] :
      ( ( ( ~ ( in @ SV704 @ SV194 )
          | ( singleton
            @ ( dsetconstr @ SV194
              @ ^ [SY3130: $i] :
                  ( ~ ( ~ $true
                      | ( SY3130 != SV561 ) )
                  | ~ ( ~ ~ $true
                      | ( SY3130 != SV704 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV561 @ SV194 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1932]) ).

thf(2136,plain,
    ! [SV562: $i,SV194: $i,SV705: $i] :
      ( ( ( ~ ( in @ SV705 @ SV194 )
          | ( singleton
            @ ( dsetconstr @ SV194
              @ ^ [SY3131: $i] :
                  ( ~ ( ~ $false
                      | ( SY3131 != SV562 ) )
                  | ~ ( ~ ~ $false
                      | ( SY3131 != SV705 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV562 @ SV194 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1933]) ).

thf(2137,plain,
    ! [SV196: $i,SV563: $i,SV422: $i,SV706: $i] :
      ( ( ( ~ ( in @ SV706 @ SV422 )
          | ( in @ ( kpair @ SV563 @ SV706 ) @ ( powerset @ ( powerset @ ( binunion @ SV196 @ SV422 ) ) ) ) )
        = $true )
      | ( ( in @ SV563 @ SV196 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1934]) ).

thf(2138,plain,
    ! [SV564: $i,SV423: $o,SV197: $i,SV707: $i] :
      ( ( ( ~ ( in @ SV707 @ SV197 )
          | ( in @ ( if @ SV197 @ SV423 @ SV564 @ SV707 ) @ SV197 ) )
        = $true )
      | ( ( in @ SV564 @ SV197 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1935]) ).

thf(2139,plain,
    ! [SV565: $i,SV197: $i,SV708: $i] :
      ( ( ( ~ ( in @ SV708 @ SV197 )
          | ( in @ ( if @ SV197 @ $true @ SV565 @ SV708 ) @ SV197 ) )
        = $true )
      | ( ( in @ SV565 @ SV197 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1936]) ).

thf(2140,plain,
    ! [SV566: $i,SV197: $i,SV709: $i] :
      ( ( ( ~ ( in @ SV709 @ SV197 )
          | ( in @ ( if @ SV197 @ $false @ SV566 @ SV709 ) @ SV197 ) )
        = $true )
      | ( ( in @ SV566 @ SV197 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1937]) ).

thf(2141,plain,
    ! [SV567: $i,SV424: $i,SV198: $i,SV710: $i] :
      ( ( ( ~ ( in @ SV710 @ SV198 )
          | ! [SY3132: $i] :
              ( ~ ( in @ SY3132 @ SV424 )
              | ~ ( in @ ( kpair @ SV710 @ SY3132 ) @ SV567 )
              | ( ( ap @ SV198 @ SV424 @ SV567 @ SV710 )
                = SY3132 ) ) )
        = $true )
      | ( ( in @ SV567 @ ( funcSet @ SV198 @ SV424 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1938]) ).

thf(2142,plain,
    ! [SV199: $i,SV568: $i > $i,SV425: $i] :
      ( ( ( ~ ( in @ ( sK23_SY3000 @ SV425 @ SV568 @ SV199 ) @ SV199 )
          | ( in @ ( SV568 @ ( sK23_SY3000 @ SV425 @ SV568 @ SV199 ) ) @ SV425 ) )
        = $false )
      | ( ( func @ SV199 @ SV425
          @ ( lam @ SV199 @ SV425
            @ ^ [SY3001: $i] : ( SV568 @ SY3001 ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[1939]) ).

thf(2143,plain,
    ! [SV200: $i,SV426: $i > $o] :
      ( ( ( ~ ( in @ ( sK16_SY2777 @ SV426 @ SV200 ) @ SV200 ) )
        = $false )
      | ( ( ~ ~ ! [SY2778: $i] :
                  ~ ~ ( ~ ( in @ SY2778 @ SV200 )
                      | ~ ( SV426 @ SY2778 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1940]) ).

thf(2144,plain,
    ! [SV200: $i,SV426: $i > $o] :
      ( ( ( ~ ( SV426 @ ( sK16_SY2777 @ SV426 @ SV200 ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2778: $i] :
                  ~ ~ ( ~ ( in @ SY2778 @ SV200 )
                      | ~ ( SV426 @ SY2778 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1940]) ).

thf(2145,plain,
    ! [SV569: $i,SV428: $i,SV202: $i,SV711: $i] :
      ( ( ( ~ ( in @ SV711 @ SV202 )
          | ( in @ ( ap @ SV202 @ SV428 @ SV569 @ SV711 ) @ SV428 ) )
        = $true )
      | ( ( in @ SV569 @ ( funcSet @ SV202 @ SV428 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1941]) ).

thf(2146,plain,
    ! [SV203: $i] :
      ( ( ( ~ ( in @ ( sK24_SY2355 @ SV203 ) @ SV203 ) )
        = $false )
      | ( ( SV203 = emptyset )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[1942]) ).

thf(2147,plain,
    ! [SV205: $i,SV430: $i] :
      ( ( ( ~ ( in @ SV430 @ ( setunion @ SV205 ) ) )
        = $true )
      | ( ( ~ ! [SY2781: $i] :
                ~ ~ ( ~ ( in @ SV430 @ SY2781 )
                    | ~ ( in @ SY2781 @ SV205 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1943]) ).

thf(2148,plain,
    ! [SV205: $i,SV430: $i] :
      ( ( ( ~ ~ ! [SY2782: $i] :
                  ~ ~ ( ~ ( in @ SV430 @ SY2782 )
                      | ~ ( in @ SY2782 @ SV205 ) ) )
        = $true )
      | ( ( in @ SV430 @ ( setunion @ SV205 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1944]) ).

thf(2149,plain,
    ! [SV712: $o,SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ( ~ ( in @ SV570 @ SV206 )
              | ~ ~ ( in @ SV570 @ SV431 )
              | SV712 )
          | ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | SV712 )
          | SV712 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[1945]) ).

thf(2150,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ( ~ ( in @ SV570 @ SV206 )
              | ~ ~ ( in @ SV570 @ SV431 )
              | $true )
          | ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | $true )
          | $true )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[1945]) ).

thf(2151,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ( ~ ( in @ SV570 @ SV206 )
              | ~ ~ ( in @ SV570 @ SV431 )
              | $false )
          | ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | $false )
          | $false )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[1945]) ).

thf(2152,plain,
    ! [SV432: $i,SV207: $i] :
      ( ( ( SV207 = SV432 )
        = $false )
      | ( ( subset @ SV207 @ SV432 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1946]) ).

thf(2153,plain,
    ! [SV208: $i,SV433: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK25_SY2785 @ SV433 @ SV208 ) @ SV208 )
                | ~ ( in @ SV433 @ ( sK25_SY2785 @ SV433 @ SV208 ) ) ) )
        = $false )
      | ( ( in @ SV433 @ ( setunion @ SV208 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[1947]) ).

thf(2154,plain,
    ! [SV713: $i > $o,SV659: $i > $o,SV434: $i,SV209: $i] :
      ( ( ( ~ ! [SY3133: $i] :
                ( ~ ( in @ SY3133 @ SV209 )
                | ! [SY3134: $i] :
                    ( ~ ( in @ SY3134 @ SV434 )
                    | ( SY3133 != SY3134 )
                    | ~ ( ~ ( ~ ( SV659 @ SY3133 )
                            | ( SV713 @ SY3134 ) )
                        | ~ ( ~ ( SV713 @ SY3134 )
                            | ( SV659 @ SY3133 ) ) ) ) )
          | ( ( dsetconstr @ SV209
              @ ^ [SY3097: $i] : ( SV659 @ SY3097 ) )
            = ( dsetconstr @ SV434
              @ ^ [SY3136: $i] : ( SV713 @ SY3136 ) ) ) )
        = $true )
      | ( ( SV209 = SV434 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1948]) ).

thf(2155,plain,
    ! [SV435: $i,SV714: $o,SV210: $i,SV571: $i] :
      ( ( ( ~ ( ( SV571 != SV210 )
              | SV714 )
          | ~ ( ~ ( in @ SV571 @ SV435 )
              | SV714 )
          | SV714 )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[1949]) ).

thf(2156,plain,
    ! [SV435: $i,SV210: $i,SV571: $i] :
      ( ( ( ~ ( ( SV571 != SV210 )
              | $true )
          | ~ ( ~ ( in @ SV571 @ SV435 )
              | $true )
          | $true )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[1949]) ).

thf(2157,plain,
    ! [SV435: $i,SV210: $i,SV571: $i] :
      ( ( ( ~ ( ( SV571 != SV210 )
              | $false )
          | ~ ( ~ ( in @ SV571 @ SV435 )
              | $false )
          | $false )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[1949]) ).

thf(2158,plain,
    ! [SV660: $i,SV211: $i > $o] :
      ( ( ( ~ ( ~ ( SV211 @ SV660 )
              | ~ ! [SY3099: $i] :
                    ( ~ ( SV211 @ SY3099 )
                    | ( SV660 = SY3099 ) ) ) )
        = $false )
      | ( ( ~ ! [SY2378: $i] :
                ~ ~ ( ~ ( SV211 @ SY2378 )
                    | ~ ! [SY2379: $i] :
                          ( ~ ( SV211 @ SY2379 )
                          | ( SY2378 = SY2379 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1950]) ).

thf(2159,plain,
    ! [SV572: $i,SV436: $i,SV212: $i,SV715: $i] :
      ( ( ( ~ ( in @ SV715 @ SV212 )
          | ( ( ap @ SV212 @ SV436 @ SV572 @ SV715 )
            = ( ap @ SV212 @ SV436 @ SV572 @ SV715 ) ) )
        = $true )
      | ( ( in @ SV572 @ ( funcSet @ SV212 @ SV436 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1951]) ).

thf(2160,plain,
    ! [SV437: $i,SV213: $i,SV661: $i] :
      ( ( ( ~ ( in @ SV661 @ SV213 ) )
        = $true )
      | ( ( ~ ( in @ SV661 @ ( setminus @ SV213 @ ( setminus @ SV213 @ SV437 ) ) )
          | ( in @ SV661 @ SV437 ) )
        = $true )
      | ( ( in @ SV437 @ ( powerset @ SV213 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1952]) ).

thf(2161,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ( ( sK17_SY2797 @ SV438 @ SV214 )
           != ( sK26_SY3100 @ SV214 @ SV438 ) )
          | ~ ( ~ ( ~ ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
                  | ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) ) )
              | ~ ( ~ ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
                  | ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) ) ) ) )
        = $false )
      | ( ( ~ ( ~ ( ~ ~ ! [SY2388: $i] :
                          ~ ~ ( ~ ( SV214 @ SY2388 )
                              | ~ ! [SY2389: $i] :
                                    ( ~ ( SV214 @ SY2389 )
                                    | ( SY2388 = SY2389 ) ) )
                  | ~ ! [SY2801: $i] :
                        ~ ~ ( ~ ( SV438 @ SY2801 )
                            | ~ ! [SY2802: $i] :
                                  ( ~ ( SV438 @ SY2802 )
                                  | ( SY2801 = SY2802 ) ) ) )
              | ~ ( ~ ~ ! [SY2803: $i] :
                          ~ ~ ( ~ ( SV438 @ SY2803 )
                              | ~ ! [SY2804: $i] :
                                    ( ~ ( SV438 @ SY2804 )
                                    | ( SY2803 = SY2804 ) ) )
                  | ~ ! [SY2394: $i] :
                        ~ ~ ( ~ ( SV214 @ SY2394 )
                            | ~ ! [SY2395: $i] :
                                  ( ~ ( SV214 @ SY2395 )
                                  | ( SY2394 = SY2395 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[1953]) ).

thf(2162,plain,
    ! [SV215: $i,SV439: $i > $o] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK27_SY2808 @ SV439 @ SV215 ) @ SV215 )
                | ~ ( SV439 @ ( sK27_SY2808 @ SV439 @ SV215 ) ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV215
            @ ^ [SY2807: $i] : ( SV439 @ SY2807 ) ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[1954]) ).

thf(2163,plain,
    ! [SV216: $i,SV573: $i,SV440: $i > $o] :
      ( ( ( ~ ( SV440 @ SV573 ) )
        = $true )
      | ( ( ~ ! [SY3006: $i] :
                ( ~ ( in @ SY3006 @ SV216 )
                | ~ ( SV440 @ SY3006 )
                | ( SY3006 = SV573 ) )
          | ( singleton
            @ ( dsetconstr @ SV216
              @ ^ [SY2811: $i] : ( SV440 @ SY2811 ) ) ) )
        = $true )
      | ( ( in @ SV573 @ SV216 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1955]) ).

thf(2164,plain,
    ! [SV218: $i,SV574: $i,SV442: $i,SV716: $i] :
      ( ( ( ~ ( in @ SV716 @ SV442 )
          | ( subset @ ( setadjoin @ ( setadjoin @ SV574 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV574 @ ( setadjoin @ SV716 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV218 @ SV442 ) ) ) )
        = $true )
      | ( ( in @ SV574 @ SV218 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1956]) ).

thf(2165,plain,
    ! [SV219: $i,SV575: $i,SV443: $i,SV717: $i] :
      ( ( ( ~ ( in @ SV717 @ SV443 )
          | ( ( ksnd @ ( kpair @ SV575 @ SV717 ) )
            = SV717 ) )
        = $true )
      | ( ( in @ SV575 @ SV219 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1957]) ).

thf(2166,plain,
    ! [SV576: $i,SV444: $o,SV220: $i,SV718: $i] :
      ( ( ( ~ ( in @ SV718 @ SV220 )
          | ~ SV444
          | ( ( dsetconstr @ SV220
              @ ^ [SY3137: $i] :
                  ( ~ ( ~ SV444
                      | ( SY3137 != SV576 ) )
                  | ~ ( ~ ~ SV444
                      | ( SY3137 != SV718 ) ) ) )
            = ( setadjoin @ SV576 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV576 @ SV220 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1958]) ).

thf(2167,plain,
    ! [SV577: $i,SV220: $i,SV719: $i] :
      ( ( ( ~ ( in @ SV719 @ SV220 )
          | ~ $true
          | ( ( dsetconstr @ SV220
              @ ^ [SY3138: $i] :
                  ( ~ ( ~ $true
                      | ( SY3138 != SV577 ) )
                  | ~ ( ~ ~ $true
                      | ( SY3138 != SV719 ) ) ) )
            = ( setadjoin @ SV577 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV577 @ SV220 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1959]) ).

thf(2168,plain,
    ! [SV578: $i,SV220: $i,SV720: $i] :
      ( ( ( ~ ( in @ SV720 @ SV220 )
          | ~ $false
          | ( ( dsetconstr @ SV220
              @ ^ [SY3139: $i] :
                  ( ~ ( ~ $false
                      | ( SY3139 != SV578 ) )
                  | ~ ( ~ ~ $false
                      | ( SY3139 != SV720 ) ) ) )
            = ( setadjoin @ SV578 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV578 @ SV220 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1960]) ).

thf(2169,plain,
    ! [SV579: $i,SV445: $i,SV221: $i,SV721: $i] :
      ( ( ( ~ ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
          | ~ ! [SY3140: $i] :
                ( ~ ( in @ SY3140 @ SV221 )
                | ! [SY3141: $i] :
                    ( ~ ( in @ SY3141 @ SV445 )
                    | ~ ( in @ ( kpair @ SY3140 @ SY3141 ) @ SV579 )
                    | ( in @ ( kpair @ SY3140 @ SY3141 ) @ SV721 ) ) )
          | ~ ! [SY3142: $i] :
                ( ~ ( in @ SY3142 @ SV221 )
                | ! [SY3143: $i] :
                    ( ~ ( in @ SY3143 @ SV445 )
                    | ~ ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV721 )
                    | ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV579 ) ) )
          | ( SV579 = SV721 ) )
        = $true )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1961]) ).

thf(2170,plain,
    ! [SV580: $i,SV446: $i,SV222: $i,SV722: $i] :
      ( ( ( ~ ( in @ SV722 @ SV222 )
          | ( singleton
            @ ( dsetconstr @ SV446
              @ ^ [SY3144: $i] : ( in @ ( kpair @ SV722 @ SY3144 ) @ SV580 ) ) ) )
        = $true )
      | ( ( func @ SV222 @ SV446 @ SV580 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1962]) ).

thf(2171,plain,
    ! [SV224: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK28_SY2426 @ SV224 ) @ SV224 )
                | ~ $true ) )
        = $false )
      | ( ( SV224 = emptyset )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[1963]) ).

thf(2172,plain,
    ! [SV225: $i,SV448: $i,SV581: $i] :
      ( ( ( ~ ( subset @ SV581 @ SV448 ) )
        = $true )
      | ( ( subset @ SV581 @ ( binintersect @ SV225 @ SV448 ) )
        = $true )
      | ( ( subset @ SV581 @ SV225 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1964]) ).

thf(2173,plain,
    ! [SV226: $i,SV449: $i,SV582: $i] :
      ( ( ( ~ ~ ( in @ SV582 @ SV449 ) )
        = $true )
      | ( ( in @ SV582 @ ( symdiff @ SV226 @ SV449 ) )
        = $true )
      | ( ( in @ SV582 @ SV226 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1965]) ).

thf(2174,plain,
    ! [SV450: $i,SV227: $i,SV662: $i] :
      ( ( ( ~ ( in @ SV662 @ ( powerset @ SV227 ) ) )
        = $true )
      | ( ( ~ ( subset @ ( setminus @ SV227 @ SV662 ) @ ( setminus @ SV227 @ SV450 ) )
          | ( subset @ SV450 @ SV662 ) )
        = $true )
      | ( ( in @ SV450 @ ( powerset @ SV227 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1966]) ).

thf(2175,plain,
    ! [SV451: $i,SV228: $i,SV663: $i] :
      ( ( ( ~ ( in @ SV663 @ ( powerset @ SV228 ) ) )
        = $true )
      | ( ( ! [SY3101: $i] :
              ( ~ ( in @ SY3101 @ ( powerset @ SV228 ) )
              | ! [SY3102: $i] :
                  ( ~ ( in @ SY3102 @ SV228 )
                  | ~ ( in @ SY3102 @ ( binintersect @ SV451 @ SV663 ) )
                  | ( in @ SY3102 @ ( binunion @ SV663 @ SY3101 ) ) ) ) )
        = $true )
      | ( ( in @ SV451 @ ( powerset @ SV228 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1967]) ).

thf(2176,plain,
    ! [SV583: $i,SV453: $o,SV230: $i,SV723: $i] :
      ( ( ( ~ ( in @ SV723 @ SV230 )
          | ~ ~ SV453
          | ( ( dsetconstr @ SV230
              @ ^ [SY3145: $i] :
                  ( ~ ( ~ SV453
                      | ( SY3145 != SV583 ) )
                  | ~ ( ~ ~ SV453
                      | ( SY3145 != SV723 ) ) ) )
            = ( setadjoin @ SV723 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV583 @ SV230 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1968]) ).

thf(2177,plain,
    ! [SV584: $i,SV230: $i,SV724: $i] :
      ( ( ( ~ ( in @ SV724 @ SV230 )
          | ~ ~ $true
          | ( ( dsetconstr @ SV230
              @ ^ [SY3146: $i] :
                  ( ~ ( ~ $true
                      | ( SY3146 != SV584 ) )
                  | ~ ( ~ ~ $true
                      | ( SY3146 != SV724 ) ) ) )
            = ( setadjoin @ SV724 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV584 @ SV230 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1969]) ).

thf(2178,plain,
    ! [SV585: $i,SV230: $i,SV725: $i] :
      ( ( ( ~ ( in @ SV725 @ SV230 )
          | ~ ~ $false
          | ( ( dsetconstr @ SV230
              @ ^ [SY3147: $i] :
                  ( ~ ( ~ $false
                      | ( SY3147 != SV585 ) )
                  | ~ ( ~ ~ $false
                      | ( SY3147 != SV725 ) ) ) )
            = ( setadjoin @ SV725 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV585 @ SV230 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1970]) ).

thf(2179,plain,
    ! [SV454: $i,SV231: $i,SV664: $i] :
      ( ( ( ~ ( in @ SV664 @ ( powerset @ SV231 ) ) )
        = $true )
      | ( ( ~ ! [SY3103: $i] :
                ( ~ ( in @ SY3103 @ SV231 )
                | ~ ( in @ SY3103 @ SV454 )
                | ( in @ SY3103 @ SV664 ) )
          | ( in @ SV454 @ ( powerset @ SV664 ) ) )
        = $true )
      | ( ( in @ SV454 @ ( powerset @ SV231 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1971]) ).

thf(2180,plain,
    ! [SV236: $i,SV588: $i,SV459: $i] :
      ( ( ( ~ ( subset @ SV459 @ SV588 ) )
        = $true )
      | ( ( subset @ SV236 @ SV588 )
        = $true )
      | ( ( subset @ SV236 @ SV459 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1974]) ).

thf(2181,plain,
    ! [SV617: $i,SV590: $i,SV462: $i,SV239: $i] :
      ( ( ( ( setadjoin @ ( setadjoin @ SV239 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV239 @ ( setadjoin @ SV462 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ SV590 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV590 @ ( setadjoin @ SV617 @ emptyset ) ) @ emptyset ) ) )
        = $false )
      | ( ( SV239 = SV590 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1976]) ).

thf(2182,plain,
    ! [SV465: $i,SV242: $i,SV593: $i] :
      ( ( ( in @ SV593 @ SV242 )
        = $true )
      | ( ( ~ ( in @ SV593 @ ( setminus @ SV242 @ SV465 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1979]) ).

thf(2183,plain,
    ! [SV466: $i,SV243: $i,SV665: $i] :
      ( ( ( ~ ( in @ SV665 @ ( powerset @ SV243 ) ) )
        = $true )
      | ( ( ~ ! [SY3104: $i] :
                ( ~ ( in @ SY3104 @ SV243 )
                | ~ ( in @ SY3104 @ SV466 )
                | ( in @ SY3104 @ SV665 ) )
          | ( subset @ SV466 @ SV665 ) )
        = $true )
      | ( ( in @ SV466 @ ( powerset @ SV243 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1980]) ).

thf(2184,plain,
    ! [SV244: $i,SV594: $i > $i,SV467: $i] :
      ( ( ( ~ ( in @ ( sK29_SY3031 @ SV467 @ SV594 @ SV244 ) @ SV244 )
          | ( in @ ( SV594 @ ( sK29_SY3031 @ SV467 @ SV594 @ SV244 ) ) @ SV467 ) )
        = $false )
      | ( ( ! [SY3032: $i] :
              ( ~ ( in @ SY3032 @ SV244 )
              | ( ( ap @ SV244 @ SV467
                  @ ( lam @ SV244 @ SV467
                    @ ^ [SY3033: $i] : ( SV594 @ SY3033 ) )
                  @ SY3032 )
                = ( SV594 @ SY3032 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[1981]) ).

thf(2185,plain,
    ! [SV595: $i,SV468: $i,SV245: $i,SV726: $i] :
      ( ( ( ~ ( in @ SV726 @ SV245 )
          | ( in @ ( kpair @ SV726 @ ( ap @ SV245 @ SV468 @ SV595 @ SV726 ) ) @ SV595 ) )
        = $true )
      | ( ( in @ SV595 @ ( funcSet @ SV245 @ SV468 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1982]) ).

thf(2186,plain,
    ! [SV469: $i,SV246: $i,SV666: $i] :
      ( ( ( ~ ( in @ SV666 @ ( powerset @ SV246 ) ) )
        = $true )
      | ( ( ! [SY3105: $i] :
              ( ~ ( in @ SY3105 @ SV246 )
              | ~ ( in @ SY3105 @ ( setminus @ SV246 @ SV469 ) )
              | ~ ( in @ SY3105 @ ( binintersect @ SV469 @ SV666 ) ) ) )
        = $true )
      | ( ( in @ SV469 @ ( powerset @ SV246 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1983]) ).

thf(2187,plain,
    ! [SV471: $i,SV249: $i,SV596: $i] :
      ( ( ( in @ SV596 @ ( setminus @ SV249 @ SV471 ) )
        = $false )
      | ( ( in @ SV596 @ SV471 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1984]) ).

thf(2188,plain,
    ! [SV250: $i,SV618: $i] :
      ( ( ( in @ SV618 @ SV250 )
        = $false )
      | ( ( ( setunion @ SV250 )
          = SV618 )
        = $true )
      | ( ( singleton @ SV250 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1985]) ).

thf(2189,plain,
    ! [SV251: $i,SV597: $i,SV472: $i,SV727: $i] :
      ( ( ( ~ ( in @ SV727 @ SV472 )
          | ( in @ ( setadjoin @ SV597 @ ( setadjoin @ SV727 @ emptyset ) ) @ ( powerset @ ( binunion @ SV251 @ SV472 ) ) ) )
        = $true )
      | ( ( in @ SV597 @ SV251 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1986]) ).

thf(2190,plain,
    ! [SV473: $i,SV252: $i,SV598: $i] :
      ( ( ( in @ SV598 @ SV252 )
        = $true )
      | ( ( in @ SV598 @ SV473 )
        = $true )
      | ( ( in @ SV598 @ ( binunion @ SV252 @ SV473 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1987]) ).

thf(2191,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ! [SY3106: $i] :
              ~ ( ~ ( ~ ( SV253 @ SY3106 )
                    | ( SY3106 = SV667 ) )
                | ~ ( ( SY3106 != SV667 )
                    | ( SV253 @ SY3106 ) ) ) )
        = $false )
      | ( ( ~ ! [SY2491: $i] :
                ~ ~ ( ~ ( SV253 @ SY2491 )
                    | ~ ! [SY2492: $i] :
                          ( ~ ( SV253 @ SY2492 )
                          | ( SY2491 = SY2492 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1988]) ).

thf(2192,plain,
    ! [SV668: $o,SV255: $i,SV475: $i] :
      ( ( ( ~ ! [SY3107: $i] :
                ( ~ ( in @ SV475 @ SY3107 )
                | ~ ( in @ SY3107 @ SV255 )
                | SV668 ) )
        = $true )
      | ( SV668 = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1990]) ).

thf(2193,plain,
    ! [SV255: $i,SV475: $i] :
      ( ( ( ~ ! [SX0: $i] :
                ( ~ ( in @ SV475 @ SX0 )
                | ~ ( in @ SX0 @ SV255 )
                | $true ) )
        = $true )
      | ( $true = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1991]) ).

thf(2194,plain,
    ! [SV255: $i,SV475: $i] :
      ( ( ( ~ ! [SX0: $i] :
                ( ~ ( in @ SV475 @ SX0 )
                | ~ ( in @ SX0 @ SV255 )
                | $false ) )
        = $true )
      | ( $false = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1992]) ).

thf(2195,plain,
    ! [SV600: $i,SV476: $o,SV256: $i,SV728: $i] :
      ( ( ( ~ ( in @ SV728 @ SV256 )
          | ( in @ ( if @ SV256 @ SV476 @ SV600 @ SV728 ) @ ( setadjoin @ SV600 @ ( setadjoin @ SV728 @ emptyset ) ) ) )
        = $true )
      | ( ( in @ SV600 @ SV256 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1993]) ).

thf(2196,plain,
    ! [SV601: $i,SV256: $i,SV729: $i] :
      ( ( ( ~ ( in @ SV729 @ SV256 )
          | ( in @ ( if @ SV256 @ $true @ SV601 @ SV729 ) @ ( setadjoin @ SV601 @ ( setadjoin @ SV729 @ emptyset ) ) ) )
        = $true )
      | ( ( in @ SV601 @ SV256 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1994]) ).

thf(2197,plain,
    ! [SV602: $i,SV256: $i,SV730: $i] :
      ( ( ( ~ ( in @ SV730 @ SV256 )
          | ( in @ ( if @ SV256 @ $false @ SV602 @ SV730 ) @ ( setadjoin @ SV602 @ ( setadjoin @ SV730 @ emptyset ) ) ) )
        = $true )
      | ( ( in @ SV602 @ SV256 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1995]) ).

thf(2198,plain,
    ! [SV257: $i,SV603: $i,SV477: $i,SV731: $i] :
      ( ( ( ~ ( in @ SV731 @ SV477 )
          | ( subset @ ( setadjoin @ SV603 @ ( setadjoin @ SV731 @ emptyset ) ) @ ( binunion @ SV257 @ SV477 ) ) )
        = $true )
      | ( ( in @ SV603 @ SV257 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1996]) ).

thf(2199,plain,
    ! [SV35: $i,SV281: $i > $o] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK30_SY2514 @ SV281 @ SV35 ) @ SV35 )
                | ~ ( SV281 @ ( sK30_SY2514 @ SV281 @ SV35 ) ) ) )
        = $false )
      | ( ( ! [SY2515: $i] :
              ( ~ ( in @ SY2515 @ SV35 )
              | ~ ( SV281 @ SY2515 ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[1997]) ).

thf(2200,plain,
    ! [SV282: $i,SV36: $i,SV619: $i] :
      ( ( ( in @ SV619 @ ( powerset @ SV36 ) )
        = $false )
      | ( ( ! [SY3055: $i] :
              ( ~ ( in @ SY3055 @ SV36 )
              | ~ ( subset @ SV282 @ SV619 )
              | ~ ~ ( in @ SY3055 @ SV619 )
              | ~ ( in @ SY3055 @ SV282 ) ) )
        = $true )
      | ( ( in @ SV282 @ ( powerset @ SV36 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1998]) ).

thf(2201,plain,
    ! [SV620: $i,SV37: $i > $o] :
      ( ( ( ~ ( SV37 @ SV620 )
          | ~ ! [SY3056: $i] :
                ( ~ ( SV37 @ SY3056 )
                | ( SV620 = SY3056 ) ) )
        = $true )
      | ( ( ~ ! [SY1897: $i] :
                ~ ! [SY1898: $i] :
                    ~ ( ~ ( ~ ( SV37 @ SY1898 )
                          | ( SY1898 = SY1897 ) )
                      | ~ ( ( SY1898 != SY1897 )
                          | ( SV37 @ SY1898 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1999]) ).

thf(2202,plain,
    ! [SV482: $i,SV283: $i,SV38: $i,SV669: $i] :
      ( ( ( ~ ( in @ SV669 @ SV38 ) )
        = $true )
      | ( ( in @ ( kpair @ SV669 @ ( ap @ SV38 @ SV283 @ SV482 @ SV669 ) ) @ SV482 )
        = $true )
      | ( ( func @ SV38 @ SV283 @ SV482 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2000]) ).

thf(2203,plain,
    ! [SV483: $i,SV284: $o,SV40: $i,SV670: $i] :
      ( ( ( ~ ( in @ SV670 @ SV40 ) )
        = $true )
      | ( ( ~ ~ SV284
          | ( in @ SV670
            @ ( dsetconstr @ SV40
              @ ^ [SY3108: $i] :
                  ( ~ ( ~ SV284
                      | ( SY3108 != SV483 ) )
                  | ~ ( ~ ~ SV284
                      | ( SY3108 != SV670 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV483 @ SV40 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2001]) ).

thf(2204,plain,
    ! [SV484: $i,SV40: $i,SV671: $i] :
      ( ( ( ~ ( in @ SV671 @ SV40 ) )
        = $true )
      | ( ( ~ ~ $true
          | ( in @ SV671
            @ ( dsetconstr @ SV40
              @ ^ [SY3109: $i] :
                  ( ~ ( ~ $true
                      | ( SY3109 != SV484 ) )
                  | ~ ( ~ ~ $true
                      | ( SY3109 != SV671 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV484 @ SV40 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2002]) ).

thf(2205,plain,
    ! [SV485: $i,SV40: $i,SV672: $i] :
      ( ( ( ~ ( in @ SV672 @ SV40 ) )
        = $true )
      | ( ( ~ ~ $false
          | ( in @ SV672
            @ ( dsetconstr @ SV40
              @ ^ [SY3110: $i] :
                  ( ~ ( ~ $false
                      | ( SY3110 != SV485 ) )
                  | ~ ( ~ ~ $false
                      | ( SY3110 != SV672 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV485 @ SV40 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2003]) ).

thf(2206,plain,
    ! [SV621: $i,SV41: $i > $o] :
      ( ( ( ~ ( SV41 @ SV621 )
          | ~ ! [SY3057: $i] :
                ( ~ ( SV41 @ SY3057 )
                | ( SV621 = SY3057 ) ) )
        = $true )
      | ( ( ! [SY1909: $i,SY1910: $i] :
              ( ~ ( SV41 @ SY1909 )
              | ~ ( SV41 @ SY1910 )
              | ( SY1909 = SY1910 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2004]) ).

thf(2207,plain,
    ! [SV42: $i,SV285: $i] :
      ( ( ( in @ SV285 @ ( powerset @ SV42 ) )
        = $false )
      | ( ( ! [SY2523: $i] :
              ( ~ ( in @ SY2523 @ SV285 )
              | ( in @ SY2523 @ SV42 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2005]) ).

thf(2208,plain,
    ! [SV42: $i,SV285: $i] :
      ( ( ( ! [SY2524: $i] :
              ( ~ ( in @ SY2524 @ SV285 )
              | ( in @ SY2524 @ SV42 ) ) )
        = $false )
      | ( ( in @ SV285 @ ( powerset @ SV42 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2006]) ).

thf(2209,plain,
    ! [SV622: $i,SV43: $i > $o] :
      ( ( ( ~ ( SV43 @ SV622 )
          | ~ ! [SY3058: $i] :
                ( ~ ( SV43 @ SY3058 )
                | ( SV622 = SY3058 ) ) )
        = $true )
      | ( ( ! [SY1916: $i,SY1917: $i] :
              ( ~ ( SV43 @ SY1916 )
              | ~ ( SV43 @ SY1917 )
              | ( SY1916 = SY1917 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2007]) ).

thf(2210,plain,
    ! [SV286: $i,SV44: $i,SV623: $i] :
      ( ( ( in @ SV623 @ ( powerset @ SV44 ) )
        = $false )
      | ( ( ! [SY3059: $i] :
              ( ~ ( in @ SY3059 @ SV44 )
              | ~ ( in @ SY3059 @ ( setminus @ SV44 @ ( binunion @ SV286 @ SV623 ) ) )
              | ~ ( in @ SY3059 @ SV286 ) ) )
        = $true )
      | ( ( in @ SV286 @ ( powerset @ SV44 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2008]) ).

thf(2211,plain,
    ! [SV287: $i > $o,SV46: $i,SV673: $i] :
      ( ( ( ~ ( ~ ( in @ SV673 @ SV46 )
              | ~ ~ ( SV287 @ SV673 ) ) )
        = $false )
      | ( ( ~ ! [SY2528: $i] :
                ( ~ ( in @ SY2528 @ SV46 )
                | ( SV287 @ SY2528 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2009]) ).

thf(2212,plain,
    ! [SV288: $i,SV47: $i,SV486: $i] :
      ( ( ( ~ ( in @ SV486 @ SV47 ) )
        = $true )
      | ( ( in @ SV486 @ SV288 )
        = $true )
      | ( ( in @ SV486 @ ( setminus @ SV47 @ SV288 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2010]) ).

thf(2213,plain,
    ! [SV624: $i,SV48: $i > $o] :
      ( ( ( ~ ( SV48 @ SV624 )
          | ~ ! [SY3060: $i] :
                ( ~ ( SV48 @ SY3060 )
                | ( SV624 = SY3060 ) ) )
        = $true )
      | ( ( ~ ! [SY1928: $i] :
                ~ ~ ( ~ ( SV48 @ SY1928 )
                    | ~ ! [SY1929: $i] :
                          ( ~ ( SV48 @ SY1929 )
                          | ( SY1928 = SY1929 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2011]) ).

thf(2214,plain,
    ! [SV49: $i,SV289: $i,SV487: $i] :
      ( ( ( ~ ( in @ SV487 @ SV289 ) )
        = $false )
      | ( ( in @ SV487 @ ( setminus @ SV49 @ SV289 ) )
        = $true )
      | ( ( in @ SV487 @ SV49 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2012]) ).

thf(2215,plain,
    ! [SV50: $i,SV488: $i,SV290: $i,SV674: $i] :
      ( ( ( ~ ( in @ SV674 @ SV290 ) )
        = $true )
      | ( ( in @ ( setadjoin @ ( setadjoin @ SV488 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV488 @ ( setadjoin @ SV674 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV50 @ SV290 ) ) ) )
        = $true )
      | ( ( in @ SV488 @ SV50 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2013]) ).

thf(2216,plain,
    ! [SV51: $i,SV291: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV51 )
              | ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV291 ) ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV291 )
              | ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV51 ) ) )
        = $true )
      | ( ( SV51 = SV291 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2014]) ).

thf(2217,plain,
    ! [SV52: $i,SV292: $i > $o] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK31_SY2534 @ SV292 @ SV52 ) @ SV52 )
                | ~ ( SV292 @ ( sK31_SY2534 @ SV292 @ SV52 ) ) ) )
        = $false )
      | ( ( ! [SY2535: $i] :
              ( ~ ( in @ SY2535 @ SV52 )
              | ~ ( SV292 @ SY2535 ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2015]) ).

thf(2218,plain,
    ! [SV55: $i,SV295: $i,SV489: $i] :
      ( ( ( ~ ~ ( in @ SV489 @ SV295 ) )
        = $true )
      | ( ( ~ ( in @ SV489 @ ( symdiff @ SV55 @ SV295 ) ) )
        = $true )
      | ( ( in @ SV489 @ SV55 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2016]) ).

thf(2219,plain,
    ! [SV490: $i > $i > $o,SV296: $i,SV56: $i,SV625: $i,SV605: $i] :
      ( ( ( in @ ( kpair @ SV605 @ SV625 )
          @ ( dpsetconstr @ SV56 @ SV296
            @ ^ [SY2884: $i,SY2885: $i] : ( SV490 @ SY2884 @ SY2885 ) ) )
        = $false )
      | ( ( in @ SV625 @ SV296 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2017]) ).

thf(2220,plain,
    ! [SV60: $i,SV299: $i,SV493: $i] :
      ( ( ( in @ SV493 @ SV299 )
        = $false )
      | ( ( ~ ( in @ SV493 @ ( symdiff @ SV60 @ SV299 ) ) )
        = $true )
      | ( ( in @ SV493 @ SV60 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2019]) ).

thf(2221,plain,
    ! [SV62: $i,SV495: $i,SV301: $i,SV675: $i] :
      ( ( ( ~ ( in @ SV675 @ SV301 ) )
        = $true )
      | ( ( ( kpair @ SV495 @ SV675 )
          = ( kpair @ SV495 @ SV675 ) )
        = $true )
      | ( ( in @ SV495 @ SV62 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2021]) ).

thf(2222,plain,
    ! [SV676: $i > $o,SV496: $i,SV302: $i,SV63: $i] :
      ( ( ( ~ ! [SY3111: $i] :
                ( ~ ( in @ SY3111 @ SV63 )
                | ! [SY3112: $i] :
                    ( ~ ( in @ SY3112 @ SV302 )
                    | ~ ( in @ ( kpair @ SY3111 @ SY3112 ) @ SV496 )
                    | ( SV676 @ ( kpair @ SY3111 @ SY3112 ) ) ) ) )
        = $true )
      | ( ( ! [SY3113: $i] :
              ( ~ ( in @ SY3113 @ SV496 )
              | ( SV676 @ SY3113 ) ) )
        = $true )
      | ( ( subset @ SV496 @ ( cartprod @ SV63 @ SV302 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2022]) ).

thf(2223,plain,
    ! [SV65: $i,SV497: $i,SV303: $i > $o] :
      ( ( ( SV303 @ SV497 )
        = $false )
      | ( ( ( dsetconstr @ SV65
            @ ^ [SY2556: $i] : ( SV303 @ SY2556 ) )
         != emptyset )
        = $true )
      | ( ( in @ SV497 @ SV65 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2023]) ).

thf(2224,plain,
    ! [SV498: $i,SV305: $o,SV67: $i,SV677: $i] :
      ( ( ( ~ ( in @ SV677 @ SV67 ) )
        = $true )
      | ( ( ~ SV305
          | ( in @ SV498
            @ ( dsetconstr @ SV67
              @ ^ [SY3114: $i] :
                  ( ~ ( ~ SV305
                      | ( SY3114 != SV498 ) )
                  | ~ ( ~ ~ SV305
                      | ( SY3114 != SV677 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV498 @ SV67 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2024]) ).

thf(2225,plain,
    ! [SV499: $i,SV67: $i,SV678: $i] :
      ( ( ( ~ ( in @ SV678 @ SV67 ) )
        = $true )
      | ( ( ~ $true
          | ( in @ SV499
            @ ( dsetconstr @ SV67
              @ ^ [SY3115: $i] :
                  ( ~ ( ~ $true
                      | ( SY3115 != SV499 ) )
                  | ~ ( ~ ~ $true
                      | ( SY3115 != SV678 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV499 @ SV67 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2025]) ).

thf(2226,plain,
    ! [SV500: $i,SV67: $i,SV679: $i] :
      ( ( ( ~ ( in @ SV679 @ SV67 ) )
        = $true )
      | ( ( ~ $false
          | ( in @ SV500
            @ ( dsetconstr @ SV67
              @ ^ [SY3116: $i] :
                  ( ~ ( ~ $false
                      | ( SY3116 != SV500 ) )
                  | ~ ( ~ ~ $false
                      | ( SY3116 != SV679 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV500 @ SV67 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2026]) ).

thf(2227,plain,
    ! [SV501: $i,SV306: $i,SV68: $i,SV680: $i] :
      ( ( ( ~ ( in @ SV680 @ SV68 ) )
        = $true )
      | ( ( in
          @ ( setunion
            @ ( dsetconstr @ SV306
              @ ^ [SY3117: $i] : ( in @ ( kpair @ SV680 @ SY3117 ) @ SV501 ) ) )
          @ SV306 )
        = $true )
      | ( ( func @ SV68 @ SV306 @ SV501 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2027]) ).

thf(2228,plain,
    ! [SV310: $i,SV72: $i,SV626: $i] :
      ( ( ( in @ SV626 @ ( powerset @ SV72 ) )
        = $false )
      | ( ( ~ ( subset @ SV310 @ ( setminus @ SV72 @ SV626 ) )
          | ( subset @ SV626 @ ( setminus @ SV72 @ SV310 ) ) )
        = $true )
      | ( ( in @ SV310 @ ( powerset @ SV72 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2028]) ).

thf(2229,plain,
    ! [SV502: $i,SV311: $i,SV73: $i,SV681: $i] :
      ( ( ( ~ ( in @ SV681 @ ( funcSet @ SV73 @ SV311 ) ) )
        = $true )
      | ( ( ~ ! [SY3118: $i] :
                ( ~ ( in @ SY3118 @ SV73 )
                | ( ( ap @ SV73 @ SV311 @ SV502 @ SY3118 )
                  = ( ap @ SV73 @ SV311 @ SV681 @ SY3118 ) ) )
          | ( SV502 = SV681 ) )
        = $true )
      | ( ( in @ SV502 @ ( funcSet @ SV73 @ SV311 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2029]) ).

thf(2230,plain,
    ! [SV74: $i,SV312: $i,SV503: $i] :
      ( ( ( ~ ~ ( in @ SV503 @ SV312 ) )
        = $true )
      | ( ( ~ ( in @ SV503 @ SV74 ) )
        = $true )
      | ( ( in @ SV503 @ ( setminus @ SV74 @ SV312 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2030]) ).

thf(2231,plain,
    ! [SV313: $i,SV75: $i,SV504: $i] :
      ( ( ( ~ ( in @ SV504 @ ( setadjoin @ SV75 @ SV313 ) ) )
        = $true )
      | ( ( ( SV504 = SV75 )
          | ( in @ SV504 @ SV313 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2031]) ).

thf(2232,plain,
    ! [SV313: $i,SV75: $i,SV504: $i] :
      ( ( ( ~ ( ( SV504 = SV75 )
              | ( in @ SV504 @ SV313 ) ) )
        = $true )
      | ( ( in @ SV504 @ ( setadjoin @ SV75 @ SV313 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2032]) ).

thf(2233,plain,
    ! [SV314: $i,SV76: $i,SV627: $i] :
      ( ( ( in @ SV627 @ ( powerset @ SV76 ) )
        = $false )
      | ( ( ! [SY3063: $i] :
              ( ~ ( in @ SY3063 @ ( powerset @ SV76 ) )
              | ! [SY3064: $i] :
                  ( ~ ( in @ SY3064 @ SV76 )
                  | ~ ( in @ SY3064 @ ( binintersect @ SV314 @ SV627 ) )
                  | ( in @ SY3064 @ ( binintersect @ ( binunion @ SV314 @ SY3063 ) @ ( binunion @ SV627 @ SY3063 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV314 @ ( powerset @ SV76 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2033]) ).

thf(2234,plain,
    ! [SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ( sK7_SY2572 @ SV315 @ SV77 )
         != ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( ~ ~ ! [SY2001: $i] :
                  ~ ~ ( ~ ( SV77 @ SY2001 )
                      | ~ ! [SY2002: $i] :
                            ( ~ ( SV77 @ SY2002 )
                            | ( SY2001 = SY2002 ) ) )
          | ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2034]) ).

thf(2235,plain,
    ! [SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ~ ( ~ ( ~ ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
                  | ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) ) )
              | ~ ( ~ ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
                  | ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) ) ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2001: $i] :
                  ~ ~ ( ~ ( SV77 @ SY2001 )
                      | ~ ! [SY2002: $i] :
                            ( ~ ( SV77 @ SY2002 )
                            | ( SY2001 = SY2002 ) ) )
          | ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2034]) ).

thf(2236,plain,
    ! [SV78: $i,SV505: $i,SV316: $i > $o] :
      ( ( ( SV316 @ SV505 )
        = $false )
      | ( ( in @ SV505
          @ ( dsetconstr @ SV78
            @ ^ [SY2581: $i] : ( SV316 @ SY2581 ) ) )
        = $true )
      | ( ( in @ SV505 @ SV78 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2035]) ).

thf(2237,plain,
    ! [SV318: $i,SV80: $i,SV628: $i] :
      ( ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( ~ ! [SY3066: $i] :
                ( ~ ( in @ SY3066 @ SV80 )
                | ~ ( in @ SY3066 @ SV318 )
                | ( in @ SY3066 @ SV628 ) )
          | ~ ! [SY3067: $i] :
                ( ~ ( in @ SY3067 @ SV80 )
                | ~ ( in @ SY3067 @ SV628 )
                | ( in @ SY3067 @ SV318 ) )
          | ( SV318 = SV628 ) )
        = $true )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2036]) ).

thf(2238,plain,
    ! [SV81: $i,SV319: $i] :
      ( ( ( in @ ( sK8_SY2585 @ SV319 @ SV81 ) @ SV81 )
        = $true )
      | ( ( ~ ! [SY2586: $i] :
                ( ~ ( in @ SY2586 @ SV319 )
                | ( in @ SY2586 @ SV81 ) )
          | ( SV81 = SV319 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2037]) ).

thf(2239,plain,
    ! [SV81: $i,SV319: $i] :
      ( ( ( ~ ! [SY2586: $i] :
                ( ~ ( in @ SY2586 @ SV319 )
                | ( in @ SY2586 @ SV81 ) ) )
        = $true )
      | ( ( SV81 = SV319 )
        = $true )
      | ( ( in @ ( sK8_SY2585 @ SV319 @ SV81 ) @ SV319 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2038]) ).

thf(2240,plain,
    ! [SV506: $i > $i > $o,SV82: $i,SV608: $i,SV320: $i,SV732: $i] :
      ( ( ( ~ ( in @ SV732 @ SV320 )
          | ~ ( in @ ( kpair @ SV608 @ SV732 )
              @ ( dpsetconstr @ SV82 @ SV320
                @ ^ [SY2907: $i,SY2908: $i] : ( SV506 @ SY2907 @ SY2908 ) ) )
          | ( SV506 @ SV608 @ SV732 ) )
        = $true )
      | ( ( in @ SV608 @ SV82 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2039]) ).

thf(2241,plain,
    ! [SV321: $i > $o,SV84: $i,SV682: $i] :
      ( ( ( ~ ( in @ SV682 @ SV84 ) )
        = $true )
      | ( ( SV321 @ SV682 )
        = $true )
      | ( ( ~ ! [SY2593: $i] :
                ~ ~ ( ~ ( in @ SY2593 @ SV84 )
                    | ~ ~ ( SV321 @ SY2593 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2040]) ).

thf(2242,plain,
    ! [SV322: $i,SV609: $o,SV85: $i,SV507: $i] :
      ( ( ( ~ ( ~ ( in @ SV507 @ SV85 )
              | SV609 ) )
        = $true )
      | ( ( ~ ( ~ ( in @ SV507 @ SV322 )
              | SV609 )
          | SV609 )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2041]) ).

thf(2243,plain,
    ! [SV322: $i,SV85: $i,SV507: $i] :
      ( ( ( ~ ( ~ ( in @ SV507 @ SV85 )
              | $true ) )
        = $true )
      | ( ( ~ ( ~ ( in @ SV507 @ SV322 )
              | $true )
          | $true )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2042]) ).

thf(2244,plain,
    ! [SV322: $i,SV85: $i,SV507: $i] :
      ( ( ( ~ ( ~ ( in @ SV507 @ SV85 )
              | $false ) )
        = $true )
      | ( ( ~ ( ~ ( in @ SV507 @ SV322 )
              | $false )
          | $false )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2043]) ).

thf(2245,plain,
    ! [SV323: $i,SV86: $i,SV508: $i] :
      ( ( ( in @ SV508 @ SV86 )
        = $false )
      | ( ( in @ SV323 @ ( setunion @ SV86 ) )
        = $true )
      | ( ( in @ SV323 @ SV508 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2044]) ).

thf(2246,plain,
    ! [SV87: $i] :
      ( ( ( ! [SY2033: $i] :
              ( ~ ~ ( ~ ( in @ SY2033 @ omega )
                    | ~ ( in @ SY2033 @ SV87 ) )
              | ( in @ ( setadjoin @ SY2033 @ SY2033 ) @ SV87 ) ) )
        = $false )
      | ( ( in @ emptyset @ SV87 )
        = $false )
      | ( ( ! [SY2034: $i] :
              ( ~ ( in @ SY2034 @ omega )
              | ( in @ SY2034 @ SV87 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2045]) ).

thf(2247,plain,
    ( ( in @ sK9_SY2910 @ ( powerset @ sK1_SX0 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2046]) ).

thf(2248,plain,
    ( ( ~ ( in @ sK32_SY3068 @ sK1_SX0 )
      | ~ ( in @ sK32_SY3068 @ ( setminus @ sK1_SX0 @ ( binunion @ sK2_SY2597 @ sK9_SY2910 ) ) )
      | ( in @ sK32_SY3068 @ ( setminus @ sK1_SX0 @ sK2_SY2597 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[2047]) ).

thf(2249,plain,
    ! [SV324: $i,SV88: $i,SV629: $i] :
      ( ( ( in @ SV629 @ ( powerset @ SV88 ) )
        = $false )
      | ( ( ~ ( subset @ SV324 @ ( setminus @ SV88 @ SV629 ) )
          | ! [SY3069: $i] :
              ( ~ ( in @ SY3069 @ SV88 )
              | ~ ( in @ SY3069 @ SV629 )
              | ( in @ SY3069 @ ( setminus @ SV88 @ SV324 ) ) ) )
        = $true )
      | ( ( in @ SV324 @ ( powerset @ SV88 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2048]) ).

thf(2250,plain,
    ! [SV325: $i > $o,SV89: $i,SV683: $i] :
      ( ( ( ~ ( ~ ( in @ SV683 @ SV89 )
              | ~ ( SV325 @ SV683 ) ) )
        = $false )
      | ( ( ( ( dsetconstr @ SV89
              @ ^ [SY2603: $i] : ( SV325 @ SY2603 ) )
           != emptyset )
          | $false )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2049]) ).

thf(2251,plain,
    ! [SV90: $i,SV326: $i] :
      ( ( ( in @ ( sK10_SY2604 @ SV326 @ SV90 ) @ SV90 )
        = $true )
      | ( ( subset @ SV90 @ SV326 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2050]) ).

thf(2252,plain,
    ! [SV327: $i,SV91: $i,SV630: $i] :
      ( ( ( in @ SV630 @ ( powerset @ SV91 ) )
        = $false )
      | ( ( in @ ( binintersect @ SV327 @ SV630 ) @ ( powerset @ SV91 ) )
        = $true )
      | ( ( in @ SV327 @ ( powerset @ SV91 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2052]) ).

thf(2253,plain,
    ! [SV328: $i,SV92: $i,SV684: $i,SV631: $i] :
      ( ( ( SV631 != SV684 )
        = $true )
      | ( ( ~ ( in @ SV631 @ SV92 )
          | ( in @ SV684 @ SV328 ) )
        = $true )
      | ( ( SV92 = SV328 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2053]) ).

thf(2254,plain,
    ! [SV509: $i > $i > $o,SV329: $i,SV93: $i,SV632: $i,SV610: $i] :
      ( ( ( in @ ( kpair @ SV610 @ SV632 )
          @ ( dpsetconstr @ SV93 @ SV329
            @ ^ [SY2914: $i,SY2915: $i] : ( SV509 @ SY2914 @ SY2915 ) ) )
        = $false )
      | ( ( SV509 @ SV610 @ SV632 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2054]) ).

thf(2255,plain,
    ! [SV331: $i,SV95: $i,SV511: $i] :
      ( ( ( in @ SV511 @ SV95 )
        = $false )
      | ( ( in @ SV511 @ SV331 )
        = $true )
      | ( ( subset @ SV95 @ SV331 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2056]) ).

thf(2256,plain,
    ! [SV512: $i,SV685: $i,SV332: $i,SV96: $i] :
      ( ( ( ~ ( func @ SV96 @ SV332 @ SV685 ) )
        = $true )
      | ( ( ~ ! [SY3119: $i] :
                ( ~ ( in @ SY3119 @ SV96 )
                | ( ( ap @ SV96 @ SV332 @ SV512 @ SY3119 )
                  = ( ap @ SV96 @ SV332 @ SV685 @ SY3119 ) ) )
          | ! [SY3120: $i] :
              ( ~ ( in @ SY3120 @ SV96 )
              | ! [SY3121: $i] :
                  ( ~ ( in @ SY3121 @ SV332 )
                  | ~ ( in @ ( kpair @ SY3120 @ SY3121 ) @ SV685 )
                  | ( in @ ( kpair @ SY3120 @ SY3121 ) @ SV512 ) ) ) )
        = $true )
      | ( ( func @ SV96 @ SV332 @ SV512 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2057]) ).

thf(2257,plain,
    ! [SV98: $i,SV333: $i,SV513: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK33_SY2921 @ SV513 @ SV333 @ SV98 ) @ SV98 )
                | ~ ~ ! [SY3150: $i] :
                        ~ ~ ( ~ ( in @ SY3150 @ SV333 )
                            | ( SV513
                             != ( kpair @ ( sK33_SY2921 @ SV513 @ SV333 @ SV98 ) @ SY3150 ) ) ) ) )
        = $false )
      | ( ( in @ SV513 @ ( cartprod @ SV98 @ SV333 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2058]) ).

thf(2258,plain,
    ! [SV334: $i,SV99: $i,SV633: $i] :
      ( ( ( in @ SV633 @ ( powerset @ SV99 ) )
        = $false )
      | ( ( ! [SY3073: $i] :
              ( ~ ( in @ SY3073 @ SV99 )
              | ~ ( in @ SV334 @ ( powerset @ SV633 ) )
              | ~ ( in @ SY3073 @ SV334 )
              | ( in @ SY3073 @ SV633 ) ) )
        = $true )
      | ( ( in @ SV334 @ ( powerset @ SV99 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2059]) ).

thf(2259,plain,
    ! [SV102: $i,SV336: $i > $o] :
      ( ( ( in @ ( sK11_SY2627 @ SV336 @ SV102 ) @ SV102 )
        = $true )
      | ( ( ~ ~ ! [SY2629: $i] :
                  ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                      | ~ ( SV336 @ SY2629 ) )
          | ( singleton
            @ ( dsetconstr @ SV102
              @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2061]) ).

thf(2260,plain,
    ! [SV102: $i,SV336: $i > $o] :
      ( ( ( ~ ( in @ ( sK34_SY3074 @ SV336 @ SV102 ) @ SV102 )
          | ~ ( SV336 @ ( sK11_SY2627 @ SV336 @ SV102 ) )
          | ~ ( SV336 @ ( sK34_SY3074 @ SV336 @ SV102 ) )
          | ( ( sK11_SY2627 @ SV336 @ SV102 )
            = ( sK34_SY3074 @ SV336 @ SV102 ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2629: $i] :
                  ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                      | ~ ( SV336 @ SY2629 ) )
          | ( singleton
            @ ( dsetconstr @ SV102
              @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2062]) ).

thf(2261,plain,
    ! [SV515: $i > $i > $o,SV337: $i,SV103: $i,SV634: $i,SV612: $i] :
      ( ( ( in @ ( kpair @ SV612 @ SV634 )
          @ ( dpsetconstr @ SV103 @ SV337
            @ ^ [SY2925: $i,SY2926: $i] : ( SV515 @ SY2925 @ SY2926 ) ) )
        = $false )
      | ( ( in @ SV612 @ SV103 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2063]) ).

thf(2262,plain,
    ! [SV105: $i,SV516: $i > $i,SV339: $i] :
      ( ( ( ~ ( in @ ( sK19_SY2927 @ SV339 @ SV516 @ SV105 ) @ SV105 ) )
        = $false )
      | ( ( ( lam @ SV105 @ SV339
            @ ^ [SY2928: $i] : ( SV516 @ SY2928 ) )
          = ( lam @ SV105 @ SV339
            @ ^ [SY2929: $i] : ( SV516 @ SY2929 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2065]) ).

thf(2263,plain,
    ! [SV105: $i,SV339: $i,SV516: $i > $i] :
      ( ( ( in @ ( SV516 @ ( sK19_SY2927 @ SV339 @ SV516 @ SV105 ) ) @ SV339 )
        = $false )
      | ( ( ( lam @ SV105 @ SV339
            @ ^ [SY2928: $i] : ( SV516 @ SY2928 ) )
          = ( lam @ SV105 @ SV339
            @ ^ [SY2929: $i] : ( SV516 @ SY2929 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2065]) ).

thf(2264,plain,
    ! [SV107: $i,SV518: $i > $i,SV341: $i] :
      ( ( ( ~ ( in @ ( sK20_SY2930 @ SV341 @ SV518 @ SV107 ) @ SV107 ) )
        = $false )
      | ( ( in
          @ ( lam @ SV107 @ SV341
            @ ^ [SY2931: $i] : ( SV518 @ SY2931 ) )
          @ ( funcSet @ SV107 @ SV341 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2066]) ).

thf(2265,plain,
    ! [SV107: $i,SV341: $i,SV518: $i > $i] :
      ( ( ( in @ ( SV518 @ ( sK20_SY2930 @ SV341 @ SV518 @ SV107 ) ) @ SV341 )
        = $false )
      | ( ( in
          @ ( lam @ SV107 @ SV341
            @ ^ [SY2931: $i] : ( SV518 @ SY2931 ) )
          @ ( funcSet @ SV107 @ SV341 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2066]) ).

thf(2266,plain,
    ! [SV109: $i] :
      ( ( ~ ( ~ ~ ( ~ ! [SY2932: $i] :
                        ( ~ ( in @ SY2932 @ ( sK3_SY2100 @ SV109 ) )
                        | ! [SY2102: $i] :
                            ( ~ ( in @ SY2102 @ SY2932 )
                            | ( in @ SY2102 @ SV109 ) ) )
                  | ~ ! [SY2934: $i,SY2935: $i] :
                        ( ~ ~ ( ~ ( in @ SY2934 @ SV109 )
                              | ~ ( in @ SY2935 @ SV109 ) )
                        | ~ ! [SY2936: $i] :
                              ( ~ ( in @ SY2936 @ ( sK3_SY2100 @ SV109 ) )
                              | ~ ( ~ ( ~ ( in @ SY2934 @ SY2936 )
                                      | ( in @ SY2935 @ SY2936 ) )
                                  | ~ ( ~ ( in @ SY2935 @ SY2936 )
                                      | ( in @ SY2934 @ SY2936 ) ) ) )
                        | ( SY2934 = SY2935 ) ) )
            | ~ ! [SY2937: $i,SY2938: $i] :
                  ( ~ ~ ( ~ ( in @ SY2937 @ ( sK3_SY2100 @ SV109 ) )
                        | ~ ( in @ SY2938 @ ( sK3_SY2100 @ SV109 ) ) )
                  | ! [SX4: $i] :
                      ( ~ ( in @ SX4 @ SY2937 )
                      | ( in @ SX4 @ SY2938 ) )
                  | ! [SX4: $i] :
                      ( ~ ( in @ SX4 @ SY2938 )
                      | ( in @ SX4 @ SY2937 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2067]) ).

thf(2267,plain,
    ! [SV109: $i] :
      ( ( ! [SY2941: $i] :
            ( ~ ~ ( ~ ! [SY2111: $i] :
                        ( ~ ( in @ SY2111 @ SY2941 )
                        | ( in @ SY2111 @ SV109 ) )
                  | ~ ~ ! [SX3: $i] :
                          ~ ( in @ SX3 @ SY2941 ) )
            | ~ ! [SY2944: $i] :
                  ~ ~ ! [SY2945: $i] :
                        ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY2944 @ ( sK3_SY2100 @ SV109 ) )
                                        | ~ ( in @ SY2945 @ SY2941 ) )
                                  | ~ ~ ~ ! [SX5: $i] :
                                            ~ ~ ( ~ ( in @ SX5 @ SY2944 )
                                                | ~ ( in @ SX5 @ SY2941 ) ) )
                            | ~ ! [SY2947: $i] :
                                  ( ~ ( in @ SY2947 @ ( sK3_SY2100 @ SV109 ) )
                                  | ! [SX6: $i] :
                                      ( ~ ( in @ SX6 @ SY2947 )
                                      | ( in @ SX6 @ SY2944 ) )
                                  | ( in @ SY2945 @ SY2947 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2068]) ).

thf(2268,plain,
    ! [SV635: $i,SV110: $i] :
      ( ( ( ! [SY2119: $i] :
              ~ ~ ( ~ ( in @ SY2119 @ SV110 )
                  | ~ ~ ~ ! [SY2120: $i] :
                            ~ ~ ( ~ ( in @ SY2120 @ SY2119 )
                                | ~ ( in @ SY2120 @ SV110 ) ) ) )
        = $false )
      | ( ( in @ SV635 @ SV110 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2069]) ).

thf(2269,plain,
    ! [SV636: $i,SV112: $i > $o] :
      ( ( ( ~ ( SV112 @ SV636 )
          | ~ ! [SY3077: $i] :
                ( ~ ( SV112 @ SY3077 )
                | ( SV636 = SY3077 ) ) )
        = $true )
      | ( ( ~ ! [SY2125: $i] :
                ~ ( SV112 @ SY2125 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2070]) ).

thf(2270,plain,
    ! [SV113: $i,SV344: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK35_SY2645 @ SV344 @ SV113 ) @ SV113 )
                | ~ ( in @ ( sK35_SY2645 @ SV344 @ SV113 ) @ SV344 ) ) )
        = $false )
      | ( ( ( binintersect @ SV113 @ SV344 )
          = emptyset )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2071]) ).

thf(2271,plain,
    ! [SV346: $i,SV116: $i,SV637: $i] :
      ( ( ( in @ SV637 @ ( powerset @ SV116 ) )
        = $false )
      | ( ( ! [SY3078: $i] :
              ( ~ ( in @ SY3078 @ SV116 )
              | ~ ~ ( in @ SY3078 @ ( binunion @ SV346 @ SV637 ) )
              | ~ ( in @ SY3078 @ SV346 ) ) )
        = $true )
      | ( ( in @ SV346 @ ( powerset @ SV116 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2072]) ).

thf(2272,plain,
    ! [SV520: $i,SV347: $o,SV118: $i,SV686: $i] :
      ( ( ( ~ ( in @ SV686 @ SV118 ) )
        = $true )
      | ( ( ~ ~ SV347
          | ( ( if @ SV118 @ SV347 @ SV520 @ SV686 )
            = SV686 ) )
        = $true )
      | ( ( in @ SV520 @ SV118 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2073]) ).

thf(2273,plain,
    ! [SV521: $i,SV118: $i,SV687: $i] :
      ( ( ( ~ ( in @ SV687 @ SV118 ) )
        = $true )
      | ( ( ~ ~ $true
          | ( ( if @ SV118 @ $true @ SV521 @ SV687 )
            = SV687 ) )
        = $true )
      | ( ( in @ SV521 @ SV118 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2074]) ).

thf(2274,plain,
    ! [SV522: $i,SV118: $i,SV688: $i] :
      ( ( ( ~ ( in @ SV688 @ SV118 ) )
        = $true )
      | ( ( ~ ~ $false
          | ( ( if @ SV118 @ $false @ SV522 @ SV688 )
            = SV688 ) )
        = $true )
      | ( ( in @ SV522 @ SV118 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2075]) ).

thf(2275,plain,
    ! [SV349: $i,SV121: $i,SV638: $i] :
      ( ( ( in @ SV638 @ SV121 )
        = $false )
      | ( ( ~ ~ ( in @ SV638 @ ( setminus @ SV121 @ SV349 ) )
          | ( in @ SV638 @ SV349 ) )
        = $true )
      | ( ( in @ SV349 @ ( powerset @ SV121 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2076]) ).

thf(2276,plain,
    ! [SV350: $i,SV122: $i,SV639: $i] :
      ( ( ( in @ SV639 @ ( powerset @ SV122 ) )
        = $false )
      | ( ( subset @ ( setminus @ SV122 @ SV350 ) @ ( setminus @ SV122 @ ( binintersect @ SV350 @ SV639 ) ) )
        = $true )
      | ( ( in @ SV350 @ ( powerset @ SV122 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2077]) ).

thf(2277,plain,
    ! [SV123: $i,SV351: $i,SV523: $i] :
      ( ( ( ~ ( in @ SV523 @ SV351 ) )
        = $false )
      | ( ( ~ ( in @ SV523 @ SV123 ) )
        = $true )
      | ( ( subset @ SV123 @ SV351 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2078]) ).

thf(2278,plain,
    ! [SV124: $i,SV524: $i > $i,SV352: $i] :
      ( ( ( ~ ( in @ ( sK21_SY2952 @ SV352 @ SV524 @ SV124 ) @ SV124 ) )
        = $false )
      | ( ( func @ SV124 @ SV352
          @ ( dpsetconstr @ SV124 @ SV352
            @ ^ [SY2953: $i,SY2954: $i] :
                ( ( SV524 @ SY2953 )
                = SY2954 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2079]) ).

thf(2279,plain,
    ! [SV124: $i,SV352: $i,SV524: $i > $i] :
      ( ( ( in @ ( SV524 @ ( sK21_SY2952 @ SV352 @ SV524 @ SV124 ) ) @ SV352 )
        = $false )
      | ( ( func @ SV124 @ SV352
          @ ( dpsetconstr @ SV124 @ SV352
            @ ^ [SY2953: $i,SY2954: $i] :
                ( ( SV524 @ SY2953 )
                = SY2954 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2079]) ).

thf(2280,plain,
    ! [SV125: $i,SV353: $i > $o] :
      ( ( ( in @ ( sK12_SY2657 @ SV353 @ SV125 ) @ SV125 )
        = $true )
      | ( ( ~ ~ ! [SY2659: $i] :
                  ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                      | ~ ( SV353 @ SY2659 ) )
          | ( singleton
            @ ( dsetconstr @ SV125
              @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2080]) ).

thf(2281,plain,
    ! [SV125: $i,SV353: $i > $o] :
      ( ( ( ~ ( in @ ( sK36_SY3079 @ SV353 @ SV125 ) @ SV125 )
          | ~ ( SV353 @ ( sK12_SY2657 @ SV353 @ SV125 ) )
          | ~ ( SV353 @ ( sK36_SY3079 @ SV353 @ SV125 ) )
          | ( ( sK12_SY2657 @ SV353 @ SV125 )
            = ( sK36_SY3079 @ SV353 @ SV125 ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2659: $i] :
                  ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                      | ~ ( SV353 @ SY2659 ) )
          | ( singleton
            @ ( dsetconstr @ SV125
              @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2081]) ).

thf(2282,plain,
    ! [SV126: $i,SV354: $i,SV525: $i] :
      ( ( ( ~ ( in @ SV525 @ SV354 ) )
        = $true )
      | ( ( in @ SV525 @ ( symdiff @ SV126 @ SV354 ) )
        = $true )
      | ( ( in @ SV525 @ SV126 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2082]) ).

thf(2283,plain,
    ! [SV356: $i,SV128: $i,SV640: $i] :
      ( ( ( in @ SV640 @ ( powerset @ SV128 ) )
        = $false )
      | ( ( in @ ( setminus @ SV128 @ SV356 ) @ ( powerset @ ( setminus @ SV128 @ ( binintersect @ SV356 @ SV640 ) ) ) )
        = $true )
      | ( ( in @ SV356 @ ( powerset @ SV128 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2084]) ).

thf(2284,plain,
    ! [SV357: $i,SV129: $i,SV641: $i] :
      ( ( ( in @ SV641 @ SV129 )
        = $false )
      | ( ( ~ ( in @ SV641 @ SV357 )
          | ~ ( in @ SV641 @ ( setminus @ SV129 @ SV357 ) ) )
        = $true )
      | ( ( in @ SV357 @ ( powerset @ SV129 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2085]) ).

thf(2285,plain,
    ! [SV360: $i,SV132: $i,SV642: $i] :
      ( ( ( in @ SV642 @ ( powerset @ SV132 ) )
        = $false )
      | ( ( ~ ( subset @ SV360 @ SV642 )
          | ( subset @ ( setminus @ SV132 @ SV642 ) @ ( setminus @ SV132 @ SV360 ) ) )
        = $true )
      | ( ( in @ SV360 @ ( powerset @ SV132 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2086]) ).

thf(2286,plain,
    ! [SV527: $i,SV361: $i,SV133: $i,SV689: $i] :
      ( ( ( ~ ( in @ SV689 @ SV133 ) )
        = $true )
      | ( ( ( ap @ SV133 @ SV361 @ SV527 @ SV689 )
          = ( ap @ SV133 @ SV361 @ SV527 @ SV689 ) )
        = $true )
      | ( ( func @ SV133 @ SV361 @ SV527 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2087]) ).

thf(2287,plain,
    ! [SV690: $i > $o,SV529: $i,SV363: $i,SV135: $i] :
      ( ( ( ~ ! [SY3122: $i] :
                ( ~ ( in @ SY3122 @ SV135 )
                | ! [SY3123: $i] :
                    ( ~ ( in @ SY3123 @ SV363 )
                    | ~ ( in @ ( kpair @ SY3122 @ SY3123 ) @ SV529 )
                    | ( SV690 @ ( kpair @ SY3122 @ SY3123 ) ) ) ) )
        = $true )
      | ( ( ! [SY3124: $i] :
              ( ~ ( in @ SY3124 @ SV529 )
              | ( SV690 @ SY3124 ) ) )
        = $true )
      | ( ( subset @ SV529 @ ( cartprod @ SV135 @ SV363 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2089]) ).

thf(2288,plain,
    ! [SV136: $i,SV364: $i,SV530: $i] :
      ( ( ( in @ SV530 @ SV364 )
        = $false )
      | ( ( in @ SV530 @ SV136 )
        = $true )
      | ( ( in @ SV364 @ ( powerset @ SV136 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2090]) ).

thf(2289,plain,
    ! [SV365: $i,SV137: $i,SV643: $i] :
      ( ( ( in @ SV643 @ ( powerset @ SV137 ) )
        = $false )
      | ( ( ! [SY3080: $i] :
              ( ~ ( in @ SY3080 @ SV137 )
              | ~ ~ ( in @ SY3080 @ SV643 )
              | ~ ( in @ SY3080 @ ( binintersect @ SV365 @ SV643 ) ) ) )
        = $true )
      | ( ( in @ SV365 @ ( powerset @ SV137 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2091]) ).

thf(2290,plain,
    ! [SV140: $i,SV531: $i,SV370: $i,SV691: $i] :
      ( ( ( ~ ( in @ SV691 @ SV370 ) )
        = $true )
      | ( ( in @ ( kpair @ SV531 @ SV691 ) @ ( cartprod @ SV140 @ SV370 ) )
        = $true )
      | ( ( in @ SV531 @ SV140 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2092]) ).

thf(2291,plain,
    ! [SV372: $i > $o,SV142: $i,SV644: $i] :
      ( ( ( in @ SV644 @ SV142 )
        = $false )
      | ( ( ! [SY3081: $i] :
              ( ~ ( in @ SY3081 @ SV142 )
              | ~ ( SV372 @ SV644 )
              | ~ ( SV372 @ SY3081 )
              | ( SV644 = SY3081 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV142
            @ ^ [SY2680: $i] : ( SV372 @ SY2680 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2093]) ).

thf(2292,plain,
    ! [SV144: $i,SV533: $i,SV374: $i,SV692: $i] :
      ( ( ( ~ ( in @ SV692 @ SV374 ) )
        = $true )
      | ( ( ( kfst @ ( kpair @ SV533 @ SV692 ) )
          = SV533 )
        = $true )
      | ( ( in @ SV533 @ SV144 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2094]) ).

thf(2293,plain,
    ! [SV377: $i,SV147: $i > $i > $o] :
      ( ( ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
        = $true )
      | ( ( ~ ! [SY2690: $i] :
                ~ ! [SY2691: $i] :
                    ~ ( ~ ( ~ ( in @ SY2691 @ SY2690 )
                          | ~ ! [SY2692: $i] :
                                ~ ~ ( ~ ( in @ SY2692 @ SV377 )
                                    | ~ ( SV147 @ SY2692 @ SY2691 ) ) )
                      | ~ ( ~ ~ ! [SY2693: $i] :
                                  ~ ~ ( ~ ( in @ SY2693 @ SV377 )
                                      | ~ ( SV147 @ SY2693 @ SY2691 ) )
                          | ( in @ SY2691 @ SY2690 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2096]) ).

thf(2294,plain,
    ! [SV377: $i,SV147: $i > $i > $o] :
      ( ( ( ! [SY3082: $i] :
              ~ ~ ( ~ ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SY3082 )
                  | ~ ! [SY3083: $i] :
                        ( ~ ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SY3083 )
                        | ( SY3082 = SY3083 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2690: $i] :
                ~ ! [SY2691: $i] :
                    ~ ( ~ ( ~ ( in @ SY2691 @ SY2690 )
                          | ~ ! [SY2692: $i] :
                                ~ ~ ( ~ ( in @ SY2692 @ SV377 )
                                    | ~ ( SV147 @ SY2692 @ SY2691 ) ) )
                      | ~ ( ~ ~ ! [SY2693: $i] :
                                  ~ ~ ( ~ ( in @ SY2693 @ SV377 )
                                      | ~ ( SV147 @ SY2693 @ SY2691 ) )
                          | ( in @ SY2691 @ SY2690 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2097]) ).

thf(2295,plain,
    ! [SV148: $i,SV378: $i] :
      ( ( ( in @ ( sK14_SY2694 @ SV378 @ SV148 ) @ SV148 )
        = $true )
      | ( ( subset @ SV148 @ SV378 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2098]) ).

thf(2296,plain,
    ! [SV381: $i,SV151: $i,SV645: $i] :
      ( ( ( in @ SV645 @ ( powerset @ SV151 ) )
        = $false )
      | ( ( ! [SY3084: $i] :
              ( ~ ( in @ SY3084 @ SV151 )
              | ~ ~ ( in @ SY3084 @ ( binunion @ SV381 @ SV645 ) )
              | ~ ( in @ SY3084 @ SV645 ) ) )
        = $true )
      | ( ( in @ SV381 @ ( powerset @ SV151 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2101]) ).

thf(2297,plain,
    ! [SV382: $i,SV152: $i,SV693: $i,SV646: $i] :
      ( ( ( SV646 != SV693 )
        = $true )
      | ( ( ( setadjoin @ SV152 @ SV646 )
          = ( setadjoin @ SV382 @ SV693 ) )
        = $true )
      | ( ( SV152 = SV382 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2102]) ).

thf(2298,plain,
    ! [SV385: $i,SV156: $i,SV647: $i] :
      ( ( ( in @ SV647 @ ( powerset @ SV156 ) )
        = $false )
      | ( ( ! [SY3086: $i] :
              ( ~ ( in @ SY3086 @ SV156 )
              | ~ ~ ( in @ SY3086 @ SV385 )
              | ~ ( in @ SY3086 @ ( binintersect @ SV385 @ SV647 ) ) ) )
        = $true )
      | ( ( in @ SV385 @ ( powerset @ SV156 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2103]) ).

thf(2299,plain,
    ! [SV648: $i,SV157: $i > $o] :
      ( ( ( ~ ( SV157 @ SV648 )
          | ~ ! [SY3087: $i] :
                ( ~ ( SV157 @ SY3087 )
                | ( SV648 = SY3087 ) ) )
        = $true )
      | ( ( SV157
          @ ( descr
            @ ^ [SY2227: $i] : ( SV157 @ SY2227 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2104]) ).

thf(2300,plain,
    ! [SV388: $i > $o,SV160: $i,SV694: $i] :
      ( ( ( ~ ( in @ SV694 @ SV160 ) )
        = $true )
      | ( ( SV388 @ SV694 )
        = $true )
      | ( ( ~ ! [SY2705: $i] :
                ~ ~ ( ~ ( in @ SY2705 @ SV160 )
                    | ~ ~ ( SV388 @ SY2705 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2106]) ).

thf(2301,plain,
    ! [SV389: $i,SV161: $i,SV649: $i] :
      ( ( ( in @ SV649 @ ( powerset @ SV161 ) )
        = $false )
      | ( ( ! [SY3088: $i] :
              ( ~ ( in @ SY3088 @ SV161 )
              | ~ ( in @ SY3088 @ ( setminus @ SV161 @ SV389 ) )
              | ( in @ SY3088 @ ( setminus @ SV161 @ ( binintersect @ SV389 @ SV649 ) ) ) ) )
        = $true )
      | ( ( in @ SV389 @ ( powerset @ SV161 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2107]) ).

thf(2302,plain,
    ! [SV390: $i,SV162: $i,SV650: $i] :
      ( ( ( in @ SV650 @ ( powerset @ SV162 ) )
        = $false )
      | ( ( in @ ( binunion @ SV390 @ SV650 ) @ ( powerset @ SV162 ) )
        = $true )
      | ( ( in @ SV390 @ ( powerset @ SV162 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2108]) ).

thf(2303,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( ~ ! [SY2242: $i,SY2243: $i] :
                ( ~ ( SV165 @ SY2242 )
                | ~ ( SV165 @ SY2243 )
                | ( SY2242 = SY2243 ) ) )
        = $true )
      | ( ( ~ ! [SY2244: $i] :
                ~ ~ ( ~ ( SV165 @ SY2244 )
                    | ~ ! [SY2245: $i] :
                          ( ~ ( SV165 @ SY2245 )
                          | ( SY2244 = SY2245 ) ) ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2109]) ).

thf(2304,plain,
    ! [SV166: $i,SV393: $i,SV538: $i] :
      ( ( ( ~ ( in @ SV538 @ SV393 ) )
        = $false )
      | ( ( ~ ( subset @ SV166 @ SV393 ) )
        = $true )
      | ( ( in @ SV538 @ SV166 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2110]) ).

thf(2305,plain,
    ! [SV394: $i,SV167: $i,SV652: $i] :
      ( ( ( in @ SV652 @ ( powerset @ SV167 ) )
        = $false )
      | ( ( ! [SY3089: $i] :
              ( ~ ( in @ SY3089 @ ( powerset @ SV167 ) )
              | ( in @ ( binintersect @ SV394 @ SV652 ) @ ( powerset @ ( binintersect @ ( binunion @ SV394 @ SY3089 ) @ ( binunion @ SV652 @ SY3089 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV394 @ ( powerset @ SV167 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2111]) ).

thf(2306,plain,
    ! [SV539: $i,SV395: $i,SV168: $i,SV695: $i] :
      ( ( ( ~ ( subset @ SV695 @ ( cartprod @ SV168 @ SV395 ) ) )
        = $true )
      | ( ( ~ ! [SY3125: $i] :
                ( ~ ( in @ SY3125 @ SV168 )
                | ! [SY3126: $i] :
                    ( ~ ( in @ SY3126 @ SV395 )
                    | ~ ( in @ ( kpair @ SY3125 @ SY3126 ) @ SV539 )
                    | ( in @ ( kpair @ SY3125 @ SY3126 ) @ SV695 ) ) )
          | ( subset @ SV539 @ SV695 ) )
        = $true )
      | ( ( subset @ SV539 @ ( cartprod @ SV168 @ SV395 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2112]) ).

thf(2307,plain,
    ! [SV540: $i,SV396: $o,SV169: $i,SV696: $i] :
      ( ( ( ~ ( in @ SV696 @ SV169 ) )
        = $true )
      | ( ( ~ SV396
          | ( ( if @ SV169 @ SV396 @ SV540 @ SV696 )
            = SV540 ) )
        = $true )
      | ( ( in @ SV540 @ SV169 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2113]) ).

thf(2308,plain,
    ! [SV541: $i,SV169: $i,SV697: $i] :
      ( ( ( ~ ( in @ SV697 @ SV169 ) )
        = $true )
      | ( ( ~ $true
          | ( ( if @ SV169 @ $true @ SV541 @ SV697 )
            = SV541 ) )
        = $true )
      | ( ( in @ SV541 @ SV169 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2114]) ).

thf(2309,plain,
    ! [SV542: $i,SV169: $i,SV698: $i] :
      ( ( ( ~ ( in @ SV698 @ SV169 ) )
        = $true )
      | ( ( ~ $false
          | ( ( if @ SV169 @ $false @ SV542 @ SV698 )
            = SV542 ) )
        = $true )
      | ( ( in @ SV542 @ SV169 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2115]) ).

thf(2310,plain,
    ! [SV170: $i,SV543: $i > $i,SV397: $i] :
      ( ( ( ~ ( in @ ( sK22_SY2969 @ SV397 @ SV543 @ SV170 ) @ SV170 ) )
        = $false )
      | ( ( ! [SY2970: $i] :
              ( ~ ( in @ SY2970 @ SV170 )
              | ( ( ap @ SV170 @ SV397
                  @ ( lam @ SV170 @ SV397
                    @ ^ [SY2971: $i] : ( SV543 @ SY2971 ) )
                  @ SY2970 )
                = ( SV543 @ SY2970 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2116]) ).

thf(2311,plain,
    ! [SV170: $i,SV397: $i,SV543: $i > $i] :
      ( ( ( in @ ( SV543 @ ( sK22_SY2969 @ SV397 @ SV543 @ SV170 ) ) @ SV397 )
        = $false )
      | ( ( ! [SY2970: $i] :
              ( ~ ( in @ SY2970 @ SV170 )
              | ( ( ap @ SV170 @ SV397
                  @ ( lam @ SV170 @ SV397
                    @ ^ [SY2971: $i] : ( SV543 @ SY2971 ) )
                  @ SY2970 )
                = ( SV543 @ SY2970 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2116]) ).

thf(2312,plain,
    ! [SV653: $i,SV171: $i] :
      ( ( ( SV171 = emptyset )
        = $false )
      | ( ( in @ SV653 @ SV171 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2117]) ).

thf(2313,plain,
    ! [SV174: $i,SV400: $i,SV614: $i,SV546: $i] :
      ( ( ( SV546 != SV614 )
        = $true )
      | ( ( SV400 = SV614 )
        = $true )
      | ( ( ( setadjoin @ ( setadjoin @ SV174 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV174 @ ( setadjoin @ SV400 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ SV546 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV546 @ ( setadjoin @ SV614 @ emptyset ) ) @ emptyset ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2118]) ).

thf(2314,plain,
    ! [SV548: $i,SV402: $i,SV176: $i,SV699: $i] :
      ( ( ( ~ ( in @ SV699 @ SV176 ) )
        = $true )
      | ( ( in @ ( ap @ SV176 @ SV402 @ SV548 @ SV699 ) @ SV402 )
        = $true )
      | ( ( func @ SV176 @ SV402 @ SV548 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2120]) ).

thf(2315,plain,
    ! [SV403: $i,SV177: $i,SV654: $i] :
      ( ( ( in @ SV654 @ ( powerset @ SV177 ) )
        = $false )
      | ( ( ! [SY3090: $i] :
              ( ~ ( in @ SY3090 @ SV177 )
              | ~ ( subset @ SV403 @ ( setminus @ SV177 @ SV654 ) )
              | ~ ( in @ SY3090 @ SV654 )
              | ~ ( in @ SY3090 @ SV403 ) ) )
        = $true )
      | ( ( in @ SV403 @ ( powerset @ SV177 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2121]) ).

thf(2316,plain,
    ! [SV178: $i,SV616: $i,SV549: $i > $i > $o,SV404: $i,SV733: $i] :
      ( ( ( ~ ( in @ SV733 @ SV404 )
          | ~ ( SV549 @ SV616 @ SV733 )
          | ( in @ ( kpair @ SV616 @ SV733 )
            @ ( dpsetconstr @ SV178 @ SV404
              @ ^ [SY2978: $i,SY2979: $i] : ( SV549 @ SY2978 @ SY2979 ) ) ) )
        = $true )
      | ( ( in @ SV616 @ SV178 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2122]) ).

thf(2317,plain,
    ! [SV179: $i,SV405: $i,SV550: $i] :
      ( ( ( ~ ( in @ SV550 @ SV405 ) )
        = $false )
      | ( ( SV179 != SV405 )
        = $true )
      | ( ( in @ SV550 @ SV179 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2123]) ).

thf(2318,plain,
    ! [SV180: $i,SV406: $i,SV551: $i] :
      ( ( ( in @ SV551 @ SV406 )
        = $false )
      | ( ( in @ SV551 @ ( binintersect @ SV180 @ SV406 ) )
        = $true )
      | ( ( in @ SV551 @ SV180 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2124]) ).

thf(2319,plain,
    ! [SV407: $i,SV181: $i] :
      ( ( ( in @ ( sK15_SY2740 @ SV181 @ SV407 ) @ SV407 )
        = $true )
      | ( ( in @ SV407 @ ( powerset @ SV181 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2125]) ).

thf(2320,plain,
    ! [SV408: $i,SV182: $i,SV655: $i] :
      ( ( ( in @ SV655 @ SV182 )
        = $false )
      | ( ( ~ ( in @ SV655 @ SV408 )
          | ( in @ SV655 @ ( setminus @ SV182 @ ( setminus @ SV182 @ SV408 ) ) ) )
        = $true )
      | ( ( in @ SV408 @ ( powerset @ SV182 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2127]) ).

thf(2321,plain,
    ! [SV554: $i,SV411: $i,SV185: $i,SV700: $i] :
      ( ( ( ~ ( in @ SV700 @ SV185 ) )
        = $true )
      | ( ( ! [SY3127: $i] :
              ( ~ ( in @ SY3127 @ SV411 )
              | ~ ( in @ ( kpair @ SV700 @ SY3127 ) @ SV554 )
              | ( ( ap @ SV185 @ SV411 @ SV554 @ SV700 )
                = SY3127 ) ) )
        = $true )
      | ( ( func @ SV185 @ SV411 @ SV554 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2128]) ).

thf(2322,plain,
    ! [SV412: $i,SV186: $i,SV656: $i] :
      ( ( ( in @ SV656 @ ( powerset @ SV186 ) )
        = $false )
      | ( ( in @ ( setminus @ SV412 @ SV656 ) @ ( powerset @ SV186 ) )
        = $true )
      | ( ( in @ SV412 @ ( powerset @ SV186 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2129]) ).

thf(2323,plain,
    ! [SV414: $i > $o,SV188: $i,SV556: $i] :
      ( ( ( ~ ( ~ ( in @ SV556
                  @ ( dsetconstr @ SV188
                    @ ^ [SY2751: $i] : ( SV414 @ SY2751 ) ) )
              | ( SV414 @ SV556 ) ) )
        = $false )
      | ( ( in @ SV556 @ SV188 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2130]) ).

thf(2324,plain,
    ! [SV188: $i,SV556: $i,SV414: $i > $o] :
      ( ( ( ~ ( ~ ( SV414 @ SV556 )
              | ( in @ SV556
                @ ( dsetconstr @ SV188
                  @ ^ [SY2752: $i] : ( SV414 @ SY2752 ) ) ) ) )
        = $false )
      | ( ( in @ SV556 @ SV188 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2130]) ).

thf(2325,plain,
    ! [SV558: $i,SV701: $i,SV416: $i,SV190: $i] :
      ( ( ( ~ ( func @ SV190 @ SV416 @ SV701 ) )
        = $true )
      | ( ( ~ ! [SY3128: $i] :
                ( ~ ( in @ SY3128 @ SV190 )
                | ( ( ap @ SV190 @ SV416 @ SV558 @ SY3128 )
                  = ( ap @ SV190 @ SV416 @ SV701 @ SY3128 ) ) )
          | ( SV558 = SV701 ) )
        = $true )
      | ( ( func @ SV190 @ SV416 @ SV558 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2131]) ).

thf(2326,plain,
    ! [SV417: $i,SV191: $i,SV657: $i] :
      ( ( ( in @ SV657 @ ( powerset @ SV191 ) )
        = $false )
      | ( ( ! [SY3091: $i] :
              ( ~ ( in @ SY3091 @ ( powerset @ SV191 ) )
              | ! [SY3092: $i] :
                  ( ~ ( in @ SY3092 @ SV191 )
                  | ~ ( in @ SY3092 @ ( binintersect @ SV417 @ SV657 ) )
                  | ( in @ SY3092 @ ( binunion @ SV417 @ SY3091 ) ) ) ) )
        = $true )
      | ( ( in @ SV417 @ ( powerset @ SV191 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2132]) ).

thf(2327,plain,
    ! [SV419: $i,SV193: $i,SV702: $i,SV658: $i] :
      ( ( ( SV658 != SV702 )
        = $true )
      | ( ( ~ ( ~ ( ~ ( in @ SV658 @ SV193 )
                  | ( in @ SV702 @ SV419 ) )
              | ~ ( ~ ( in @ SV702 @ SV419 )
                  | ( in @ SV658 @ SV193 ) ) ) )
        = $true )
      | ( ( SV193 = SV419 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2133]) ).

thf(2328,plain,
    ! [SV560: $i,SV420: $o,SV194: $i,SV703: $i] :
      ( ( ( ~ ( in @ SV703 @ SV194 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV194
            @ ^ [SY3129: $i] :
                ( ~ ( ~ SV420
                    | ( SY3129 != SV560 ) )
                | ~ ( ~ ~ SV420
                    | ( SY3129 != SV703 ) ) ) ) )
        = $true )
      | ( ( in @ SV560 @ SV194 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2134]) ).

thf(2329,plain,
    ! [SV561: $i,SV194: $i,SV704: $i] :
      ( ( ( ~ ( in @ SV704 @ SV194 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV194
            @ ^ [SY3130: $i] :
                ( ~ ( ~ $true
                    | ( SY3130 != SV561 ) )
                | ~ ( ~ ~ $true
                    | ( SY3130 != SV704 ) ) ) ) )
        = $true )
      | ( ( in @ SV561 @ SV194 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2135]) ).

thf(2330,plain,
    ! [SV562: $i,SV194: $i,SV705: $i] :
      ( ( ( ~ ( in @ SV705 @ SV194 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV194
            @ ^ [SY3131: $i] :
                ( ~ ( ~ $false
                    | ( SY3131 != SV562 ) )
                | ~ ( ~ ~ $false
                    | ( SY3131 != SV705 ) ) ) ) )
        = $true )
      | ( ( in @ SV562 @ SV194 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2136]) ).

thf(2331,plain,
    ! [SV196: $i,SV563: $i,SV422: $i,SV706: $i] :
      ( ( ( ~ ( in @ SV706 @ SV422 ) )
        = $true )
      | ( ( in @ ( kpair @ SV563 @ SV706 ) @ ( powerset @ ( powerset @ ( binunion @ SV196 @ SV422 ) ) ) )
        = $true )
      | ( ( in @ SV563 @ SV196 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2137]) ).

thf(2332,plain,
    ! [SV564: $i,SV423: $o,SV197: $i,SV707: $i] :
      ( ( ( ~ ( in @ SV707 @ SV197 ) )
        = $true )
      | ( ( in @ ( if @ SV197 @ SV423 @ SV564 @ SV707 ) @ SV197 )
        = $true )
      | ( ( in @ SV564 @ SV197 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2138]) ).

thf(2333,plain,
    ! [SV565: $i,SV197: $i,SV708: $i] :
      ( ( ( ~ ( in @ SV708 @ SV197 ) )
        = $true )
      | ( ( in @ ( if @ SV197 @ $true @ SV565 @ SV708 ) @ SV197 )
        = $true )
      | ( ( in @ SV565 @ SV197 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2139]) ).

thf(2334,plain,
    ! [SV566: $i,SV197: $i,SV709: $i] :
      ( ( ( ~ ( in @ SV709 @ SV197 ) )
        = $true )
      | ( ( in @ ( if @ SV197 @ $false @ SV566 @ SV709 ) @ SV197 )
        = $true )
      | ( ( in @ SV566 @ SV197 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2140]) ).

thf(2335,plain,
    ! [SV567: $i,SV424: $i,SV198: $i,SV710: $i] :
      ( ( ( ~ ( in @ SV710 @ SV198 ) )
        = $true )
      | ( ( ! [SY3132: $i] :
              ( ~ ( in @ SY3132 @ SV424 )
              | ~ ( in @ ( kpair @ SV710 @ SY3132 ) @ SV567 )
              | ( ( ap @ SV198 @ SV424 @ SV567 @ SV710 )
                = SY3132 ) ) )
        = $true )
      | ( ( in @ SV567 @ ( funcSet @ SV198 @ SV424 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2141]) ).

thf(2336,plain,
    ! [SV199: $i,SV568: $i > $i,SV425: $i] :
      ( ( ( ~ ( in @ ( sK23_SY3000 @ SV425 @ SV568 @ SV199 ) @ SV199 ) )
        = $false )
      | ( ( func @ SV199 @ SV425
          @ ( lam @ SV199 @ SV425
            @ ^ [SY3001: $i] : ( SV568 @ SY3001 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2142]) ).

thf(2337,plain,
    ! [SV199: $i,SV425: $i,SV568: $i > $i] :
      ( ( ( in @ ( SV568 @ ( sK23_SY3000 @ SV425 @ SV568 @ SV199 ) ) @ SV425 )
        = $false )
      | ( ( func @ SV199 @ SV425
          @ ( lam @ SV199 @ SV425
            @ ^ [SY3001: $i] : ( SV568 @ SY3001 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2142]) ).

thf(2338,plain,
    ! [SV200: $i,SV426: $i > $o] :
      ( ( ( in @ ( sK16_SY2777 @ SV426 @ SV200 ) @ SV200 )
        = $true )
      | ( ( ~ ~ ! [SY2778: $i] :
                  ~ ~ ( ~ ( in @ SY2778 @ SV200 )
                      | ~ ( SV426 @ SY2778 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2143]) ).

thf(2339,plain,
    ! [SV200: $i,SV426: $i > $o] :
      ( ( ( SV426 @ ( sK16_SY2777 @ SV426 @ SV200 ) )
        = $true )
      | ( ( ~ ~ ! [SY2778: $i] :
                  ~ ~ ( ~ ( in @ SY2778 @ SV200 )
                      | ~ ( SV426 @ SY2778 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2144]) ).

thf(2340,plain,
    ! [SV569: $i,SV428: $i,SV202: $i,SV711: $i] :
      ( ( ( ~ ( in @ SV711 @ SV202 ) )
        = $true )
      | ( ( in @ ( ap @ SV202 @ SV428 @ SV569 @ SV711 ) @ SV428 )
        = $true )
      | ( ( in @ SV569 @ ( funcSet @ SV202 @ SV428 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2145]) ).

thf(2341,plain,
    ! [SV203: $i] :
      ( ( ( in @ ( sK24_SY2355 @ SV203 ) @ SV203 )
        = $true )
      | ( ( SV203 = emptyset )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2146]) ).

thf(2342,plain,
    ! [SV205: $i,SV430: $i] :
      ( ( ( in @ SV430 @ ( setunion @ SV205 ) )
        = $false )
      | ( ( ~ ! [SY2781: $i] :
                ~ ~ ( ~ ( in @ SV430 @ SY2781 )
                    | ~ ( in @ SY2781 @ SV205 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2147]) ).

thf(2343,plain,
    ! [SV205: $i,SV430: $i] :
      ( ( ( ~ ! [SY2782: $i] :
                ~ ~ ( ~ ( in @ SV430 @ SY2782 )
                    | ~ ( in @ SY2782 @ SV205 ) ) )
        = $false )
      | ( ( in @ SV430 @ ( setunion @ SV205 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2148]) ).

thf(2344,plain,
    ! [SV712: $o,SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ( ~ ( in @ SV570 @ SV206 )
              | ~ ~ ( in @ SV570 @ SV431 )
              | SV712 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | SV712 )
          | SV712 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2149]) ).

thf(2345,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ( ~ ( in @ SV570 @ SV206 )
              | ~ ~ ( in @ SV570 @ SV431 )
              | $true ) )
        = $true )
      | ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | $true )
          | $true )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2150]) ).

thf(2346,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ( ~ ( in @ SV570 @ SV206 )
              | ~ ~ ( in @ SV570 @ SV431 )
              | $false ) )
        = $true )
      | ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | $false )
          | $false )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2151]) ).

thf(2347,plain,
    ! [SV208: $i,SV433: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK25_SY2785 @ SV433 @ SV208 ) @ SV208 )
              | ~ ( in @ SV433 @ ( sK25_SY2785 @ SV433 @ SV208 ) ) ) )
        = $true )
      | ( ( in @ SV433 @ ( setunion @ SV208 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2153]) ).

thf(2348,plain,
    ! [SV713: $i > $o,SV659: $i > $o,SV434: $i,SV209: $i] :
      ( ( ( ~ ! [SY3133: $i] :
                ( ~ ( in @ SY3133 @ SV209 )
                | ! [SY3134: $i] :
                    ( ~ ( in @ SY3134 @ SV434 )
                    | ( SY3133 != SY3134 )
                    | ~ ( ~ ( ~ ( SV659 @ SY3133 )
                            | ( SV713 @ SY3134 ) )
                        | ~ ( ~ ( SV713 @ SY3134 )
                            | ( SV659 @ SY3133 ) ) ) ) ) )
        = $true )
      | ( ( ( dsetconstr @ SV209
            @ ^ [SY3097: $i] : ( SV659 @ SY3097 ) )
          = ( dsetconstr @ SV434
            @ ^ [SY3136: $i] : ( SV713 @ SY3136 ) ) )
        = $true )
      | ( ( SV209 = SV434 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2154]) ).

thf(2349,plain,
    ! [SV435: $i,SV714: $o,SV210: $i,SV571: $i] :
      ( ( ( ~ ( ( SV571 != SV210 )
              | SV714 ) )
        = $true )
      | ( ( ~ ( ~ ( in @ SV571 @ SV435 )
              | SV714 )
          | SV714 )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2155]) ).

thf(2350,plain,
    ! [SV435: $i,SV210: $i,SV571: $i] :
      ( ( ( ~ ( ( SV571 != SV210 )
              | $true ) )
        = $true )
      | ( ( ~ ( ~ ( in @ SV571 @ SV435 )
              | $true )
          | $true )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2156]) ).

thf(2351,plain,
    ! [SV435: $i,SV210: $i,SV571: $i] :
      ( ( ( ~ ( ( SV571 != SV210 )
              | $false ) )
        = $true )
      | ( ( ~ ( ~ ( in @ SV571 @ SV435 )
              | $false )
          | $false )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2157]) ).

thf(2352,plain,
    ! [SV660: $i,SV211: $i > $o] :
      ( ( ( ~ ( SV211 @ SV660 )
          | ~ ! [SY3099: $i] :
                ( ~ ( SV211 @ SY3099 )
                | ( SV660 = SY3099 ) ) )
        = $true )
      | ( ( ~ ! [SY2378: $i] :
                ~ ~ ( ~ ( SV211 @ SY2378 )
                    | ~ ! [SY2379: $i] :
                          ( ~ ( SV211 @ SY2379 )
                          | ( SY2378 = SY2379 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2158]) ).

thf(2353,plain,
    ! [SV572: $i,SV436: $i,SV212: $i,SV715: $i] :
      ( ( ( ~ ( in @ SV715 @ SV212 ) )
        = $true )
      | ( ( ( ap @ SV212 @ SV436 @ SV572 @ SV715 )
          = ( ap @ SV212 @ SV436 @ SV572 @ SV715 ) )
        = $true )
      | ( ( in @ SV572 @ ( funcSet @ SV212 @ SV436 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2159]) ).

thf(2354,plain,
    ! [SV437: $i,SV213: $i,SV661: $i] :
      ( ( ( in @ SV661 @ SV213 )
        = $false )
      | ( ( ~ ( in @ SV661 @ ( setminus @ SV213 @ ( setminus @ SV213 @ SV437 ) ) )
          | ( in @ SV661 @ SV437 ) )
        = $true )
      | ( ( in @ SV437 @ ( powerset @ SV213 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2160]) ).

thf(2355,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ( sK17_SY2797 @ SV438 @ SV214 )
         != ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( ~ ( ~ ( ~ ~ ! [SY2388: $i] :
                          ~ ~ ( ~ ( SV214 @ SY2388 )
                              | ~ ! [SY2389: $i] :
                                    ( ~ ( SV214 @ SY2389 )
                                    | ( SY2388 = SY2389 ) ) )
                  | ~ ! [SY2801: $i] :
                        ~ ~ ( ~ ( SV438 @ SY2801 )
                            | ~ ! [SY2802: $i] :
                                  ( ~ ( SV438 @ SY2802 )
                                  | ( SY2801 = SY2802 ) ) ) )
              | ~ ( ~ ~ ! [SY2803: $i] :
                          ~ ~ ( ~ ( SV438 @ SY2803 )
                              | ~ ! [SY2804: $i] :
                                    ( ~ ( SV438 @ SY2804 )
                                    | ( SY2803 = SY2804 ) ) )
                  | ~ ! [SY2394: $i] :
                        ~ ~ ( ~ ( SV214 @ SY2394 )
                            | ~ ! [SY2395: $i] :
                                  ( ~ ( SV214 @ SY2395 )
                                  | ( SY2394 = SY2395 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2161]) ).

thf(2356,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ( ~ ( ~ ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
                  | ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) ) )
              | ~ ( ~ ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
                  | ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) ) ) ) )
        = $false )
      | ( ( ~ ( ~ ( ~ ~ ! [SY2388: $i] :
                          ~ ~ ( ~ ( SV214 @ SY2388 )
                              | ~ ! [SY2389: $i] :
                                    ( ~ ( SV214 @ SY2389 )
                                    | ( SY2388 = SY2389 ) ) )
                  | ~ ! [SY2801: $i] :
                        ~ ~ ( ~ ( SV438 @ SY2801 )
                            | ~ ! [SY2802: $i] :
                                  ( ~ ( SV438 @ SY2802 )
                                  | ( SY2801 = SY2802 ) ) ) )
              | ~ ( ~ ~ ! [SY2803: $i] :
                          ~ ~ ( ~ ( SV438 @ SY2803 )
                              | ~ ! [SY2804: $i] :
                                    ( ~ ( SV438 @ SY2804 )
                                    | ( SY2803 = SY2804 ) ) )
                  | ~ ! [SY2394: $i] :
                        ~ ~ ( ~ ( SV214 @ SY2394 )
                            | ~ ! [SY2395: $i] :
                                  ( ~ ( SV214 @ SY2395 )
                                  | ( SY2394 = SY2395 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2161]) ).

thf(2357,plain,
    ! [SV215: $i,SV439: $i > $o] :
      ( ( ( ~ ( ~ ( in @ ( sK27_SY2808 @ SV439 @ SV215 ) @ SV215 )
              | ~ ( SV439 @ ( sK27_SY2808 @ SV439 @ SV215 ) ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV215
            @ ^ [SY2807: $i] : ( SV439 @ SY2807 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2162]) ).

thf(2358,plain,
    ! [SV216: $i,SV573: $i,SV440: $i > $o] :
      ( ( ( SV440 @ SV573 )
        = $false )
      | ( ( ~ ! [SY3006: $i] :
                ( ~ ( in @ SY3006 @ SV216 )
                | ~ ( SV440 @ SY3006 )
                | ( SY3006 = SV573 ) )
          | ( singleton
            @ ( dsetconstr @ SV216
              @ ^ [SY2811: $i] : ( SV440 @ SY2811 ) ) ) )
        = $true )
      | ( ( in @ SV573 @ SV216 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2163]) ).

thf(2359,plain,
    ! [SV218: $i,SV574: $i,SV442: $i,SV716: $i] :
      ( ( ( ~ ( in @ SV716 @ SV442 ) )
        = $true )
      | ( ( subset @ ( setadjoin @ ( setadjoin @ SV574 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV574 @ ( setadjoin @ SV716 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV218 @ SV442 ) ) )
        = $true )
      | ( ( in @ SV574 @ SV218 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2164]) ).

thf(2360,plain,
    ! [SV219: $i,SV575: $i,SV443: $i,SV717: $i] :
      ( ( ( ~ ( in @ SV717 @ SV443 ) )
        = $true )
      | ( ( ( ksnd @ ( kpair @ SV575 @ SV717 ) )
          = SV717 )
        = $true )
      | ( ( in @ SV575 @ SV219 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2165]) ).

thf(2361,plain,
    ! [SV576: $i,SV444: $o,SV220: $i,SV718: $i] :
      ( ( ( ~ ( in @ SV718 @ SV220 ) )
        = $true )
      | ( ( ~ SV444
          | ( ( dsetconstr @ SV220
              @ ^ [SY3137: $i] :
                  ( ~ ( ~ SV444
                      | ( SY3137 != SV576 ) )
                  | ~ ( ~ ~ SV444
                      | ( SY3137 != SV718 ) ) ) )
            = ( setadjoin @ SV576 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV576 @ SV220 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2166]) ).

thf(2362,plain,
    ! [SV577: $i,SV220: $i,SV719: $i] :
      ( ( ( ~ ( in @ SV719 @ SV220 ) )
        = $true )
      | ( ( ~ $true
          | ( ( dsetconstr @ SV220
              @ ^ [SY3138: $i] :
                  ( ~ ( ~ $true
                      | ( SY3138 != SV577 ) )
                  | ~ ( ~ ~ $true
                      | ( SY3138 != SV719 ) ) ) )
            = ( setadjoin @ SV577 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV577 @ SV220 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2167]) ).

thf(2363,plain,
    ! [SV578: $i,SV220: $i,SV720: $i] :
      ( ( ( ~ ( in @ SV720 @ SV220 ) )
        = $true )
      | ( ( ~ $false
          | ( ( dsetconstr @ SV220
              @ ^ [SY3139: $i] :
                  ( ~ ( ~ $false
                      | ( SY3139 != SV578 ) )
                  | ~ ( ~ ~ $false
                      | ( SY3139 != SV720 ) ) ) )
            = ( setadjoin @ SV578 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV578 @ SV220 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2168]) ).

thf(2364,plain,
    ! [SV579: $i,SV445: $i,SV221: $i,SV721: $i] :
      ( ( ( ~ ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) ) )
        = $true )
      | ( ( ~ ! [SY3140: $i] :
                ( ~ ( in @ SY3140 @ SV221 )
                | ! [SY3141: $i] :
                    ( ~ ( in @ SY3141 @ SV445 )
                    | ~ ( in @ ( kpair @ SY3140 @ SY3141 ) @ SV579 )
                    | ( in @ ( kpair @ SY3140 @ SY3141 ) @ SV721 ) ) )
          | ~ ! [SY3142: $i] :
                ( ~ ( in @ SY3142 @ SV221 )
                | ! [SY3143: $i] :
                    ( ~ ( in @ SY3143 @ SV445 )
                    | ~ ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV721 )
                    | ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV579 ) ) )
          | ( SV579 = SV721 ) )
        = $true )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2169]) ).

thf(2365,plain,
    ! [SV580: $i,SV446: $i,SV222: $i,SV722: $i] :
      ( ( ( ~ ( in @ SV722 @ SV222 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV446
            @ ^ [SY3144: $i] : ( in @ ( kpair @ SV722 @ SY3144 ) @ SV580 ) ) )
        = $true )
      | ( ( func @ SV222 @ SV446 @ SV580 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2170]) ).

thf(2366,plain,
    ! [SV224: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK28_SY2426 @ SV224 ) @ SV224 )
              | ~ $true ) )
        = $true )
      | ( ( SV224 = emptyset )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2171]) ).

thf(2367,plain,
    ! [SV225: $i,SV448: $i,SV581: $i] :
      ( ( ( subset @ SV581 @ SV448 )
        = $false )
      | ( ( subset @ SV581 @ ( binintersect @ SV225 @ SV448 ) )
        = $true )
      | ( ( subset @ SV581 @ SV225 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2172]) ).

thf(2368,plain,
    ! [SV226: $i,SV449: $i,SV582: $i] :
      ( ( ( ~ ( in @ SV582 @ SV449 ) )
        = $false )
      | ( ( in @ SV582 @ ( symdiff @ SV226 @ SV449 ) )
        = $true )
      | ( ( in @ SV582 @ SV226 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2173]) ).

thf(2369,plain,
    ! [SV450: $i,SV227: $i,SV662: $i] :
      ( ( ( in @ SV662 @ ( powerset @ SV227 ) )
        = $false )
      | ( ( ~ ( subset @ ( setminus @ SV227 @ SV662 ) @ ( setminus @ SV227 @ SV450 ) )
          | ( subset @ SV450 @ SV662 ) )
        = $true )
      | ( ( in @ SV450 @ ( powerset @ SV227 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2174]) ).

thf(2370,plain,
    ! [SV451: $i,SV228: $i,SV663: $i] :
      ( ( ( in @ SV663 @ ( powerset @ SV228 ) )
        = $false )
      | ( ( ! [SY3101: $i] :
              ( ~ ( in @ SY3101 @ ( powerset @ SV228 ) )
              | ! [SY3102: $i] :
                  ( ~ ( in @ SY3102 @ SV228 )
                  | ~ ( in @ SY3102 @ ( binintersect @ SV451 @ SV663 ) )
                  | ( in @ SY3102 @ ( binunion @ SV663 @ SY3101 ) ) ) ) )
        = $true )
      | ( ( in @ SV451 @ ( powerset @ SV228 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2175]) ).

thf(2371,plain,
    ! [SV583: $i,SV453: $o,SV230: $i,SV723: $i] :
      ( ( ( ~ ( in @ SV723 @ SV230 ) )
        = $true )
      | ( ( ~ ~ SV453
          | ( ( dsetconstr @ SV230
              @ ^ [SY3145: $i] :
                  ( ~ ( ~ SV453
                      | ( SY3145 != SV583 ) )
                  | ~ ( ~ ~ SV453
                      | ( SY3145 != SV723 ) ) ) )
            = ( setadjoin @ SV723 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV583 @ SV230 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2176]) ).

thf(2372,plain,
    ! [SV584: $i,SV230: $i,SV724: $i] :
      ( ( ( ~ ( in @ SV724 @ SV230 ) )
        = $true )
      | ( ( ~ ~ $true
          | ( ( dsetconstr @ SV230
              @ ^ [SY3146: $i] :
                  ( ~ ( ~ $true
                      | ( SY3146 != SV584 ) )
                  | ~ ( ~ ~ $true
                      | ( SY3146 != SV724 ) ) ) )
            = ( setadjoin @ SV724 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV584 @ SV230 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2177]) ).

thf(2373,plain,
    ! [SV585: $i,SV230: $i,SV725: $i] :
      ( ( ( ~ ( in @ SV725 @ SV230 ) )
        = $true )
      | ( ( ~ ~ $false
          | ( ( dsetconstr @ SV230
              @ ^ [SY3147: $i] :
                  ( ~ ( ~ $false
                      | ( SY3147 != SV585 ) )
                  | ~ ( ~ ~ $false
                      | ( SY3147 != SV725 ) ) ) )
            = ( setadjoin @ SV725 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV585 @ SV230 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2178]) ).

thf(2374,plain,
    ! [SV454: $i,SV231: $i,SV664: $i] :
      ( ( ( in @ SV664 @ ( powerset @ SV231 ) )
        = $false )
      | ( ( ~ ! [SY3103: $i] :
                ( ~ ( in @ SY3103 @ SV231 )
                | ~ ( in @ SY3103 @ SV454 )
                | ( in @ SY3103 @ SV664 ) )
          | ( in @ SV454 @ ( powerset @ SV664 ) ) )
        = $true )
      | ( ( in @ SV454 @ ( powerset @ SV231 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2179]) ).

thf(2375,plain,
    ! [SV236: $i,SV588: $i,SV459: $i] :
      ( ( ( subset @ SV459 @ SV588 )
        = $false )
      | ( ( subset @ SV236 @ SV588 )
        = $true )
      | ( ( subset @ SV236 @ SV459 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2180]) ).

thf(2376,plain,
    ! [SV465: $i,SV242: $i,SV593: $i] :
      ( ( ( in @ SV593 @ ( setminus @ SV242 @ SV465 ) )
        = $false )
      | ( ( in @ SV593 @ SV242 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2182]) ).

thf(2377,plain,
    ! [SV466: $i,SV243: $i,SV665: $i] :
      ( ( ( in @ SV665 @ ( powerset @ SV243 ) )
        = $false )
      | ( ( ~ ! [SY3104: $i] :
                ( ~ ( in @ SY3104 @ SV243 )
                | ~ ( in @ SY3104 @ SV466 )
                | ( in @ SY3104 @ SV665 ) )
          | ( subset @ SV466 @ SV665 ) )
        = $true )
      | ( ( in @ SV466 @ ( powerset @ SV243 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2183]) ).

thf(2378,plain,
    ! [SV244: $i,SV594: $i > $i,SV467: $i] :
      ( ( ( ~ ( in @ ( sK29_SY3031 @ SV467 @ SV594 @ SV244 ) @ SV244 ) )
        = $false )
      | ( ( ! [SY3032: $i] :
              ( ~ ( in @ SY3032 @ SV244 )
              | ( ( ap @ SV244 @ SV467
                  @ ( lam @ SV244 @ SV467
                    @ ^ [SY3033: $i] : ( SV594 @ SY3033 ) )
                  @ SY3032 )
                = ( SV594 @ SY3032 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2184]) ).

thf(2379,plain,
    ! [SV244: $i,SV467: $i,SV594: $i > $i] :
      ( ( ( in @ ( SV594 @ ( sK29_SY3031 @ SV467 @ SV594 @ SV244 ) ) @ SV467 )
        = $false )
      | ( ( ! [SY3032: $i] :
              ( ~ ( in @ SY3032 @ SV244 )
              | ( ( ap @ SV244 @ SV467
                  @ ( lam @ SV244 @ SV467
                    @ ^ [SY3033: $i] : ( SV594 @ SY3033 ) )
                  @ SY3032 )
                = ( SV594 @ SY3032 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2184]) ).

thf(2380,plain,
    ! [SV595: $i,SV468: $i,SV245: $i,SV726: $i] :
      ( ( ( ~ ( in @ SV726 @ SV245 ) )
        = $true )
      | ( ( in @ ( kpair @ SV726 @ ( ap @ SV245 @ SV468 @ SV595 @ SV726 ) ) @ SV595 )
        = $true )
      | ( ( in @ SV595 @ ( funcSet @ SV245 @ SV468 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2185]) ).

thf(2381,plain,
    ! [SV469: $i,SV246: $i,SV666: $i] :
      ( ( ( in @ SV666 @ ( powerset @ SV246 ) )
        = $false )
      | ( ( ! [SY3105: $i] :
              ( ~ ( in @ SY3105 @ SV246 )
              | ~ ( in @ SY3105 @ ( setminus @ SV246 @ SV469 ) )
              | ~ ( in @ SY3105 @ ( binintersect @ SV469 @ SV666 ) ) ) )
        = $true )
      | ( ( in @ SV469 @ ( powerset @ SV246 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2186]) ).

thf(2382,plain,
    ! [SV251: $i,SV597: $i,SV472: $i,SV727: $i] :
      ( ( ( ~ ( in @ SV727 @ SV472 ) )
        = $true )
      | ( ( in @ ( setadjoin @ SV597 @ ( setadjoin @ SV727 @ emptyset ) ) @ ( powerset @ ( binunion @ SV251 @ SV472 ) ) )
        = $true )
      | ( ( in @ SV597 @ SV251 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2189]) ).

thf(2383,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ~ ( ~ ( ~ ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
                  | ( ( sK37_SY3106 @ SV667 @ SV253 )
                    = SV667 ) )
              | ~ ( ( ( sK37_SY3106 @ SV667 @ SV253 )
                   != SV667 )
                  | ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) ) ) ) )
        = $false )
      | ( ( ~ ! [SY2491: $i] :
                ~ ~ ( ~ ( SV253 @ SY2491 )
                    | ~ ! [SY2492: $i] :
                          ( ~ ( SV253 @ SY2492 )
                          | ( SY2491 = SY2492 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2191]) ).

thf(2384,plain,
    ! [SV668: $o,SV255: $i,SV475: $i] :
      ( ( ( ! [SY3107: $i] :
              ( ~ ( in @ SV475 @ SY3107 )
              | ~ ( in @ SY3107 @ SV255 )
              | SV668 ) )
        = $false )
      | ( SV668 = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2192]) ).

thf(2385,plain,
    ! [SV255: $i,SV475: $i] :
      ( ( ( ! [SX0: $i] :
              ( ~ ( in @ SV475 @ SX0 )
              | ~ ( in @ SX0 @ SV255 )
              | $true ) )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2193]) ).

thf(2386,plain,
    ! [SV255: $i,SV475: $i] :
      ( ( ( ! [SX0: $i] :
              ( ~ ( in @ SV475 @ SX0 )
              | ~ ( in @ SX0 @ SV255 )
              | $false ) )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2194]) ).

thf(2387,plain,
    ! [SV600: $i,SV476: $o,SV256: $i,SV728: $i] :
      ( ( ( ~ ( in @ SV728 @ SV256 ) )
        = $true )
      | ( ( in @ ( if @ SV256 @ SV476 @ SV600 @ SV728 ) @ ( setadjoin @ SV600 @ ( setadjoin @ SV728 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV600 @ SV256 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2195]) ).

thf(2388,plain,
    ! [SV601: $i,SV256: $i,SV729: $i] :
      ( ( ( ~ ( in @ SV729 @ SV256 ) )
        = $true )
      | ( ( in @ ( if @ SV256 @ $true @ SV601 @ SV729 ) @ ( setadjoin @ SV601 @ ( setadjoin @ SV729 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV601 @ SV256 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2196]) ).

thf(2389,plain,
    ! [SV602: $i,SV256: $i,SV730: $i] :
      ( ( ( ~ ( in @ SV730 @ SV256 ) )
        = $true )
      | ( ( in @ ( if @ SV256 @ $false @ SV602 @ SV730 ) @ ( setadjoin @ SV602 @ ( setadjoin @ SV730 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV602 @ SV256 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2197]) ).

thf(2390,plain,
    ! [SV257: $i,SV603: $i,SV477: $i,SV731: $i] :
      ( ( ( ~ ( in @ SV731 @ SV477 ) )
        = $true )
      | ( ( subset @ ( setadjoin @ SV603 @ ( setadjoin @ SV731 @ emptyset ) ) @ ( binunion @ SV257 @ SV477 ) )
        = $true )
      | ( ( in @ SV603 @ SV257 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2198]) ).

thf(2391,plain,
    ! [SV35: $i,SV281: $i > $o] :
      ( ( ( ~ ( ~ ( in @ ( sK30_SY2514 @ SV281 @ SV35 ) @ SV35 )
              | ~ ( SV281 @ ( sK30_SY2514 @ SV281 @ SV35 ) ) ) )
        = $true )
      | ( ( ! [SY2515: $i] :
              ( ~ ( in @ SY2515 @ SV35 )
              | ~ ( SV281 @ SY2515 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2199]) ).

thf(2392,plain,
    ! [SV619: $i,SV282: $i,SV36: $i,SV734: $i] :
      ( ( ( ~ ( in @ SV734 @ SV36 )
          | ~ ( subset @ SV282 @ SV619 )
          | ~ ~ ( in @ SV734 @ SV619 )
          | ~ ( in @ SV734 @ SV282 ) )
        = $true )
      | ( ( in @ SV619 @ ( powerset @ SV36 ) )
        = $false )
      | ( ( in @ SV282 @ ( powerset @ SV36 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2200]) ).

thf(2393,plain,
    ! [SV620: $i,SV37: $i > $o] :
      ( ( ( ~ ( SV37 @ SV620 ) )
        = $true )
      | ( ( ~ ! [SY3056: $i] :
                ( ~ ( SV37 @ SY3056 )
                | ( SV620 = SY3056 ) ) )
        = $true )
      | ( ( ~ ! [SY1897: $i] :
                ~ ! [SY1898: $i] :
                    ~ ( ~ ( ~ ( SV37 @ SY1898 )
                          | ( SY1898 = SY1897 ) )
                      | ~ ( ( SY1898 != SY1897 )
                          | ( SV37 @ SY1898 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2201]) ).

thf(2394,plain,
    ! [SV482: $i,SV283: $i,SV38: $i,SV669: $i] :
      ( ( ( in @ SV669 @ SV38 )
        = $false )
      | ( ( in @ ( kpair @ SV669 @ ( ap @ SV38 @ SV283 @ SV482 @ SV669 ) ) @ SV482 )
        = $true )
      | ( ( func @ SV38 @ SV283 @ SV482 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2202]) ).

thf(2395,plain,
    ! [SV483: $i,SV284: $o,SV40: $i,SV670: $i] :
      ( ( ( in @ SV670 @ SV40 )
        = $false )
      | ( ( ~ ~ SV284
          | ( in @ SV670
            @ ( dsetconstr @ SV40
              @ ^ [SY3108: $i] :
                  ( ~ ( ~ SV284
                      | ( SY3108 != SV483 ) )
                  | ~ ( ~ ~ SV284
                      | ( SY3108 != SV670 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV483 @ SV40 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2203]) ).

thf(2396,plain,
    ! [SV484: $i,SV40: $i,SV671: $i] :
      ( ( ( in @ SV671 @ SV40 )
        = $false )
      | ( ( ~ ~ $true
          | ( in @ SV671
            @ ( dsetconstr @ SV40
              @ ^ [SY3109: $i] :
                  ( ~ ( ~ $true
                      | ( SY3109 != SV484 ) )
                  | ~ ( ~ ~ $true
                      | ( SY3109 != SV671 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV484 @ SV40 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2204]) ).

thf(2397,plain,
    ! [SV485: $i,SV40: $i,SV672: $i] :
      ( ( ( in @ SV672 @ SV40 )
        = $false )
      | ( ( ~ ~ $false
          | ( in @ SV672
            @ ( dsetconstr @ SV40
              @ ^ [SY3110: $i] :
                  ( ~ ( ~ $false
                      | ( SY3110 != SV485 ) )
                  | ~ ( ~ ~ $false
                      | ( SY3110 != SV672 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV485 @ SV40 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2205]) ).

thf(2398,plain,
    ! [SV621: $i,SV41: $i > $o] :
      ( ( ( ~ ( SV41 @ SV621 ) )
        = $true )
      | ( ( ~ ! [SY3057: $i] :
                ( ~ ( SV41 @ SY3057 )
                | ( SV621 = SY3057 ) ) )
        = $true )
      | ( ( ! [SY1909: $i,SY1910: $i] :
              ( ~ ( SV41 @ SY1909 )
              | ~ ( SV41 @ SY1910 )
              | ( SY1909 = SY1910 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2206]) ).

thf(2399,plain,
    ! [SV42: $i,SV285: $i,SV735: $i] :
      ( ( ( ~ ( in @ SV735 @ SV285 )
          | ( in @ SV735 @ SV42 ) )
        = $true )
      | ( ( in @ SV285 @ ( powerset @ SV42 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2207]) ).

thf(2400,plain,
    ! [SV285: $i,SV42: $i] :
      ( ( ( ~ ( in @ ( sK38_SY2524 @ SV42 @ SV285 ) @ SV285 )
          | ( in @ ( sK38_SY2524 @ SV42 @ SV285 ) @ SV42 ) )
        = $false )
      | ( ( in @ SV285 @ ( powerset @ SV42 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2208]) ).

thf(2401,plain,
    ! [SV622: $i,SV43: $i > $o] :
      ( ( ( ~ ( SV43 @ SV622 ) )
        = $true )
      | ( ( ~ ! [SY3058: $i] :
                ( ~ ( SV43 @ SY3058 )
                | ( SV622 = SY3058 ) ) )
        = $true )
      | ( ( ! [SY1916: $i,SY1917: $i] :
              ( ~ ( SV43 @ SY1916 )
              | ~ ( SV43 @ SY1917 )
              | ( SY1916 = SY1917 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2209]) ).

thf(2402,plain,
    ! [SV623: $i,SV286: $i,SV44: $i,SV736: $i] :
      ( ( ( ~ ( in @ SV736 @ SV44 )
          | ~ ( in @ SV736 @ ( setminus @ SV44 @ ( binunion @ SV286 @ SV623 ) ) )
          | ~ ( in @ SV736 @ SV286 ) )
        = $true )
      | ( ( in @ SV623 @ ( powerset @ SV44 ) )
        = $false )
      | ( ( in @ SV286 @ ( powerset @ SV44 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2210]) ).

thf(2403,plain,
    ! [SV287: $i > $o,SV46: $i,SV673: $i] :
      ( ( ( ~ ( in @ SV673 @ SV46 )
          | ~ ~ ( SV287 @ SV673 ) )
        = $true )
      | ( ( ~ ! [SY2528: $i] :
                ( ~ ( in @ SY2528 @ SV46 )
                | ( SV287 @ SY2528 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2211]) ).

thf(2404,plain,
    ! [SV288: $i,SV47: $i,SV486: $i] :
      ( ( ( in @ SV486 @ SV47 )
        = $false )
      | ( ( in @ SV486 @ SV288 )
        = $true )
      | ( ( in @ SV486 @ ( setminus @ SV47 @ SV288 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2212]) ).

thf(2405,plain,
    ! [SV624: $i,SV48: $i > $o] :
      ( ( ( ~ ( SV48 @ SV624 ) )
        = $true )
      | ( ( ~ ! [SY3060: $i] :
                ( ~ ( SV48 @ SY3060 )
                | ( SV624 = SY3060 ) ) )
        = $true )
      | ( ( ~ ! [SY1928: $i] :
                ~ ~ ( ~ ( SV48 @ SY1928 )
                    | ~ ! [SY1929: $i] :
                          ( ~ ( SV48 @ SY1929 )
                          | ( SY1928 = SY1929 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2213]) ).

thf(2406,plain,
    ! [SV49: $i,SV289: $i,SV487: $i] :
      ( ( ( in @ SV487 @ SV289 )
        = $true )
      | ( ( in @ SV487 @ ( setminus @ SV49 @ SV289 ) )
        = $true )
      | ( ( in @ SV487 @ SV49 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2214]) ).

thf(2407,plain,
    ! [SV50: $i,SV488: $i,SV290: $i,SV674: $i] :
      ( ( ( in @ SV674 @ SV290 )
        = $false )
      | ( ( in @ ( setadjoin @ ( setadjoin @ SV488 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV488 @ ( setadjoin @ SV674 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV50 @ SV290 ) ) ) )
        = $true )
      | ( ( in @ SV488 @ SV50 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2215]) ).

thf(2408,plain,
    ! [SV51: $i,SV291: $i] :
      ( ( ( ~ ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV51 )
          | ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV291 ) )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV291 )
              | ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV51 ) ) )
        = $true )
      | ( ( SV51 = SV291 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2216]) ).

thf(2409,plain,
    ! [SV52: $i,SV292: $i > $o] :
      ( ( ( ~ ( ~ ( in @ ( sK31_SY2534 @ SV292 @ SV52 ) @ SV52 )
              | ~ ( SV292 @ ( sK31_SY2534 @ SV292 @ SV52 ) ) ) )
        = $true )
      | ( ( ! [SY2535: $i] :
              ( ~ ( in @ SY2535 @ SV52 )
              | ~ ( SV292 @ SY2535 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2217]) ).

thf(2410,plain,
    ! [SV55: $i,SV295: $i,SV489: $i] :
      ( ( ( ~ ( in @ SV489 @ SV295 ) )
        = $false )
      | ( ( ~ ( in @ SV489 @ ( symdiff @ SV55 @ SV295 ) ) )
        = $true )
      | ( ( in @ SV489 @ SV55 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2218]) ).

thf(2411,plain,
    ! [SV299: $i,SV60: $i,SV493: $i] :
      ( ( ( in @ SV493 @ ( symdiff @ SV60 @ SV299 ) )
        = $false )
      | ( ( in @ SV493 @ SV299 )
        = $false )
      | ( ( in @ SV493 @ SV60 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2220]) ).

thf(2412,plain,
    ! [SV62: $i,SV495: $i,SV301: $i,SV675: $i] :
      ( ( ( in @ SV675 @ SV301 )
        = $false )
      | ( ( ( kpair @ SV495 @ SV675 )
          = ( kpair @ SV495 @ SV675 ) )
        = $true )
      | ( ( in @ SV495 @ SV62 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2221]) ).

thf(2413,plain,
    ! [SV676: $i > $o,SV496: $i,SV302: $i,SV63: $i] :
      ( ( ( ! [SY3111: $i] :
              ( ~ ( in @ SY3111 @ SV63 )
              | ! [SY3112: $i] :
                  ( ~ ( in @ SY3112 @ SV302 )
                  | ~ ( in @ ( kpair @ SY3111 @ SY3112 ) @ SV496 )
                  | ( SV676 @ ( kpair @ SY3111 @ SY3112 ) ) ) ) )
        = $false )
      | ( ( ! [SY3113: $i] :
              ( ~ ( in @ SY3113 @ SV496 )
              | ( SV676 @ SY3113 ) ) )
        = $true )
      | ( ( subset @ SV496 @ ( cartprod @ SV63 @ SV302 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2222]) ).

thf(2414,plain,
    ! [SV497: $i,SV303: $i > $o,SV65: $i] :
      ( ( ( ( dsetconstr @ SV65
            @ ^ [SY2556: $i] : ( SV303 @ SY2556 ) )
          = emptyset )
        = $false )
      | ( ( SV303 @ SV497 )
        = $false )
      | ( ( in @ SV497 @ SV65 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2223]) ).

thf(2415,plain,
    ! [SV498: $i,SV305: $o,SV67: $i,SV677: $i] :
      ( ( ( in @ SV677 @ SV67 )
        = $false )
      | ( ( ~ SV305
          | ( in @ SV498
            @ ( dsetconstr @ SV67
              @ ^ [SY3114: $i] :
                  ( ~ ( ~ SV305
                      | ( SY3114 != SV498 ) )
                  | ~ ( ~ ~ SV305
                      | ( SY3114 != SV677 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV498 @ SV67 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2224]) ).

thf(2416,plain,
    ! [SV499: $i,SV67: $i,SV678: $i] :
      ( ( ( in @ SV678 @ SV67 )
        = $false )
      | ( ( ~ $true
          | ( in @ SV499
            @ ( dsetconstr @ SV67
              @ ^ [SY3115: $i] :
                  ( ~ ( ~ $true
                      | ( SY3115 != SV499 ) )
                  | ~ ( ~ ~ $true
                      | ( SY3115 != SV678 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV499 @ SV67 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2225]) ).

thf(2417,plain,
    ! [SV500: $i,SV67: $i,SV679: $i] :
      ( ( ( in @ SV679 @ SV67 )
        = $false )
      | ( ( ~ $false
          | ( in @ SV500
            @ ( dsetconstr @ SV67
              @ ^ [SY3116: $i] :
                  ( ~ ( ~ $false
                      | ( SY3116 != SV500 ) )
                  | ~ ( ~ ~ $false
                      | ( SY3116 != SV679 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV500 @ SV67 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2226]) ).

thf(2418,plain,
    ! [SV501: $i,SV306: $i,SV68: $i,SV680: $i] :
      ( ( ( in @ SV680 @ SV68 )
        = $false )
      | ( ( in
          @ ( setunion
            @ ( dsetconstr @ SV306
              @ ^ [SY3117: $i] : ( in @ ( kpair @ SV680 @ SY3117 ) @ SV501 ) ) )
          @ SV306 )
        = $true )
      | ( ( func @ SV68 @ SV306 @ SV501 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2227]) ).

thf(2419,plain,
    ! [SV626: $i,SV72: $i,SV310: $i] :
      ( ( ( ~ ( subset @ SV310 @ ( setminus @ SV72 @ SV626 ) ) )
        = $true )
      | ( ( subset @ SV626 @ ( setminus @ SV72 @ SV310 ) )
        = $true )
      | ( ( in @ SV626 @ ( powerset @ SV72 ) )
        = $false )
      | ( ( in @ SV310 @ ( powerset @ SV72 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2228]) ).

thf(2420,plain,
    ! [SV502: $i,SV311: $i,SV73: $i,SV681: $i] :
      ( ( ( in @ SV681 @ ( funcSet @ SV73 @ SV311 ) )
        = $false )
      | ( ( ~ ! [SY3118: $i] :
                ( ~ ( in @ SY3118 @ SV73 )
                | ( ( ap @ SV73 @ SV311 @ SV502 @ SY3118 )
                  = ( ap @ SV73 @ SV311 @ SV681 @ SY3118 ) ) )
          | ( SV502 = SV681 ) )
        = $true )
      | ( ( in @ SV502 @ ( funcSet @ SV73 @ SV311 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2229]) ).

thf(2421,plain,
    ! [SV74: $i,SV312: $i,SV503: $i] :
      ( ( ( ~ ( in @ SV503 @ SV312 ) )
        = $false )
      | ( ( ~ ( in @ SV503 @ SV74 ) )
        = $true )
      | ( ( in @ SV503 @ ( setminus @ SV74 @ SV312 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2230]) ).

thf(2422,plain,
    ! [SV313: $i,SV75: $i,SV504: $i] :
      ( ( ( in @ SV504 @ ( setadjoin @ SV75 @ SV313 ) )
        = $false )
      | ( ( ( SV504 = SV75 )
          | ( in @ SV504 @ SV313 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2231]) ).

thf(2423,plain,
    ! [SV313: $i,SV75: $i,SV504: $i] :
      ( ( ( ( SV504 = SV75 )
          | ( in @ SV504 @ SV313 ) )
        = $false )
      | ( ( in @ SV504 @ ( setadjoin @ SV75 @ SV313 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2232]) ).

thf(2424,plain,
    ! [SV627: $i,SV314: $i,SV76: $i,SV737: $i] :
      ( ( ( ~ ( in @ SV737 @ ( powerset @ SV76 ) )
          | ! [SY3153: $i] :
              ( ~ ( in @ SY3153 @ SV76 )
              | ~ ( in @ SY3153 @ ( binintersect @ SV314 @ SV627 ) )
              | ( in @ SY3153 @ ( binintersect @ ( binunion @ SV314 @ SV737 ) @ ( binunion @ SV627 @ SV737 ) ) ) ) )
        = $true )
      | ( ( in @ SV627 @ ( powerset @ SV76 ) )
        = $false )
      | ( ( in @ SV314 @ ( powerset @ SV76 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2233]) ).

thf(2425,plain,
    ! [SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true )
      | ( ( ~ ~ ! [SY2001: $i] :
                  ~ ~ ( ~ ( SV77 @ SY2001 )
                      | ~ ! [SY2002: $i] :
                            ( ~ ( SV77 @ SY2002 )
                            | ( SY2001 = SY2002 ) ) )
          | ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2234]) ).

thf(2426,plain,
    ! [SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ~ ( ~ ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
              | ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) ) )
          | ~ ( ~ ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
              | ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2001: $i] :
                  ~ ~ ( ~ ( SV77 @ SY2001 )
                      | ~ ! [SY2002: $i] :
                            ( ~ ( SV77 @ SY2002 )
                            | ( SY2001 = SY2002 ) ) )
          | ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2235]) ).

thf(2427,plain,
    ! [SV628: $i,SV318: $i,SV80: $i] :
      ( ( ( ~ ! [SY3066: $i] :
                ( ~ ( in @ SY3066 @ SV80 )
                | ~ ( in @ SY3066 @ SV318 )
                | ( in @ SY3066 @ SV628 ) ) )
        = $true )
      | ( ( ~ ! [SY3067: $i] :
                ( ~ ( in @ SY3067 @ SV80 )
                | ~ ( in @ SY3067 @ SV628 )
                | ( in @ SY3067 @ SV318 ) )
          | ( SV318 = SV628 ) )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2237]) ).

thf(2428,plain,
    ! [SV81: $i,SV319: $i] :
      ( ( ( ~ ! [SY2586: $i] :
                ( ~ ( in @ SY2586 @ SV319 )
                | ( in @ SY2586 @ SV81 ) ) )
        = $true )
      | ( ( SV81 = SV319 )
        = $true )
      | ( ( in @ ( sK8_SY2585 @ SV319 @ SV81 ) @ SV81 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2238]) ).

thf(2429,plain,
    ! [SV81: $i,SV319: $i] :
      ( ( ( ! [SY2586: $i] :
              ( ~ ( in @ SY2586 @ SV319 )
              | ( in @ SY2586 @ SV81 ) ) )
        = $false )
      | ( ( SV81 = SV319 )
        = $true )
      | ( ( in @ ( sK8_SY2585 @ SV319 @ SV81 ) @ SV319 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2239]) ).

thf(2430,plain,
    ! [SV506: $i > $i > $o,SV82: $i,SV608: $i,SV320: $i,SV732: $i] :
      ( ( ( ~ ( in @ SV732 @ SV320 ) )
        = $true )
      | ( ( ~ ( in @ ( kpair @ SV608 @ SV732 )
              @ ( dpsetconstr @ SV82 @ SV320
                @ ^ [SY2907: $i,SY2908: $i] : ( SV506 @ SY2907 @ SY2908 ) ) )
          | ( SV506 @ SV608 @ SV732 ) )
        = $true )
      | ( ( in @ SV608 @ SV82 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2240]) ).

thf(2431,plain,
    ! [SV321: $i > $o,SV84: $i,SV682: $i] :
      ( ( ( in @ SV682 @ SV84 )
        = $false )
      | ( ( SV321 @ SV682 )
        = $true )
      | ( ( ~ ! [SY2593: $i] :
                ~ ~ ( ~ ( in @ SY2593 @ SV84 )
                    | ~ ~ ( SV321 @ SY2593 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2241]) ).

thf(2432,plain,
    ! [SV322: $i,SV609: $o,SV85: $i,SV507: $i] :
      ( ( ( ~ ( in @ SV507 @ SV85 )
          | SV609 )
        = $false )
      | ( ( ~ ( ~ ( in @ SV507 @ SV322 )
              | SV609 )
          | SV609 )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2242]) ).

thf(2433,plain,
    ! [SV322: $i,SV85: $i,SV507: $i] :
      ( ( ( ~ ( in @ SV507 @ SV85 )
          | $true )
        = $false )
      | ( ( ~ ( ~ ( in @ SV507 @ SV322 )
              | $true )
          | $true )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2243]) ).

thf(2434,plain,
    ! [SV322: $i,SV85: $i,SV507: $i] :
      ( ( ( ~ ( in @ SV507 @ SV85 )
          | $false )
        = $false )
      | ( ( ~ ( ~ ( in @ SV507 @ SV322 )
              | $false )
          | $false )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2244]) ).

thf(2435,plain,
    ! [SV87: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK39_SY2033 @ SV87 ) @ omega )
                | ~ ( in @ ( sK39_SY2033 @ SV87 ) @ SV87 ) )
          | ( in @ ( setadjoin @ ( sK39_SY2033 @ SV87 ) @ ( sK39_SY2033 @ SV87 ) ) @ SV87 ) )
        = $false )
      | ( ( in @ emptyset @ SV87 )
        = $false )
      | ( ( ! [SY2034: $i] :
              ( ~ ( in @ SY2034 @ omega )
              | ( in @ SY2034 @ SV87 ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2246]) ).

thf(2436,plain,
    ( ( ~ ( in @ sK32_SY3068 @ sK1_SX0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2248]) ).

thf(2437,plain,
    ( ( ~ ( in @ sK32_SY3068 @ ( setminus @ sK1_SX0 @ ( binunion @ sK2_SY2597 @ sK9_SY2910 ) ) )
      | ( in @ sK32_SY3068 @ ( setminus @ sK1_SX0 @ sK2_SY2597 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2248]) ).

thf(2438,plain,
    ! [SV629: $i,SV88: $i,SV324: $i] :
      ( ( ( ~ ( subset @ SV324 @ ( setminus @ SV88 @ SV629 ) ) )
        = $true )
      | ( ( ! [SY3069: $i] :
              ( ~ ( in @ SY3069 @ SV88 )
              | ~ ( in @ SY3069 @ SV629 )
              | ( in @ SY3069 @ ( setminus @ SV88 @ SV324 ) ) ) )
        = $true )
      | ( ( in @ SV629 @ ( powerset @ SV88 ) )
        = $false )
      | ( ( in @ SV324 @ ( powerset @ SV88 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2249]) ).

thf(2439,plain,
    ! [SV325: $i > $o,SV89: $i,SV683: $i] :
      ( ( ( ~ ( in @ SV683 @ SV89 )
          | ~ ( SV325 @ SV683 ) )
        = $true )
      | ( ( ( ( dsetconstr @ SV89
              @ ^ [SY2603: $i] : ( SV325 @ SY2603 ) )
           != emptyset )
          | $false )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2250]) ).

thf(2440,plain,
    ! [SV328: $i,SV92: $i,SV684: $i,SV631: $i] :
      ( ( ( SV631 = SV684 )
        = $false )
      | ( ( ~ ( in @ SV631 @ SV92 )
          | ( in @ SV684 @ SV328 ) )
        = $true )
      | ( ( SV92 = SV328 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2253]) ).

thf(2441,plain,
    ! [SV512: $i,SV685: $i,SV332: $i,SV96: $i] :
      ( ( ( func @ SV96 @ SV332 @ SV685 )
        = $false )
      | ( ( ~ ! [SY3119: $i] :
                ( ~ ( in @ SY3119 @ SV96 )
                | ( ( ap @ SV96 @ SV332 @ SV512 @ SY3119 )
                  = ( ap @ SV96 @ SV332 @ SV685 @ SY3119 ) ) )
          | ! [SY3120: $i] :
              ( ~ ( in @ SY3120 @ SV96 )
              | ! [SY3121: $i] :
                  ( ~ ( in @ SY3121 @ SV332 )
                  | ~ ( in @ ( kpair @ SY3120 @ SY3121 ) @ SV685 )
                  | ( in @ ( kpair @ SY3120 @ SY3121 ) @ SV512 ) ) ) )
        = $true )
      | ( ( func @ SV96 @ SV332 @ SV512 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2256]) ).

thf(2442,plain,
    ! [SV98: $i,SV333: $i,SV513: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK33_SY2921 @ SV513 @ SV333 @ SV98 ) @ SV98 )
              | ~ ~ ! [SY3150: $i] :
                      ~ ~ ( ~ ( in @ SY3150 @ SV333 )
                          | ( SV513
                           != ( kpair @ ( sK33_SY2921 @ SV513 @ SV333 @ SV98 ) @ SY3150 ) ) ) ) )
        = $true )
      | ( ( in @ SV513 @ ( cartprod @ SV98 @ SV333 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2257]) ).

thf(2443,plain,
    ! [SV633: $i,SV334: $i,SV99: $i,SV738: $i] :
      ( ( ( ~ ( in @ SV738 @ SV99 )
          | ~ ( in @ SV334 @ ( powerset @ SV633 ) )
          | ~ ( in @ SV738 @ SV334 )
          | ( in @ SV738 @ SV633 ) )
        = $true )
      | ( ( in @ SV633 @ ( powerset @ SV99 ) )
        = $false )
      | ( ( in @ SV334 @ ( powerset @ SV99 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2258]) ).

thf(2444,plain,
    ! [SV336: $i > $o,SV102: $i] :
      ( ( ( ~ ~ ! [SY2629: $i] :
                  ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                      | ~ ( SV336 @ SY2629 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( in @ ( sK11_SY2627 @ SV336 @ SV102 ) @ SV102 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2259]) ).

thf(2445,plain,
    ! [SV102: $i,SV336: $i > $o] :
      ( ( ( ~ ( in @ ( sK34_SY3074 @ SV336 @ SV102 ) @ SV102 ) )
        = $false )
      | ( ( ~ ~ ! [SY2629: $i] :
                  ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                      | ~ ( SV336 @ SY2629 ) )
          | ( singleton
            @ ( dsetconstr @ SV102
              @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2260]) ).

thf(2446,plain,
    ! [SV102: $i,SV336: $i > $o] :
      ( ( ( ~ ( SV336 @ ( sK11_SY2627 @ SV336 @ SV102 ) )
          | ~ ( SV336 @ ( sK34_SY3074 @ SV336 @ SV102 ) )
          | ( ( sK11_SY2627 @ SV336 @ SV102 )
            = ( sK34_SY3074 @ SV336 @ SV102 ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2629: $i] :
                  ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                      | ~ ( SV336 @ SY2629 ) )
          | ( singleton
            @ ( dsetconstr @ SV102
              @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2260]) ).

thf(2447,plain,
    ! [SV105: $i,SV516: $i > $i,SV339: $i] :
      ( ( ( in @ ( sK19_SY2927 @ SV339 @ SV516 @ SV105 ) @ SV105 )
        = $true )
      | ( ( ( lam @ SV105 @ SV339
            @ ^ [SY2928: $i] : ( SV516 @ SY2928 ) )
          = ( lam @ SV105 @ SV339
            @ ^ [SY2929: $i] : ( SV516 @ SY2929 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2262]) ).

thf(2448,plain,
    ! [SV107: $i,SV518: $i > $i,SV341: $i] :
      ( ( ( in @ ( sK20_SY2930 @ SV341 @ SV518 @ SV107 ) @ SV107 )
        = $true )
      | ( ( in
          @ ( lam @ SV107 @ SV341
            @ ^ [SY2931: $i] : ( SV518 @ SY2931 ) )
          @ ( funcSet @ SV107 @ SV341 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2264]) ).

thf(2449,plain,
    ! [SV109: $i] :
      ( ( ~ ~ ( ~ ! [SY2932: $i] :
                    ( ~ ( in @ SY2932 @ ( sK3_SY2100 @ SV109 ) )
                    | ! [SY2102: $i] :
                        ( ~ ( in @ SY2102 @ SY2932 )
                        | ( in @ SY2102 @ SV109 ) ) )
              | ~ ! [SY2934: $i,SY2935: $i] :
                    ( ~ ~ ( ~ ( in @ SY2934 @ SV109 )
                          | ~ ( in @ SY2935 @ SV109 ) )
                    | ~ ! [SY2936: $i] :
                          ( ~ ( in @ SY2936 @ ( sK3_SY2100 @ SV109 ) )
                          | ~ ( ~ ( ~ ( in @ SY2934 @ SY2936 )
                                  | ( in @ SY2935 @ SY2936 ) )
                              | ~ ( ~ ( in @ SY2935 @ SY2936 )
                                  | ( in @ SY2934 @ SY2936 ) ) ) )
                    | ( SY2934 = SY2935 ) ) )
        | ~ ! [SY2937: $i,SY2938: $i] :
              ( ~ ~ ( ~ ( in @ SY2937 @ ( sK3_SY2100 @ SV109 ) )
                    | ~ ( in @ SY2938 @ ( sK3_SY2100 @ SV109 ) ) )
              | ! [SX4: $i] :
                  ( ~ ( in @ SX4 @ SY2937 )
                  | ( in @ SX4 @ SY2938 ) )
              | ! [SX4: $i] :
                  ( ~ ( in @ SX4 @ SY2938 )
                  | ( in @ SX4 @ SY2937 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[2266]) ).

thf(2450,plain,
    ! [SV109: $i,SV739: $i] :
      ( ( ~ ~ ( ~ ! [SY3154: $i] :
                    ( ~ ( in @ SY3154 @ SV739 )
                    | ( in @ SY3154 @ SV109 ) )
              | ~ ~ ! [SY3155: $i] :
                      ~ ( in @ SY3155 @ SV739 ) )
        | ~ ! [SY3156: $i] :
              ~ ~ ! [SY3157: $i] :
                    ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3156 @ ( sK3_SY2100 @ SV109 ) )
                                    | ~ ( in @ SY3157 @ SV739 ) )
                              | ~ ~ ~ ! [SY3158: $i] :
                                        ~ ~ ( ~ ( in @ SY3158 @ SY3156 )
                                            | ~ ( in @ SY3158 @ SV739 ) ) )
                        | ~ ! [SY2947: $i] :
                              ( ~ ( in @ SY2947 @ ( sK3_SY2100 @ SV109 ) )
                              | ! [SX6: $i] :
                                  ( ~ ( in @ SX6 @ SY2947 )
                                  | ( in @ SX6 @ SY3156 ) )
                              | ( in @ SY3157 @ SY2947 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2267]) ).

thf(2451,plain,
    ! [SV110: $i,SV635: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK40_SY2119 @ SV635 @ SV110 ) @ SV110 )
                | ~ ~ ~ ! [SY3161: $i] :
                          ~ ~ ( ~ ( in @ SY3161 @ ( sK40_SY2119 @ SV635 @ SV110 ) )
                              | ~ ( in @ SY3161 @ SV110 ) ) ) )
        = $false )
      | ( ( in @ SV635 @ SV110 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2268]) ).

thf(2452,plain,
    ! [SV636: $i,SV112: $i > $o] :
      ( ( ( ~ ( SV112 @ SV636 ) )
        = $true )
      | ( ( ~ ! [SY3077: $i] :
                ( ~ ( SV112 @ SY3077 )
                | ( SV636 = SY3077 ) ) )
        = $true )
      | ( ( ~ ! [SY2125: $i] :
                ~ ( SV112 @ SY2125 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2269]) ).

thf(2453,plain,
    ! [SV113: $i,SV344: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK35_SY2645 @ SV344 @ SV113 ) @ SV113 )
              | ~ ( in @ ( sK35_SY2645 @ SV344 @ SV113 ) @ SV344 ) ) )
        = $true )
      | ( ( ( binintersect @ SV113 @ SV344 )
          = emptyset )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2270]) ).

thf(2454,plain,
    ! [SV637: $i,SV346: $i,SV116: $i,SV740: $i] :
      ( ( ( ~ ( in @ SV740 @ SV116 )
          | ~ ~ ( in @ SV740 @ ( binunion @ SV346 @ SV637 ) )
          | ~ ( in @ SV740 @ SV346 ) )
        = $true )
      | ( ( in @ SV637 @ ( powerset @ SV116 ) )
        = $false )
      | ( ( in @ SV346 @ ( powerset @ SV116 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2271]) ).

thf(2455,plain,
    ! [SV520: $i,SV347: $o,SV118: $i,SV686: $i] :
      ( ( ( in @ SV686 @ SV118 )
        = $false )
      | ( ( ~ ~ SV347
          | ( ( if @ SV118 @ SV347 @ SV520 @ SV686 )
            = SV686 ) )
        = $true )
      | ( ( in @ SV520 @ SV118 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2272]) ).

thf(2456,plain,
    ! [SV521: $i,SV118: $i,SV687: $i] :
      ( ( ( in @ SV687 @ SV118 )
        = $false )
      | ( ( ~ ~ $true
          | ( ( if @ SV118 @ $true @ SV521 @ SV687 )
            = SV687 ) )
        = $true )
      | ( ( in @ SV521 @ SV118 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2273]) ).

thf(2457,plain,
    ! [SV522: $i,SV118: $i,SV688: $i] :
      ( ( ( in @ SV688 @ SV118 )
        = $false )
      | ( ( ~ ~ $false
          | ( ( if @ SV118 @ $false @ SV522 @ SV688 )
            = SV688 ) )
        = $true )
      | ( ( in @ SV522 @ SV118 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2274]) ).

thf(2458,plain,
    ! [SV349: $i,SV121: $i,SV638: $i] :
      ( ( ( ~ ~ ( in @ SV638 @ ( setminus @ SV121 @ SV349 ) ) )
        = $true )
      | ( ( in @ SV638 @ SV349 )
        = $true )
      | ( ( in @ SV638 @ SV121 )
        = $false )
      | ( ( in @ SV349 @ ( powerset @ SV121 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2275]) ).

thf(2459,plain,
    ! [SV123: $i,SV351: $i,SV523: $i] :
      ( ( ( in @ SV523 @ SV351 )
        = $true )
      | ( ( ~ ( in @ SV523 @ SV123 ) )
        = $true )
      | ( ( subset @ SV123 @ SV351 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2277]) ).

thf(2460,plain,
    ! [SV124: $i,SV524: $i > $i,SV352: $i] :
      ( ( ( in @ ( sK21_SY2952 @ SV352 @ SV524 @ SV124 ) @ SV124 )
        = $true )
      | ( ( func @ SV124 @ SV352
          @ ( dpsetconstr @ SV124 @ SV352
            @ ^ [SY2953: $i,SY2954: $i] :
                ( ( SV524 @ SY2953 )
                = SY2954 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2278]) ).

thf(2461,plain,
    ! [SV353: $i > $o,SV125: $i] :
      ( ( ( ~ ~ ! [SY2659: $i] :
                  ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                      | ~ ( SV353 @ SY2659 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( in @ ( sK12_SY2657 @ SV353 @ SV125 ) @ SV125 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2280]) ).

thf(2462,plain,
    ! [SV125: $i,SV353: $i > $o] :
      ( ( ( ~ ( in @ ( sK36_SY3079 @ SV353 @ SV125 ) @ SV125 ) )
        = $false )
      | ( ( ~ ~ ! [SY2659: $i] :
                  ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                      | ~ ( SV353 @ SY2659 ) )
          | ( singleton
            @ ( dsetconstr @ SV125
              @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2281]) ).

thf(2463,plain,
    ! [SV125: $i,SV353: $i > $o] :
      ( ( ( ~ ( SV353 @ ( sK12_SY2657 @ SV353 @ SV125 ) )
          | ~ ( SV353 @ ( sK36_SY3079 @ SV353 @ SV125 ) )
          | ( ( sK12_SY2657 @ SV353 @ SV125 )
            = ( sK36_SY3079 @ SV353 @ SV125 ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2659: $i] :
                  ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                      | ~ ( SV353 @ SY2659 ) )
          | ( singleton
            @ ( dsetconstr @ SV125
              @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2281]) ).

thf(2464,plain,
    ! [SV126: $i,SV354: $i,SV525: $i] :
      ( ( ( in @ SV525 @ SV354 )
        = $false )
      | ( ( in @ SV525 @ ( symdiff @ SV126 @ SV354 ) )
        = $true )
      | ( ( in @ SV525 @ SV126 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2282]) ).

thf(2465,plain,
    ! [SV129: $i,SV357: $i,SV641: $i] :
      ( ( ( ~ ( in @ SV641 @ SV357 ) )
        = $true )
      | ( ( ~ ( in @ SV641 @ ( setminus @ SV129 @ SV357 ) ) )
        = $true )
      | ( ( in @ SV641 @ SV129 )
        = $false )
      | ( ( in @ SV357 @ ( powerset @ SV129 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2284]) ).

thf(2466,plain,
    ! [SV132: $i,SV642: $i,SV360: $i] :
      ( ( ( ~ ( subset @ SV360 @ SV642 ) )
        = $true )
      | ( ( subset @ ( setminus @ SV132 @ SV642 ) @ ( setminus @ SV132 @ SV360 ) )
        = $true )
      | ( ( in @ SV642 @ ( powerset @ SV132 ) )
        = $false )
      | ( ( in @ SV360 @ ( powerset @ SV132 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2285]) ).

thf(2467,plain,
    ! [SV527: $i,SV361: $i,SV133: $i,SV689: $i] :
      ( ( ( in @ SV689 @ SV133 )
        = $false )
      | ( ( ( ap @ SV133 @ SV361 @ SV527 @ SV689 )
          = ( ap @ SV133 @ SV361 @ SV527 @ SV689 ) )
        = $true )
      | ( ( func @ SV133 @ SV361 @ SV527 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2286]) ).

thf(2468,plain,
    ! [SV690: $i > $o,SV529: $i,SV363: $i,SV135: $i] :
      ( ( ( ! [SY3122: $i] :
              ( ~ ( in @ SY3122 @ SV135 )
              | ! [SY3123: $i] :
                  ( ~ ( in @ SY3123 @ SV363 )
                  | ~ ( in @ ( kpair @ SY3122 @ SY3123 ) @ SV529 )
                  | ( SV690 @ ( kpair @ SY3122 @ SY3123 ) ) ) ) )
        = $false )
      | ( ( ! [SY3124: $i] :
              ( ~ ( in @ SY3124 @ SV529 )
              | ( SV690 @ SY3124 ) ) )
        = $true )
      | ( ( subset @ SV529 @ ( cartprod @ SV135 @ SV363 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2287]) ).

thf(2469,plain,
    ! [SV365: $i,SV643: $i,SV137: $i,SV741: $i] :
      ( ( ( ~ ( in @ SV741 @ SV137 )
          | ~ ~ ( in @ SV741 @ SV643 )
          | ~ ( in @ SV741 @ ( binintersect @ SV365 @ SV643 ) ) )
        = $true )
      | ( ( in @ SV643 @ ( powerset @ SV137 ) )
        = $false )
      | ( ( in @ SV365 @ ( powerset @ SV137 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2289]) ).

thf(2470,plain,
    ! [SV140: $i,SV531: $i,SV370: $i,SV691: $i] :
      ( ( ( in @ SV691 @ SV370 )
        = $false )
      | ( ( in @ ( kpair @ SV531 @ SV691 ) @ ( cartprod @ SV140 @ SV370 ) )
        = $true )
      | ( ( in @ SV531 @ SV140 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2290]) ).

thf(2471,plain,
    ! [SV644: $i,SV372: $i > $o,SV142: $i,SV742: $i] :
      ( ( ( ~ ( in @ SV742 @ SV142 )
          | ~ ( SV372 @ SV644 )
          | ~ ( SV372 @ SV742 )
          | ( SV644 = SV742 ) )
        = $true )
      | ( ( in @ SV644 @ SV142 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV142
            @ ^ [SY2680: $i] : ( SV372 @ SY2680 ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2291]) ).

thf(2472,plain,
    ! [SV144: $i,SV533: $i,SV374: $i,SV692: $i] :
      ( ( ( in @ SV692 @ SV374 )
        = $false )
      | ( ( ( kfst @ ( kpair @ SV533 @ SV692 ) )
          = SV533 )
        = $true )
      | ( ( in @ SV533 @ SV144 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2292]) ).

thf(2473,plain,
    ! [SV147: $i > $i > $o,SV377: $i] :
      ( ( ( ! [SY2690: $i] :
              ~ ! [SY2691: $i] :
                  ~ ( ~ ( ~ ( in @ SY2691 @ SY2690 )
                        | ~ ! [SY2692: $i] :
                              ~ ~ ( ~ ( in @ SY2692 @ SV377 )
                                  | ~ ( SV147 @ SY2692 @ SY2691 ) ) )
                    | ~ ( ~ ~ ! [SY2693: $i] :
                                ~ ~ ( ~ ( in @ SY2693 @ SV377 )
                                    | ~ ( SV147 @ SY2693 @ SY2691 ) )
                        | ( in @ SY2691 @ SY2690 ) ) ) )
        = $false )
      | ( ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2293]) ).

thf(2474,plain,
    ! [SV743: $i,SV377: $i,SV147: $i > $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
                | ~ ! [SY3162: $i] :
                      ( ~ ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SY3162 )
                      | ( SV743 = SY3162 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2690: $i] :
                ~ ! [SY2691: $i] :
                    ~ ( ~ ( ~ ( in @ SY2691 @ SY2690 )
                          | ~ ! [SY2692: $i] :
                                ~ ~ ( ~ ( in @ SY2692 @ SV377 )
                                    | ~ ( SV147 @ SY2692 @ SY2691 ) ) )
                      | ~ ( ~ ~ ! [SY2693: $i] :
                                  ~ ~ ( ~ ( in @ SY2693 @ SV377 )
                                      | ~ ( SV147 @ SY2693 @ SY2691 ) )
                          | ( in @ SY2691 @ SY2690 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2294]) ).

thf(2475,plain,
    ! [SV645: $i,SV381: $i,SV151: $i,SV744: $i] :
      ( ( ( ~ ( in @ SV744 @ SV151 )
          | ~ ~ ( in @ SV744 @ ( binunion @ SV381 @ SV645 ) )
          | ~ ( in @ SV744 @ SV645 ) )
        = $true )
      | ( ( in @ SV645 @ ( powerset @ SV151 ) )
        = $false )
      | ( ( in @ SV381 @ ( powerset @ SV151 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2296]) ).

thf(2476,plain,
    ! [SV382: $i,SV152: $i,SV693: $i,SV646: $i] :
      ( ( ( SV646 = SV693 )
        = $false )
      | ( ( ( setadjoin @ SV152 @ SV646 )
          = ( setadjoin @ SV382 @ SV693 ) )
        = $true )
      | ( ( SV152 = SV382 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2297]) ).

thf(2477,plain,
    ! [SV647: $i,SV385: $i,SV156: $i,SV745: $i] :
      ( ( ( ~ ( in @ SV745 @ SV156 )
          | ~ ~ ( in @ SV745 @ SV385 )
          | ~ ( in @ SV745 @ ( binintersect @ SV385 @ SV647 ) ) )
        = $true )
      | ( ( in @ SV647 @ ( powerset @ SV156 ) )
        = $false )
      | ( ( in @ SV385 @ ( powerset @ SV156 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2298]) ).

thf(2478,plain,
    ! [SV648: $i,SV157: $i > $o] :
      ( ( ( ~ ( SV157 @ SV648 ) )
        = $true )
      | ( ( ~ ! [SY3087: $i] :
                ( ~ ( SV157 @ SY3087 )
                | ( SV648 = SY3087 ) ) )
        = $true )
      | ( ( SV157
          @ ( descr
            @ ^ [SY2227: $i] : ( SV157 @ SY2227 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2299]) ).

thf(2479,plain,
    ! [SV388: $i > $o,SV160: $i,SV694: $i] :
      ( ( ( in @ SV694 @ SV160 )
        = $false )
      | ( ( SV388 @ SV694 )
        = $true )
      | ( ( ~ ! [SY2705: $i] :
                ~ ~ ( ~ ( in @ SY2705 @ SV160 )
                    | ~ ~ ( SV388 @ SY2705 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2300]) ).

thf(2480,plain,
    ! [SV649: $i,SV389: $i,SV161: $i,SV746: $i] :
      ( ( ( ~ ( in @ SV746 @ SV161 )
          | ~ ( in @ SV746 @ ( setminus @ SV161 @ SV389 ) )
          | ( in @ SV746 @ ( setminus @ SV161 @ ( binintersect @ SV389 @ SV649 ) ) ) )
        = $true )
      | ( ( in @ SV649 @ ( powerset @ SV161 ) )
        = $false )
      | ( ( in @ SV389 @ ( powerset @ SV161 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2301]) ).

thf(2481,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( ! [SY2242: $i,SY2243: $i] :
              ( ~ ( SV165 @ SY2242 )
              | ~ ( SV165 @ SY2243 )
              | ( SY2242 = SY2243 ) ) )
        = $false )
      | ( ( ~ ! [SY2244: $i] :
                ~ ~ ( ~ ( SV165 @ SY2244 )
                    | ~ ! [SY2245: $i] :
                          ( ~ ( SV165 @ SY2245 )
                          | ( SY2244 = SY2245 ) ) ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2303]) ).

thf(2482,plain,
    ! [SV166: $i,SV393: $i,SV538: $i] :
      ( ( ( in @ SV538 @ SV393 )
        = $true )
      | ( ( ~ ( subset @ SV166 @ SV393 ) )
        = $true )
      | ( ( in @ SV538 @ SV166 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2304]) ).

thf(2483,plain,
    ! [SV652: $i,SV394: $i,SV167: $i,SV747: $i] :
      ( ( ( ~ ( in @ SV747 @ ( powerset @ SV167 ) )
          | ( in @ ( binintersect @ SV394 @ SV652 ) @ ( powerset @ ( binintersect @ ( binunion @ SV394 @ SV747 ) @ ( binunion @ SV652 @ SV747 ) ) ) ) )
        = $true )
      | ( ( in @ SV652 @ ( powerset @ SV167 ) )
        = $false )
      | ( ( in @ SV394 @ ( powerset @ SV167 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2305]) ).

thf(2484,plain,
    ! [SV539: $i,SV395: $i,SV168: $i,SV695: $i] :
      ( ( ( subset @ SV695 @ ( cartprod @ SV168 @ SV395 ) )
        = $false )
      | ( ( ~ ! [SY3125: $i] :
                ( ~ ( in @ SY3125 @ SV168 )
                | ! [SY3126: $i] :
                    ( ~ ( in @ SY3126 @ SV395 )
                    | ~ ( in @ ( kpair @ SY3125 @ SY3126 ) @ SV539 )
                    | ( in @ ( kpair @ SY3125 @ SY3126 ) @ SV695 ) ) )
          | ( subset @ SV539 @ SV695 ) )
        = $true )
      | ( ( subset @ SV539 @ ( cartprod @ SV168 @ SV395 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2306]) ).

thf(2485,plain,
    ! [SV540: $i,SV396: $o,SV169: $i,SV696: $i] :
      ( ( ( in @ SV696 @ SV169 )
        = $false )
      | ( ( ~ SV396
          | ( ( if @ SV169 @ SV396 @ SV540 @ SV696 )
            = SV540 ) )
        = $true )
      | ( ( in @ SV540 @ SV169 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2307]) ).

thf(2486,plain,
    ! [SV541: $i,SV169: $i,SV697: $i] :
      ( ( ( in @ SV697 @ SV169 )
        = $false )
      | ( ( ~ $true
          | ( ( if @ SV169 @ $true @ SV541 @ SV697 )
            = SV541 ) )
        = $true )
      | ( ( in @ SV541 @ SV169 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2308]) ).

thf(2487,plain,
    ! [SV542: $i,SV169: $i,SV698: $i] :
      ( ( ( in @ SV698 @ SV169 )
        = $false )
      | ( ( ~ $false
          | ( ( if @ SV169 @ $false @ SV542 @ SV698 )
            = SV542 ) )
        = $true )
      | ( ( in @ SV542 @ SV169 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2309]) ).

thf(2488,plain,
    ! [SV170: $i,SV543: $i > $i,SV397: $i] :
      ( ( ( in @ ( sK22_SY2969 @ SV397 @ SV543 @ SV170 ) @ SV170 )
        = $true )
      | ( ( ! [SY2970: $i] :
              ( ~ ( in @ SY2970 @ SV170 )
              | ( ( ap @ SV170 @ SV397
                  @ ( lam @ SV170 @ SV397
                    @ ^ [SY2971: $i] : ( SV543 @ SY2971 ) )
                  @ SY2970 )
                = ( SV543 @ SY2970 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2310]) ).

thf(2489,plain,
    ! [SV543: $i > $i,SV397: $i,SV170: $i,SV748: $i] :
      ( ( ( ~ ( in @ SV748 @ SV170 )
          | ( ( ap @ SV170 @ SV397
              @ ( lam @ SV170 @ SV397
                @ ^ [SY2971: $i] : ( SV543 @ SY2971 ) )
              @ SV748 )
            = ( SV543 @ SV748 ) ) )
        = $true )
      | ( ( in @ ( SV543 @ ( sK22_SY2969 @ SV397 @ SV543 @ SV170 ) ) @ SV397 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2311]) ).

thf(2490,plain,
    ! [SV174: $i,SV400: $i,SV614: $i,SV546: $i] :
      ( ( ( SV546 = SV614 )
        = $false )
      | ( ( SV400 = SV614 )
        = $true )
      | ( ( ( setadjoin @ ( setadjoin @ SV174 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV174 @ ( setadjoin @ SV400 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ SV546 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV546 @ ( setadjoin @ SV614 @ emptyset ) ) @ emptyset ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2313]) ).

thf(2491,plain,
    ! [SV548: $i,SV402: $i,SV176: $i,SV699: $i] :
      ( ( ( in @ SV699 @ SV176 )
        = $false )
      | ( ( in @ ( ap @ SV176 @ SV402 @ SV548 @ SV699 ) @ SV402 )
        = $true )
      | ( ( func @ SV176 @ SV402 @ SV548 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2314]) ).

thf(2492,plain,
    ! [SV654: $i,SV403: $i,SV177: $i,SV749: $i] :
      ( ( ( ~ ( in @ SV749 @ SV177 )
          | ~ ( subset @ SV403 @ ( setminus @ SV177 @ SV654 ) )
          | ~ ( in @ SV749 @ SV654 )
          | ~ ( in @ SV749 @ SV403 ) )
        = $true )
      | ( ( in @ SV654 @ ( powerset @ SV177 ) )
        = $false )
      | ( ( in @ SV403 @ ( powerset @ SV177 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2315]) ).

thf(2493,plain,
    ! [SV178: $i,SV616: $i,SV549: $i > $i > $o,SV404: $i,SV733: $i] :
      ( ( ( ~ ( in @ SV733 @ SV404 ) )
        = $true )
      | ( ( ~ ( SV549 @ SV616 @ SV733 )
          | ( in @ ( kpair @ SV616 @ SV733 )
            @ ( dpsetconstr @ SV178 @ SV404
              @ ^ [SY2978: $i,SY2979: $i] : ( SV549 @ SY2978 @ SY2979 ) ) ) )
        = $true )
      | ( ( in @ SV616 @ SV178 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2316]) ).

thf(2494,plain,
    ! [SV179: $i,SV405: $i,SV550: $i] :
      ( ( ( in @ SV550 @ SV405 )
        = $true )
      | ( ( SV179 != SV405 )
        = $true )
      | ( ( in @ SV550 @ SV179 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2317]) ).

thf(2495,plain,
    ! [SV182: $i,SV408: $i,SV655: $i] :
      ( ( ( ~ ( in @ SV655 @ SV408 ) )
        = $true )
      | ( ( in @ SV655 @ ( setminus @ SV182 @ ( setminus @ SV182 @ SV408 ) ) )
        = $true )
      | ( ( in @ SV655 @ SV182 )
        = $false )
      | ( ( in @ SV408 @ ( powerset @ SV182 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2320]) ).

thf(2496,plain,
    ! [SV554: $i,SV411: $i,SV185: $i,SV700: $i] :
      ( ( ( in @ SV700 @ SV185 )
        = $false )
      | ( ( ! [SY3127: $i] :
              ( ~ ( in @ SY3127 @ SV411 )
              | ~ ( in @ ( kpair @ SV700 @ SY3127 ) @ SV554 )
              | ( ( ap @ SV185 @ SV411 @ SV554 @ SV700 )
                = SY3127 ) ) )
        = $true )
      | ( ( func @ SV185 @ SV411 @ SV554 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2321]) ).

thf(2497,plain,
    ! [SV414: $i > $o,SV188: $i,SV556: $i] :
      ( ( ( ~ ( in @ SV556
              @ ( dsetconstr @ SV188
                @ ^ [SY2751: $i] : ( SV414 @ SY2751 ) ) )
          | ( SV414 @ SV556 ) )
        = $true )
      | ( ( in @ SV556 @ SV188 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2323]) ).

thf(2498,plain,
    ! [SV188: $i,SV556: $i,SV414: $i > $o] :
      ( ( ( ~ ( SV414 @ SV556 )
          | ( in @ SV556
            @ ( dsetconstr @ SV188
              @ ^ [SY2752: $i] : ( SV414 @ SY2752 ) ) ) )
        = $true )
      | ( ( in @ SV556 @ SV188 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2324]) ).

thf(2499,plain,
    ! [SV558: $i,SV701: $i,SV416: $i,SV190: $i] :
      ( ( ( func @ SV190 @ SV416 @ SV701 )
        = $false )
      | ( ( ~ ! [SY3128: $i] :
                ( ~ ( in @ SY3128 @ SV190 )
                | ( ( ap @ SV190 @ SV416 @ SV558 @ SY3128 )
                  = ( ap @ SV190 @ SV416 @ SV701 @ SY3128 ) ) )
          | ( SV558 = SV701 ) )
        = $true )
      | ( ( func @ SV190 @ SV416 @ SV558 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2325]) ).

thf(2500,plain,
    ! [SV657: $i,SV417: $i,SV191: $i,SV750: $i] :
      ( ( ( ~ ( in @ SV750 @ ( powerset @ SV191 ) )
          | ! [SY3164: $i] :
              ( ~ ( in @ SY3164 @ SV191 )
              | ~ ( in @ SY3164 @ ( binintersect @ SV417 @ SV657 ) )
              | ( in @ SY3164 @ ( binunion @ SV417 @ SV750 ) ) ) )
        = $true )
      | ( ( in @ SV657 @ ( powerset @ SV191 ) )
        = $false )
      | ( ( in @ SV417 @ ( powerset @ SV191 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2326]) ).

thf(2501,plain,
    ! [SV419: $i,SV193: $i,SV702: $i,SV658: $i] :
      ( ( ( SV658 = SV702 )
        = $false )
      | ( ( ~ ( ~ ( ~ ( in @ SV658 @ SV193 )
                  | ( in @ SV702 @ SV419 ) )
              | ~ ( ~ ( in @ SV702 @ SV419 )
                  | ( in @ SV658 @ SV193 ) ) ) )
        = $true )
      | ( ( SV193 = SV419 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2327]) ).

thf(2502,plain,
    ! [SV560: $i,SV420: $o,SV194: $i,SV703: $i] :
      ( ( ( in @ SV703 @ SV194 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV194
            @ ^ [SY3129: $i] :
                ( ~ ( ~ SV420
                    | ( SY3129 != SV560 ) )
                | ~ ( ~ ~ SV420
                    | ( SY3129 != SV703 ) ) ) ) )
        = $true )
      | ( ( in @ SV560 @ SV194 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2328]) ).

thf(2503,plain,
    ! [SV561: $i,SV194: $i,SV704: $i] :
      ( ( ( in @ SV704 @ SV194 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV194
            @ ^ [SY3130: $i] :
                ( ~ ( ~ $true
                    | ( SY3130 != SV561 ) )
                | ~ ( ~ ~ $true
                    | ( SY3130 != SV704 ) ) ) ) )
        = $true )
      | ( ( in @ SV561 @ SV194 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2329]) ).

thf(2504,plain,
    ! [SV562: $i,SV194: $i,SV705: $i] :
      ( ( ( in @ SV705 @ SV194 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV194
            @ ^ [SY3131: $i] :
                ( ~ ( ~ $false
                    | ( SY3131 != SV562 ) )
                | ~ ( ~ ~ $false
                    | ( SY3131 != SV705 ) ) ) ) )
        = $true )
      | ( ( in @ SV562 @ SV194 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2330]) ).

thf(2505,plain,
    ! [SV196: $i,SV563: $i,SV422: $i,SV706: $i] :
      ( ( ( in @ SV706 @ SV422 )
        = $false )
      | ( ( in @ ( kpair @ SV563 @ SV706 ) @ ( powerset @ ( powerset @ ( binunion @ SV196 @ SV422 ) ) ) )
        = $true )
      | ( ( in @ SV563 @ SV196 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2331]) ).

thf(2506,plain,
    ! [SV564: $i,SV423: $o,SV197: $i,SV707: $i] :
      ( ( ( in @ SV707 @ SV197 )
        = $false )
      | ( ( in @ ( if @ SV197 @ SV423 @ SV564 @ SV707 ) @ SV197 )
        = $true )
      | ( ( in @ SV564 @ SV197 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2332]) ).

thf(2507,plain,
    ! [SV565: $i,SV197: $i,SV708: $i] :
      ( ( ( in @ SV708 @ SV197 )
        = $false )
      | ( ( in @ ( if @ SV197 @ $true @ SV565 @ SV708 ) @ SV197 )
        = $true )
      | ( ( in @ SV565 @ SV197 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2333]) ).

thf(2508,plain,
    ! [SV566: $i,SV197: $i,SV709: $i] :
      ( ( ( in @ SV709 @ SV197 )
        = $false )
      | ( ( in @ ( if @ SV197 @ $false @ SV566 @ SV709 ) @ SV197 )
        = $true )
      | ( ( in @ SV566 @ SV197 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2334]) ).

thf(2509,plain,
    ! [SV567: $i,SV424: $i,SV198: $i,SV710: $i] :
      ( ( ( in @ SV710 @ SV198 )
        = $false )
      | ( ( ! [SY3132: $i] :
              ( ~ ( in @ SY3132 @ SV424 )
              | ~ ( in @ ( kpair @ SV710 @ SY3132 ) @ SV567 )
              | ( ( ap @ SV198 @ SV424 @ SV567 @ SV710 )
                = SY3132 ) ) )
        = $true )
      | ( ( in @ SV567 @ ( funcSet @ SV198 @ SV424 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2335]) ).

thf(2510,plain,
    ! [SV199: $i,SV568: $i > $i,SV425: $i] :
      ( ( ( in @ ( sK23_SY3000 @ SV425 @ SV568 @ SV199 ) @ SV199 )
        = $true )
      | ( ( func @ SV199 @ SV425
          @ ( lam @ SV199 @ SV425
            @ ^ [SY3001: $i] : ( SV568 @ SY3001 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2336]) ).

thf(2511,plain,
    ! [SV426: $i > $o,SV200: $i] :
      ( ( ( ~ ! [SY2778: $i] :
                ~ ~ ( ~ ( in @ SY2778 @ SV200 )
                    | ~ ( SV426 @ SY2778 ) ) )
        = $false )
      | ( ( in @ ( sK16_SY2777 @ SV426 @ SV200 ) @ SV200 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2338]) ).

thf(2512,plain,
    ! [SV426: $i > $o,SV200: $i] :
      ( ( ( ~ ! [SY2778: $i] :
                ~ ~ ( ~ ( in @ SY2778 @ SV200 )
                    | ~ ( SV426 @ SY2778 ) ) )
        = $false )
      | ( ( SV426 @ ( sK16_SY2777 @ SV426 @ SV200 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2339]) ).

thf(2513,plain,
    ! [SV569: $i,SV428: $i,SV202: $i,SV711: $i] :
      ( ( ( in @ SV711 @ SV202 )
        = $false )
      | ( ( in @ ( ap @ SV202 @ SV428 @ SV569 @ SV711 ) @ SV428 )
        = $true )
      | ( ( in @ SV569 @ ( funcSet @ SV202 @ SV428 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2340]) ).

thf(2514,plain,
    ! [SV205: $i,SV430: $i] :
      ( ( ( ! [SY2781: $i] :
              ~ ~ ( ~ ( in @ SV430 @ SY2781 )
                  | ~ ( in @ SY2781 @ SV205 ) ) )
        = $false )
      | ( ( in @ SV430 @ ( setunion @ SV205 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2342]) ).

thf(2515,plain,
    ! [SV205: $i,SV430: $i] :
      ( ( ( ! [SY2782: $i] :
              ~ ~ ( ~ ( in @ SV430 @ SY2782 )
                  | ~ ( in @ SY2782 @ SV205 ) ) )
        = $true )
      | ( ( in @ SV430 @ ( setunion @ SV205 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2343]) ).

thf(2516,plain,
    ! [SV712: $o,SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV206 )
          | ~ ~ ( in @ SV570 @ SV431 )
          | SV712 )
        = $false )
      | ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | SV712 )
          | SV712 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2344]) ).

thf(2517,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV206 )
          | ~ ~ ( in @ SV570 @ SV431 )
          | $true )
        = $false )
      | ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | $true )
          | $true )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2345]) ).

thf(2518,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV206 )
          | ~ ~ ( in @ SV570 @ SV431 )
          | $false )
        = $false )
      | ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | $false )
          | $false )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2346]) ).

thf(2519,plain,
    ! [SV208: $i,SV433: $i] :
      ( ( ( ~ ( in @ ( sK25_SY2785 @ SV433 @ SV208 ) @ SV208 )
          | ~ ( in @ SV433 @ ( sK25_SY2785 @ SV433 @ SV208 ) ) )
        = $false )
      | ( ( in @ SV433 @ ( setunion @ SV208 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2347]) ).

thf(2520,plain,
    ! [SV713: $i > $o,SV659: $i > $o,SV434: $i,SV209: $i] :
      ( ( ( ! [SY3133: $i] :
              ( ~ ( in @ SY3133 @ SV209 )
              | ! [SY3134: $i] :
                  ( ~ ( in @ SY3134 @ SV434 )
                  | ( SY3133 != SY3134 )
                  | ~ ( ~ ( ~ ( SV659 @ SY3133 )
                          | ( SV713 @ SY3134 ) )
                      | ~ ( ~ ( SV713 @ SY3134 )
                          | ( SV659 @ SY3133 ) ) ) ) ) )
        = $false )
      | ( ( ( dsetconstr @ SV209
            @ ^ [SY3097: $i] : ( SV659 @ SY3097 ) )
          = ( dsetconstr @ SV434
            @ ^ [SY3136: $i] : ( SV713 @ SY3136 ) ) )
        = $true )
      | ( ( SV209 = SV434 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2348]) ).

thf(2521,plain,
    ! [SV435: $i,SV714: $o,SV210: $i,SV571: $i] :
      ( ( ( ( SV571 != SV210 )
          | SV714 )
        = $false )
      | ( ( ~ ( ~ ( in @ SV571 @ SV435 )
              | SV714 )
          | SV714 )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2349]) ).

thf(2522,plain,
    ! [SV435: $i,SV210: $i,SV571: $i] :
      ( ( ( ( SV571 != SV210 )
          | $true )
        = $false )
      | ( ( ~ ( ~ ( in @ SV571 @ SV435 )
              | $true )
          | $true )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2350]) ).

thf(2523,plain,
    ! [SV435: $i,SV210: $i,SV571: $i] :
      ( ( ( ( SV571 != SV210 )
          | $false )
        = $false )
      | ( ( ~ ( ~ ( in @ SV571 @ SV435 )
              | $false )
          | $false )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2351]) ).

thf(2524,plain,
    ! [SV660: $i,SV211: $i > $o] :
      ( ( ( ~ ( SV211 @ SV660 ) )
        = $true )
      | ( ( ~ ! [SY3099: $i] :
                ( ~ ( SV211 @ SY3099 )
                | ( SV660 = SY3099 ) ) )
        = $true )
      | ( ( ~ ! [SY2378: $i] :
                ~ ~ ( ~ ( SV211 @ SY2378 )
                    | ~ ! [SY2379: $i] :
                          ( ~ ( SV211 @ SY2379 )
                          | ( SY2378 = SY2379 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2352]) ).

thf(2525,plain,
    ! [SV572: $i,SV436: $i,SV212: $i,SV715: $i] :
      ( ( ( in @ SV715 @ SV212 )
        = $false )
      | ( ( ( ap @ SV212 @ SV436 @ SV572 @ SV715 )
          = ( ap @ SV212 @ SV436 @ SV572 @ SV715 ) )
        = $true )
      | ( ( in @ SV572 @ ( funcSet @ SV212 @ SV436 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2353]) ).

thf(2526,plain,
    ! [SV437: $i,SV213: $i,SV661: $i] :
      ( ( ( ~ ( in @ SV661 @ ( setminus @ SV213 @ ( setminus @ SV213 @ SV437 ) ) ) )
        = $true )
      | ( ( in @ SV661 @ SV437 )
        = $true )
      | ( ( in @ SV661 @ SV213 )
        = $false )
      | ( ( in @ SV437 @ ( powerset @ SV213 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2354]) ).

thf(2527,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ~ ! [SY2388: $i] :
                          ~ ~ ( ~ ( SV214 @ SY2388 )
                              | ~ ! [SY2389: $i] :
                                    ( ~ ( SV214 @ SY2389 )
                                    | ( SY2388 = SY2389 ) ) )
                  | ~ ! [SY2801: $i] :
                        ~ ~ ( ~ ( SV438 @ SY2801 )
                            | ~ ! [SY2802: $i] :
                                  ( ~ ( SV438 @ SY2802 )
                                  | ( SY2801 = SY2802 ) ) ) )
              | ~ ( ~ ~ ! [SY2803: $i] :
                          ~ ~ ( ~ ( SV438 @ SY2803 )
                              | ~ ! [SY2804: $i] :
                                    ( ~ ( SV438 @ SY2804 )
                                    | ( SY2803 = SY2804 ) ) )
                  | ~ ! [SY2394: $i] :
                        ~ ~ ( ~ ( SV214 @ SY2394 )
                            | ~ ! [SY2395: $i] :
                                  ( ~ ( SV214 @ SY2395 )
                                  | ( SY2394 = SY2395 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2355]) ).

thf(2528,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ( ~ ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
              | ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) ) )
          | ~ ( ~ ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
              | ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ~ ! [SY2388: $i] :
                          ~ ~ ( ~ ( SV214 @ SY2388 )
                              | ~ ! [SY2389: $i] :
                                    ( ~ ( SV214 @ SY2389 )
                                    | ( SY2388 = SY2389 ) ) )
                  | ~ ! [SY2801: $i] :
                        ~ ~ ( ~ ( SV438 @ SY2801 )
                            | ~ ! [SY2802: $i] :
                                  ( ~ ( SV438 @ SY2802 )
                                  | ( SY2801 = SY2802 ) ) ) )
              | ~ ( ~ ~ ! [SY2803: $i] :
                          ~ ~ ( ~ ( SV438 @ SY2803 )
                              | ~ ! [SY2804: $i] :
                                    ( ~ ( SV438 @ SY2804 )
                                    | ( SY2803 = SY2804 ) ) )
                  | ~ ! [SY2394: $i] :
                        ~ ~ ( ~ ( SV214 @ SY2394 )
                            | ~ ! [SY2395: $i] :
                                  ( ~ ( SV214 @ SY2395 )
                                  | ( SY2394 = SY2395 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2356]) ).

thf(2529,plain,
    ! [SV215: $i,SV439: $i > $o] :
      ( ( ( ~ ( in @ ( sK27_SY2808 @ SV439 @ SV215 ) @ SV215 )
          | ~ ( SV439 @ ( sK27_SY2808 @ SV439 @ SV215 ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV215
            @ ^ [SY2807: $i] : ( SV439 @ SY2807 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2357]) ).

thf(2530,plain,
    ! [SV573: $i,SV440: $i > $o,SV216: $i] :
      ( ( ( ~ ! [SY3006: $i] :
                ( ~ ( in @ SY3006 @ SV216 )
                | ~ ( SV440 @ SY3006 )
                | ( SY3006 = SV573 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV216
            @ ^ [SY2811: $i] : ( SV440 @ SY2811 ) ) )
        = $true )
      | ( ( SV440 @ SV573 )
        = $false )
      | ( ( in @ SV573 @ SV216 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2358]) ).

thf(2531,plain,
    ! [SV218: $i,SV574: $i,SV442: $i,SV716: $i] :
      ( ( ( in @ SV716 @ SV442 )
        = $false )
      | ( ( subset @ ( setadjoin @ ( setadjoin @ SV574 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV574 @ ( setadjoin @ SV716 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV218 @ SV442 ) ) )
        = $true )
      | ( ( in @ SV574 @ SV218 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2359]) ).

thf(2532,plain,
    ! [SV219: $i,SV575: $i,SV443: $i,SV717: $i] :
      ( ( ( in @ SV717 @ SV443 )
        = $false )
      | ( ( ( ksnd @ ( kpair @ SV575 @ SV717 ) )
          = SV717 )
        = $true )
      | ( ( in @ SV575 @ SV219 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2360]) ).

thf(2533,plain,
    ! [SV576: $i,SV444: $o,SV220: $i,SV718: $i] :
      ( ( ( in @ SV718 @ SV220 )
        = $false )
      | ( ( ~ SV444
          | ( ( dsetconstr @ SV220
              @ ^ [SY3137: $i] :
                  ( ~ ( ~ SV444
                      | ( SY3137 != SV576 ) )
                  | ~ ( ~ ~ SV444
                      | ( SY3137 != SV718 ) ) ) )
            = ( setadjoin @ SV576 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV576 @ SV220 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2361]) ).

thf(2534,plain,
    ! [SV577: $i,SV220: $i,SV719: $i] :
      ( ( ( in @ SV719 @ SV220 )
        = $false )
      | ( ( ~ $true
          | ( ( dsetconstr @ SV220
              @ ^ [SY3138: $i] :
                  ( ~ ( ~ $true
                      | ( SY3138 != SV577 ) )
                  | ~ ( ~ ~ $true
                      | ( SY3138 != SV719 ) ) ) )
            = ( setadjoin @ SV577 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV577 @ SV220 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2362]) ).

thf(2535,plain,
    ! [SV578: $i,SV220: $i,SV720: $i] :
      ( ( ( in @ SV720 @ SV220 )
        = $false )
      | ( ( ~ $false
          | ( ( dsetconstr @ SV220
              @ ^ [SY3139: $i] :
                  ( ~ ( ~ $false
                      | ( SY3139 != SV578 ) )
                  | ~ ( ~ ~ $false
                      | ( SY3139 != SV720 ) ) ) )
            = ( setadjoin @ SV578 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV578 @ SV220 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2363]) ).

thf(2536,plain,
    ! [SV579: $i,SV445: $i,SV221: $i,SV721: $i] :
      ( ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( ~ ! [SY3140: $i] :
                ( ~ ( in @ SY3140 @ SV221 )
                | ! [SY3141: $i] :
                    ( ~ ( in @ SY3141 @ SV445 )
                    | ~ ( in @ ( kpair @ SY3140 @ SY3141 ) @ SV579 )
                    | ( in @ ( kpair @ SY3140 @ SY3141 ) @ SV721 ) ) )
          | ~ ! [SY3142: $i] :
                ( ~ ( in @ SY3142 @ SV221 )
                | ! [SY3143: $i] :
                    ( ~ ( in @ SY3143 @ SV445 )
                    | ~ ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV721 )
                    | ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV579 ) ) )
          | ( SV579 = SV721 ) )
        = $true )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2364]) ).

thf(2537,plain,
    ! [SV580: $i,SV446: $i,SV222: $i,SV722: $i] :
      ( ( ( in @ SV722 @ SV222 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV446
            @ ^ [SY3144: $i] : ( in @ ( kpair @ SV722 @ SY3144 ) @ SV580 ) ) )
        = $true )
      | ( ( func @ SV222 @ SV446 @ SV580 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2365]) ).

thf(2538,plain,
    ! [SV224: $i] :
      ( ( ( ~ ( in @ ( sK28_SY2426 @ SV224 ) @ SV224 )
          | ~ $true )
        = $false )
      | ( ( SV224 = emptyset )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2366]) ).

thf(2539,plain,
    ! [SV226: $i,SV449: $i,SV582: $i] :
      ( ( ( in @ SV582 @ SV449 )
        = $true )
      | ( ( in @ SV582 @ ( symdiff @ SV226 @ SV449 ) )
        = $true )
      | ( ( in @ SV582 @ SV226 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2368]) ).

thf(2540,plain,
    ! [SV450: $i,SV662: $i,SV227: $i] :
      ( ( ( ~ ( subset @ ( setminus @ SV227 @ SV662 ) @ ( setminus @ SV227 @ SV450 ) ) )
        = $true )
      | ( ( subset @ SV450 @ SV662 )
        = $true )
      | ( ( in @ SV662 @ ( powerset @ SV227 ) )
        = $false )
      | ( ( in @ SV450 @ ( powerset @ SV227 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2369]) ).

thf(2541,plain,
    ! [SV663: $i,SV451: $i,SV228: $i,SV751: $i] :
      ( ( ( ~ ( in @ SV751 @ ( powerset @ SV228 ) )
          | ! [SY3165: $i] :
              ( ~ ( in @ SY3165 @ SV228 )
              | ~ ( in @ SY3165 @ ( binintersect @ SV451 @ SV663 ) )
              | ( in @ SY3165 @ ( binunion @ SV663 @ SV751 ) ) ) )
        = $true )
      | ( ( in @ SV663 @ ( powerset @ SV228 ) )
        = $false )
      | ( ( in @ SV451 @ ( powerset @ SV228 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2370]) ).

thf(2542,plain,
    ! [SV583: $i,SV453: $o,SV230: $i,SV723: $i] :
      ( ( ( in @ SV723 @ SV230 )
        = $false )
      | ( ( ~ ~ SV453
          | ( ( dsetconstr @ SV230
              @ ^ [SY3145: $i] :
                  ( ~ ( ~ SV453
                      | ( SY3145 != SV583 ) )
                  | ~ ( ~ ~ SV453
                      | ( SY3145 != SV723 ) ) ) )
            = ( setadjoin @ SV723 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV583 @ SV230 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2371]) ).

thf(2543,plain,
    ! [SV584: $i,SV230: $i,SV724: $i] :
      ( ( ( in @ SV724 @ SV230 )
        = $false )
      | ( ( ~ ~ $true
          | ( ( dsetconstr @ SV230
              @ ^ [SY3146: $i] :
                  ( ~ ( ~ $true
                      | ( SY3146 != SV584 ) )
                  | ~ ( ~ ~ $true
                      | ( SY3146 != SV724 ) ) ) )
            = ( setadjoin @ SV724 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV584 @ SV230 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2372]) ).

thf(2544,plain,
    ! [SV585: $i,SV230: $i,SV725: $i] :
      ( ( ( in @ SV725 @ SV230 )
        = $false )
      | ( ( ~ ~ $false
          | ( ( dsetconstr @ SV230
              @ ^ [SY3147: $i] :
                  ( ~ ( ~ $false
                      | ( SY3147 != SV585 ) )
                  | ~ ( ~ ~ $false
                      | ( SY3147 != SV725 ) ) ) )
            = ( setadjoin @ SV725 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV585 @ SV230 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2373]) ).

thf(2545,plain,
    ! [SV664: $i,SV454: $i,SV231: $i] :
      ( ( ( ~ ! [SY3103: $i] :
                ( ~ ( in @ SY3103 @ SV231 )
                | ~ ( in @ SY3103 @ SV454 )
                | ( in @ SY3103 @ SV664 ) ) )
        = $true )
      | ( ( in @ SV454 @ ( powerset @ SV664 ) )
        = $true )
      | ( ( in @ SV664 @ ( powerset @ SV231 ) )
        = $false )
      | ( ( in @ SV454 @ ( powerset @ SV231 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2374]) ).

thf(2546,plain,
    ! [SV665: $i,SV466: $i,SV243: $i] :
      ( ( ( ~ ! [SY3104: $i] :
                ( ~ ( in @ SY3104 @ SV243 )
                | ~ ( in @ SY3104 @ SV466 )
                | ( in @ SY3104 @ SV665 ) ) )
        = $true )
      | ( ( subset @ SV466 @ SV665 )
        = $true )
      | ( ( in @ SV665 @ ( powerset @ SV243 ) )
        = $false )
      | ( ( in @ SV466 @ ( powerset @ SV243 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2377]) ).

thf(2547,plain,
    ! [SV244: $i,SV594: $i > $i,SV467: $i] :
      ( ( ( in @ ( sK29_SY3031 @ SV467 @ SV594 @ SV244 ) @ SV244 )
        = $true )
      | ( ( ! [SY3032: $i] :
              ( ~ ( in @ SY3032 @ SV244 )
              | ( ( ap @ SV244 @ SV467
                  @ ( lam @ SV244 @ SV467
                    @ ^ [SY3033: $i] : ( SV594 @ SY3033 ) )
                  @ SY3032 )
                = ( SV594 @ SY3032 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2378]) ).

thf(2548,plain,
    ! [SV594: $i > $i,SV467: $i,SV244: $i,SV752: $i] :
      ( ( ( ~ ( in @ SV752 @ SV244 )
          | ( ( ap @ SV244 @ SV467
              @ ( lam @ SV244 @ SV467
                @ ^ [SY3033: $i] : ( SV594 @ SY3033 ) )
              @ SV752 )
            = ( SV594 @ SV752 ) ) )
        = $true )
      | ( ( in @ ( SV594 @ ( sK29_SY3031 @ SV467 @ SV594 @ SV244 ) ) @ SV467 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2379]) ).

thf(2549,plain,
    ! [SV595: $i,SV468: $i,SV245: $i,SV726: $i] :
      ( ( ( in @ SV726 @ SV245 )
        = $false )
      | ( ( in @ ( kpair @ SV726 @ ( ap @ SV245 @ SV468 @ SV595 @ SV726 ) ) @ SV595 )
        = $true )
      | ( ( in @ SV595 @ ( funcSet @ SV245 @ SV468 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2380]) ).

thf(2550,plain,
    ! [SV666: $i,SV469: $i,SV246: $i,SV753: $i] :
      ( ( ( ~ ( in @ SV753 @ SV246 )
          | ~ ( in @ SV753 @ ( setminus @ SV246 @ SV469 ) )
          | ~ ( in @ SV753 @ ( binintersect @ SV469 @ SV666 ) ) )
        = $true )
      | ( ( in @ SV666 @ ( powerset @ SV246 ) )
        = $false )
      | ( ( in @ SV469 @ ( powerset @ SV246 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2381]) ).

thf(2551,plain,
    ! [SV251: $i,SV597: $i,SV472: $i,SV727: $i] :
      ( ( ( in @ SV727 @ SV472 )
        = $false )
      | ( ( in @ ( setadjoin @ SV597 @ ( setadjoin @ SV727 @ emptyset ) ) @ ( powerset @ ( binunion @ SV251 @ SV472 ) ) )
        = $true )
      | ( ( in @ SV597 @ SV251 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2382]) ).

thf(2552,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ~ ( ~ ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
              | ( ( sK37_SY3106 @ SV667 @ SV253 )
                = SV667 ) )
          | ~ ( ( ( sK37_SY3106 @ SV667 @ SV253 )
               != SV667 )
              | ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2491: $i] :
                ~ ~ ( ~ ( SV253 @ SY2491 )
                    | ~ ! [SY2492: $i] :
                          ( ~ ( SV253 @ SY2492 )
                          | ( SY2491 = SY2492 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2383]) ).

thf(2553,plain,
    ! [SV255: $i,SV668: $o,SV475: $i] :
      ( ( ( ~ ( in @ SV475 @ ( sK41_SY3107 @ SV668 @ SV255 @ SV475 ) )
          | ~ ( in @ ( sK41_SY3107 @ SV668 @ SV255 @ SV475 ) @ SV255 )
          | SV668 )
        = $false )
      | ( SV668 = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2384]) ).

thf(2554,plain,
    ! [SV255: $i,SV475: $i] :
      ( ( ( ~ ( in @ SV475 @ ( sK42_SX0 @ SV255 @ SV475 ) )
          | ~ ( in @ ( sK42_SX0 @ SV255 @ SV475 ) @ SV255 )
          | $true )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2385]) ).

thf(2555,plain,
    ! [SV255: $i,SV475: $i] :
      ( ( ( ~ ( in @ SV475 @ ( sK43_SX0 @ SV255 @ SV475 ) )
          | ~ ( in @ ( sK43_SX0 @ SV255 @ SV475 ) @ SV255 )
          | $false )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2386]) ).

thf(2556,plain,
    ! [SV600: $i,SV476: $o,SV256: $i,SV728: $i] :
      ( ( ( in @ SV728 @ SV256 )
        = $false )
      | ( ( in @ ( if @ SV256 @ SV476 @ SV600 @ SV728 ) @ ( setadjoin @ SV600 @ ( setadjoin @ SV728 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV600 @ SV256 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2387]) ).

thf(2557,plain,
    ! [SV601: $i,SV256: $i,SV729: $i] :
      ( ( ( in @ SV729 @ SV256 )
        = $false )
      | ( ( in @ ( if @ SV256 @ $true @ SV601 @ SV729 ) @ ( setadjoin @ SV601 @ ( setadjoin @ SV729 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV601 @ SV256 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2388]) ).

thf(2558,plain,
    ! [SV602: $i,SV256: $i,SV730: $i] :
      ( ( ( in @ SV730 @ SV256 )
        = $false )
      | ( ( in @ ( if @ SV256 @ $false @ SV602 @ SV730 ) @ ( setadjoin @ SV602 @ ( setadjoin @ SV730 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV602 @ SV256 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2389]) ).

thf(2559,plain,
    ! [SV257: $i,SV603: $i,SV477: $i,SV731: $i] :
      ( ( ( in @ SV731 @ SV477 )
        = $false )
      | ( ( subset @ ( setadjoin @ SV603 @ ( setadjoin @ SV731 @ emptyset ) ) @ ( binunion @ SV257 @ SV477 ) )
        = $true )
      | ( ( in @ SV603 @ SV257 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2390]) ).

thf(2560,plain,
    ! [SV35: $i,SV281: $i > $o] :
      ( ( ( ~ ( in @ ( sK30_SY2514 @ SV281 @ SV35 ) @ SV35 )
          | ~ ( SV281 @ ( sK30_SY2514 @ SV281 @ SV35 ) ) )
        = $false )
      | ( ( ! [SY2515: $i] :
              ( ~ ( in @ SY2515 @ SV35 )
              | ~ ( SV281 @ SY2515 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2391]) ).

thf(2561,plain,
    ! [SV619: $i,SV282: $i,SV36: $i,SV734: $i] :
      ( ( ( ~ ( in @ SV734 @ SV36 ) )
        = $true )
      | ( ( ~ ( subset @ SV282 @ SV619 )
          | ~ ~ ( in @ SV734 @ SV619 )
          | ~ ( in @ SV734 @ SV282 ) )
        = $true )
      | ( ( in @ SV619 @ ( powerset @ SV36 ) )
        = $false )
      | ( ( in @ SV282 @ ( powerset @ SV36 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2392]) ).

thf(2562,plain,
    ! [SV620: $i,SV37: $i > $o] :
      ( ( ( SV37 @ SV620 )
        = $false )
      | ( ( ~ ! [SY3056: $i] :
                ( ~ ( SV37 @ SY3056 )
                | ( SV620 = SY3056 ) ) )
        = $true )
      | ( ( ~ ! [SY1897: $i] :
                ~ ! [SY1898: $i] :
                    ~ ( ~ ( ~ ( SV37 @ SY1898 )
                          | ( SY1898 = SY1897 ) )
                      | ~ ( ( SY1898 != SY1897 )
                          | ( SV37 @ SY1898 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2393]) ).

thf(2563,plain,
    ! [SV483: $i,SV40: $i,SV670: $i,SV284: $o] :
      ( ( ( ~ ~ SV284 )
        = $true )
      | ( ( in @ SV670
          @ ( dsetconstr @ SV40
            @ ^ [SY3108: $i] :
                ( ~ ( ~ SV284
                    | ( SY3108 != SV483 ) )
                | ~ ( ~ ~ SV284
                    | ( SY3108 != SV670 ) ) ) ) )
        = $true )
      | ( ( in @ SV670 @ SV40 )
        = $false )
      | ( ( in @ SV483 @ SV40 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2395]) ).

thf(2564,plain,
    ! [SV484: $i,SV40: $i,SV671: $i] :
      ( ( ( ~ ~ $true )
        = $true )
      | ( ( in @ SV671
          @ ( dsetconstr @ SV40
            @ ^ [SY3109: $i] :
                ( ~ ( ~ $true
                    | ( SY3109 != SV484 ) )
                | ~ ( ~ ~ $true
                    | ( SY3109 != SV671 ) ) ) ) )
        = $true )
      | ( ( in @ SV671 @ SV40 )
        = $false )
      | ( ( in @ SV484 @ SV40 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2396]) ).

thf(2565,plain,
    ! [SV485: $i,SV40: $i,SV672: $i] :
      ( ( ( ~ ~ $false )
        = $true )
      | ( ( in @ SV672
          @ ( dsetconstr @ SV40
            @ ^ [SY3110: $i] :
                ( ~ ( ~ $false
                    | ( SY3110 != SV485 ) )
                | ~ ( ~ ~ $false
                    | ( SY3110 != SV672 ) ) ) ) )
        = $true )
      | ( ( in @ SV672 @ SV40 )
        = $false )
      | ( ( in @ SV485 @ SV40 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2397]) ).

thf(2566,plain,
    ! [SV621: $i,SV41: $i > $o] :
      ( ( ( SV41 @ SV621 )
        = $false )
      | ( ( ~ ! [SY3057: $i] :
                ( ~ ( SV41 @ SY3057 )
                | ( SV621 = SY3057 ) ) )
        = $true )
      | ( ( ! [SY1909: $i,SY1910: $i] :
              ( ~ ( SV41 @ SY1909 )
              | ~ ( SV41 @ SY1910 )
              | ( SY1909 = SY1910 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2398]) ).

thf(2567,plain,
    ! [SV42: $i,SV285: $i,SV735: $i] :
      ( ( ( ~ ( in @ SV735 @ SV285 ) )
        = $true )
      | ( ( in @ SV735 @ SV42 )
        = $true )
      | ( ( in @ SV285 @ ( powerset @ SV42 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2399]) ).

thf(2568,plain,
    ! [SV285: $i,SV42: $i] :
      ( ( ( ~ ( in @ ( sK38_SY2524 @ SV42 @ SV285 ) @ SV285 ) )
        = $false )
      | ( ( in @ SV285 @ ( powerset @ SV42 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2400]) ).

thf(2569,plain,
    ! [SV285: $i,SV42: $i] :
      ( ( ( in @ ( sK38_SY2524 @ SV42 @ SV285 ) @ SV42 )
        = $false )
      | ( ( in @ SV285 @ ( powerset @ SV42 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2400]) ).

thf(2570,plain,
    ! [SV622: $i,SV43: $i > $o] :
      ( ( ( SV43 @ SV622 )
        = $false )
      | ( ( ~ ! [SY3058: $i] :
                ( ~ ( SV43 @ SY3058 )
                | ( SV622 = SY3058 ) ) )
        = $true )
      | ( ( ! [SY1916: $i,SY1917: $i] :
              ( ~ ( SV43 @ SY1916 )
              | ~ ( SV43 @ SY1917 )
              | ( SY1916 = SY1917 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2401]) ).

thf(2571,plain,
    ! [SV623: $i,SV286: $i,SV44: $i,SV736: $i] :
      ( ( ( ~ ( in @ SV736 @ SV44 ) )
        = $true )
      | ( ( ~ ( in @ SV736 @ ( setminus @ SV44 @ ( binunion @ SV286 @ SV623 ) ) )
          | ~ ( in @ SV736 @ SV286 ) )
        = $true )
      | ( ( in @ SV623 @ ( powerset @ SV44 ) )
        = $false )
      | ( ( in @ SV286 @ ( powerset @ SV44 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2402]) ).

thf(2572,plain,
    ! [SV287: $i > $o,SV46: $i,SV673: $i] :
      ( ( ( ~ ( in @ SV673 @ SV46 ) )
        = $true )
      | ( ( ~ ~ ( SV287 @ SV673 ) )
        = $true )
      | ( ( ~ ! [SY2528: $i] :
                ( ~ ( in @ SY2528 @ SV46 )
                | ( SV287 @ SY2528 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2403]) ).

thf(2573,plain,
    ! [SV624: $i,SV48: $i > $o] :
      ( ( ( SV48 @ SV624 )
        = $false )
      | ( ( ~ ! [SY3060: $i] :
                ( ~ ( SV48 @ SY3060 )
                | ( SV624 = SY3060 ) ) )
        = $true )
      | ( ( ~ ! [SY1928: $i] :
                ~ ~ ( ~ ( SV48 @ SY1928 )
                    | ~ ! [SY1929: $i] :
                          ( ~ ( SV48 @ SY1929 )
                          | ( SY1928 = SY1929 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2405]) ).

thf(2574,plain,
    ! [SV51: $i,SV291: $i] :
      ( ( ( ~ ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV51 ) )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV291 )
              | ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV51 ) ) )
        = $true )
      | ( ( SV51 = SV291 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2408]) ).

thf(2575,plain,
    ! [SV51: $i,SV291: $i] :
      ( ( ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV291 )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV291 )
              | ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV51 ) ) )
        = $true )
      | ( ( SV51 = SV291 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2408]) ).

thf(2576,plain,
    ! [SV52: $i,SV292: $i > $o] :
      ( ( ( ~ ( in @ ( sK31_SY2534 @ SV292 @ SV52 ) @ SV52 )
          | ~ ( SV292 @ ( sK31_SY2534 @ SV292 @ SV52 ) ) )
        = $false )
      | ( ( ! [SY2535: $i] :
              ( ~ ( in @ SY2535 @ SV52 )
              | ~ ( SV292 @ SY2535 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2409]) ).

thf(2577,plain,
    ! [SV55: $i,SV295: $i,SV489: $i] :
      ( ( ( in @ SV489 @ SV295 )
        = $true )
      | ( ( ~ ( in @ SV489 @ ( symdiff @ SV55 @ SV295 ) ) )
        = $true )
      | ( ( in @ SV489 @ SV55 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2410]) ).

thf(2578,plain,
    ! [SV63: $i,SV302: $i,SV496: $i,SV676: $i > $o] :
      ( ( ( ~ ( in @ ( sK44_SY3111 @ SV676 @ SV496 @ SV302 @ SV63 ) @ SV63 )
          | ! [SY3167: $i] :
              ( ~ ( in @ SY3167 @ SV302 )
              | ~ ( in @ ( kpair @ ( sK44_SY3111 @ SV676 @ SV496 @ SV302 @ SV63 ) @ SY3167 ) @ SV496 )
              | ( SV676 @ ( kpair @ ( sK44_SY3111 @ SV676 @ SV496 @ SV302 @ SV63 ) @ SY3167 ) ) ) )
        = $false )
      | ( ( ! [SY3113: $i] :
              ( ~ ( in @ SY3113 @ SV496 )
              | ( SV676 @ SY3113 ) ) )
        = $true )
      | ( ( subset @ SV496 @ ( cartprod @ SV63 @ SV302 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2413]) ).

thf(2579,plain,
    ! [SV677: $i,SV67: $i,SV498: $i,SV305: $o] :
      ( ( ( ~ SV305 ) = $true )
      | ( ( in @ SV498
          @ ( dsetconstr @ SV67
            @ ^ [SY3114: $i] :
                ( ~ ( ~ SV305
                    | ( SY3114 != SV498 ) )
                | ~ ( ~ ~ SV305
                    | ( SY3114 != SV677 ) ) ) ) )
        = $true )
      | ( ( in @ SV677 @ SV67 )
        = $false )
      | ( ( in @ SV498 @ SV67 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2415]) ).

thf(2580,plain,
    ! [SV678: $i,SV67: $i,SV499: $i] :
      ( ( ( ~ $true ) = $true )
      | ( ( in @ SV499
          @ ( dsetconstr @ SV67
            @ ^ [SY3115: $i] :
                ( ~ ( ~ $true
                    | ( SY3115 != SV499 ) )
                | ~ ( ~ ~ $true
                    | ( SY3115 != SV678 ) ) ) ) )
        = $true )
      | ( ( in @ SV678 @ SV67 )
        = $false )
      | ( ( in @ SV499 @ SV67 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2416]) ).

thf(2581,plain,
    ! [SV679: $i,SV67: $i,SV500: $i] :
      ( ( ( ~ $false ) = $true )
      | ( ( in @ SV500
          @ ( dsetconstr @ SV67
            @ ^ [SY3116: $i] :
                ( ~ ( ~ $false
                    | ( SY3116 != SV500 ) )
                | ~ ( ~ ~ $false
                    | ( SY3116 != SV679 ) ) ) ) )
        = $true )
      | ( ( in @ SV679 @ SV67 )
        = $false )
      | ( ( in @ SV500 @ SV67 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2417]) ).

thf(2582,plain,
    ! [SV626: $i,SV72: $i,SV310: $i] :
      ( ( ( subset @ SV310 @ ( setminus @ SV72 @ SV626 ) )
        = $false )
      | ( ( subset @ SV626 @ ( setminus @ SV72 @ SV310 ) )
        = $true )
      | ( ( in @ SV626 @ ( powerset @ SV72 ) )
        = $false )
      | ( ( in @ SV310 @ ( powerset @ SV72 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2419]) ).

thf(2583,plain,
    ! [SV681: $i,SV502: $i,SV311: $i,SV73: $i] :
      ( ( ( ~ ! [SY3118: $i] :
                ( ~ ( in @ SY3118 @ SV73 )
                | ( ( ap @ SV73 @ SV311 @ SV502 @ SY3118 )
                  = ( ap @ SV73 @ SV311 @ SV681 @ SY3118 ) ) ) )
        = $true )
      | ( ( SV502 = SV681 )
        = $true )
      | ( ( in @ SV681 @ ( funcSet @ SV73 @ SV311 ) )
        = $false )
      | ( ( in @ SV502 @ ( funcSet @ SV73 @ SV311 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2420]) ).

thf(2584,plain,
    ! [SV74: $i,SV312: $i,SV503: $i] :
      ( ( ( in @ SV503 @ SV312 )
        = $true )
      | ( ( ~ ( in @ SV503 @ SV74 ) )
        = $true )
      | ( ( in @ SV503 @ ( setminus @ SV74 @ SV312 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2421]) ).

thf(2585,plain,
    ! [SV313: $i,SV75: $i,SV504: $i] :
      ( ( ( SV504 = SV75 )
        = $true )
      | ( ( in @ SV504 @ SV313 )
        = $true )
      | ( ( in @ SV504 @ ( setadjoin @ SV75 @ SV313 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2422]) ).

thf(2586,plain,
    ! [SV313: $i,SV75: $i,SV504: $i] :
      ( ( ( SV504 = SV75 )
        = $false )
      | ( ( in @ SV504 @ ( setadjoin @ SV75 @ SV313 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2423]) ).

thf(2587,plain,
    ! [SV75: $i,SV313: $i,SV504: $i] :
      ( ( ( in @ SV504 @ SV313 )
        = $false )
      | ( ( in @ SV504 @ ( setadjoin @ SV75 @ SV313 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2423]) ).

thf(2588,plain,
    ! [SV627: $i,SV314: $i,SV76: $i,SV737: $i] :
      ( ( ( ~ ( in @ SV737 @ ( powerset @ SV76 ) ) )
        = $true )
      | ( ( ! [SY3153: $i] :
              ( ~ ( in @ SY3153 @ SV76 )
              | ~ ( in @ SY3153 @ ( binintersect @ SV314 @ SV627 ) )
              | ( in @ SY3153 @ ( binintersect @ ( binunion @ SV314 @ SV737 ) @ ( binunion @ SV627 @ SV737 ) ) ) ) )
        = $true )
      | ( ( in @ SV627 @ ( powerset @ SV76 ) )
        = $false )
      | ( ( in @ SV314 @ ( powerset @ SV76 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2424]) ).

thf(2589,plain,
    ! [SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ~ ~ ! [SY2001: $i] :
                  ~ ~ ( ~ ( SV77 @ SY2001 )
                      | ~ ! [SY2002: $i] :
                            ( ~ ( SV77 @ SY2002 )
                            | ( SY2001 = SY2002 ) ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2425]) ).

thf(2590,plain,
    ! [SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ~ ( ~ ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
              | ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
              | ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2001: $i] :
                  ~ ~ ( ~ ( SV77 @ SY2001 )
                      | ~ ! [SY2002: $i] :
                            ( ~ ( SV77 @ SY2002 )
                            | ( SY2001 = SY2002 ) ) )
          | ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2426]) ).

thf(2591,plain,
    ! [SV628: $i,SV318: $i,SV80: $i] :
      ( ( ( ! [SY3066: $i] :
              ( ~ ( in @ SY3066 @ SV80 )
              | ~ ( in @ SY3066 @ SV318 )
              | ( in @ SY3066 @ SV628 ) ) )
        = $false )
      | ( ( ~ ! [SY3067: $i] :
                ( ~ ( in @ SY3067 @ SV80 )
                | ~ ( in @ SY3067 @ SV628 )
                | ( in @ SY3067 @ SV318 ) )
          | ( SV318 = SV628 ) )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2427]) ).

thf(2592,plain,
    ! [SV81: $i,SV319: $i] :
      ( ( ( ! [SY2586: $i] :
              ( ~ ( in @ SY2586 @ SV319 )
              | ( in @ SY2586 @ SV81 ) ) )
        = $false )
      | ( ( SV81 = SV319 )
        = $true )
      | ( ( in @ ( sK8_SY2585 @ SV319 @ SV81 ) @ SV81 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2428]) ).

thf(2593,plain,
    ! [SV319: $i,SV81: $i] :
      ( ( ( ~ ( in @ ( sK45_SY2586 @ SV81 @ SV319 ) @ SV319 )
          | ( in @ ( sK45_SY2586 @ SV81 @ SV319 ) @ SV81 ) )
        = $false )
      | ( ( SV81 = SV319 )
        = $true )
      | ( ( in @ ( sK8_SY2585 @ SV319 @ SV81 ) @ SV319 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2429]) ).

thf(2594,plain,
    ! [SV506: $i > $i > $o,SV82: $i,SV608: $i,SV320: $i,SV732: $i] :
      ( ( ( in @ SV732 @ SV320 )
        = $false )
      | ( ( ~ ( in @ ( kpair @ SV608 @ SV732 )
              @ ( dpsetconstr @ SV82 @ SV320
                @ ^ [SY2907: $i,SY2908: $i] : ( SV506 @ SY2907 @ SY2908 ) ) )
          | ( SV506 @ SV608 @ SV732 ) )
        = $true )
      | ( ( in @ SV608 @ SV82 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2430]) ).

thf(2595,plain,
    ! [SV682: $i,SV321: $i > $o,SV84: $i] :
      ( ( ( ! [SY2593: $i] :
              ~ ~ ( ~ ( in @ SY2593 @ SV84 )
                  | ~ ~ ( SV321 @ SY2593 ) ) )
        = $false )
      | ( ( SV321 @ SV682 )
        = $true )
      | ( ( in @ SV682 @ SV84 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2431]) ).

thf(2596,plain,
    ! [SV609: $o,SV322: $i,SV85: $i,SV507: $i] :
      ( ( ( ~ ( in @ SV507 @ SV85 ) )
        = $false )
      | ( ( ~ ( ~ ( in @ SV507 @ SV322 )
              | SV609 )
          | SV609 )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2432]) ).

thf(2597,plain,
    ! [SV85: $i,SV322: $i,SV507: $i,SV609: $o] :
      ( ( SV609 = $false )
      | ( ( ~ ( ~ ( in @ SV507 @ SV322 )
              | SV609 )
          | SV609 )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2432]) ).

thf(2598,plain,
    ! [SV322: $i,SV85: $i,SV507: $i] :
      ( ( ( ~ ( in @ SV507 @ SV85 ) )
        = $false )
      | ( ( ~ ( ~ ( in @ SV507 @ SV322 )
              | $true )
          | $true )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2433]) ).

thf(2599,plain,
    ! [SV85: $i,SV322: $i,SV507: $i] :
      ( ( $true = $false )
      | ( ( ~ ( ~ ( in @ SV507 @ SV322 )
              | $true )
          | $true )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2433]) ).

thf(2600,plain,
    ! [SV322: $i,SV85: $i,SV507: $i] :
      ( ( ( ~ ( in @ SV507 @ SV85 ) )
        = $false )
      | ( ( ~ ( ~ ( in @ SV507 @ SV322 )
              | $false )
          | $false )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2434]) ).

thf(2601,plain,
    ! [SV85: $i,SV322: $i,SV507: $i] :
      ( ( $false = $false )
      | ( ( ~ ( ~ ( in @ SV507 @ SV322 )
              | $false )
          | $false )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2434]) ).

thf(2602,plain,
    ! [SV87: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK39_SY2033 @ SV87 ) @ omega )
                | ~ ( in @ ( sK39_SY2033 @ SV87 ) @ SV87 ) ) )
        = $false )
      | ( ( in @ emptyset @ SV87 )
        = $false )
      | ( ( ! [SY2034: $i] :
              ( ~ ( in @ SY2034 @ omega )
              | ( in @ SY2034 @ SV87 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2435]) ).

thf(2603,plain,
    ! [SV87: $i] :
      ( ( ( in @ ( setadjoin @ ( sK39_SY2033 @ SV87 ) @ ( sK39_SY2033 @ SV87 ) ) @ SV87 )
        = $false )
      | ( ( in @ emptyset @ SV87 )
        = $false )
      | ( ( ! [SY2034: $i] :
              ( ~ ( in @ SY2034 @ omega )
              | ( in @ SY2034 @ SV87 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2435]) ).

thf(2604,plain,
    ( ( in @ sK32_SY3068 @ sK1_SX0 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2436]) ).

thf(2605,plain,
    ( ( ~ ( in @ sK32_SY3068 @ ( setminus @ sK1_SX0 @ ( binunion @ sK2_SY2597 @ sK9_SY2910 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2437]) ).

thf(2606,plain,
    ( ( in @ sK32_SY3068 @ ( setminus @ sK1_SX0 @ sK2_SY2597 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2437]) ).

thf(2607,plain,
    ! [SV629: $i,SV88: $i,SV324: $i] :
      ( ( ( subset @ SV324 @ ( setminus @ SV88 @ SV629 ) )
        = $false )
      | ( ( ! [SY3069: $i] :
              ( ~ ( in @ SY3069 @ SV88 )
              | ~ ( in @ SY3069 @ SV629 )
              | ( in @ SY3069 @ ( setminus @ SV88 @ SV324 ) ) ) )
        = $true )
      | ( ( in @ SV629 @ ( powerset @ SV88 ) )
        = $false )
      | ( ( in @ SV324 @ ( powerset @ SV88 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2438]) ).

thf(2608,plain,
    ! [SV325: $i > $o,SV89: $i,SV683: $i] :
      ( ( ( ~ ( in @ SV683 @ SV89 ) )
        = $true )
      | ( ( ~ ( SV325 @ SV683 ) )
        = $true )
      | ( ( ( ( dsetconstr @ SV89
              @ ^ [SY2603: $i] : ( SV325 @ SY2603 ) )
           != emptyset )
          | $false )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2439]) ).

thf(2609,plain,
    ! [SV328: $i,SV684: $i,SV92: $i,SV631: $i] :
      ( ( ( ~ ( in @ SV631 @ SV92 ) )
        = $true )
      | ( ( in @ SV684 @ SV328 )
        = $true )
      | ( ( SV631 = SV684 )
        = $false )
      | ( ( SV92 = SV328 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2440]) ).

thf(2610,plain,
    ! [SV685: $i,SV512: $i,SV332: $i,SV96: $i] :
      ( ( ( ~ ! [SY3119: $i] :
                ( ~ ( in @ SY3119 @ SV96 )
                | ( ( ap @ SV96 @ SV332 @ SV512 @ SY3119 )
                  = ( ap @ SV96 @ SV332 @ SV685 @ SY3119 ) ) ) )
        = $true )
      | ( ( ! [SY3120: $i] :
              ( ~ ( in @ SY3120 @ SV96 )
              | ! [SY3121: $i] :
                  ( ~ ( in @ SY3121 @ SV332 )
                  | ~ ( in @ ( kpair @ SY3120 @ SY3121 ) @ SV685 )
                  | ( in @ ( kpair @ SY3120 @ SY3121 ) @ SV512 ) ) ) )
        = $true )
      | ( ( func @ SV96 @ SV332 @ SV685 )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV512 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2441]) ).

thf(2611,plain,
    ! [SV98: $i,SV333: $i,SV513: $i] :
      ( ( ( ~ ( in @ ( sK33_SY2921 @ SV513 @ SV333 @ SV98 ) @ SV98 )
          | ~ ~ ! [SY3150: $i] :
                  ~ ~ ( ~ ( in @ SY3150 @ SV333 )
                      | ( SV513
                       != ( kpair @ ( sK33_SY2921 @ SV513 @ SV333 @ SV98 ) @ SY3150 ) ) ) )
        = $false )
      | ( ( in @ SV513 @ ( cartprod @ SV98 @ SV333 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2442]) ).

thf(2612,plain,
    ! [SV633: $i,SV334: $i,SV99: $i,SV738: $i] :
      ( ( ( ~ ( in @ SV738 @ SV99 ) )
        = $true )
      | ( ( ~ ( in @ SV334 @ ( powerset @ SV633 ) )
          | ~ ( in @ SV738 @ SV334 )
          | ( in @ SV738 @ SV633 ) )
        = $true )
      | ( ( in @ SV633 @ ( powerset @ SV99 ) )
        = $false )
      | ( ( in @ SV334 @ ( powerset @ SV99 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2443]) ).

thf(2613,plain,
    ! [SV336: $i > $o,SV102: $i] :
      ( ( ( ~ ! [SY2629: $i] :
                ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                    | ~ ( SV336 @ SY2629 ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( in @ ( sK11_SY2627 @ SV336 @ SV102 ) @ SV102 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2444]) ).

thf(2614,plain,
    ! [SV102: $i,SV336: $i > $o] :
      ( ( ( in @ ( sK34_SY3074 @ SV336 @ SV102 ) @ SV102 )
        = $true )
      | ( ( ~ ~ ! [SY2629: $i] :
                  ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                      | ~ ( SV336 @ SY2629 ) )
          | ( singleton
            @ ( dsetconstr @ SV102
              @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2445]) ).

thf(2615,plain,
    ! [SV102: $i,SV336: $i > $o] :
      ( ( ( ~ ( SV336 @ ( sK11_SY2627 @ SV336 @ SV102 ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2629: $i] :
                  ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                      | ~ ( SV336 @ SY2629 ) )
          | ( singleton
            @ ( dsetconstr @ SV102
              @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2446]) ).

thf(2616,plain,
    ! [SV102: $i,SV336: $i > $o] :
      ( ( ( ~ ( SV336 @ ( sK34_SY3074 @ SV336 @ SV102 ) )
          | ( ( sK11_SY2627 @ SV336 @ SV102 )
            = ( sK34_SY3074 @ SV336 @ SV102 ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2629: $i] :
                  ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                      | ~ ( SV336 @ SY2629 ) )
          | ( singleton
            @ ( dsetconstr @ SV102
              @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2446]) ).

thf(2617,plain,
    ! [SV109: $i] :
      ( ( ~ ~ ( ~ ! [SY2932: $i] :
                    ( ~ ( in @ SY2932 @ ( sK3_SY2100 @ SV109 ) )
                    | ! [SY2102: $i] :
                        ( ~ ( in @ SY2102 @ SY2932 )
                        | ( in @ SY2102 @ SV109 ) ) )
              | ~ ! [SY2934: $i,SY2935: $i] :
                    ( ~ ~ ( ~ ( in @ SY2934 @ SV109 )
                          | ~ ( in @ SY2935 @ SV109 ) )
                    | ~ ! [SY2936: $i] :
                          ( ~ ( in @ SY2936 @ ( sK3_SY2100 @ SV109 ) )
                          | ~ ( ~ ( ~ ( in @ SY2934 @ SY2936 )
                                  | ( in @ SY2935 @ SY2936 ) )
                              | ~ ( ~ ( in @ SY2935 @ SY2936 )
                                  | ( in @ SY2934 @ SY2936 ) ) ) )
                    | ( SY2934 = SY2935 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2449]) ).

thf(2618,plain,
    ! [SV109: $i] :
      ( ( ~ ! [SY2937: $i,SY2938: $i] :
              ( ~ ~ ( ~ ( in @ SY2937 @ ( sK3_SY2100 @ SV109 ) )
                    | ~ ( in @ SY2938 @ ( sK3_SY2100 @ SV109 ) ) )
              | ! [SX4: $i] :
                  ( ~ ( in @ SX4 @ SY2937 )
                  | ( in @ SX4 @ SY2938 ) )
              | ! [SX4: $i] :
                  ( ~ ( in @ SX4 @ SY2938 )
                  | ( in @ SX4 @ SY2937 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2449]) ).

thf(2619,plain,
    ! [SV109: $i,SV739: $i] :
      ( ( ( ~ ~ ( ~ ! [SY3154: $i] :
                      ( ~ ( in @ SY3154 @ SV739 )
                      | ( in @ SY3154 @ SV109 ) )
                | ~ ~ ! [SY3155: $i] :
                        ~ ( in @ SY3155 @ SV739 ) ) )
        = $true )
      | ( ( ~ ! [SY3156: $i] :
                ~ ~ ! [SY3157: $i] :
                      ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3156 @ ( sK3_SY2100 @ SV109 ) )
                                      | ~ ( in @ SY3157 @ SV739 ) )
                                | ~ ~ ~ ! [SY3158: $i] :
                                          ~ ~ ( ~ ( in @ SY3158 @ SY3156 )
                                              | ~ ( in @ SY3158 @ SV739 ) ) )
                          | ~ ! [SY2947: $i] :
                                ( ~ ( in @ SY2947 @ ( sK3_SY2100 @ SV109 ) )
                                | ! [SX6: $i] :
                                    ( ~ ( in @ SX6 @ SY2947 )
                                    | ( in @ SX6 @ SY3156 ) )
                                | ( in @ SY3157 @ SY2947 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2450]) ).

thf(2620,plain,
    ! [SV110: $i,SV635: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK40_SY2119 @ SV635 @ SV110 ) @ SV110 )
              | ~ ~ ~ ! [SY3161: $i] :
                        ~ ~ ( ~ ( in @ SY3161 @ ( sK40_SY2119 @ SV635 @ SV110 ) )
                            | ~ ( in @ SY3161 @ SV110 ) ) ) )
        = $true )
      | ( ( in @ SV635 @ SV110 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2451]) ).

thf(2621,plain,
    ! [SV636: $i,SV112: $i > $o] :
      ( ( ( SV112 @ SV636 )
        = $false )
      | ( ( ~ ! [SY3077: $i] :
                ( ~ ( SV112 @ SY3077 )
                | ( SV636 = SY3077 ) ) )
        = $true )
      | ( ( ~ ! [SY2125: $i] :
                ~ ( SV112 @ SY2125 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2452]) ).

thf(2622,plain,
    ! [SV113: $i,SV344: $i] :
      ( ( ( ~ ( in @ ( sK35_SY2645 @ SV344 @ SV113 ) @ SV113 )
          | ~ ( in @ ( sK35_SY2645 @ SV344 @ SV113 ) @ SV344 ) )
        = $false )
      | ( ( ( binintersect @ SV113 @ SV344 )
          = emptyset )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2453]) ).

thf(2623,plain,
    ! [SV637: $i,SV346: $i,SV116: $i,SV740: $i] :
      ( ( ( ~ ( in @ SV740 @ SV116 ) )
        = $true )
      | ( ( ~ ~ ( in @ SV740 @ ( binunion @ SV346 @ SV637 ) )
          | ~ ( in @ SV740 @ SV346 ) )
        = $true )
      | ( ( in @ SV637 @ ( powerset @ SV116 ) )
        = $false )
      | ( ( in @ SV346 @ ( powerset @ SV116 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2454]) ).

thf(2624,plain,
    ! [SV686: $i,SV520: $i,SV118: $i,SV347: $o] :
      ( ( ( ~ ~ SV347 )
        = $true )
      | ( ( ( if @ SV118 @ SV347 @ SV520 @ SV686 )
          = SV686 )
        = $true )
      | ( ( in @ SV686 @ SV118 )
        = $false )
      | ( ( in @ SV520 @ SV118 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2455]) ).

thf(2625,plain,
    ! [SV687: $i,SV521: $i,SV118: $i] :
      ( ( ( ~ ~ $true )
        = $true )
      | ( ( ( if @ SV118 @ $true @ SV521 @ SV687 )
          = SV687 )
        = $true )
      | ( ( in @ SV687 @ SV118 )
        = $false )
      | ( ( in @ SV521 @ SV118 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2456]) ).

thf(2626,plain,
    ! [SV688: $i,SV522: $i,SV118: $i] :
      ( ( ( ~ ~ $false )
        = $true )
      | ( ( ( if @ SV118 @ $false @ SV522 @ SV688 )
          = SV688 )
        = $true )
      | ( ( in @ SV688 @ SV118 )
        = $false )
      | ( ( in @ SV522 @ SV118 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2457]) ).

thf(2627,plain,
    ! [SV349: $i,SV121: $i,SV638: $i] :
      ( ( ( ~ ( in @ SV638 @ ( setminus @ SV121 @ SV349 ) ) )
        = $false )
      | ( ( in @ SV638 @ SV349 )
        = $true )
      | ( ( in @ SV638 @ SV121 )
        = $false )
      | ( ( in @ SV349 @ ( powerset @ SV121 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2458]) ).

thf(2628,plain,
    ! [SV351: $i,SV123: $i,SV523: $i] :
      ( ( ( in @ SV523 @ SV123 )
        = $false )
      | ( ( in @ SV523 @ SV351 )
        = $true )
      | ( ( subset @ SV123 @ SV351 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2459]) ).

thf(2629,plain,
    ! [SV353: $i > $o,SV125: $i] :
      ( ( ( ~ ! [SY2659: $i] :
                ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                    | ~ ( SV353 @ SY2659 ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( in @ ( sK12_SY2657 @ SV353 @ SV125 ) @ SV125 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2461]) ).

thf(2630,plain,
    ! [SV125: $i,SV353: $i > $o] :
      ( ( ( in @ ( sK36_SY3079 @ SV353 @ SV125 ) @ SV125 )
        = $true )
      | ( ( ~ ~ ! [SY2659: $i] :
                  ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                      | ~ ( SV353 @ SY2659 ) )
          | ( singleton
            @ ( dsetconstr @ SV125
              @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2462]) ).

thf(2631,plain,
    ! [SV125: $i,SV353: $i > $o] :
      ( ( ( ~ ( SV353 @ ( sK12_SY2657 @ SV353 @ SV125 ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2659: $i] :
                  ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                      | ~ ( SV353 @ SY2659 ) )
          | ( singleton
            @ ( dsetconstr @ SV125
              @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2463]) ).

thf(2632,plain,
    ! [SV125: $i,SV353: $i > $o] :
      ( ( ( ~ ( SV353 @ ( sK36_SY3079 @ SV353 @ SV125 ) )
          | ( ( sK12_SY2657 @ SV353 @ SV125 )
            = ( sK36_SY3079 @ SV353 @ SV125 ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2659: $i] :
                  ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                      | ~ ( SV353 @ SY2659 ) )
          | ( singleton
            @ ( dsetconstr @ SV125
              @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2463]) ).

thf(2633,plain,
    ! [SV129: $i,SV357: $i,SV641: $i] :
      ( ( ( in @ SV641 @ SV357 )
        = $false )
      | ( ( ~ ( in @ SV641 @ ( setminus @ SV129 @ SV357 ) ) )
        = $true )
      | ( ( in @ SV641 @ SV129 )
        = $false )
      | ( ( in @ SV357 @ ( powerset @ SV129 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2465]) ).

thf(2634,plain,
    ! [SV132: $i,SV642: $i,SV360: $i] :
      ( ( ( subset @ SV360 @ SV642 )
        = $false )
      | ( ( subset @ ( setminus @ SV132 @ SV642 ) @ ( setminus @ SV132 @ SV360 ) )
        = $true )
      | ( ( in @ SV642 @ ( powerset @ SV132 ) )
        = $false )
      | ( ( in @ SV360 @ ( powerset @ SV132 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2466]) ).

thf(2635,plain,
    ! [SV135: $i,SV363: $i,SV529: $i,SV690: $i > $o] :
      ( ( ( ~ ( in @ ( sK46_SY3122 @ SV690 @ SV529 @ SV363 @ SV135 ) @ SV135 )
          | ! [SY3168: $i] :
              ( ~ ( in @ SY3168 @ SV363 )
              | ~ ( in @ ( kpair @ ( sK46_SY3122 @ SV690 @ SV529 @ SV363 @ SV135 ) @ SY3168 ) @ SV529 )
              | ( SV690 @ ( kpair @ ( sK46_SY3122 @ SV690 @ SV529 @ SV363 @ SV135 ) @ SY3168 ) ) ) )
        = $false )
      | ( ( ! [SY3124: $i] :
              ( ~ ( in @ SY3124 @ SV529 )
              | ( SV690 @ SY3124 ) ) )
        = $true )
      | ( ( subset @ SV529 @ ( cartprod @ SV135 @ SV363 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2468]) ).

thf(2636,plain,
    ! [SV365: $i,SV643: $i,SV137: $i,SV741: $i] :
      ( ( ( ~ ( in @ SV741 @ SV137 ) )
        = $true )
      | ( ( ~ ~ ( in @ SV741 @ SV643 )
          | ~ ( in @ SV741 @ ( binintersect @ SV365 @ SV643 ) ) )
        = $true )
      | ( ( in @ SV643 @ ( powerset @ SV137 ) )
        = $false )
      | ( ( in @ SV365 @ ( powerset @ SV137 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2469]) ).

thf(2637,plain,
    ! [SV644: $i,SV372: $i > $o,SV142: $i,SV742: $i] :
      ( ( ( ~ ( in @ SV742 @ SV142 ) )
        = $true )
      | ( ( ~ ( SV372 @ SV644 )
          | ~ ( SV372 @ SV742 )
          | ( SV644 = SV742 ) )
        = $true )
      | ( ( in @ SV644 @ SV142 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV142
            @ ^ [SY2680: $i] : ( SV372 @ SY2680 ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2471]) ).

thf(2638,plain,
    ! [SV377: $i,SV147: $i > $i > $o] :
      ( ( ( ~ ! [SY3169: $i] :
                ~ ( ~ ( ~ ( in @ SY3169 @ ( sK47_SY2690 @ SV147 @ SV377 ) )
                      | ~ ! [SY2692: $i] :
                            ~ ~ ( ~ ( in @ SY2692 @ SV377 )
                                | ~ ( SV147 @ SY2692 @ SY3169 ) ) )
                  | ~ ( ~ ~ ! [SY2693: $i] :
                              ~ ~ ( ~ ( in @ SY2693 @ SV377 )
                                  | ~ ( SV147 @ SY2693 @ SY3169 ) )
                      | ( in @ SY3169 @ ( sK47_SY2690 @ SV147 @ SV377 ) ) ) ) )
        = $false )
      | ( ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2473]) ).

thf(2639,plain,
    ! [SV743: $i,SV377: $i,SV147: $i > $i > $o] :
      ( ( ( ~ ( ~ ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
              | ~ ! [SY3162: $i] :
                    ( ~ ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SY3162 )
                    | ( SV743 = SY3162 ) ) ) )
        = $false )
      | ( ( ~ ! [SY2690: $i] :
                ~ ! [SY2691: $i] :
                    ~ ( ~ ( ~ ( in @ SY2691 @ SY2690 )
                          | ~ ! [SY2692: $i] :
                                ~ ~ ( ~ ( in @ SY2692 @ SV377 )
                                    | ~ ( SV147 @ SY2692 @ SY2691 ) ) )
                      | ~ ( ~ ~ ! [SY2693: $i] :
                                  ~ ~ ( ~ ( in @ SY2693 @ SV377 )
                                      | ~ ( SV147 @ SY2693 @ SY2691 ) )
                          | ( in @ SY2691 @ SY2690 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2474]) ).

thf(2640,plain,
    ! [SV645: $i,SV381: $i,SV151: $i,SV744: $i] :
      ( ( ( ~ ( in @ SV744 @ SV151 ) )
        = $true )
      | ( ( ~ ~ ( in @ SV744 @ ( binunion @ SV381 @ SV645 ) )
          | ~ ( in @ SV744 @ SV645 ) )
        = $true )
      | ( ( in @ SV645 @ ( powerset @ SV151 ) )
        = $false )
      | ( ( in @ SV381 @ ( powerset @ SV151 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2475]) ).

thf(2641,plain,
    ! [SV647: $i,SV385: $i,SV156: $i,SV745: $i] :
      ( ( ( ~ ( in @ SV745 @ SV156 ) )
        = $true )
      | ( ( ~ ~ ( in @ SV745 @ SV385 )
          | ~ ( in @ SV745 @ ( binintersect @ SV385 @ SV647 ) ) )
        = $true )
      | ( ( in @ SV647 @ ( powerset @ SV156 ) )
        = $false )
      | ( ( in @ SV385 @ ( powerset @ SV156 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2477]) ).

thf(2642,plain,
    ! [SV648: $i,SV157: $i > $o] :
      ( ( ( SV157 @ SV648 )
        = $false )
      | ( ( ~ ! [SY3087: $i] :
                ( ~ ( SV157 @ SY3087 )
                | ( SV648 = SY3087 ) ) )
        = $true )
      | ( ( SV157
          @ ( descr
            @ ^ [SY2227: $i] : ( SV157 @ SY2227 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2478]) ).

thf(2643,plain,
    ! [SV694: $i,SV388: $i > $o,SV160: $i] :
      ( ( ( ! [SY2705: $i] :
              ~ ~ ( ~ ( in @ SY2705 @ SV160 )
                  | ~ ~ ( SV388 @ SY2705 ) ) )
        = $false )
      | ( ( SV388 @ SV694 )
        = $true )
      | ( ( in @ SV694 @ SV160 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2479]) ).

thf(2644,plain,
    ! [SV649: $i,SV389: $i,SV161: $i,SV746: $i] :
      ( ( ( ~ ( in @ SV746 @ SV161 ) )
        = $true )
      | ( ( ~ ( in @ SV746 @ ( setminus @ SV161 @ SV389 ) )
          | ( in @ SV746 @ ( setminus @ SV161 @ ( binintersect @ SV389 @ SV649 ) ) ) )
        = $true )
      | ( ( in @ SV649 @ ( powerset @ SV161 ) )
        = $false )
      | ( ( in @ SV389 @ ( powerset @ SV161 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2480]) ).

thf(2645,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( ! [SY3172: $i] :
              ( ~ ( SV165 @ ( sK48_SY2242 @ SV651 @ SV165 ) )
              | ~ ( SV165 @ SY3172 )
              | ( ( sK48_SY2242 @ SV651 @ SV165 )
                = SY3172 ) ) )
        = $false )
      | ( ( ~ ! [SY2244: $i] :
                ~ ~ ( ~ ( SV165 @ SY2244 )
                    | ~ ! [SY2245: $i] :
                          ( ~ ( SV165 @ SY2245 )
                          | ( SY2244 = SY2245 ) ) ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2481]) ).

thf(2646,plain,
    ! [SV538: $i,SV393: $i,SV166: $i] :
      ( ( ( subset @ SV166 @ SV393 )
        = $false )
      | ( ( in @ SV538 @ SV393 )
        = $true )
      | ( ( in @ SV538 @ SV166 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2482]) ).

thf(2647,plain,
    ! [SV652: $i,SV394: $i,SV167: $i,SV747: $i] :
      ( ( ( ~ ( in @ SV747 @ ( powerset @ SV167 ) ) )
        = $true )
      | ( ( in @ ( binintersect @ SV394 @ SV652 ) @ ( powerset @ ( binintersect @ ( binunion @ SV394 @ SV747 ) @ ( binunion @ SV652 @ SV747 ) ) ) )
        = $true )
      | ( ( in @ SV652 @ ( powerset @ SV167 ) )
        = $false )
      | ( ( in @ SV394 @ ( powerset @ SV167 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2483]) ).

thf(2648,plain,
    ! [SV695: $i,SV539: $i,SV395: $i,SV168: $i] :
      ( ( ( ~ ! [SY3125: $i] :
                ( ~ ( in @ SY3125 @ SV168 )
                | ! [SY3126: $i] :
                    ( ~ ( in @ SY3126 @ SV395 )
                    | ~ ( in @ ( kpair @ SY3125 @ SY3126 ) @ SV539 )
                    | ( in @ ( kpair @ SY3125 @ SY3126 ) @ SV695 ) ) ) )
        = $true )
      | ( ( subset @ SV539 @ SV695 )
        = $true )
      | ( ( subset @ SV695 @ ( cartprod @ SV168 @ SV395 ) )
        = $false )
      | ( ( subset @ SV539 @ ( cartprod @ SV168 @ SV395 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2484]) ).

thf(2649,plain,
    ! [SV696: $i,SV540: $i,SV169: $i,SV396: $o] :
      ( ( ( ~ SV396 ) = $true )
      | ( ( ( if @ SV169 @ SV396 @ SV540 @ SV696 )
          = SV540 )
        = $true )
      | ( ( in @ SV696 @ SV169 )
        = $false )
      | ( ( in @ SV540 @ SV169 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2485]) ).

thf(2650,plain,
    ! [SV697: $i,SV541: $i,SV169: $i] :
      ( ( ( ~ $true ) = $true )
      | ( ( ( if @ SV169 @ $true @ SV541 @ SV697 )
          = SV541 )
        = $true )
      | ( ( in @ SV697 @ SV169 )
        = $false )
      | ( ( in @ SV541 @ SV169 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2486]) ).

thf(2651,plain,
    ! [SV698: $i,SV542: $i,SV169: $i] :
      ( ( ( ~ $false ) = $true )
      | ( ( ( if @ SV169 @ $false @ SV542 @ SV698 )
          = SV542 )
        = $true )
      | ( ( in @ SV698 @ SV169 )
        = $false )
      | ( ( in @ SV542 @ SV169 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2487]) ).

thf(2652,plain,
    ! [SV543: $i > $i,SV397: $i,SV170: $i,SV754: $i] :
      ( ( ( ~ ( in @ SV754 @ SV170 )
          | ( ( ap @ SV170 @ SV397
              @ ( lam @ SV170 @ SV397
                @ ^ [SY2971: $i] : ( SV543 @ SY2971 ) )
              @ SV754 )
            = ( SV543 @ SV754 ) ) )
        = $true )
      | ( ( in @ ( sK22_SY2969 @ SV397 @ SV543 @ SV170 ) @ SV170 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2488]) ).

thf(2653,plain,
    ! [SV543: $i > $i,SV397: $i,SV170: $i,SV748: $i] :
      ( ( ( ~ ( in @ SV748 @ SV170 ) )
        = $true )
      | ( ( ( ap @ SV170 @ SV397
            @ ( lam @ SV170 @ SV397
              @ ^ [SY2971: $i] : ( SV543 @ SY2971 ) )
            @ SV748 )
          = ( SV543 @ SV748 ) )
        = $true )
      | ( ( in @ ( SV543 @ ( sK22_SY2969 @ SV397 @ SV543 @ SV170 ) ) @ SV397 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2489]) ).

thf(2654,plain,
    ! [SV654: $i,SV403: $i,SV177: $i,SV749: $i] :
      ( ( ( ~ ( in @ SV749 @ SV177 ) )
        = $true )
      | ( ( ~ ( subset @ SV403 @ ( setminus @ SV177 @ SV654 ) )
          | ~ ( in @ SV749 @ SV654 )
          | ~ ( in @ SV749 @ SV403 ) )
        = $true )
      | ( ( in @ SV654 @ ( powerset @ SV177 ) )
        = $false )
      | ( ( in @ SV403 @ ( powerset @ SV177 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2492]) ).

thf(2655,plain,
    ! [SV178: $i,SV616: $i,SV549: $i > $i > $o,SV404: $i,SV733: $i] :
      ( ( ( in @ SV733 @ SV404 )
        = $false )
      | ( ( ~ ( SV549 @ SV616 @ SV733 )
          | ( in @ ( kpair @ SV616 @ SV733 )
            @ ( dpsetconstr @ SV178 @ SV404
              @ ^ [SY2978: $i,SY2979: $i] : ( SV549 @ SY2978 @ SY2979 ) ) ) )
        = $true )
      | ( ( in @ SV616 @ SV178 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2493]) ).

thf(2656,plain,
    ! [SV550: $i,SV405: $i,SV179: $i] :
      ( ( ( SV179 = SV405 )
        = $false )
      | ( ( in @ SV550 @ SV405 )
        = $true )
      | ( ( in @ SV550 @ SV179 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2494]) ).

thf(2657,plain,
    ! [SV182: $i,SV408: $i,SV655: $i] :
      ( ( ( in @ SV655 @ SV408 )
        = $false )
      | ( ( in @ SV655 @ ( setminus @ SV182 @ ( setminus @ SV182 @ SV408 ) ) )
        = $true )
      | ( ( in @ SV655 @ SV182 )
        = $false )
      | ( ( in @ SV408 @ ( powerset @ SV182 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2495]) ).

thf(2658,plain,
    ! [SV185: $i,SV554: $i,SV700: $i,SV411: $i,SV755: $i] :
      ( ( ( ~ ( in @ SV755 @ SV411 )
          | ~ ( in @ ( kpair @ SV700 @ SV755 ) @ SV554 )
          | ( ( ap @ SV185 @ SV411 @ SV554 @ SV700 )
            = SV755 ) )
        = $true )
      | ( ( in @ SV700 @ SV185 )
        = $false )
      | ( ( func @ SV185 @ SV411 @ SV554 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2496]) ).

thf(2659,plain,
    ! [SV414: $i > $o,SV188: $i,SV556: $i] :
      ( ( ( ~ ( in @ SV556
              @ ( dsetconstr @ SV188
                @ ^ [SY2751: $i] : ( SV414 @ SY2751 ) ) ) )
        = $true )
      | ( ( SV414 @ SV556 )
        = $true )
      | ( ( in @ SV556 @ SV188 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2497]) ).

thf(2660,plain,
    ! [SV188: $i,SV556: $i,SV414: $i > $o] :
      ( ( ( ~ ( SV414 @ SV556 ) )
        = $true )
      | ( ( in @ SV556
          @ ( dsetconstr @ SV188
            @ ^ [SY2752: $i] : ( SV414 @ SY2752 ) ) )
        = $true )
      | ( ( in @ SV556 @ SV188 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2498]) ).

thf(2661,plain,
    ! [SV701: $i,SV558: $i,SV416: $i,SV190: $i] :
      ( ( ( ~ ! [SY3128: $i] :
                ( ~ ( in @ SY3128 @ SV190 )
                | ( ( ap @ SV190 @ SV416 @ SV558 @ SY3128 )
                  = ( ap @ SV190 @ SV416 @ SV701 @ SY3128 ) ) ) )
        = $true )
      | ( ( SV558 = SV701 )
        = $true )
      | ( ( func @ SV190 @ SV416 @ SV701 )
        = $false )
      | ( ( func @ SV190 @ SV416 @ SV558 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2499]) ).

thf(2662,plain,
    ! [SV657: $i,SV417: $i,SV191: $i,SV750: $i] :
      ( ( ( ~ ( in @ SV750 @ ( powerset @ SV191 ) ) )
        = $true )
      | ( ( ! [SY3164: $i] :
              ( ~ ( in @ SY3164 @ SV191 )
              | ~ ( in @ SY3164 @ ( binintersect @ SV417 @ SV657 ) )
              | ( in @ SY3164 @ ( binunion @ SV417 @ SV750 ) ) ) )
        = $true )
      | ( ( in @ SV657 @ ( powerset @ SV191 ) )
        = $false )
      | ( ( in @ SV417 @ ( powerset @ SV191 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2500]) ).

thf(2663,plain,
    ! [SV419: $i,SV702: $i,SV193: $i,SV658: $i] :
      ( ( ( ~ ( ~ ( in @ SV658 @ SV193 )
              | ( in @ SV702 @ SV419 ) )
          | ~ ( ~ ( in @ SV702 @ SV419 )
              | ( in @ SV658 @ SV193 ) ) )
        = $false )
      | ( ( SV658 = SV702 )
        = $false )
      | ( ( SV193 = SV419 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2501]) ).

thf(2664,plain,
    ! [SV198: $i,SV567: $i,SV710: $i,SV424: $i,SV756: $i] :
      ( ( ( ~ ( in @ SV756 @ SV424 )
          | ~ ( in @ ( kpair @ SV710 @ SV756 ) @ SV567 )
          | ( ( ap @ SV198 @ SV424 @ SV567 @ SV710 )
            = SV756 ) )
        = $true )
      | ( ( in @ SV710 @ SV198 )
        = $false )
      | ( ( in @ SV567 @ ( funcSet @ SV198 @ SV424 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2509]) ).

thf(2665,plain,
    ! [SV426: $i > $o,SV200: $i] :
      ( ( ( ! [SY2778: $i] :
              ~ ~ ( ~ ( in @ SY2778 @ SV200 )
                  | ~ ( SV426 @ SY2778 ) ) )
        = $true )
      | ( ( in @ ( sK16_SY2777 @ SV426 @ SV200 ) @ SV200 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2511]) ).

thf(2666,plain,
    ! [SV426: $i > $o,SV200: $i] :
      ( ( ( ! [SY2778: $i] :
              ~ ~ ( ~ ( in @ SY2778 @ SV200 )
                  | ~ ( SV426 @ SY2778 ) ) )
        = $true )
      | ( ( SV426 @ ( sK16_SY2777 @ SV426 @ SV200 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2512]) ).

thf(2667,plain,
    ! [SV205: $i,SV430: $i] :
      ( ( ( ~ ~ ( ~ ( in @ SV430 @ ( sK49_SY2781 @ SV205 @ SV430 ) )
                | ~ ( in @ ( sK49_SY2781 @ SV205 @ SV430 ) @ SV205 ) ) )
        = $false )
      | ( ( in @ SV430 @ ( setunion @ SV205 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2514]) ).

thf(2668,plain,
    ! [SV205: $i,SV757: $i,SV430: $i] :
      ( ( ( ~ ~ ( ~ ( in @ SV430 @ SV757 )
                | ~ ( in @ SV757 @ SV205 ) ) )
        = $true )
      | ( ( in @ SV430 @ ( setunion @ SV205 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2515]) ).

thf(2669,plain,
    ! [SV712: $o,SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV206 ) )
        = $false )
      | ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | SV712 )
          | SV712 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2516]) ).

thf(2670,plain,
    ! [SV206: $i,SV712: $o,SV431: $i,SV570: $i] :
      ( ( ( ~ ~ ( in @ SV570 @ SV431 )
          | SV712 )
        = $false )
      | ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | SV712 )
          | SV712 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2516]) ).

thf(2671,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV206 ) )
        = $false )
      | ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | $true )
          | $true )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2517]) ).

thf(2672,plain,
    ! [SV206: $i,SV431: $i,SV570: $i] :
      ( ( ( ~ ~ ( in @ SV570 @ SV431 )
          | $true )
        = $false )
      | ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | $true )
          | $true )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2517]) ).

thf(2673,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV206 ) )
        = $false )
      | ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | $false )
          | $false )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2518]) ).

thf(2674,plain,
    ! [SV206: $i,SV431: $i,SV570: $i] :
      ( ( ( ~ ~ ( in @ SV570 @ SV431 )
          | $false )
        = $false )
      | ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | $false )
          | $false )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2518]) ).

thf(2675,plain,
    ! [SV208: $i,SV433: $i] :
      ( ( ( ~ ( in @ ( sK25_SY2785 @ SV433 @ SV208 ) @ SV208 ) )
        = $false )
      | ( ( in @ SV433 @ ( setunion @ SV208 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2519]) ).

thf(2676,plain,
    ! [SV208: $i,SV433: $i] :
      ( ( ( ~ ( in @ SV433 @ ( sK25_SY2785 @ SV433 @ SV208 ) ) )
        = $false )
      | ( ( in @ SV433 @ ( setunion @ SV208 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2519]) ).

thf(2677,plain,
    ! [SV209: $i,SV434: $i,SV659: $i > $o,SV713: $i > $o] :
      ( ( ( ~ ( in @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) @ SV209 )
          | ! [SY3174: $i] :
              ( ~ ( in @ SY3174 @ SV434 )
              | ( ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 )
               != SY3174 )
              | ~ ( ~ ( ~ ( SV659 @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) )
                      | ( SV713 @ SY3174 ) )
                  | ~ ( ~ ( SV713 @ SY3174 )
                      | ( SV659 @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) ) ) ) ) )
        = $false )
      | ( ( ( dsetconstr @ SV209
            @ ^ [SY3097: $i] : ( SV659 @ SY3097 ) )
          = ( dsetconstr @ SV434
            @ ^ [SY3136: $i] : ( SV713 @ SY3136 ) ) )
        = $true )
      | ( ( SV209 = SV434 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2520]) ).

thf(2678,plain,
    ! [SV714: $o,SV435: $i,SV210: $i,SV571: $i] :
      ( ( ( SV571 != SV210 )
        = $false )
      | ( ( ~ ( ~ ( in @ SV571 @ SV435 )
              | SV714 )
          | SV714 )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2521]) ).

thf(2679,plain,
    ! [SV210: $i,SV435: $i,SV571: $i,SV714: $o] :
      ( ( SV714 = $false )
      | ( ( ~ ( ~ ( in @ SV571 @ SV435 )
              | SV714 )
          | SV714 )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2521]) ).

thf(2680,plain,
    ! [SV435: $i,SV210: $i,SV571: $i] :
      ( ( ( SV571 != SV210 )
        = $false )
      | ( ( ~ ( ~ ( in @ SV571 @ SV435 )
              | $true )
          | $true )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2522]) ).

thf(2681,plain,
    ! [SV210: $i,SV435: $i,SV571: $i] :
      ( ( $true = $false )
      | ( ( ~ ( ~ ( in @ SV571 @ SV435 )
              | $true )
          | $true )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2522]) ).

thf(2682,plain,
    ! [SV435: $i,SV210: $i,SV571: $i] :
      ( ( ( SV571 != SV210 )
        = $false )
      | ( ( ~ ( ~ ( in @ SV571 @ SV435 )
              | $false )
          | $false )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2523]) ).

thf(2683,plain,
    ! [SV210: $i,SV435: $i,SV571: $i] :
      ( ( $false = $false )
      | ( ( ~ ( ~ ( in @ SV571 @ SV435 )
              | $false )
          | $false )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2523]) ).

thf(2684,plain,
    ! [SV660: $i,SV211: $i > $o] :
      ( ( ( SV211 @ SV660 )
        = $false )
      | ( ( ~ ! [SY3099: $i] :
                ( ~ ( SV211 @ SY3099 )
                | ( SV660 = SY3099 ) ) )
        = $true )
      | ( ( ~ ! [SY2378: $i] :
                ~ ~ ( ~ ( SV211 @ SY2378 )
                    | ~ ! [SY2379: $i] :
                          ( ~ ( SV211 @ SY2379 )
                          | ( SY2378 = SY2379 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2524]) ).

thf(2685,plain,
    ! [SV437: $i,SV213: $i,SV661: $i] :
      ( ( ( in @ SV661 @ ( setminus @ SV213 @ ( setminus @ SV213 @ SV437 ) ) )
        = $false )
      | ( ( in @ SV661 @ SV437 )
        = $true )
      | ( ( in @ SV661 @ SV213 )
        = $false )
      | ( ( in @ SV437 @ ( powerset @ SV213 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2526]) ).

thf(2686,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ( ~ ~ ! [SY2388: $i] :
                      ~ ~ ( ~ ( SV214 @ SY2388 )
                          | ~ ! [SY2389: $i] :
                                ( ~ ( SV214 @ SY2389 )
                                | ( SY2388 = SY2389 ) ) )
              | ~ ! [SY2801: $i] :
                    ~ ~ ( ~ ( SV438 @ SY2801 )
                        | ~ ! [SY2802: $i] :
                              ( ~ ( SV438 @ SY2802 )
                              | ( SY2801 = SY2802 ) ) ) )
          | ~ ( ~ ~ ! [SY2803: $i] :
                      ~ ~ ( ~ ( SV438 @ SY2803 )
                          | ~ ! [SY2804: $i] :
                                ( ~ ( SV438 @ SY2804 )
                                | ( SY2803 = SY2804 ) ) )
              | ~ ! [SY2394: $i] :
                    ~ ~ ( ~ ( SV214 @ SY2394 )
                        | ~ ! [SY2395: $i] :
                              ( ~ ( SV214 @ SY2395 )
                              | ( SY2394 = SY2395 ) ) ) ) )
        = $false )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2527]) ).

thf(2687,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ( ~ ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
              | ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
              | ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ~ ! [SY2388: $i] :
                          ~ ~ ( ~ ( SV214 @ SY2388 )
                              | ~ ! [SY2389: $i] :
                                    ( ~ ( SV214 @ SY2389 )
                                    | ( SY2388 = SY2389 ) ) )
                  | ~ ! [SY2801: $i] :
                        ~ ~ ( ~ ( SV438 @ SY2801 )
                            | ~ ! [SY2802: $i] :
                                  ( ~ ( SV438 @ SY2802 )
                                  | ( SY2801 = SY2802 ) ) ) )
              | ~ ( ~ ~ ! [SY2803: $i] :
                          ~ ~ ( ~ ( SV438 @ SY2803 )
                              | ~ ! [SY2804: $i] :
                                    ( ~ ( SV438 @ SY2804 )
                                    | ( SY2803 = SY2804 ) ) )
                  | ~ ! [SY2394: $i] :
                        ~ ~ ( ~ ( SV214 @ SY2394 )
                            | ~ ! [SY2395: $i] :
                                  ( ~ ( SV214 @ SY2395 )
                                  | ( SY2394 = SY2395 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2528]) ).

thf(2688,plain,
    ! [SV215: $i,SV439: $i > $o] :
      ( ( ( ~ ( in @ ( sK27_SY2808 @ SV439 @ SV215 ) @ SV215 ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV215
            @ ^ [SY2807: $i] : ( SV439 @ SY2807 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2529]) ).

thf(2689,plain,
    ! [SV215: $i,SV439: $i > $o] :
      ( ( ( ~ ( SV439 @ ( sK27_SY2808 @ SV439 @ SV215 ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV215
            @ ^ [SY2807: $i] : ( SV439 @ SY2807 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2529]) ).

thf(2690,plain,
    ! [SV573: $i,SV440: $i > $o,SV216: $i] :
      ( ( ( ! [SY3006: $i] :
              ( ~ ( in @ SY3006 @ SV216 )
              | ~ ( SV440 @ SY3006 )
              | ( SY3006 = SV573 ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV216
            @ ^ [SY2811: $i] : ( SV440 @ SY2811 ) ) )
        = $true )
      | ( ( SV440 @ SV573 )
        = $false )
      | ( ( in @ SV573 @ SV216 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2530]) ).

thf(2691,plain,
    ! [SV718: $i,SV576: $i,SV220: $i,SV444: $o] :
      ( ( ( ~ SV444 ) = $true )
      | ( ( ( dsetconstr @ SV220
            @ ^ [SY3137: $i] :
                ( ~ ( ~ SV444
                    | ( SY3137 != SV576 ) )
                | ~ ( ~ ~ SV444
                    | ( SY3137 != SV718 ) ) ) )
          = ( setadjoin @ SV576 @ emptyset ) )
        = $true )
      | ( ( in @ SV718 @ SV220 )
        = $false )
      | ( ( in @ SV576 @ SV220 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2533]) ).

thf(2692,plain,
    ! [SV719: $i,SV577: $i,SV220: $i] :
      ( ( ( ~ $true ) = $true )
      | ( ( ( dsetconstr @ SV220
            @ ^ [SY3138: $i] :
                ( ~ ( ~ $true
                    | ( SY3138 != SV577 ) )
                | ~ ( ~ ~ $true
                    | ( SY3138 != SV719 ) ) ) )
          = ( setadjoin @ SV577 @ emptyset ) )
        = $true )
      | ( ( in @ SV719 @ SV220 )
        = $false )
      | ( ( in @ SV577 @ SV220 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2534]) ).

thf(2693,plain,
    ! [SV720: $i,SV578: $i,SV220: $i] :
      ( ( ( ~ $false ) = $true )
      | ( ( ( dsetconstr @ SV220
            @ ^ [SY3139: $i] :
                ( ~ ( ~ $false
                    | ( SY3139 != SV578 ) )
                | ~ ( ~ ~ $false
                    | ( SY3139 != SV720 ) ) ) )
          = ( setadjoin @ SV578 @ emptyset ) )
        = $true )
      | ( ( in @ SV720 @ SV220 )
        = $false )
      | ( ( in @ SV578 @ SV220 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2535]) ).

thf(2694,plain,
    ! [SV721: $i,SV579: $i,SV445: $i,SV221: $i] :
      ( ( ( ~ ! [SY3140: $i] :
                ( ~ ( in @ SY3140 @ SV221 )
                | ! [SY3141: $i] :
                    ( ~ ( in @ SY3141 @ SV445 )
                    | ~ ( in @ ( kpair @ SY3140 @ SY3141 ) @ SV579 )
                    | ( in @ ( kpair @ SY3140 @ SY3141 ) @ SV721 ) ) ) )
        = $true )
      | ( ( ~ ! [SY3142: $i] :
                ( ~ ( in @ SY3142 @ SV221 )
                | ! [SY3143: $i] :
                    ( ~ ( in @ SY3143 @ SV445 )
                    | ~ ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV721 )
                    | ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV579 ) ) )
          | ( SV579 = SV721 ) )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2536]) ).

thf(2695,plain,
    ! [SV224: $i] :
      ( ( ( ~ ( in @ ( sK28_SY2426 @ SV224 ) @ SV224 ) )
        = $false )
      | ( ( SV224 = emptyset )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2538]) ).

thf(2696,plain,
    ! [SV224: $i] :
      ( ( ( ~ $true ) = $false )
      | ( ( SV224 = emptyset )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2538]) ).

thf(2697,plain,
    ! [SV450: $i,SV662: $i,SV227: $i] :
      ( ( ( subset @ ( setminus @ SV227 @ SV662 ) @ ( setminus @ SV227 @ SV450 ) )
        = $false )
      | ( ( subset @ SV450 @ SV662 )
        = $true )
      | ( ( in @ SV662 @ ( powerset @ SV227 ) )
        = $false )
      | ( ( in @ SV450 @ ( powerset @ SV227 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2540]) ).

thf(2698,plain,
    ! [SV663: $i,SV451: $i,SV228: $i,SV751: $i] :
      ( ( ( ~ ( in @ SV751 @ ( powerset @ SV228 ) ) )
        = $true )
      | ( ( ! [SY3165: $i] :
              ( ~ ( in @ SY3165 @ SV228 )
              | ~ ( in @ SY3165 @ ( binintersect @ SV451 @ SV663 ) )
              | ( in @ SY3165 @ ( binunion @ SV663 @ SV751 ) ) ) )
        = $true )
      | ( ( in @ SV663 @ ( powerset @ SV228 ) )
        = $false )
      | ( ( in @ SV451 @ ( powerset @ SV228 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2541]) ).

thf(2699,plain,
    ! [SV723: $i,SV583: $i,SV230: $i,SV453: $o] :
      ( ( ( ~ ~ SV453 )
        = $true )
      | ( ( ( dsetconstr @ SV230
            @ ^ [SY3145: $i] :
                ( ~ ( ~ SV453
                    | ( SY3145 != SV583 ) )
                | ~ ( ~ ~ SV453
                    | ( SY3145 != SV723 ) ) ) )
          = ( setadjoin @ SV723 @ emptyset ) )
        = $true )
      | ( ( in @ SV723 @ SV230 )
        = $false )
      | ( ( in @ SV583 @ SV230 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2542]) ).

thf(2700,plain,
    ! [SV724: $i,SV584: $i,SV230: $i] :
      ( ( ( ~ ~ $true )
        = $true )
      | ( ( ( dsetconstr @ SV230
            @ ^ [SY3146: $i] :
                ( ~ ( ~ $true
                    | ( SY3146 != SV584 ) )
                | ~ ( ~ ~ $true
                    | ( SY3146 != SV724 ) ) ) )
          = ( setadjoin @ SV724 @ emptyset ) )
        = $true )
      | ( ( in @ SV724 @ SV230 )
        = $false )
      | ( ( in @ SV584 @ SV230 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2543]) ).

thf(2701,plain,
    ! [SV725: $i,SV585: $i,SV230: $i] :
      ( ( ( ~ ~ $false )
        = $true )
      | ( ( ( dsetconstr @ SV230
            @ ^ [SY3147: $i] :
                ( ~ ( ~ $false
                    | ( SY3147 != SV585 ) )
                | ~ ( ~ ~ $false
                    | ( SY3147 != SV725 ) ) ) )
          = ( setadjoin @ SV725 @ emptyset ) )
        = $true )
      | ( ( in @ SV725 @ SV230 )
        = $false )
      | ( ( in @ SV585 @ SV230 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2544]) ).

thf(2702,plain,
    ! [SV664: $i,SV454: $i,SV231: $i] :
      ( ( ( ! [SY3103: $i] :
              ( ~ ( in @ SY3103 @ SV231 )
              | ~ ( in @ SY3103 @ SV454 )
              | ( in @ SY3103 @ SV664 ) ) )
        = $false )
      | ( ( in @ SV454 @ ( powerset @ SV664 ) )
        = $true )
      | ( ( in @ SV664 @ ( powerset @ SV231 ) )
        = $false )
      | ( ( in @ SV454 @ ( powerset @ SV231 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2545]) ).

thf(2703,plain,
    ! [SV665: $i,SV466: $i,SV243: $i] :
      ( ( ( ! [SY3104: $i] :
              ( ~ ( in @ SY3104 @ SV243 )
              | ~ ( in @ SY3104 @ SV466 )
              | ( in @ SY3104 @ SV665 ) ) )
        = $false )
      | ( ( subset @ SV466 @ SV665 )
        = $true )
      | ( ( in @ SV665 @ ( powerset @ SV243 ) )
        = $false )
      | ( ( in @ SV466 @ ( powerset @ SV243 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2546]) ).

thf(2704,plain,
    ! [SV594: $i > $i,SV467: $i,SV244: $i,SV758: $i] :
      ( ( ( ~ ( in @ SV758 @ SV244 )
          | ( ( ap @ SV244 @ SV467
              @ ( lam @ SV244 @ SV467
                @ ^ [SY3033: $i] : ( SV594 @ SY3033 ) )
              @ SV758 )
            = ( SV594 @ SV758 ) ) )
        = $true )
      | ( ( in @ ( sK29_SY3031 @ SV467 @ SV594 @ SV244 ) @ SV244 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2547]) ).

thf(2705,plain,
    ! [SV594: $i > $i,SV467: $i,SV244: $i,SV752: $i] :
      ( ( ( ~ ( in @ SV752 @ SV244 ) )
        = $true )
      | ( ( ( ap @ SV244 @ SV467
            @ ( lam @ SV244 @ SV467
              @ ^ [SY3033: $i] : ( SV594 @ SY3033 ) )
            @ SV752 )
          = ( SV594 @ SV752 ) )
        = $true )
      | ( ( in @ ( SV594 @ ( sK29_SY3031 @ SV467 @ SV594 @ SV244 ) ) @ SV467 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2548]) ).

thf(2706,plain,
    ! [SV666: $i,SV469: $i,SV246: $i,SV753: $i] :
      ( ( ( ~ ( in @ SV753 @ SV246 ) )
        = $true )
      | ( ( ~ ( in @ SV753 @ ( setminus @ SV246 @ SV469 ) )
          | ~ ( in @ SV753 @ ( binintersect @ SV469 @ SV666 ) ) )
        = $true )
      | ( ( in @ SV666 @ ( powerset @ SV246 ) )
        = $false )
      | ( ( in @ SV469 @ ( powerset @ SV246 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2550]) ).

thf(2707,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ~ ( ~ ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
              | ( ( sK37_SY3106 @ SV667 @ SV253 )
                = SV667 ) ) )
        = $true )
      | ( ( ~ ( ( ( sK37_SY3106 @ SV667 @ SV253 )
               != SV667 )
              | ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2491: $i] :
                ~ ~ ( ~ ( SV253 @ SY2491 )
                    | ~ ! [SY2492: $i] :
                          ( ~ ( SV253 @ SY2492 )
                          | ( SY2491 = SY2492 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2552]) ).

thf(2708,plain,
    ! [SV255: $i,SV668: $o,SV475: $i] :
      ( ( ( ~ ( in @ SV475 @ ( sK41_SY3107 @ SV668 @ SV255 @ SV475 ) ) )
        = $false )
      | ( SV668 = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2553]) ).

thf(2709,plain,
    ! [SV475: $i,SV255: $i,SV668: $o] :
      ( ( ( ~ ( in @ ( sK41_SY3107 @ SV668 @ SV255 @ SV475 ) @ SV255 )
          | SV668 )
        = $false )
      | ( SV668 = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2553]) ).

thf(2710,plain,
    ! [SV255: $i,SV475: $i] :
      ( ( ( ~ ( in @ SV475 @ ( sK42_SX0 @ SV255 @ SV475 ) ) )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2554]) ).

thf(2711,plain,
    ! [SV475: $i,SV255: $i] :
      ( ( ( ~ ( in @ ( sK42_SX0 @ SV255 @ SV475 ) @ SV255 )
          | $true )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2554]) ).

thf(2712,plain,
    ! [SV255: $i,SV475: $i] :
      ( ( ( ~ ( in @ SV475 @ ( sK43_SX0 @ SV255 @ SV475 ) ) )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2555]) ).

thf(2713,plain,
    ! [SV475: $i,SV255: $i] :
      ( ( ( ~ ( in @ ( sK43_SX0 @ SV255 @ SV475 ) @ SV255 )
          | $false )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2555]) ).

thf(2714,plain,
    ! [SV35: $i,SV281: $i > $o] :
      ( ( ( ~ ( in @ ( sK30_SY2514 @ SV281 @ SV35 ) @ SV35 ) )
        = $false )
      | ( ( ! [SY2515: $i] :
              ( ~ ( in @ SY2515 @ SV35 )
              | ~ ( SV281 @ SY2515 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2560]) ).

thf(2715,plain,
    ! [SV35: $i,SV281: $i > $o] :
      ( ( ( ~ ( SV281 @ ( sK30_SY2514 @ SV281 @ SV35 ) ) )
        = $false )
      | ( ( ! [SY2515: $i] :
              ( ~ ( in @ SY2515 @ SV35 )
              | ~ ( SV281 @ SY2515 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2560]) ).

thf(2716,plain,
    ! [SV619: $i,SV282: $i,SV36: $i,SV734: $i] :
      ( ( ( in @ SV734 @ SV36 )
        = $false )
      | ( ( ~ ( subset @ SV282 @ SV619 )
          | ~ ~ ( in @ SV734 @ SV619 )
          | ~ ( in @ SV734 @ SV282 ) )
        = $true )
      | ( ( in @ SV619 @ ( powerset @ SV36 ) )
        = $false )
      | ( ( in @ SV282 @ ( powerset @ SV36 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2561]) ).

thf(2717,plain,
    ! [SV620: $i,SV37: $i > $o] :
      ( ( ( ! [SY3056: $i] :
              ( ~ ( SV37 @ SY3056 )
              | ( SV620 = SY3056 ) ) )
        = $false )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( ~ ! [SY1897: $i] :
                ~ ! [SY1898: $i] :
                    ~ ( ~ ( ~ ( SV37 @ SY1898 )
                          | ( SY1898 = SY1897 ) )
                      | ~ ( ( SY1898 != SY1897 )
                          | ( SV37 @ SY1898 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2562]) ).

thf(2718,plain,
    ! [SV483: $i,SV40: $i,SV670: $i,SV284: $o] :
      ( ( ( ~ SV284 ) = $false )
      | ( ( in @ SV670
          @ ( dsetconstr @ SV40
            @ ^ [SY3108: $i] :
                ( ~ ( ~ SV284
                    | ( SY3108 != SV483 ) )
                | ~ ( ~ ~ SV284
                    | ( SY3108 != SV670 ) ) ) ) )
        = $true )
      | ( ( in @ SV670 @ SV40 )
        = $false )
      | ( ( in @ SV483 @ SV40 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2563]) ).

thf(2719,plain,
    ! [SV484: $i,SV40: $i,SV671: $i] :
      ( ( ( ~ $true ) = $false )
      | ( ( in @ SV671
          @ ( dsetconstr @ SV40
            @ ^ [SY3109: $i] :
                ( ~ ( ~ $true
                    | ( SY3109 != SV484 ) )
                | ~ ( ~ ~ $true
                    | ( SY3109 != SV671 ) ) ) ) )
        = $true )
      | ( ( in @ SV671 @ SV40 )
        = $false )
      | ( ( in @ SV484 @ SV40 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2564]) ).

thf(2720,plain,
    ! [SV485: $i,SV40: $i,SV672: $i] :
      ( ( ( ~ $false ) = $false )
      | ( ( in @ SV672
          @ ( dsetconstr @ SV40
            @ ^ [SY3110: $i] :
                ( ~ ( ~ $false
                    | ( SY3110 != SV485 ) )
                | ~ ( ~ ~ $false
                    | ( SY3110 != SV672 ) ) ) ) )
        = $true )
      | ( ( in @ SV672 @ SV40 )
        = $false )
      | ( ( in @ SV485 @ SV40 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2565]) ).

thf(2721,plain,
    ! [SV621: $i,SV41: $i > $o] :
      ( ( ( ! [SY3057: $i] :
              ( ~ ( SV41 @ SY3057 )
              | ( SV621 = SY3057 ) ) )
        = $false )
      | ( ( SV41 @ SV621 )
        = $false )
      | ( ( ! [SY1909: $i,SY1910: $i] :
              ( ~ ( SV41 @ SY1909 )
              | ~ ( SV41 @ SY1910 )
              | ( SY1909 = SY1910 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2566]) ).

thf(2722,plain,
    ! [SV42: $i,SV285: $i,SV735: $i] :
      ( ( ( in @ SV735 @ SV285 )
        = $false )
      | ( ( in @ SV735 @ SV42 )
        = $true )
      | ( ( in @ SV285 @ ( powerset @ SV42 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2567]) ).

thf(2723,plain,
    ! [SV285: $i,SV42: $i] :
      ( ( ( in @ ( sK38_SY2524 @ SV42 @ SV285 ) @ SV285 )
        = $true )
      | ( ( in @ SV285 @ ( powerset @ SV42 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2568]) ).

thf(2724,plain,
    ! [SV622: $i,SV43: $i > $o] :
      ( ( ( ! [SY3058: $i] :
              ( ~ ( SV43 @ SY3058 )
              | ( SV622 = SY3058 ) ) )
        = $false )
      | ( ( SV43 @ SV622 )
        = $false )
      | ( ( ! [SY1916: $i,SY1917: $i] :
              ( ~ ( SV43 @ SY1916 )
              | ~ ( SV43 @ SY1917 )
              | ( SY1916 = SY1917 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2570]) ).

thf(2725,plain,
    ! [SV623: $i,SV286: $i,SV44: $i,SV736: $i] :
      ( ( ( in @ SV736 @ SV44 )
        = $false )
      | ( ( ~ ( in @ SV736 @ ( setminus @ SV44 @ ( binunion @ SV286 @ SV623 ) ) )
          | ~ ( in @ SV736 @ SV286 ) )
        = $true )
      | ( ( in @ SV623 @ ( powerset @ SV44 ) )
        = $false )
      | ( ( in @ SV286 @ ( powerset @ SV44 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2571]) ).

thf(2726,plain,
    ! [SV287: $i > $o,SV46: $i,SV673: $i] :
      ( ( ( in @ SV673 @ SV46 )
        = $false )
      | ( ( ~ ~ ( SV287 @ SV673 ) )
        = $true )
      | ( ( ~ ! [SY2528: $i] :
                ( ~ ( in @ SY2528 @ SV46 )
                | ( SV287 @ SY2528 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2572]) ).

thf(2727,plain,
    ! [SV624: $i,SV48: $i > $o] :
      ( ( ( ! [SY3060: $i] :
              ( ~ ( SV48 @ SY3060 )
              | ( SV624 = SY3060 ) ) )
        = $false )
      | ( ( SV48 @ SV624 )
        = $false )
      | ( ( ~ ! [SY1928: $i] :
                ~ ~ ( ~ ( SV48 @ SY1928 )
                    | ~ ! [SY1929: $i] :
                          ( ~ ( SV48 @ SY1929 )
                          | ( SY1928 = SY1929 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2573]) ).

thf(2728,plain,
    ! [SV51: $i,SV291: $i] :
      ( ( ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV51 )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV291 )
              | ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV51 ) ) )
        = $true )
      | ( ( SV51 = SV291 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2574]) ).

thf(2729,plain,
    ! [SV51: $i,SV291: $i] :
      ( ( ( ~ ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV291 )
          | ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV51 ) )
        = $false )
      | ( ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV291 )
        = $false )
      | ( ( SV51 = SV291 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2575]) ).

thf(2730,plain,
    ! [SV52: $i,SV292: $i > $o] :
      ( ( ( ~ ( in @ ( sK31_SY2534 @ SV292 @ SV52 ) @ SV52 ) )
        = $false )
      | ( ( ! [SY2535: $i] :
              ( ~ ( in @ SY2535 @ SV52 )
              | ~ ( SV292 @ SY2535 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2576]) ).

thf(2731,plain,
    ! [SV52: $i,SV292: $i > $o] :
      ( ( ( ~ ( SV292 @ ( sK31_SY2534 @ SV292 @ SV52 ) ) )
        = $false )
      | ( ( ! [SY2535: $i] :
              ( ~ ( in @ SY2535 @ SV52 )
              | ~ ( SV292 @ SY2535 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2576]) ).

thf(2732,plain,
    ! [SV295: $i,SV55: $i,SV489: $i] :
      ( ( ( in @ SV489 @ ( symdiff @ SV55 @ SV295 ) )
        = $false )
      | ( ( in @ SV489 @ SV295 )
        = $true )
      | ( ( in @ SV489 @ SV55 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2577]) ).

thf(2733,plain,
    ! [SV63: $i,SV302: $i,SV496: $i,SV676: $i > $o] :
      ( ( ( ~ ( in @ ( sK44_SY3111 @ SV676 @ SV496 @ SV302 @ SV63 ) @ SV63 ) )
        = $false )
      | ( ( ! [SY3113: $i] :
              ( ~ ( in @ SY3113 @ SV496 )
              | ( SV676 @ SY3113 ) ) )
        = $true )
      | ( ( subset @ SV496 @ ( cartprod @ SV63 @ SV302 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2578]) ).

thf(2734,plain,
    ! [SV63: $i,SV496: $i,SV676: $i > $o,SV302: $i] :
      ( ( ( ! [SY3167: $i] :
              ( ~ ( in @ SY3167 @ SV302 )
              | ~ ( in @ ( kpair @ ( sK44_SY3111 @ SV676 @ SV496 @ SV302 @ SV63 ) @ SY3167 ) @ SV496 )
              | ( SV676 @ ( kpair @ ( sK44_SY3111 @ SV676 @ SV496 @ SV302 @ SV63 ) @ SY3167 ) ) ) )
        = $false )
      | ( ( ! [SY3113: $i] :
              ( ~ ( in @ SY3113 @ SV496 )
              | ( SV676 @ SY3113 ) ) )
        = $true )
      | ( ( subset @ SV496 @ ( cartprod @ SV63 @ SV302 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2578]) ).

thf(2735,plain,
    ! [SV677: $i,SV67: $i,SV498: $i,SV305: $o] :
      ( ( SV305 = $false )
      | ( ( in @ SV498
          @ ( dsetconstr @ SV67
            @ ^ [SY3114: $i] :
                ( ~ ( ~ SV305
                    | ( SY3114 != SV498 ) )
                | ~ ( ~ ~ SV305
                    | ( SY3114 != SV677 ) ) ) ) )
        = $true )
      | ( ( in @ SV677 @ SV67 )
        = $false )
      | ( ( in @ SV498 @ SV67 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2579]) ).

thf(2736,plain,
    ! [SV678: $i,SV67: $i,SV499: $i] :
      ( ( $true = $false )
      | ( ( in @ SV499
          @ ( dsetconstr @ SV67
            @ ^ [SY3115: $i] :
                ( ~ ( ~ $true
                    | ( SY3115 != SV499 ) )
                | ~ ( ~ ~ $true
                    | ( SY3115 != SV678 ) ) ) ) )
        = $true )
      | ( ( in @ SV678 @ SV67 )
        = $false )
      | ( ( in @ SV499 @ SV67 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2580]) ).

thf(2737,plain,
    ! [SV679: $i,SV67: $i,SV500: $i] :
      ( ( $false = $false )
      | ( ( in @ SV500
          @ ( dsetconstr @ SV67
            @ ^ [SY3116: $i] :
                ( ~ ( ~ $false
                    | ( SY3116 != SV500 ) )
                | ~ ( ~ ~ $false
                    | ( SY3116 != SV679 ) ) ) ) )
        = $true )
      | ( ( in @ SV679 @ SV67 )
        = $false )
      | ( ( in @ SV500 @ SV67 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2581]) ).

thf(2738,plain,
    ! [SV681: $i,SV502: $i,SV311: $i,SV73: $i] :
      ( ( ( ! [SY3118: $i] :
              ( ~ ( in @ SY3118 @ SV73 )
              | ( ( ap @ SV73 @ SV311 @ SV502 @ SY3118 )
                = ( ap @ SV73 @ SV311 @ SV681 @ SY3118 ) ) ) )
        = $false )
      | ( ( SV502 = SV681 )
        = $true )
      | ( ( in @ SV681 @ ( funcSet @ SV73 @ SV311 ) )
        = $false )
      | ( ( in @ SV502 @ ( funcSet @ SV73 @ SV311 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2583]) ).

thf(2739,plain,
    ! [SV312: $i,SV74: $i,SV503: $i] :
      ( ( ( in @ SV503 @ SV74 )
        = $false )
      | ( ( in @ SV503 @ SV312 )
        = $true )
      | ( ( in @ SV503 @ ( setminus @ SV74 @ SV312 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2584]) ).

thf(2740,plain,
    ! [SV627: $i,SV314: $i,SV76: $i,SV737: $i] :
      ( ( ( in @ SV737 @ ( powerset @ SV76 ) )
        = $false )
      | ( ( ! [SY3153: $i] :
              ( ~ ( in @ SY3153 @ SV76 )
              | ~ ( in @ SY3153 @ ( binintersect @ SV314 @ SV627 ) )
              | ( in @ SY3153 @ ( binintersect @ ( binunion @ SV314 @ SV737 ) @ ( binunion @ SV627 @ SV737 ) ) ) ) )
        = $true )
      | ( ( in @ SV627 @ ( powerset @ SV76 ) )
        = $false )
      | ( ( in @ SV314 @ ( powerset @ SV76 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2588]) ).

thf(2741,plain,
    ! [SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ~ ! [SY2001: $i] :
                ~ ~ ( ~ ( SV77 @ SY2001 )
                    | ~ ! [SY2002: $i] :
                          ( ~ ( SV77 @ SY2002 )
                          | ( SY2001 = SY2002 ) ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2589]) ).

thf(2742,plain,
    ! [SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ~ ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
          | ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) ) )
        = $false )
      | ( ( ~ ( ~ ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
              | ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2001: $i] :
                  ~ ~ ( ~ ( SV77 @ SY2001 )
                      | ~ ! [SY2002: $i] :
                            ( ~ ( SV77 @ SY2002 )
                            | ( SY2001 = SY2002 ) ) )
          | ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2590]) ).

thf(2743,plain,
    ! [SV80: $i,SV318: $i,SV628: $i] :
      ( ( ( ~ ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV80 )
          | ~ ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV318 )
          | ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV628 ) )
        = $false )
      | ( ( ~ ! [SY3067: $i] :
                ( ~ ( in @ SY3067 @ SV80 )
                | ~ ( in @ SY3067 @ SV628 )
                | ( in @ SY3067 @ SV318 ) )
          | ( SV318 = SV628 ) )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2591]) ).

thf(2744,plain,
    ! [SV319: $i,SV81: $i] :
      ( ( ( ~ ( in @ ( sK52_SY2586 @ SV81 @ SV319 ) @ SV319 )
          | ( in @ ( sK52_SY2586 @ SV81 @ SV319 ) @ SV81 ) )
        = $false )
      | ( ( SV81 = SV319 )
        = $true )
      | ( ( in @ ( sK8_SY2585 @ SV319 @ SV81 ) @ SV81 )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2592]) ).

thf(2745,plain,
    ! [SV319: $i,SV81: $i] :
      ( ( ( ~ ( in @ ( sK45_SY2586 @ SV81 @ SV319 ) @ SV319 ) )
        = $false )
      | ( ( SV81 = SV319 )
        = $true )
      | ( ( in @ ( sK8_SY2585 @ SV319 @ SV81 ) @ SV319 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2593]) ).

thf(2746,plain,
    ! [SV319: $i,SV81: $i] :
      ( ( ( in @ ( sK45_SY2586 @ SV81 @ SV319 ) @ SV81 )
        = $false )
      | ( ( SV81 = SV319 )
        = $true )
      | ( ( in @ ( sK8_SY2585 @ SV319 @ SV81 ) @ SV319 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2593]) ).

thf(2747,plain,
    ! [SV506: $i > $i > $o,SV320: $i,SV82: $i,SV732: $i,SV608: $i] :
      ( ( ( ~ ( in @ ( kpair @ SV608 @ SV732 )
              @ ( dpsetconstr @ SV82 @ SV320
                @ ^ [SY2907: $i,SY2908: $i] : ( SV506 @ SY2907 @ SY2908 ) ) ) )
        = $true )
      | ( ( SV506 @ SV608 @ SV732 )
        = $true )
      | ( ( in @ SV732 @ SV320 )
        = $false )
      | ( ( in @ SV608 @ SV82 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2594]) ).

thf(2748,plain,
    ! [SV84: $i,SV321: $i > $o,SV682: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK53_SY2593 @ SV682 @ SV321 @ SV84 ) @ SV84 )
                | ~ ~ ( SV321 @ ( sK53_SY2593 @ SV682 @ SV321 @ SV84 ) ) ) )
        = $false )
      | ( ( SV321 @ SV682 )
        = $true )
      | ( ( in @ SV682 @ SV84 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2595]) ).

thf(2749,plain,
    ! [SV609: $o,SV322: $i,SV85: $i,SV507: $i] :
      ( ( ( in @ SV507 @ SV85 )
        = $true )
      | ( ( ~ ( ~ ( in @ SV507 @ SV322 )
              | SV609 )
          | SV609 )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2596]) ).

thf(2750,plain,
    ! [SV85: $i,SV609: $o,SV322: $i,SV507: $i] :
      ( ( ( ~ ( ~ ( in @ SV507 @ SV322 )
              | SV609 ) )
        = $true )
      | ( SV609 = $true )
      | ( SV609 = $false )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2597]) ).

thf(2751,plain,
    ! [SV322: $i,SV85: $i,SV507: $i] :
      ( ( ( in @ SV507 @ SV85 )
        = $true )
      | ( ( ~ ( ~ ( in @ SV507 @ SV322 )
              | $true )
          | $true )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2598]) ).

thf(2752,plain,
    ! [SV85: $i,SV322: $i,SV507: $i] :
      ( ( ( ~ ( ~ ( in @ SV507 @ SV322 )
              | $true ) )
        = $true )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2599]) ).

thf(2753,plain,
    ! [SV322: $i,SV85: $i,SV507: $i] :
      ( ( ( in @ SV507 @ SV85 )
        = $true )
      | ( ( ~ ( ~ ( in @ SV507 @ SV322 )
              | $false )
          | $false )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2600]) ).

thf(2754,plain,
    ! [SV85: $i,SV322: $i,SV507: $i] :
      ( ( ( ~ ( ~ ( in @ SV507 @ SV322 )
              | $false ) )
        = $true )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2601]) ).

thf(2755,plain,
    ! [SV87: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK39_SY2033 @ SV87 ) @ omega )
              | ~ ( in @ ( sK39_SY2033 @ SV87 ) @ SV87 ) ) )
        = $true )
      | ( ( in @ emptyset @ SV87 )
        = $false )
      | ( ( ! [SY2034: $i] :
              ( ~ ( in @ SY2034 @ omega )
              | ( in @ SY2034 @ SV87 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2602]) ).

thf(2756,plain,
    ! [SV87: $i,SV759: $i] :
      ( ( ( ~ ( in @ SV759 @ omega )
          | ( in @ SV759 @ SV87 ) )
        = $true )
      | ( ( in @ emptyset @ SV87 )
        = $false )
      | ( ( in @ ( setadjoin @ ( sK39_SY2033 @ SV87 ) @ ( sK39_SY2033 @ SV87 ) ) @ SV87 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2603]) ).

thf(2757,plain,
    ( ( in @ sK32_SY3068 @ ( setminus @ sK1_SX0 @ ( binunion @ sK2_SY2597 @ sK9_SY2910 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2605]) ).

thf(2758,plain,
    ! [SV324: $i,SV629: $i,SV88: $i,SV760: $i] :
      ( ( ( ~ ( in @ SV760 @ SV88 )
          | ~ ( in @ SV760 @ SV629 )
          | ( in @ SV760 @ ( setminus @ SV88 @ SV324 ) ) )
        = $true )
      | ( ( subset @ SV324 @ ( setminus @ SV88 @ SV629 ) )
        = $false )
      | ( ( in @ SV629 @ ( powerset @ SV88 ) )
        = $false )
      | ( ( in @ SV324 @ ( powerset @ SV88 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2607]) ).

thf(2759,plain,
    ! [SV325: $i > $o,SV89: $i,SV683: $i] :
      ( ( ( in @ SV683 @ SV89 )
        = $false )
      | ( ( ~ ( SV325 @ SV683 ) )
        = $true )
      | ( ( ( ( dsetconstr @ SV89
              @ ^ [SY2603: $i] : ( SV325 @ SY2603 ) )
           != emptyset )
          | $false )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2608]) ).

thf(2760,plain,
    ! [SV328: $i,SV684: $i,SV92: $i,SV631: $i] :
      ( ( ( in @ SV631 @ SV92 )
        = $false )
      | ( ( in @ SV684 @ SV328 )
        = $true )
      | ( ( SV631 = SV684 )
        = $false )
      | ( ( SV92 = SV328 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2609]) ).

thf(2761,plain,
    ! [SV685: $i,SV512: $i,SV332: $i,SV96: $i] :
      ( ( ( ! [SY3119: $i] :
              ( ~ ( in @ SY3119 @ SV96 )
              | ( ( ap @ SV96 @ SV332 @ SV512 @ SY3119 )
                = ( ap @ SV96 @ SV332 @ SV685 @ SY3119 ) ) ) )
        = $false )
      | ( ( ! [SY3120: $i] :
              ( ~ ( in @ SY3120 @ SV96 )
              | ! [SY3121: $i] :
                  ( ~ ( in @ SY3121 @ SV332 )
                  | ~ ( in @ ( kpair @ SY3120 @ SY3121 ) @ SV685 )
                  | ( in @ ( kpair @ SY3120 @ SY3121 ) @ SV512 ) ) ) )
        = $true )
      | ( ( func @ SV96 @ SV332 @ SV685 )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV512 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2610]) ).

thf(2762,plain,
    ! [SV98: $i,SV333: $i,SV513: $i] :
      ( ( ( ~ ( in @ ( sK33_SY2921 @ SV513 @ SV333 @ SV98 ) @ SV98 ) )
        = $false )
      | ( ( in @ SV513 @ ( cartprod @ SV98 @ SV333 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2611]) ).

thf(2763,plain,
    ! [SV98: $i,SV513: $i,SV333: $i] :
      ( ( ( ~ ~ ! [SY3150: $i] :
                  ~ ~ ( ~ ( in @ SY3150 @ SV333 )
                      | ( SV513
                       != ( kpair @ ( sK33_SY2921 @ SV513 @ SV333 @ SV98 ) @ SY3150 ) ) ) )
        = $false )
      | ( ( in @ SV513 @ ( cartprod @ SV98 @ SV333 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2611]) ).

thf(2764,plain,
    ! [SV633: $i,SV334: $i,SV99: $i,SV738: $i] :
      ( ( ( in @ SV738 @ SV99 )
        = $false )
      | ( ( ~ ( in @ SV334 @ ( powerset @ SV633 ) )
          | ~ ( in @ SV738 @ SV334 )
          | ( in @ SV738 @ SV633 ) )
        = $true )
      | ( ( in @ SV633 @ ( powerset @ SV99 ) )
        = $false )
      | ( ( in @ SV334 @ ( powerset @ SV99 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2612]) ).

thf(2765,plain,
    ! [SV336: $i > $o,SV102: $i] :
      ( ( ( ! [SY2629: $i] :
              ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                  | ~ ( SV336 @ SY2629 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( in @ ( sK11_SY2627 @ SV336 @ SV102 ) @ SV102 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2613]) ).

thf(2766,plain,
    ! [SV336: $i > $o,SV102: $i] :
      ( ( ( ~ ~ ! [SY2629: $i] :
                  ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                      | ~ ( SV336 @ SY2629 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( in @ ( sK34_SY3074 @ SV336 @ SV102 ) @ SV102 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2614]) ).

thf(2767,plain,
    ! [SV102: $i,SV336: $i > $o] :
      ( ( ( SV336 @ ( sK11_SY2627 @ SV336 @ SV102 ) )
        = $true )
      | ( ( ~ ~ ! [SY2629: $i] :
                  ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                      | ~ ( SV336 @ SY2629 ) )
          | ( singleton
            @ ( dsetconstr @ SV102
              @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2615]) ).

thf(2768,plain,
    ! [SV102: $i,SV336: $i > $o] :
      ( ( ( ~ ( SV336 @ ( sK34_SY3074 @ SV336 @ SV102 ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2629: $i] :
                  ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                      | ~ ( SV336 @ SY2629 ) )
          | ( singleton
            @ ( dsetconstr @ SV102
              @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2616]) ).

thf(2769,plain,
    ! [SV102: $i,SV336: $i > $o] :
      ( ( ( ( sK11_SY2627 @ SV336 @ SV102 )
          = ( sK34_SY3074 @ SV336 @ SV102 ) )
        = $false )
      | ( ( ~ ~ ! [SY2629: $i] :
                  ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                      | ~ ( SV336 @ SY2629 ) )
          | ( singleton
            @ ( dsetconstr @ SV102
              @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2616]) ).

thf(2770,plain,
    ! [SV109: $i] :
      ( ( ~ ( ~ ! [SY2932: $i] :
                  ( ~ ( in @ SY2932 @ ( sK3_SY2100 @ SV109 ) )
                  | ! [SY2102: $i] :
                      ( ~ ( in @ SY2102 @ SY2932 )
                      | ( in @ SY2102 @ SV109 ) ) )
            | ~ ! [SY2934: $i,SY2935: $i] :
                  ( ~ ~ ( ~ ( in @ SY2934 @ SV109 )
                        | ~ ( in @ SY2935 @ SV109 ) )
                  | ~ ! [SY2936: $i] :
                        ( ~ ( in @ SY2936 @ ( sK3_SY2100 @ SV109 ) )
                        | ~ ( ~ ( ~ ( in @ SY2934 @ SY2936 )
                                | ( in @ SY2935 @ SY2936 ) )
                            | ~ ( ~ ( in @ SY2935 @ SY2936 )
                                | ( in @ SY2934 @ SY2936 ) ) ) )
                  | ( SY2934 = SY2935 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2617]) ).

thf(2771,plain,
    ! [SV109: $i] :
      ( ( ! [SY2937: $i,SY2938: $i] :
            ( ~ ~ ( ~ ( in @ SY2937 @ ( sK3_SY2100 @ SV109 ) )
                  | ~ ( in @ SY2938 @ ( sK3_SY2100 @ SV109 ) ) )
            | ! [SX4: $i] :
                ( ~ ( in @ SX4 @ SY2937 )
                | ( in @ SX4 @ SY2938 ) )
            | ! [SX4: $i] :
                ( ~ ( in @ SX4 @ SY2938 )
                | ( in @ SX4 @ SY2937 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2618]) ).

thf(2772,plain,
    ! [SV109: $i,SV739: $i] :
      ( ( ( ~ ( ~ ! [SY3154: $i] :
                    ( ~ ( in @ SY3154 @ SV739 )
                    | ( in @ SY3154 @ SV109 ) )
              | ~ ~ ! [SY3155: $i] :
                      ~ ( in @ SY3155 @ SV739 ) ) )
        = $false )
      | ( ( ~ ! [SY3156: $i] :
                ~ ~ ! [SY3157: $i] :
                      ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3156 @ ( sK3_SY2100 @ SV109 ) )
                                      | ~ ( in @ SY3157 @ SV739 ) )
                                | ~ ~ ~ ! [SY3158: $i] :
                                          ~ ~ ( ~ ( in @ SY3158 @ SY3156 )
                                              | ~ ( in @ SY3158 @ SV739 ) ) )
                          | ~ ! [SY2947: $i] :
                                ( ~ ( in @ SY2947 @ ( sK3_SY2100 @ SV109 ) )
                                | ! [SX6: $i] :
                                    ( ~ ( in @ SX6 @ SY2947 )
                                    | ( in @ SX6 @ SY3156 ) )
                                | ( in @ SY3157 @ SY2947 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2619]) ).

thf(2773,plain,
    ! [SV110: $i,SV635: $i] :
      ( ( ( ~ ( in @ ( sK40_SY2119 @ SV635 @ SV110 ) @ SV110 )
          | ~ ~ ~ ! [SY3161: $i] :
                    ~ ~ ( ~ ( in @ SY3161 @ ( sK40_SY2119 @ SV635 @ SV110 ) )
                        | ~ ( in @ SY3161 @ SV110 ) ) )
        = $false )
      | ( ( in @ SV635 @ SV110 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2620]) ).

thf(2774,plain,
    ! [SV636: $i,SV112: $i > $o] :
      ( ( ( ! [SY3077: $i] :
              ( ~ ( SV112 @ SY3077 )
              | ( SV636 = SY3077 ) ) )
        = $false )
      | ( ( SV112 @ SV636 )
        = $false )
      | ( ( ~ ! [SY2125: $i] :
                ~ ( SV112 @ SY2125 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2621]) ).

thf(2775,plain,
    ! [SV113: $i,SV344: $i] :
      ( ( ( ~ ( in @ ( sK35_SY2645 @ SV344 @ SV113 ) @ SV113 ) )
        = $false )
      | ( ( ( binintersect @ SV113 @ SV344 )
          = emptyset )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2622]) ).

thf(2776,plain,
    ! [SV113: $i,SV344: $i] :
      ( ( ( ~ ( in @ ( sK35_SY2645 @ SV344 @ SV113 ) @ SV344 ) )
        = $false )
      | ( ( ( binintersect @ SV113 @ SV344 )
          = emptyset )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2622]) ).

thf(2777,plain,
    ! [SV637: $i,SV346: $i,SV116: $i,SV740: $i] :
      ( ( ( in @ SV740 @ SV116 )
        = $false )
      | ( ( ~ ~ ( in @ SV740 @ ( binunion @ SV346 @ SV637 ) )
          | ~ ( in @ SV740 @ SV346 ) )
        = $true )
      | ( ( in @ SV637 @ ( powerset @ SV116 ) )
        = $false )
      | ( ( in @ SV346 @ ( powerset @ SV116 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2623]) ).

thf(2778,plain,
    ! [SV686: $i,SV520: $i,SV118: $i,SV347: $o] :
      ( ( ( ~ SV347 ) = $false )
      | ( ( ( if @ SV118 @ SV347 @ SV520 @ SV686 )
          = SV686 )
        = $true )
      | ( ( in @ SV686 @ SV118 )
        = $false )
      | ( ( in @ SV520 @ SV118 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2624]) ).

thf(2779,plain,
    ! [SV687: $i,SV521: $i,SV118: $i] :
      ( ( ( ~ $true ) = $false )
      | ( ( ( if @ SV118 @ $true @ SV521 @ SV687 )
          = SV687 )
        = $true )
      | ( ( in @ SV687 @ SV118 )
        = $false )
      | ( ( in @ SV521 @ SV118 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2625]) ).

thf(2780,plain,
    ! [SV688: $i,SV522: $i,SV118: $i] :
      ( ( ( ~ $false ) = $false )
      | ( ( ( if @ SV118 @ $false @ SV522 @ SV688 )
          = SV688 )
        = $true )
      | ( ( in @ SV688 @ SV118 )
        = $false )
      | ( ( in @ SV522 @ SV118 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2626]) ).

thf(2781,plain,
    ! [SV349: $i,SV121: $i,SV638: $i] :
      ( ( ( in @ SV638 @ ( setminus @ SV121 @ SV349 ) )
        = $true )
      | ( ( in @ SV638 @ SV349 )
        = $true )
      | ( ( in @ SV638 @ SV121 )
        = $false )
      | ( ( in @ SV349 @ ( powerset @ SV121 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2627]) ).

thf(2782,plain,
    ! [SV353: $i > $o,SV125: $i] :
      ( ( ( ! [SY2659: $i] :
              ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                  | ~ ( SV353 @ SY2659 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( in @ ( sK12_SY2657 @ SV353 @ SV125 ) @ SV125 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2629]) ).

thf(2783,plain,
    ! [SV353: $i > $o,SV125: $i] :
      ( ( ( ~ ~ ! [SY2659: $i] :
                  ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                      | ~ ( SV353 @ SY2659 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( in @ ( sK36_SY3079 @ SV353 @ SV125 ) @ SV125 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2630]) ).

thf(2784,plain,
    ! [SV125: $i,SV353: $i > $o] :
      ( ( ( SV353 @ ( sK12_SY2657 @ SV353 @ SV125 ) )
        = $true )
      | ( ( ~ ~ ! [SY2659: $i] :
                  ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                      | ~ ( SV353 @ SY2659 ) )
          | ( singleton
            @ ( dsetconstr @ SV125
              @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2631]) ).

thf(2785,plain,
    ! [SV125: $i,SV353: $i > $o] :
      ( ( ( ~ ( SV353 @ ( sK36_SY3079 @ SV353 @ SV125 ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2659: $i] :
                  ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                      | ~ ( SV353 @ SY2659 ) )
          | ( singleton
            @ ( dsetconstr @ SV125
              @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2632]) ).

thf(2786,plain,
    ! [SV125: $i,SV353: $i > $o] :
      ( ( ( ( sK12_SY2657 @ SV353 @ SV125 )
          = ( sK36_SY3079 @ SV353 @ SV125 ) )
        = $false )
      | ( ( ~ ~ ! [SY2659: $i] :
                  ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                      | ~ ( SV353 @ SY2659 ) )
          | ( singleton
            @ ( dsetconstr @ SV125
              @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2632]) ).

thf(2787,plain,
    ! [SV357: $i,SV129: $i,SV641: $i] :
      ( ( ( in @ SV641 @ ( setminus @ SV129 @ SV357 ) )
        = $false )
      | ( ( in @ SV641 @ SV357 )
        = $false )
      | ( ( in @ SV641 @ SV129 )
        = $false )
      | ( ( in @ SV357 @ ( powerset @ SV129 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2633]) ).

thf(2788,plain,
    ! [SV135: $i,SV363: $i,SV529: $i,SV690: $i > $o] :
      ( ( ( ~ ( in @ ( sK46_SY3122 @ SV690 @ SV529 @ SV363 @ SV135 ) @ SV135 ) )
        = $false )
      | ( ( ! [SY3124: $i] :
              ( ~ ( in @ SY3124 @ SV529 )
              | ( SV690 @ SY3124 ) ) )
        = $true )
      | ( ( subset @ SV529 @ ( cartprod @ SV135 @ SV363 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2635]) ).

thf(2789,plain,
    ! [SV135: $i,SV529: $i,SV690: $i > $o,SV363: $i] :
      ( ( ( ! [SY3168: $i] :
              ( ~ ( in @ SY3168 @ SV363 )
              | ~ ( in @ ( kpair @ ( sK46_SY3122 @ SV690 @ SV529 @ SV363 @ SV135 ) @ SY3168 ) @ SV529 )
              | ( SV690 @ ( kpair @ ( sK46_SY3122 @ SV690 @ SV529 @ SV363 @ SV135 ) @ SY3168 ) ) ) )
        = $false )
      | ( ( ! [SY3124: $i] :
              ( ~ ( in @ SY3124 @ SV529 )
              | ( SV690 @ SY3124 ) ) )
        = $true )
      | ( ( subset @ SV529 @ ( cartprod @ SV135 @ SV363 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2635]) ).

thf(2790,plain,
    ! [SV365: $i,SV643: $i,SV137: $i,SV741: $i] :
      ( ( ( in @ SV741 @ SV137 )
        = $false )
      | ( ( ~ ~ ( in @ SV741 @ SV643 )
          | ~ ( in @ SV741 @ ( binintersect @ SV365 @ SV643 ) ) )
        = $true )
      | ( ( in @ SV643 @ ( powerset @ SV137 ) )
        = $false )
      | ( ( in @ SV365 @ ( powerset @ SV137 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2636]) ).

thf(2791,plain,
    ! [SV644: $i,SV372: $i > $o,SV142: $i,SV742: $i] :
      ( ( ( in @ SV742 @ SV142 )
        = $false )
      | ( ( ~ ( SV372 @ SV644 )
          | ~ ( SV372 @ SV742 )
          | ( SV644 = SV742 ) )
        = $true )
      | ( ( in @ SV644 @ SV142 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV142
            @ ^ [SY2680: $i] : ( SV372 @ SY2680 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2637]) ).

thf(2792,plain,
    ! [SV377: $i,SV147: $i > $i > $o] :
      ( ( ( ! [SY3169: $i] :
              ~ ( ~ ( ~ ( in @ SY3169 @ ( sK47_SY2690 @ SV147 @ SV377 ) )
                    | ~ ! [SY2692: $i] :
                          ~ ~ ( ~ ( in @ SY2692 @ SV377 )
                              | ~ ( SV147 @ SY2692 @ SY3169 ) ) )
                | ~ ( ~ ~ ! [SY2693: $i] :
                            ~ ~ ( ~ ( in @ SY2693 @ SV377 )
                                | ~ ( SV147 @ SY2693 @ SY3169 ) )
                    | ( in @ SY3169 @ ( sK47_SY2690 @ SV147 @ SV377 ) ) ) ) )
        = $true )
      | ( ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2638]) ).

thf(2793,plain,
    ! [SV743: $i,SV377: $i,SV147: $i > $i > $o] :
      ( ( ( ~ ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
          | ~ ! [SY3162: $i] :
                ( ~ ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SY3162 )
                | ( SV743 = SY3162 ) ) )
        = $true )
      | ( ( ~ ! [SY2690: $i] :
                ~ ! [SY2691: $i] :
                    ~ ( ~ ( ~ ( in @ SY2691 @ SY2690 )
                          | ~ ! [SY2692: $i] :
                                ~ ~ ( ~ ( in @ SY2692 @ SV377 )
                                    | ~ ( SV147 @ SY2692 @ SY2691 ) ) )
                      | ~ ( ~ ~ ! [SY2693: $i] :
                                  ~ ~ ( ~ ( in @ SY2693 @ SV377 )
                                      | ~ ( SV147 @ SY2693 @ SY2691 ) )
                          | ( in @ SY2691 @ SY2690 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2639]) ).

thf(2794,plain,
    ! [SV645: $i,SV381: $i,SV151: $i,SV744: $i] :
      ( ( ( in @ SV744 @ SV151 )
        = $false )
      | ( ( ~ ~ ( in @ SV744 @ ( binunion @ SV381 @ SV645 ) )
          | ~ ( in @ SV744 @ SV645 ) )
        = $true )
      | ( ( in @ SV645 @ ( powerset @ SV151 ) )
        = $false )
      | ( ( in @ SV381 @ ( powerset @ SV151 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2640]) ).

thf(2795,plain,
    ! [SV647: $i,SV385: $i,SV156: $i,SV745: $i] :
      ( ( ( in @ SV745 @ SV156 )
        = $false )
      | ( ( ~ ~ ( in @ SV745 @ SV385 )
          | ~ ( in @ SV745 @ ( binintersect @ SV385 @ SV647 ) ) )
        = $true )
      | ( ( in @ SV647 @ ( powerset @ SV156 ) )
        = $false )
      | ( ( in @ SV385 @ ( powerset @ SV156 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2641]) ).

thf(2796,plain,
    ! [SV648: $i,SV157: $i > $o] :
      ( ( ( ! [SY3087: $i] :
              ( ~ ( SV157 @ SY3087 )
              | ( SV648 = SY3087 ) ) )
        = $false )
      | ( ( SV157 @ SV648 )
        = $false )
      | ( ( SV157
          @ ( descr
            @ ^ [SY2227: $i] : ( SV157 @ SY2227 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2642]) ).

thf(2797,plain,
    ! [SV160: $i,SV388: $i > $o,SV694: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK54_SY2705 @ SV694 @ SV388 @ SV160 ) @ SV160 )
                | ~ ~ ( SV388 @ ( sK54_SY2705 @ SV694 @ SV388 @ SV160 ) ) ) )
        = $false )
      | ( ( SV388 @ SV694 )
        = $true )
      | ( ( in @ SV694 @ SV160 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2643]) ).

thf(2798,plain,
    ! [SV649: $i,SV389: $i,SV161: $i,SV746: $i] :
      ( ( ( in @ SV746 @ SV161 )
        = $false )
      | ( ( ~ ( in @ SV746 @ ( setminus @ SV161 @ SV389 ) )
          | ( in @ SV746 @ ( setminus @ SV161 @ ( binintersect @ SV389 @ SV649 ) ) ) )
        = $true )
      | ( ( in @ SV649 @ ( powerset @ SV161 ) )
        = $false )
      | ( ( in @ SV389 @ ( powerset @ SV161 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2644]) ).

thf(2799,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( ~ ( SV165 @ ( sK48_SY2242 @ SV651 @ SV165 ) )
          | ~ ( SV165 @ ( sK55_SY3172 @ SV651 @ SV165 ) )
          | ( ( sK48_SY2242 @ SV651 @ SV165 )
            = ( sK55_SY3172 @ SV651 @ SV165 ) ) )
        = $false )
      | ( ( ~ ! [SY2244: $i] :
                ~ ~ ( ~ ( SV165 @ SY2244 )
                    | ~ ! [SY2245: $i] :
                          ( ~ ( SV165 @ SY2245 )
                          | ( SY2244 = SY2245 ) ) ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2645]) ).

thf(2800,plain,
    ! [SV652: $i,SV394: $i,SV167: $i,SV747: $i] :
      ( ( ( in @ SV747 @ ( powerset @ SV167 ) )
        = $false )
      | ( ( in @ ( binintersect @ SV394 @ SV652 ) @ ( powerset @ ( binintersect @ ( binunion @ SV394 @ SV747 ) @ ( binunion @ SV652 @ SV747 ) ) ) )
        = $true )
      | ( ( in @ SV652 @ ( powerset @ SV167 ) )
        = $false )
      | ( ( in @ SV394 @ ( powerset @ SV167 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2647]) ).

thf(2801,plain,
    ! [SV695: $i,SV539: $i,SV395: $i,SV168: $i] :
      ( ( ( ! [SY3125: $i] :
              ( ~ ( in @ SY3125 @ SV168 )
              | ! [SY3126: $i] :
                  ( ~ ( in @ SY3126 @ SV395 )
                  | ~ ( in @ ( kpair @ SY3125 @ SY3126 ) @ SV539 )
                  | ( in @ ( kpair @ SY3125 @ SY3126 ) @ SV695 ) ) ) )
        = $false )
      | ( ( subset @ SV539 @ SV695 )
        = $true )
      | ( ( subset @ SV695 @ ( cartprod @ SV168 @ SV395 ) )
        = $false )
      | ( ( subset @ SV539 @ ( cartprod @ SV168 @ SV395 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2648]) ).

thf(2802,plain,
    ! [SV696: $i,SV540: $i,SV169: $i,SV396: $o] :
      ( ( SV396 = $false )
      | ( ( ( if @ SV169 @ SV396 @ SV540 @ SV696 )
          = SV540 )
        = $true )
      | ( ( in @ SV696 @ SV169 )
        = $false )
      | ( ( in @ SV540 @ SV169 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2649]) ).

thf(2803,plain,
    ! [SV697: $i,SV541: $i,SV169: $i] :
      ( ( $true = $false )
      | ( ( ( if @ SV169 @ $true @ SV541 @ SV697 )
          = SV541 )
        = $true )
      | ( ( in @ SV697 @ SV169 )
        = $false )
      | ( ( in @ SV541 @ SV169 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2650]) ).

thf(2804,plain,
    ! [SV698: $i,SV542: $i,SV169: $i] :
      ( ( $false = $false )
      | ( ( ( if @ SV169 @ $false @ SV542 @ SV698 )
          = SV542 )
        = $true )
      | ( ( in @ SV698 @ SV169 )
        = $false )
      | ( ( in @ SV542 @ SV169 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2651]) ).

thf(2805,plain,
    ! [SV543: $i > $i,SV397: $i,SV170: $i,SV754: $i] :
      ( ( ( ~ ( in @ SV754 @ SV170 ) )
        = $true )
      | ( ( ( ap @ SV170 @ SV397
            @ ( lam @ SV170 @ SV397
              @ ^ [SY2971: $i] : ( SV543 @ SY2971 ) )
            @ SV754 )
          = ( SV543 @ SV754 ) )
        = $true )
      | ( ( in @ ( sK22_SY2969 @ SV397 @ SV543 @ SV170 ) @ SV170 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2652]) ).

thf(2806,plain,
    ! [SV543: $i > $i,SV397: $i,SV170: $i,SV748: $i] :
      ( ( ( in @ SV748 @ SV170 )
        = $false )
      | ( ( ( ap @ SV170 @ SV397
            @ ( lam @ SV170 @ SV397
              @ ^ [SY2971: $i] : ( SV543 @ SY2971 ) )
            @ SV748 )
          = ( SV543 @ SV748 ) )
        = $true )
      | ( ( in @ ( SV543 @ ( sK22_SY2969 @ SV397 @ SV543 @ SV170 ) ) @ SV397 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2653]) ).

thf(2807,plain,
    ! [SV654: $i,SV403: $i,SV177: $i,SV749: $i] :
      ( ( ( in @ SV749 @ SV177 )
        = $false )
      | ( ( ~ ( subset @ SV403 @ ( setminus @ SV177 @ SV654 ) )
          | ~ ( in @ SV749 @ SV654 )
          | ~ ( in @ SV749 @ SV403 ) )
        = $true )
      | ( ( in @ SV654 @ ( powerset @ SV177 ) )
        = $false )
      | ( ( in @ SV403 @ ( powerset @ SV177 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2654]) ).

thf(2808,plain,
    ! [SV404: $i,SV178: $i,SV733: $i,SV616: $i,SV549: $i > $i > $o] :
      ( ( ( ~ ( SV549 @ SV616 @ SV733 ) )
        = $true )
      | ( ( in @ ( kpair @ SV616 @ SV733 )
          @ ( dpsetconstr @ SV178 @ SV404
            @ ^ [SY2978: $i,SY2979: $i] : ( SV549 @ SY2978 @ SY2979 ) ) )
        = $true )
      | ( ( in @ SV733 @ SV404 )
        = $false )
      | ( ( in @ SV616 @ SV178 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2655]) ).

thf(2809,plain,
    ! [SV185: $i,SV554: $i,SV700: $i,SV411: $i,SV755: $i] :
      ( ( ( ~ ( in @ SV755 @ SV411 ) )
        = $true )
      | ( ( ~ ( in @ ( kpair @ SV700 @ SV755 ) @ SV554 )
          | ( ( ap @ SV185 @ SV411 @ SV554 @ SV700 )
            = SV755 ) )
        = $true )
      | ( ( in @ SV700 @ SV185 )
        = $false )
      | ( ( func @ SV185 @ SV411 @ SV554 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2658]) ).

thf(2810,plain,
    ! [SV414: $i > $o,SV188: $i,SV556: $i] :
      ( ( ( in @ SV556
          @ ( dsetconstr @ SV188
            @ ^ [SY2751: $i] : ( SV414 @ SY2751 ) ) )
        = $false )
      | ( ( SV414 @ SV556 )
        = $true )
      | ( ( in @ SV556 @ SV188 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2659]) ).

thf(2811,plain,
    ! [SV188: $i,SV556: $i,SV414: $i > $o] :
      ( ( ( SV414 @ SV556 )
        = $false )
      | ( ( in @ SV556
          @ ( dsetconstr @ SV188
            @ ^ [SY2752: $i] : ( SV414 @ SY2752 ) ) )
        = $true )
      | ( ( in @ SV556 @ SV188 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2660]) ).

thf(2812,plain,
    ! [SV701: $i,SV558: $i,SV416: $i,SV190: $i] :
      ( ( ( ! [SY3128: $i] :
              ( ~ ( in @ SY3128 @ SV190 )
              | ( ( ap @ SV190 @ SV416 @ SV558 @ SY3128 )
                = ( ap @ SV190 @ SV416 @ SV701 @ SY3128 ) ) ) )
        = $false )
      | ( ( SV558 = SV701 )
        = $true )
      | ( ( func @ SV190 @ SV416 @ SV701 )
        = $false )
      | ( ( func @ SV190 @ SV416 @ SV558 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2661]) ).

thf(2813,plain,
    ! [SV657: $i,SV417: $i,SV191: $i,SV750: $i] :
      ( ( ( in @ SV750 @ ( powerset @ SV191 ) )
        = $false )
      | ( ( ! [SY3164: $i] :
              ( ~ ( in @ SY3164 @ SV191 )
              | ~ ( in @ SY3164 @ ( binintersect @ SV417 @ SV657 ) )
              | ( in @ SY3164 @ ( binunion @ SV417 @ SV750 ) ) ) )
        = $true )
      | ( ( in @ SV657 @ ( powerset @ SV191 ) )
        = $false )
      | ( ( in @ SV417 @ ( powerset @ SV191 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2662]) ).

thf(2814,plain,
    ! [SV419: $i,SV702: $i,SV193: $i,SV658: $i] :
      ( ( ( ~ ( ~ ( in @ SV658 @ SV193 )
              | ( in @ SV702 @ SV419 ) ) )
        = $false )
      | ( ( SV658 = SV702 )
        = $false )
      | ( ( SV193 = SV419 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2663]) ).

thf(2815,plain,
    ! [SV193: $i,SV658: $i,SV419: $i,SV702: $i] :
      ( ( ( ~ ( ~ ( in @ SV702 @ SV419 )
              | ( in @ SV658 @ SV193 ) ) )
        = $false )
      | ( ( SV658 = SV702 )
        = $false )
      | ( ( SV193 = SV419 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2663]) ).

thf(2816,plain,
    ! [SV198: $i,SV567: $i,SV710: $i,SV424: $i,SV756: $i] :
      ( ( ( ~ ( in @ SV756 @ SV424 ) )
        = $true )
      | ( ( ~ ( in @ ( kpair @ SV710 @ SV756 ) @ SV567 )
          | ( ( ap @ SV198 @ SV424 @ SV567 @ SV710 )
            = SV756 ) )
        = $true )
      | ( ( in @ SV710 @ SV198 )
        = $false )
      | ( ( in @ SV567 @ ( funcSet @ SV198 @ SV424 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2664]) ).

thf(2817,plain,
    ! [SV426: $i > $o,SV200: $i,SV761: $i] :
      ( ( ( ~ ~ ( ~ ( in @ SV761 @ SV200 )
                | ~ ( SV426 @ SV761 ) ) )
        = $true )
      | ( ( in @ ( sK16_SY2777 @ SV426 @ SV200 ) @ SV200 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2665]) ).

thf(2818,plain,
    ! [SV426: $i > $o,SV200: $i,SV762: $i] :
      ( ( ( ~ ~ ( ~ ( in @ SV762 @ SV200 )
                | ~ ( SV426 @ SV762 ) ) )
        = $true )
      | ( ( SV426 @ ( sK16_SY2777 @ SV426 @ SV200 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2666]) ).

thf(2819,plain,
    ! [SV205: $i,SV430: $i] :
      ( ( ( ~ ( ~ ( in @ SV430 @ ( sK49_SY2781 @ SV205 @ SV430 ) )
              | ~ ( in @ ( sK49_SY2781 @ SV205 @ SV430 ) @ SV205 ) ) )
        = $true )
      | ( ( in @ SV430 @ ( setunion @ SV205 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2667]) ).

thf(2820,plain,
    ! [SV205: $i,SV757: $i,SV430: $i] :
      ( ( ( ~ ( ~ ( in @ SV430 @ SV757 )
              | ~ ( in @ SV757 @ SV205 ) ) )
        = $false )
      | ( ( in @ SV430 @ ( setunion @ SV205 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2668]) ).

thf(2821,plain,
    ! [SV712: $o,SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | SV712 )
          | SV712 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2669]) ).

thf(2822,plain,
    ! [SV712: $o,SV206: $i,SV431: $i,SV570: $i] :
      ( ( ( ~ ~ ( in @ SV570 @ SV431 ) )
        = $false )
      | ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | SV712 )
          | SV712 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2670]) ).

thf(2823,plain,
    ! [SV431: $i,SV206: $i,SV570: $i,SV712: $o] :
      ( ( SV712 = $false )
      | ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | SV712 )
          | SV712 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2670]) ).

thf(2824,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | $true )
          | $true )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2671]) ).

thf(2825,plain,
    ! [SV206: $i,SV431: $i,SV570: $i] :
      ( ( ( ~ ~ ( in @ SV570 @ SV431 ) )
        = $false )
      | ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | $true )
          | $true )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2672]) ).

thf(2826,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( $true = $false )
      | ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | $true )
          | $true )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2672]) ).

thf(2827,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | $false )
          | $false )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2673]) ).

thf(2828,plain,
    ! [SV206: $i,SV431: $i,SV570: $i] :
      ( ( ( ~ ~ ( in @ SV570 @ SV431 ) )
        = $false )
      | ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | $false )
          | $false )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2674]) ).

thf(2829,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( $false = $false )
      | ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | $false )
          | $false )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2674]) ).

thf(2830,plain,
    ! [SV208: $i,SV433: $i] :
      ( ( ( in @ ( sK25_SY2785 @ SV433 @ SV208 ) @ SV208 )
        = $true )
      | ( ( in @ SV433 @ ( setunion @ SV208 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2675]) ).

thf(2831,plain,
    ! [SV208: $i,SV433: $i] :
      ( ( ( in @ SV433 @ ( sK25_SY2785 @ SV433 @ SV208 ) )
        = $true )
      | ( ( in @ SV433 @ ( setunion @ SV208 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2676]) ).

thf(2832,plain,
    ! [SV209: $i,SV434: $i,SV659: $i > $o,SV713: $i > $o] :
      ( ( ( ~ ( in @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) @ SV209 ) )
        = $false )
      | ( ( ( dsetconstr @ SV209
            @ ^ [SY3097: $i] : ( SV659 @ SY3097 ) )
          = ( dsetconstr @ SV434
            @ ^ [SY3136: $i] : ( SV713 @ SY3136 ) ) )
        = $true )
      | ( ( SV209 = SV434 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2677]) ).

thf(2833,plain,
    ! [SV209: $i,SV659: $i > $o,SV713: $i > $o,SV434: $i] :
      ( ( ( ! [SY3174: $i] :
              ( ~ ( in @ SY3174 @ SV434 )
              | ( ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 )
               != SY3174 )
              | ~ ( ~ ( ~ ( SV659 @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) )
                      | ( SV713 @ SY3174 ) )
                  | ~ ( ~ ( SV713 @ SY3174 )
                      | ( SV659 @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) ) ) ) ) )
        = $false )
      | ( ( ( dsetconstr @ SV209
            @ ^ [SY3097: $i] : ( SV659 @ SY3097 ) )
          = ( dsetconstr @ SV434
            @ ^ [SY3136: $i] : ( SV713 @ SY3136 ) ) )
        = $true )
      | ( ( SV209 = SV434 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2677]) ).

thf(2834,plain,
    ! [SV714: $o,SV435: $i,SV210: $i,SV571: $i] :
      ( ( ( SV571 = SV210 )
        = $true )
      | ( ( ~ ( ~ ( in @ SV571 @ SV435 )
              | SV714 )
          | SV714 )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2678]) ).

thf(2835,plain,
    ! [SV210: $i,SV714: $o,SV435: $i,SV571: $i] :
      ( ( ( ~ ( ~ ( in @ SV571 @ SV435 )
              | SV714 ) )
        = $true )
      | ( SV714 = $true )
      | ( SV714 = $false )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2679]) ).

thf(2836,plain,
    ! [SV435: $i,SV210: $i,SV571: $i] :
      ( ( ( SV571 = SV210 )
        = $true )
      | ( ( ~ ( ~ ( in @ SV571 @ SV435 )
              | $true )
          | $true )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2680]) ).

thf(2837,plain,
    ! [SV210: $i,SV435: $i,SV571: $i] :
      ( ( ( ~ ( ~ ( in @ SV571 @ SV435 )
              | $true ) )
        = $true )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2681]) ).

thf(2838,plain,
    ! [SV435: $i,SV210: $i,SV571: $i] :
      ( ( ( SV571 = SV210 )
        = $true )
      | ( ( ~ ( ~ ( in @ SV571 @ SV435 )
              | $false )
          | $false )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2682]) ).

thf(2839,plain,
    ! [SV210: $i,SV435: $i,SV571: $i] :
      ( ( ( ~ ( ~ ( in @ SV571 @ SV435 )
              | $false ) )
        = $true )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2683]) ).

thf(2840,plain,
    ! [SV660: $i,SV211: $i > $o] :
      ( ( ( ! [SY3099: $i] :
              ( ~ ( SV211 @ SY3099 )
              | ( SV660 = SY3099 ) ) )
        = $false )
      | ( ( SV211 @ SV660 )
        = $false )
      | ( ( ~ ! [SY2378: $i] :
                ~ ~ ( ~ ( SV211 @ SY2378 )
                    | ~ ! [SY2379: $i] :
                          ( ~ ( SV211 @ SY2379 )
                          | ( SY2378 = SY2379 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2684]) ).

thf(2841,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ( ~ ~ ! [SY2388: $i] :
                      ~ ~ ( ~ ( SV214 @ SY2388 )
                          | ~ ! [SY2389: $i] :
                                ( ~ ( SV214 @ SY2389 )
                                | ( SY2388 = SY2389 ) ) )
              | ~ ! [SY2801: $i] :
                    ~ ~ ( ~ ( SV438 @ SY2801 )
                        | ~ ! [SY2802: $i] :
                              ( ~ ( SV438 @ SY2802 )
                              | ( SY2801 = SY2802 ) ) ) ) )
        = $false )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2686]) ).

thf(2842,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ( ~ ~ ! [SY2803: $i] :
                      ~ ~ ( ~ ( SV438 @ SY2803 )
                          | ~ ! [SY2804: $i] :
                                ( ~ ( SV438 @ SY2804 )
                                | ( SY2803 = SY2804 ) ) )
              | ~ ! [SY2394: $i] :
                    ~ ~ ( ~ ( SV214 @ SY2394 )
                        | ~ ! [SY2395: $i] :
                              ( ~ ( SV214 @ SY2395 )
                              | ( SY2394 = SY2395 ) ) ) ) )
        = $false )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2686]) ).

thf(2843,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
          | ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) ) )
        = $false )
      | ( ( ~ ( ~ ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
              | ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ~ ! [SY2388: $i] :
                          ~ ~ ( ~ ( SV214 @ SY2388 )
                              | ~ ! [SY2389: $i] :
                                    ( ~ ( SV214 @ SY2389 )
                                    | ( SY2388 = SY2389 ) ) )
                  | ~ ! [SY2801: $i] :
                        ~ ~ ( ~ ( SV438 @ SY2801 )
                            | ~ ! [SY2802: $i] :
                                  ( ~ ( SV438 @ SY2802 )
                                  | ( SY2801 = SY2802 ) ) ) )
              | ~ ( ~ ~ ! [SY2803: $i] :
                          ~ ~ ( ~ ( SV438 @ SY2803 )
                              | ~ ! [SY2804: $i] :
                                    ( ~ ( SV438 @ SY2804 )
                                    | ( SY2803 = SY2804 ) ) )
                  | ~ ! [SY2394: $i] :
                        ~ ~ ( ~ ( SV214 @ SY2394 )
                            | ~ ! [SY2395: $i] :
                                  ( ~ ( SV214 @ SY2395 )
                                  | ( SY2394 = SY2395 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2687]) ).

thf(2844,plain,
    ! [SV215: $i,SV439: $i > $o] :
      ( ( ( in @ ( sK27_SY2808 @ SV439 @ SV215 ) @ SV215 )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV215
            @ ^ [SY2807: $i] : ( SV439 @ SY2807 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2688]) ).

thf(2845,plain,
    ! [SV215: $i,SV439: $i > $o] :
      ( ( ( SV439 @ ( sK27_SY2808 @ SV439 @ SV215 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV215
            @ ^ [SY2807: $i] : ( SV439 @ SY2807 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2689]) ).

thf(2846,plain,
    ! [SV216: $i,SV440: $i > $o,SV573: $i] :
      ( ( ( ~ ( in @ ( sK56_SY3006 @ SV573 @ SV440 @ SV216 ) @ SV216 )
          | ~ ( SV440 @ ( sK56_SY3006 @ SV573 @ SV440 @ SV216 ) )
          | ( ( sK56_SY3006 @ SV573 @ SV440 @ SV216 )
            = SV573 ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV216
            @ ^ [SY2811: $i] : ( SV440 @ SY2811 ) ) )
        = $true )
      | ( ( SV440 @ SV573 )
        = $false )
      | ( ( in @ SV573 @ SV216 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2690]) ).

thf(2847,plain,
    ! [SV718: $i,SV576: $i,SV220: $i,SV444: $o] :
      ( ( SV444 = $false )
      | ( ( ( dsetconstr @ SV220
            @ ^ [SY3137: $i] :
                ( ~ ( ~ SV444
                    | ( SY3137 != SV576 ) )
                | ~ ( ~ ~ SV444
                    | ( SY3137 != SV718 ) ) ) )
          = ( setadjoin @ SV576 @ emptyset ) )
        = $true )
      | ( ( in @ SV718 @ SV220 )
        = $false )
      | ( ( in @ SV576 @ SV220 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2691]) ).

thf(2848,plain,
    ! [SV719: $i,SV577: $i,SV220: $i] :
      ( ( $true = $false )
      | ( ( ( dsetconstr @ SV220
            @ ^ [SY3138: $i] :
                ( ~ ( ~ $true
                    | ( SY3138 != SV577 ) )
                | ~ ( ~ ~ $true
                    | ( SY3138 != SV719 ) ) ) )
          = ( setadjoin @ SV577 @ emptyset ) )
        = $true )
      | ( ( in @ SV719 @ SV220 )
        = $false )
      | ( ( in @ SV577 @ SV220 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2692]) ).

thf(2849,plain,
    ! [SV720: $i,SV578: $i,SV220: $i] :
      ( ( $false = $false )
      | ( ( ( dsetconstr @ SV220
            @ ^ [SY3139: $i] :
                ( ~ ( ~ $false
                    | ( SY3139 != SV578 ) )
                | ~ ( ~ ~ $false
                    | ( SY3139 != SV720 ) ) ) )
          = ( setadjoin @ SV578 @ emptyset ) )
        = $true )
      | ( ( in @ SV720 @ SV220 )
        = $false )
      | ( ( in @ SV578 @ SV220 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2693]) ).

thf(2850,plain,
    ! [SV721: $i,SV579: $i,SV445: $i,SV221: $i] :
      ( ( ( ! [SY3140: $i] :
              ( ~ ( in @ SY3140 @ SV221 )
              | ! [SY3141: $i] :
                  ( ~ ( in @ SY3141 @ SV445 )
                  | ~ ( in @ ( kpair @ SY3140 @ SY3141 ) @ SV579 )
                  | ( in @ ( kpair @ SY3140 @ SY3141 ) @ SV721 ) ) ) )
        = $false )
      | ( ( ~ ! [SY3142: $i] :
                ( ~ ( in @ SY3142 @ SV221 )
                | ! [SY3143: $i] :
                    ( ~ ( in @ SY3143 @ SV445 )
                    | ~ ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV721 )
                    | ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV579 ) ) )
          | ( SV579 = SV721 ) )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2694]) ).

thf(2851,plain,
    ! [SV224: $i] :
      ( ( ( in @ ( sK28_SY2426 @ SV224 ) @ SV224 )
        = $true )
      | ( ( SV224 = emptyset )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2695]) ).

thf(2852,plain,
    ! [SV224: $i] :
      ( ( $true = $true )
      | ( ( SV224 = emptyset )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2696]) ).

thf(2853,plain,
    ! [SV663: $i,SV451: $i,SV228: $i,SV751: $i] :
      ( ( ( in @ SV751 @ ( powerset @ SV228 ) )
        = $false )
      | ( ( ! [SY3165: $i] :
              ( ~ ( in @ SY3165 @ SV228 )
              | ~ ( in @ SY3165 @ ( binintersect @ SV451 @ SV663 ) )
              | ( in @ SY3165 @ ( binunion @ SV663 @ SV751 ) ) ) )
        = $true )
      | ( ( in @ SV663 @ ( powerset @ SV228 ) )
        = $false )
      | ( ( in @ SV451 @ ( powerset @ SV228 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2698]) ).

thf(2854,plain,
    ! [SV723: $i,SV583: $i,SV230: $i,SV453: $o] :
      ( ( ( ~ SV453 ) = $false )
      | ( ( ( dsetconstr @ SV230
            @ ^ [SY3145: $i] :
                ( ~ ( ~ SV453
                    | ( SY3145 != SV583 ) )
                | ~ ( ~ ~ SV453
                    | ( SY3145 != SV723 ) ) ) )
          = ( setadjoin @ SV723 @ emptyset ) )
        = $true )
      | ( ( in @ SV723 @ SV230 )
        = $false )
      | ( ( in @ SV583 @ SV230 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2699]) ).

thf(2855,plain,
    ! [SV724: $i,SV584: $i,SV230: $i] :
      ( ( ( ~ $true ) = $false )
      | ( ( ( dsetconstr @ SV230
            @ ^ [SY3146: $i] :
                ( ~ ( ~ $true
                    | ( SY3146 != SV584 ) )
                | ~ ( ~ ~ $true
                    | ( SY3146 != SV724 ) ) ) )
          = ( setadjoin @ SV724 @ emptyset ) )
        = $true )
      | ( ( in @ SV724 @ SV230 )
        = $false )
      | ( ( in @ SV584 @ SV230 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2700]) ).

thf(2856,plain,
    ! [SV725: $i,SV585: $i,SV230: $i] :
      ( ( ( ~ $false ) = $false )
      | ( ( ( dsetconstr @ SV230
            @ ^ [SY3147: $i] :
                ( ~ ( ~ $false
                    | ( SY3147 != SV585 ) )
                | ~ ( ~ ~ $false
                    | ( SY3147 != SV725 ) ) ) )
          = ( setadjoin @ SV725 @ emptyset ) )
        = $true )
      | ( ( in @ SV725 @ SV230 )
        = $false )
      | ( ( in @ SV585 @ SV230 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2701]) ).

thf(2857,plain,
    ! [SV231: $i,SV454: $i,SV664: $i] :
      ( ( ( ~ ( in @ ( sK57_SY3103 @ SV664 @ SV454 @ SV231 ) @ SV231 )
          | ~ ( in @ ( sK57_SY3103 @ SV664 @ SV454 @ SV231 ) @ SV454 )
          | ( in @ ( sK57_SY3103 @ SV664 @ SV454 @ SV231 ) @ SV664 ) )
        = $false )
      | ( ( in @ SV454 @ ( powerset @ SV664 ) )
        = $true )
      | ( ( in @ SV664 @ ( powerset @ SV231 ) )
        = $false )
      | ( ( in @ SV454 @ ( powerset @ SV231 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2702]) ).

thf(2858,plain,
    ! [SV243: $i,SV466: $i,SV665: $i] :
      ( ( ( ~ ( in @ ( sK58_SY3104 @ SV665 @ SV466 @ SV243 ) @ SV243 )
          | ~ ( in @ ( sK58_SY3104 @ SV665 @ SV466 @ SV243 ) @ SV466 )
          | ( in @ ( sK58_SY3104 @ SV665 @ SV466 @ SV243 ) @ SV665 ) )
        = $false )
      | ( ( subset @ SV466 @ SV665 )
        = $true )
      | ( ( in @ SV665 @ ( powerset @ SV243 ) )
        = $false )
      | ( ( in @ SV466 @ ( powerset @ SV243 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2703]) ).

thf(2859,plain,
    ! [SV594: $i > $i,SV467: $i,SV244: $i,SV758: $i] :
      ( ( ( ~ ( in @ SV758 @ SV244 ) )
        = $true )
      | ( ( ( ap @ SV244 @ SV467
            @ ( lam @ SV244 @ SV467
              @ ^ [SY3033: $i] : ( SV594 @ SY3033 ) )
            @ SV758 )
          = ( SV594 @ SV758 ) )
        = $true )
      | ( ( in @ ( sK29_SY3031 @ SV467 @ SV594 @ SV244 ) @ SV244 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2704]) ).

thf(2860,plain,
    ! [SV594: $i > $i,SV467: $i,SV244: $i,SV752: $i] :
      ( ( ( in @ SV752 @ SV244 )
        = $false )
      | ( ( ( ap @ SV244 @ SV467
            @ ( lam @ SV244 @ SV467
              @ ^ [SY3033: $i] : ( SV594 @ SY3033 ) )
            @ SV752 )
          = ( SV594 @ SV752 ) )
        = $true )
      | ( ( in @ ( SV594 @ ( sK29_SY3031 @ SV467 @ SV594 @ SV244 ) ) @ SV467 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2705]) ).

thf(2861,plain,
    ! [SV666: $i,SV469: $i,SV246: $i,SV753: $i] :
      ( ( ( in @ SV753 @ SV246 )
        = $false )
      | ( ( ~ ( in @ SV753 @ ( setminus @ SV246 @ SV469 ) )
          | ~ ( in @ SV753 @ ( binintersect @ SV469 @ SV666 ) ) )
        = $true )
      | ( ( in @ SV666 @ ( powerset @ SV246 ) )
        = $false )
      | ( ( in @ SV469 @ ( powerset @ SV246 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2706]) ).

thf(2862,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ~ ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
          | ( ( sK37_SY3106 @ SV667 @ SV253 )
            = SV667 ) )
        = $false )
      | ( ( ~ ( ( ( sK37_SY3106 @ SV667 @ SV253 )
               != SV667 )
              | ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2491: $i] :
                ~ ~ ( ~ ( SV253 @ SY2491 )
                    | ~ ! [SY2492: $i] :
                          ( ~ ( SV253 @ SY2492 )
                          | ( SY2491 = SY2492 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2707]) ).

thf(2863,plain,
    ! [SV255: $i,SV668: $o,SV475: $i] :
      ( ( ( in @ SV475 @ ( sK41_SY3107 @ SV668 @ SV255 @ SV475 ) )
        = $true )
      | ( SV668 = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2708]) ).

thf(2864,plain,
    ! [SV475: $i,SV255: $i,SV668: $o] :
      ( ( ( ~ ( in @ ( sK41_SY3107 @ SV668 @ SV255 @ SV475 ) @ SV255 ) )
        = $false )
      | ( SV668 = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2709]) ).

thf(2865,plain,
    ! [SV255: $i,SV475: $i,SV668: $o] :
      ( ( SV668 = $false )
      | ( SV668 = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2709]) ).

thf(2866,plain,
    ! [SV255: $i,SV475: $i] :
      ( ( ( in @ SV475 @ ( sK42_SX0 @ SV255 @ SV475 ) )
        = $true )
      | ( $true = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2710]) ).

thf(2867,plain,
    ! [SV475: $i,SV255: $i] :
      ( ( ( ~ ( in @ ( sK42_SX0 @ SV255 @ SV475 ) @ SV255 ) )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2711]) ).

thf(2868,plain,
    ! [SV255: $i,SV475: $i] :
      ( ( $true = $false )
      | ( $true = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2711]) ).

thf(2869,plain,
    ! [SV255: $i,SV475: $i] :
      ( ( ( in @ SV475 @ ( sK43_SX0 @ SV255 @ SV475 ) )
        = $true )
      | ( $false = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2712]) ).

thf(2870,plain,
    ! [SV475: $i,SV255: $i] :
      ( ( ( ~ ( in @ ( sK43_SX0 @ SV255 @ SV475 ) @ SV255 ) )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2713]) ).

thf(2871,plain,
    ! [SV255: $i,SV475: $i] :
      ( ( $false = $false )
      | ( $false = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2713]) ).

thf(2872,plain,
    ! [SV35: $i,SV281: $i > $o] :
      ( ( ( in @ ( sK30_SY2514 @ SV281 @ SV35 ) @ SV35 )
        = $true )
      | ( ( ! [SY2515: $i] :
              ( ~ ( in @ SY2515 @ SV35 )
              | ~ ( SV281 @ SY2515 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2714]) ).

thf(2873,plain,
    ! [SV35: $i,SV281: $i > $o] :
      ( ( ( SV281 @ ( sK30_SY2514 @ SV281 @ SV35 ) )
        = $true )
      | ( ( ! [SY2515: $i] :
              ( ~ ( in @ SY2515 @ SV35 )
              | ~ ( SV281 @ SY2515 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2715]) ).

thf(2874,plain,
    ! [SV36: $i,SV734: $i,SV619: $i,SV282: $i] :
      ( ( ( ~ ( subset @ SV282 @ SV619 ) )
        = $true )
      | ( ( ~ ~ ( in @ SV734 @ SV619 )
          | ~ ( in @ SV734 @ SV282 ) )
        = $true )
      | ( ( in @ SV734 @ SV36 )
        = $false )
      | ( ( in @ SV619 @ ( powerset @ SV36 ) )
        = $false )
      | ( ( in @ SV282 @ ( powerset @ SV36 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2716]) ).

thf(2875,plain,
    ! [SV620: $i,SV37: $i > $o] :
      ( ( ( ~ ( SV37 @ ( sK59_SY3056 @ SV620 @ SV37 ) )
          | ( SV620
            = ( sK59_SY3056 @ SV620 @ SV37 ) ) )
        = $false )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( ~ ! [SY1897: $i] :
                ~ ! [SY1898: $i] :
                    ~ ( ~ ( ~ ( SV37 @ SY1898 )
                          | ( SY1898 = SY1897 ) )
                      | ~ ( ( SY1898 != SY1897 )
                          | ( SV37 @ SY1898 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2717]) ).

thf(2876,plain,
    ! [SV483: $i,SV40: $i,SV670: $i,SV284: $o] :
      ( ( SV284 = $true )
      | ( ( in @ SV670
          @ ( dsetconstr @ SV40
            @ ^ [SY3108: $i] :
                ( ~ ( ~ SV284
                    | ( SY3108 != SV483 ) )
                | ~ ( ~ ~ SV284
                    | ( SY3108 != SV670 ) ) ) ) )
        = $true )
      | ( ( in @ SV670 @ SV40 )
        = $false )
      | ( ( in @ SV483 @ SV40 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2718]) ).

thf(2877,plain,
    ! [SV484: $i,SV40: $i,SV671: $i] :
      ( ( $true = $true )
      | ( ( in @ SV671
          @ ( dsetconstr @ SV40
            @ ^ [SY3109: $i] :
                ( ~ ( ~ $true
                    | ( SY3109 != SV484 ) )
                | ~ ( ~ ~ $true
                    | ( SY3109 != SV671 ) ) ) ) )
        = $true )
      | ( ( in @ SV671 @ SV40 )
        = $false )
      | ( ( in @ SV484 @ SV40 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2719]) ).

thf(2878,plain,
    ! [SV485: $i,SV40: $i,SV672: $i] :
      ( ( $false = $true )
      | ( ( in @ SV672
          @ ( dsetconstr @ SV40
            @ ^ [SY3110: $i] :
                ( ~ ( ~ $false
                    | ( SY3110 != SV485 ) )
                | ~ ( ~ ~ $false
                    | ( SY3110 != SV672 ) ) ) ) )
        = $true )
      | ( ( in @ SV672 @ SV40 )
        = $false )
      | ( ( in @ SV485 @ SV40 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2720]) ).

thf(2879,plain,
    ! [SV621: $i,SV41: $i > $o] :
      ( ( ( ~ ( SV41 @ ( sK60_SY3057 @ SV621 @ SV41 ) )
          | ( SV621
            = ( sK60_SY3057 @ SV621 @ SV41 ) ) )
        = $false )
      | ( ( SV41 @ SV621 )
        = $false )
      | ( ( ! [SY1909: $i,SY1910: $i] :
              ( ~ ( SV41 @ SY1909 )
              | ~ ( SV41 @ SY1910 )
              | ( SY1909 = SY1910 ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2721]) ).

thf(2880,plain,
    ! [SV622: $i,SV43: $i > $o] :
      ( ( ( ~ ( SV43 @ ( sK61_SY3058 @ SV622 @ SV43 ) )
          | ( SV622
            = ( sK61_SY3058 @ SV622 @ SV43 ) ) )
        = $false )
      | ( ( SV43 @ SV622 )
        = $false )
      | ( ( ! [SY1916: $i,SY1917: $i] :
              ( ~ ( SV43 @ SY1916 )
              | ~ ( SV43 @ SY1917 )
              | ( SY1916 = SY1917 ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2724]) ).

thf(2881,plain,
    ! [SV623: $i,SV286: $i,SV44: $i,SV736: $i] :
      ( ( ( ~ ( in @ SV736 @ ( setminus @ SV44 @ ( binunion @ SV286 @ SV623 ) ) ) )
        = $true )
      | ( ( ~ ( in @ SV736 @ SV286 ) )
        = $true )
      | ( ( in @ SV736 @ SV44 )
        = $false )
      | ( ( in @ SV623 @ ( powerset @ SV44 ) )
        = $false )
      | ( ( in @ SV286 @ ( powerset @ SV44 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2725]) ).

thf(2882,plain,
    ! [SV46: $i,SV673: $i,SV287: $i > $o] :
      ( ( ( ~ ( SV287 @ SV673 ) )
        = $false )
      | ( ( in @ SV673 @ SV46 )
        = $false )
      | ( ( ~ ! [SY2528: $i] :
                ( ~ ( in @ SY2528 @ SV46 )
                | ( SV287 @ SY2528 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2726]) ).

thf(2883,plain,
    ! [SV624: $i,SV48: $i > $o] :
      ( ( ( ~ ( SV48 @ ( sK62_SY3060 @ SV624 @ SV48 ) )
          | ( SV624
            = ( sK62_SY3060 @ SV624 @ SV48 ) ) )
        = $false )
      | ( ( SV48 @ SV624 )
        = $false )
      | ( ( ~ ! [SY1928: $i] :
                ~ ~ ( ~ ( SV48 @ SY1928 )
                    | ~ ! [SY1929: $i] :
                          ( ~ ( SV48 @ SY1929 )
                          | ( SY1928 = SY1929 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2727]) ).

thf(2884,plain,
    ! [SV51: $i,SV291: $i] :
      ( ( ( ~ ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV291 )
          | ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV51 ) )
        = $false )
      | ( ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV51 )
        = $true )
      | ( ( SV51 = SV291 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2728]) ).

thf(2885,plain,
    ! [SV51: $i,SV291: $i] :
      ( ( ( ~ ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV291 ) )
        = $false )
      | ( ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV291 )
        = $false )
      | ( ( SV51 = SV291 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2729]) ).

thf(2886,plain,
    ! [SV51: $i,SV291: $i] :
      ( ( ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV51 )
        = $false )
      | ( ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV291 )
        = $false )
      | ( ( SV51 = SV291 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2729]) ).

thf(2887,plain,
    ! [SV52: $i,SV292: $i > $o] :
      ( ( ( in @ ( sK31_SY2534 @ SV292 @ SV52 ) @ SV52 )
        = $true )
      | ( ( ! [SY2535: $i] :
              ( ~ ( in @ SY2535 @ SV52 )
              | ~ ( SV292 @ SY2535 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2730]) ).

thf(2888,plain,
    ! [SV52: $i,SV292: $i > $o] :
      ( ( ( SV292 @ ( sK31_SY2534 @ SV292 @ SV52 ) )
        = $true )
      | ( ( ! [SY2535: $i] :
              ( ~ ( in @ SY2535 @ SV52 )
              | ~ ( SV292 @ SY2535 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2731]) ).

thf(2889,plain,
    ! [SV63: $i,SV302: $i,SV496: $i,SV676: $i > $o] :
      ( ( ( in @ ( sK44_SY3111 @ SV676 @ SV496 @ SV302 @ SV63 ) @ SV63 )
        = $true )
      | ( ( ! [SY3113: $i] :
              ( ~ ( in @ SY3113 @ SV496 )
              | ( SV676 @ SY3113 ) ) )
        = $true )
      | ( ( subset @ SV496 @ ( cartprod @ SV63 @ SV302 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2733]) ).

thf(2890,plain,
    ! [SV302: $i,SV676: $i > $o,SV496: $i,SV63: $i] :
      ( ( ( ~ ( in @ ( sK63_SY3167 @ SV63 @ SV496 @ SV676 @ SV302 ) @ SV302 )
          | ~ ( in @ ( kpair @ ( sK44_SY3111 @ SV676 @ SV496 @ SV302 @ SV63 ) @ ( sK63_SY3167 @ SV63 @ SV496 @ SV676 @ SV302 ) ) @ SV496 )
          | ( SV676 @ ( kpair @ ( sK44_SY3111 @ SV676 @ SV496 @ SV302 @ SV63 ) @ ( sK63_SY3167 @ SV63 @ SV496 @ SV676 @ SV302 ) ) ) )
        = $false )
      | ( ( ! [SY3113: $i] :
              ( ~ ( in @ SY3113 @ SV496 )
              | ( SV676 @ SY3113 ) ) )
        = $true )
      | ( ( subset @ SV496 @ ( cartprod @ SV63 @ SV302 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2734]) ).

thf(2891,plain,
    ! [SV73: $i,SV311: $i,SV502: $i,SV681: $i] :
      ( ( ( ~ ( in @ ( sK64_SY3118 @ SV681 @ SV502 @ SV311 @ SV73 ) @ SV73 )
          | ( ( ap @ SV73 @ SV311 @ SV502 @ ( sK64_SY3118 @ SV681 @ SV502 @ SV311 @ SV73 ) )
            = ( ap @ SV73 @ SV311 @ SV681 @ ( sK64_SY3118 @ SV681 @ SV502 @ SV311 @ SV73 ) ) ) )
        = $false )
      | ( ( SV502 = SV681 )
        = $true )
      | ( ( in @ SV681 @ ( funcSet @ SV73 @ SV311 ) )
        = $false )
      | ( ( in @ SV502 @ ( funcSet @ SV73 @ SV311 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2738]) ).

thf(2892,plain,
    ! [SV737: $i,SV627: $i,SV314: $i,SV76: $i,SV763: $i] :
      ( ( ( ~ ( in @ SV763 @ SV76 )
          | ~ ( in @ SV763 @ ( binintersect @ SV314 @ SV627 ) )
          | ( in @ SV763 @ ( binintersect @ ( binunion @ SV314 @ SV737 ) @ ( binunion @ SV627 @ SV737 ) ) ) )
        = $true )
      | ( ( in @ SV737 @ ( powerset @ SV76 ) )
        = $false )
      | ( ( in @ SV627 @ ( powerset @ SV76 ) )
        = $false )
      | ( ( in @ SV314 @ ( powerset @ SV76 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2740]) ).

thf(2893,plain,
    ! [SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ! [SY2001: $i] :
              ~ ~ ( ~ ( SV77 @ SY2001 )
                  | ~ ! [SY2002: $i] :
                        ( ~ ( SV77 @ SY2002 )
                        | ( SY2001 = SY2002 ) ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2741]) ).

thf(2894,plain,
    ! [SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ~ ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) ) )
        = $false )
      | ( ( ~ ( ~ ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
              | ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2001: $i] :
                  ~ ~ ( ~ ( SV77 @ SY2001 )
                      | ~ ! [SY2002: $i] :
                            ( ~ ( SV77 @ SY2002 )
                            | ( SY2001 = SY2002 ) ) )
          | ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2742]) ).

thf(2895,plain,
    ! [SV77: $i > $o,SV315: $i > $o] :
      ( ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( ~ ( ~ ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
              | ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2001: $i] :
                  ~ ~ ( ~ ( SV77 @ SY2001 )
                      | ~ ! [SY2002: $i] :
                            ( ~ ( SV77 @ SY2002 )
                            | ( SY2001 = SY2002 ) ) )
          | ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2742]) ).

thf(2896,plain,
    ! [SV80: $i,SV318: $i,SV628: $i] :
      ( ( ( ~ ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV80 ) )
        = $false )
      | ( ( ~ ! [SY3067: $i] :
                ( ~ ( in @ SY3067 @ SV80 )
                | ~ ( in @ SY3067 @ SV628 )
                | ( in @ SY3067 @ SV318 ) )
          | ( SV318 = SV628 ) )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2743]) ).

thf(2897,plain,
    ! [SV80: $i,SV318: $i,SV628: $i] :
      ( ( ( ~ ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV318 )
          | ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV628 ) )
        = $false )
      | ( ( ~ ! [SY3067: $i] :
                ( ~ ( in @ SY3067 @ SV80 )
                | ~ ( in @ SY3067 @ SV628 )
                | ( in @ SY3067 @ SV318 ) )
          | ( SV318 = SV628 ) )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2743]) ).

thf(2898,plain,
    ! [SV319: $i,SV81: $i] :
      ( ( ( ~ ( in @ ( sK52_SY2586 @ SV81 @ SV319 ) @ SV319 ) )
        = $false )
      | ( ( SV81 = SV319 )
        = $true )
      | ( ( in @ ( sK8_SY2585 @ SV319 @ SV81 ) @ SV81 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2744]) ).

thf(2899,plain,
    ! [SV319: $i,SV81: $i] :
      ( ( ( in @ ( sK52_SY2586 @ SV81 @ SV319 ) @ SV81 )
        = $false )
      | ( ( SV81 = SV319 )
        = $true )
      | ( ( in @ ( sK8_SY2585 @ SV319 @ SV81 ) @ SV81 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2744]) ).

thf(2900,plain,
    ! [SV319: $i,SV81: $i] :
      ( ( ( in @ ( sK45_SY2586 @ SV81 @ SV319 ) @ SV319 )
        = $true )
      | ( ( SV81 = SV319 )
        = $true )
      | ( ( in @ ( sK8_SY2585 @ SV319 @ SV81 ) @ SV319 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2745]) ).

thf(2901,plain,
    ! [SV506: $i > $i > $o,SV320: $i,SV82: $i,SV732: $i,SV608: $i] :
      ( ( ( in @ ( kpair @ SV608 @ SV732 )
          @ ( dpsetconstr @ SV82 @ SV320
            @ ^ [SY2907: $i,SY2908: $i] : ( SV506 @ SY2907 @ SY2908 ) ) )
        = $false )
      | ( ( SV506 @ SV608 @ SV732 )
        = $true )
      | ( ( in @ SV732 @ SV320 )
        = $false )
      | ( ( in @ SV608 @ SV82 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2747]) ).

thf(2902,plain,
    ! [SV84: $i,SV321: $i > $o,SV682: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK53_SY2593 @ SV682 @ SV321 @ SV84 ) @ SV84 )
              | ~ ~ ( SV321 @ ( sK53_SY2593 @ SV682 @ SV321 @ SV84 ) ) ) )
        = $true )
      | ( ( SV321 @ SV682 )
        = $true )
      | ( ( in @ SV682 @ SV84 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2748]) ).

thf(2903,plain,
    ! [SV85: $i,SV609: $o,SV322: $i,SV507: $i] :
      ( ( ( ~ ( ~ ( in @ SV507 @ SV322 )
              | SV609 ) )
        = $true )
      | ( SV609 = $true )
      | ( ( in @ SV507 @ SV85 )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2749]) ).

thf(2904,plain,
    ! [SV85: $i,SV609: $o,SV322: $i,SV507: $i] :
      ( ( ( ~ ( in @ SV507 @ SV322 )
          | SV609 )
        = $false )
      | ( SV609 = $true )
      | ( SV609 = $false )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2750]) ).

thf(2905,plain,
    ! [SV85: $i,SV322: $i,SV507: $i] :
      ( ( ( ~ ( ~ ( in @ SV507 @ SV322 )
              | $true ) )
        = $true )
      | ( $true = $true )
      | ( ( in @ SV507 @ SV85 )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2751]) ).

thf(2906,plain,
    ! [SV85: $i,SV322: $i,SV507: $i] :
      ( ( ( ~ ( in @ SV507 @ SV322 )
          | $true )
        = $false )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2752]) ).

thf(2907,plain,
    ! [SV85: $i,SV322: $i,SV507: $i] :
      ( ( ( ~ ( ~ ( in @ SV507 @ SV322 )
              | $false ) )
        = $true )
      | ( $false = $true )
      | ( ( in @ SV507 @ SV85 )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2753]) ).

thf(2908,plain,
    ! [SV85: $i,SV322: $i,SV507: $i] :
      ( ( ( ~ ( in @ SV507 @ SV322 )
          | $false )
        = $false )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2754]) ).

thf(2909,plain,
    ! [SV87: $i] :
      ( ( ( ~ ( in @ ( sK39_SY2033 @ SV87 ) @ omega )
          | ~ ( in @ ( sK39_SY2033 @ SV87 ) @ SV87 ) )
        = $false )
      | ( ( in @ emptyset @ SV87 )
        = $false )
      | ( ( ! [SY2034: $i] :
              ( ~ ( in @ SY2034 @ omega )
              | ( in @ SY2034 @ SV87 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2755]) ).

thf(2910,plain,
    ! [SV87: $i,SV759: $i] :
      ( ( ( ~ ( in @ SV759 @ omega ) )
        = $true )
      | ( ( in @ SV759 @ SV87 )
        = $true )
      | ( ( in @ emptyset @ SV87 )
        = $false )
      | ( ( in @ ( setadjoin @ ( sK39_SY2033 @ SV87 ) @ ( sK39_SY2033 @ SV87 ) ) @ SV87 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2756]) ).

thf(2911,plain,
    ! [SV324: $i,SV629: $i,SV88: $i,SV760: $i] :
      ( ( ( ~ ( in @ SV760 @ SV88 ) )
        = $true )
      | ( ( ~ ( in @ SV760 @ SV629 )
          | ( in @ SV760 @ ( setminus @ SV88 @ SV324 ) ) )
        = $true )
      | ( ( subset @ SV324 @ ( setminus @ SV88 @ SV629 ) )
        = $false )
      | ( ( in @ SV629 @ ( powerset @ SV88 ) )
        = $false )
      | ( ( in @ SV324 @ ( powerset @ SV88 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2758]) ).

thf(2912,plain,
    ! [SV89: $i,SV683: $i,SV325: $i > $o] :
      ( ( ( SV325 @ SV683 )
        = $false )
      | ( ( in @ SV683 @ SV89 )
        = $false )
      | ( ( ( ( dsetconstr @ SV89
              @ ^ [SY2603: $i] : ( SV325 @ SY2603 ) )
           != emptyset )
          | $false )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2759]) ).

thf(2913,plain,
    ! [SV96: $i,SV332: $i,SV512: $i,SV685: $i] :
      ( ( ( ~ ( in @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) @ SV96 )
          | ( ( ap @ SV96 @ SV332 @ SV512 @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) )
            = ( ap @ SV96 @ SV332 @ SV685 @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) ) ) )
        = $false )
      | ( ( ! [SY3120: $i] :
              ( ~ ( in @ SY3120 @ SV96 )
              | ! [SY3121: $i] :
                  ( ~ ( in @ SY3121 @ SV332 )
                  | ~ ( in @ ( kpair @ SY3120 @ SY3121 ) @ SV685 )
                  | ( in @ ( kpair @ SY3120 @ SY3121 ) @ SV512 ) ) ) )
        = $true )
      | ( ( func @ SV96 @ SV332 @ SV685 )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV512 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2761]) ).

thf(2914,plain,
    ! [SV98: $i,SV333: $i,SV513: $i] :
      ( ( ( in @ ( sK33_SY2921 @ SV513 @ SV333 @ SV98 ) @ SV98 )
        = $true )
      | ( ( in @ SV513 @ ( cartprod @ SV98 @ SV333 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2762]) ).

thf(2915,plain,
    ! [SV98: $i,SV513: $i,SV333: $i] :
      ( ( ( ~ ! [SY3150: $i] :
                ~ ~ ( ~ ( in @ SY3150 @ SV333 )
                    | ( SV513
                     != ( kpair @ ( sK33_SY2921 @ SV513 @ SV333 @ SV98 ) @ SY3150 ) ) ) )
        = $true )
      | ( ( in @ SV513 @ ( cartprod @ SV98 @ SV333 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2763]) ).

thf(2916,plain,
    ! [SV99: $i,SV738: $i,SV633: $i,SV334: $i] :
      ( ( ( ~ ( in @ SV334 @ ( powerset @ SV633 ) ) )
        = $true )
      | ( ( ~ ( in @ SV738 @ SV334 )
          | ( in @ SV738 @ SV633 ) )
        = $true )
      | ( ( in @ SV738 @ SV99 )
        = $false )
      | ( ( in @ SV633 @ ( powerset @ SV99 ) )
        = $false )
      | ( ( in @ SV334 @ ( powerset @ SV99 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2764]) ).

thf(2917,plain,
    ! [SV336: $i > $o,SV102: $i,SV764: $i] :
      ( ( ( ~ ~ ( ~ ( in @ SV764 @ SV102 )
                | ~ ( SV336 @ SV764 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( in @ ( sK11_SY2627 @ SV336 @ SV102 ) @ SV102 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2765]) ).

thf(2918,plain,
    ! [SV336: $i > $o,SV102: $i] :
      ( ( ( ~ ! [SY2629: $i] :
                ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                    | ~ ( SV336 @ SY2629 ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( in @ ( sK34_SY3074 @ SV336 @ SV102 ) @ SV102 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2766]) ).

thf(2919,plain,
    ! [SV336: $i > $o,SV102: $i] :
      ( ( ( ~ ~ ! [SY2629: $i] :
                  ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                      | ~ ( SV336 @ SY2629 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( SV336 @ ( sK11_SY2627 @ SV336 @ SV102 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2767]) ).

thf(2920,plain,
    ! [SV102: $i,SV336: $i > $o] :
      ( ( ( SV336 @ ( sK34_SY3074 @ SV336 @ SV102 ) )
        = $true )
      | ( ( ~ ~ ! [SY2629: $i] :
                  ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                      | ~ ( SV336 @ SY2629 ) )
          | ( singleton
            @ ( dsetconstr @ SV102
              @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2768]) ).

thf(2921,plain,
    ! [SV336: $i > $o,SV102: $i] :
      ( ( ( ~ ~ ! [SY2629: $i] :
                  ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                      | ~ ( SV336 @ SY2629 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( ( sK11_SY2627 @ SV336 @ SV102 )
          = ( sK34_SY3074 @ SV336 @ SV102 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2769]) ).

thf(2922,plain,
    ! [SV109: $i] :
      ( ( ~ ! [SY2932: $i] :
              ( ~ ( in @ SY2932 @ ( sK3_SY2100 @ SV109 ) )
              | ! [SY2102: $i] :
                  ( ~ ( in @ SY2102 @ SY2932 )
                  | ( in @ SY2102 @ SV109 ) ) )
        | ~ ! [SY2934: $i,SY2935: $i] :
              ( ~ ~ ( ~ ( in @ SY2934 @ SV109 )
                    | ~ ( in @ SY2935 @ SV109 ) )
              | ~ ! [SY2936: $i] :
                    ( ~ ( in @ SY2936 @ ( sK3_SY2100 @ SV109 ) )
                    | ~ ( ~ ( ~ ( in @ SY2934 @ SY2936 )
                            | ( in @ SY2935 @ SY2936 ) )
                        | ~ ( ~ ( in @ SY2935 @ SY2936 )
                            | ( in @ SY2934 @ SY2936 ) ) ) )
              | ( SY2934 = SY2935 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[2770]) ).

thf(2923,plain,
    ! [SV109: $i,SV765: $i] :
      ( ( ! [SY3176: $i] :
            ( ~ ~ ( ~ ( in @ SV765 @ ( sK3_SY2100 @ SV109 ) )
                  | ~ ( in @ SY3176 @ ( sK3_SY2100 @ SV109 ) ) )
            | ! [SY3177: $i] :
                ( ~ ( in @ SY3177 @ SV765 )
                | ( in @ SY3177 @ SY3176 ) )
            | ! [SY3178: $i] :
                ( ~ ( in @ SY3178 @ SY3176 )
                | ( in @ SY3178 @ SV765 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2771]) ).

thf(2924,plain,
    ! [SV109: $i,SV739: $i] :
      ( ( ( ~ ! [SY3154: $i] :
                ( ~ ( in @ SY3154 @ SV739 )
                | ( in @ SY3154 @ SV109 ) )
          | ~ ~ ! [SY3155: $i] :
                  ~ ( in @ SY3155 @ SV739 ) )
        = $true )
      | ( ( ~ ! [SY3156: $i] :
                ~ ~ ! [SY3157: $i] :
                      ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3156 @ ( sK3_SY2100 @ SV109 ) )
                                      | ~ ( in @ SY3157 @ SV739 ) )
                                | ~ ~ ~ ! [SY3158: $i] :
                                          ~ ~ ( ~ ( in @ SY3158 @ SY3156 )
                                              | ~ ( in @ SY3158 @ SV739 ) ) )
                          | ~ ! [SY2947: $i] :
                                ( ~ ( in @ SY2947 @ ( sK3_SY2100 @ SV109 ) )
                                | ! [SX6: $i] :
                                    ( ~ ( in @ SX6 @ SY2947 )
                                    | ( in @ SX6 @ SY3156 ) )
                                | ( in @ SY3157 @ SY2947 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2772]) ).

thf(2925,plain,
    ! [SV110: $i,SV635: $i] :
      ( ( ( ~ ( in @ ( sK40_SY2119 @ SV635 @ SV110 ) @ SV110 ) )
        = $false )
      | ( ( in @ SV635 @ SV110 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2773]) ).

thf(2926,plain,
    ! [SV110: $i,SV635: $i] :
      ( ( ( ~ ~ ~ ! [SY3161: $i] :
                    ~ ~ ( ~ ( in @ SY3161 @ ( sK40_SY2119 @ SV635 @ SV110 ) )
                        | ~ ( in @ SY3161 @ SV110 ) ) )
        = $false )
      | ( ( in @ SV635 @ SV110 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2773]) ).

thf(2927,plain,
    ! [SV636: $i,SV112: $i > $o] :
      ( ( ( ~ ( SV112 @ ( sK66_SY3077 @ SV636 @ SV112 ) )
          | ( SV636
            = ( sK66_SY3077 @ SV636 @ SV112 ) ) )
        = $false )
      | ( ( SV112 @ SV636 )
        = $false )
      | ( ( ~ ! [SY2125: $i] :
                ~ ( SV112 @ SY2125 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2774]) ).

thf(2928,plain,
    ! [SV113: $i,SV344: $i] :
      ( ( ( in @ ( sK35_SY2645 @ SV344 @ SV113 ) @ SV113 )
        = $true )
      | ( ( ( binintersect @ SV113 @ SV344 )
          = emptyset )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2775]) ).

thf(2929,plain,
    ! [SV113: $i,SV344: $i] :
      ( ( ( in @ ( sK35_SY2645 @ SV344 @ SV113 ) @ SV344 )
        = $true )
      | ( ( ( binintersect @ SV113 @ SV344 )
          = emptyset )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2776]) ).

thf(2930,plain,
    ! [SV116: $i,SV637: $i,SV346: $i,SV740: $i] :
      ( ( ( ~ ~ ( in @ SV740 @ ( binunion @ SV346 @ SV637 ) ) )
        = $true )
      | ( ( ~ ( in @ SV740 @ SV346 ) )
        = $true )
      | ( ( in @ SV740 @ SV116 )
        = $false )
      | ( ( in @ SV637 @ ( powerset @ SV116 ) )
        = $false )
      | ( ( in @ SV346 @ ( powerset @ SV116 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2777]) ).

thf(2931,plain,
    ! [SV686: $i,SV520: $i,SV118: $i,SV347: $o] :
      ( ( SV347 = $true )
      | ( ( ( if @ SV118 @ SV347 @ SV520 @ SV686 )
          = SV686 )
        = $true )
      | ( ( in @ SV686 @ SV118 )
        = $false )
      | ( ( in @ SV520 @ SV118 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2778]) ).

thf(2932,plain,
    ! [SV687: $i,SV521: $i,SV118: $i] :
      ( ( $true = $true )
      | ( ( ( if @ SV118 @ $true @ SV521 @ SV687 )
          = SV687 )
        = $true )
      | ( ( in @ SV687 @ SV118 )
        = $false )
      | ( ( in @ SV521 @ SV118 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2779]) ).

thf(2933,plain,
    ! [SV688: $i,SV522: $i,SV118: $i] :
      ( ( $false = $true )
      | ( ( ( if @ SV118 @ $false @ SV522 @ SV688 )
          = SV688 )
        = $true )
      | ( ( in @ SV688 @ SV118 )
        = $false )
      | ( ( in @ SV522 @ SV118 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2780]) ).

thf(2934,plain,
    ! [SV353: $i > $o,SV125: $i,SV766: $i] :
      ( ( ( ~ ~ ( ~ ( in @ SV766 @ SV125 )
                | ~ ( SV353 @ SV766 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( in @ ( sK12_SY2657 @ SV353 @ SV125 ) @ SV125 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2782]) ).

thf(2935,plain,
    ! [SV353: $i > $o,SV125: $i] :
      ( ( ( ~ ! [SY2659: $i] :
                ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                    | ~ ( SV353 @ SY2659 ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( in @ ( sK36_SY3079 @ SV353 @ SV125 ) @ SV125 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2783]) ).

thf(2936,plain,
    ! [SV353: $i > $o,SV125: $i] :
      ( ( ( ~ ~ ! [SY2659: $i] :
                  ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                      | ~ ( SV353 @ SY2659 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( SV353 @ ( sK12_SY2657 @ SV353 @ SV125 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2784]) ).

thf(2937,plain,
    ! [SV125: $i,SV353: $i > $o] :
      ( ( ( SV353 @ ( sK36_SY3079 @ SV353 @ SV125 ) )
        = $true )
      | ( ( ~ ~ ! [SY2659: $i] :
                  ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                      | ~ ( SV353 @ SY2659 ) )
          | ( singleton
            @ ( dsetconstr @ SV125
              @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2785]) ).

thf(2938,plain,
    ! [SV353: $i > $o,SV125: $i] :
      ( ( ( ~ ~ ! [SY2659: $i] :
                  ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                      | ~ ( SV353 @ SY2659 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( ( sK12_SY2657 @ SV353 @ SV125 )
          = ( sK36_SY3079 @ SV353 @ SV125 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2786]) ).

thf(2939,plain,
    ! [SV135: $i,SV363: $i,SV529: $i,SV690: $i > $o] :
      ( ( ( in @ ( sK46_SY3122 @ SV690 @ SV529 @ SV363 @ SV135 ) @ SV135 )
        = $true )
      | ( ( ! [SY3124: $i] :
              ( ~ ( in @ SY3124 @ SV529 )
              | ( SV690 @ SY3124 ) ) )
        = $true )
      | ( ( subset @ SV529 @ ( cartprod @ SV135 @ SV363 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2788]) ).

thf(2940,plain,
    ! [SV363: $i,SV690: $i > $o,SV529: $i,SV135: $i] :
      ( ( ( ~ ( in @ ( sK67_SY3168 @ SV135 @ SV529 @ SV690 @ SV363 ) @ SV363 )
          | ~ ( in @ ( kpair @ ( sK46_SY3122 @ SV690 @ SV529 @ SV363 @ SV135 ) @ ( sK67_SY3168 @ SV135 @ SV529 @ SV690 @ SV363 ) ) @ SV529 )
          | ( SV690 @ ( kpair @ ( sK46_SY3122 @ SV690 @ SV529 @ SV363 @ SV135 ) @ ( sK67_SY3168 @ SV135 @ SV529 @ SV690 @ SV363 ) ) ) )
        = $false )
      | ( ( ! [SY3124: $i] :
              ( ~ ( in @ SY3124 @ SV529 )
              | ( SV690 @ SY3124 ) ) )
        = $true )
      | ( ( subset @ SV529 @ ( cartprod @ SV135 @ SV363 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2789]) ).

thf(2941,plain,
    ! [SV137: $i,SV365: $i,SV643: $i,SV741: $i] :
      ( ( ( ~ ~ ( in @ SV741 @ SV643 ) )
        = $true )
      | ( ( ~ ( in @ SV741 @ ( binintersect @ SV365 @ SV643 ) ) )
        = $true )
      | ( ( in @ SV741 @ SV137 )
        = $false )
      | ( ( in @ SV643 @ ( powerset @ SV137 ) )
        = $false )
      | ( ( in @ SV365 @ ( powerset @ SV137 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2790]) ).

thf(2942,plain,
    ! [SV142: $i,SV742: $i,SV644: $i,SV372: $i > $o] :
      ( ( ( ~ ( SV372 @ SV644 ) )
        = $true )
      | ( ( ~ ( SV372 @ SV742 )
          | ( SV644 = SV742 ) )
        = $true )
      | ( ( in @ SV742 @ SV142 )
        = $false )
      | ( ( in @ SV644 @ SV142 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV142
            @ ^ [SY2680: $i] : ( SV372 @ SY2680 ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2791]) ).

thf(2943,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV767: $i] :
      ( ( ( ~ ( ~ ( ~ ( in @ SV767 @ ( sK47_SY2690 @ SV147 @ SV377 ) )
                  | ~ ! [SY3179: $i] :
                        ~ ~ ( ~ ( in @ SY3179 @ SV377 )
                            | ~ ( SV147 @ SY3179 @ SV767 ) ) )
              | ~ ( ~ ~ ! [SY3180: $i] :
                          ~ ~ ( ~ ( in @ SY3180 @ SV377 )
                              | ~ ( SV147 @ SY3180 @ SV767 ) )
                  | ( in @ SV767 @ ( sK47_SY2690 @ SV147 @ SV377 ) ) ) ) )
        = $true )
      | ( ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2792]) ).

thf(2944,plain,
    ! [SV743: $i,SV377: $i,SV147: $i > $i > $o] :
      ( ( ( ~ ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 ) )
        = $true )
      | ( ( ~ ! [SY3162: $i] :
                ( ~ ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SY3162 )
                | ( SV743 = SY3162 ) ) )
        = $true )
      | ( ( ~ ! [SY2690: $i] :
                ~ ! [SY2691: $i] :
                    ~ ( ~ ( ~ ( in @ SY2691 @ SY2690 )
                          | ~ ! [SY2692: $i] :
                                ~ ~ ( ~ ( in @ SY2692 @ SV377 )
                                    | ~ ( SV147 @ SY2692 @ SY2691 ) ) )
                      | ~ ( ~ ~ ! [SY2693: $i] :
                                  ~ ~ ( ~ ( in @ SY2693 @ SV377 )
                                      | ~ ( SV147 @ SY2693 @ SY2691 ) )
                          | ( in @ SY2691 @ SY2690 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2793]) ).

thf(2945,plain,
    ! [SV151: $i,SV645: $i,SV381: $i,SV744: $i] :
      ( ( ( ~ ~ ( in @ SV744 @ ( binunion @ SV381 @ SV645 ) ) )
        = $true )
      | ( ( ~ ( in @ SV744 @ SV645 ) )
        = $true )
      | ( ( in @ SV744 @ SV151 )
        = $false )
      | ( ( in @ SV645 @ ( powerset @ SV151 ) )
        = $false )
      | ( ( in @ SV381 @ ( powerset @ SV151 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2794]) ).

thf(2946,plain,
    ! [SV156: $i,SV647: $i,SV385: $i,SV745: $i] :
      ( ( ( ~ ~ ( in @ SV745 @ SV385 ) )
        = $true )
      | ( ( ~ ( in @ SV745 @ ( binintersect @ SV385 @ SV647 ) ) )
        = $true )
      | ( ( in @ SV745 @ SV156 )
        = $false )
      | ( ( in @ SV647 @ ( powerset @ SV156 ) )
        = $false )
      | ( ( in @ SV385 @ ( powerset @ SV156 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2795]) ).

thf(2947,plain,
    ! [SV648: $i,SV157: $i > $o] :
      ( ( ( ~ ( SV157 @ ( sK68_SY3087 @ SV648 @ SV157 ) )
          | ( SV648
            = ( sK68_SY3087 @ SV648 @ SV157 ) ) )
        = $false )
      | ( ( SV157 @ SV648 )
        = $false )
      | ( ( SV157
          @ ( descr
            @ ^ [SY2227: $i] : ( SV157 @ SY2227 ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2796]) ).

thf(2948,plain,
    ! [SV160: $i,SV388: $i > $o,SV694: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK54_SY2705 @ SV694 @ SV388 @ SV160 ) @ SV160 )
              | ~ ~ ( SV388 @ ( sK54_SY2705 @ SV694 @ SV388 @ SV160 ) ) ) )
        = $true )
      | ( ( SV388 @ SV694 )
        = $true )
      | ( ( in @ SV694 @ SV160 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2797]) ).

thf(2949,plain,
    ! [SV649: $i,SV389: $i,SV161: $i,SV746: $i] :
      ( ( ( ~ ( in @ SV746 @ ( setminus @ SV161 @ SV389 ) ) )
        = $true )
      | ( ( in @ SV746 @ ( setminus @ SV161 @ ( binintersect @ SV389 @ SV649 ) ) )
        = $true )
      | ( ( in @ SV746 @ SV161 )
        = $false )
      | ( ( in @ SV649 @ ( powerset @ SV161 ) )
        = $false )
      | ( ( in @ SV389 @ ( powerset @ SV161 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2798]) ).

thf(2950,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( ~ ( SV165 @ ( sK48_SY2242 @ SV651 @ SV165 ) ) )
        = $false )
      | ( ( ~ ! [SY2244: $i] :
                ~ ~ ( ~ ( SV165 @ SY2244 )
                    | ~ ! [SY2245: $i] :
                          ( ~ ( SV165 @ SY2245 )
                          | ( SY2244 = SY2245 ) ) ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2799]) ).

thf(2951,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( ~ ( SV165 @ ( sK55_SY3172 @ SV651 @ SV165 ) )
          | ( ( sK48_SY2242 @ SV651 @ SV165 )
            = ( sK55_SY3172 @ SV651 @ SV165 ) ) )
        = $false )
      | ( ( ~ ! [SY2244: $i] :
                ~ ~ ( ~ ( SV165 @ SY2244 )
                    | ~ ! [SY2245: $i] :
                          ( ~ ( SV165 @ SY2245 )
                          | ( SY2244 = SY2245 ) ) ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2799]) ).

thf(2952,plain,
    ! [SV168: $i,SV395: $i,SV539: $i,SV695: $i] :
      ( ( ( ~ ( in @ ( sK69_SY3125 @ SV695 @ SV539 @ SV395 @ SV168 ) @ SV168 )
          | ! [SY3181: $i] :
              ( ~ ( in @ SY3181 @ SV395 )
              | ~ ( in @ ( kpair @ ( sK69_SY3125 @ SV695 @ SV539 @ SV395 @ SV168 ) @ SY3181 ) @ SV539 )
              | ( in @ ( kpair @ ( sK69_SY3125 @ SV695 @ SV539 @ SV395 @ SV168 ) @ SY3181 ) @ SV695 ) ) )
        = $false )
      | ( ( subset @ SV539 @ SV695 )
        = $true )
      | ( ( subset @ SV695 @ ( cartprod @ SV168 @ SV395 ) )
        = $false )
      | ( ( subset @ SV539 @ ( cartprod @ SV168 @ SV395 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2801]) ).

thf(2953,plain,
    ! [SV543: $i > $i,SV397: $i,SV170: $i,SV754: $i] :
      ( ( ( in @ SV754 @ SV170 )
        = $false )
      | ( ( ( ap @ SV170 @ SV397
            @ ( lam @ SV170 @ SV397
              @ ^ [SY2971: $i] : ( SV543 @ SY2971 ) )
            @ SV754 )
          = ( SV543 @ SV754 ) )
        = $true )
      | ( ( in @ ( sK22_SY2969 @ SV397 @ SV543 @ SV170 ) @ SV170 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2805]) ).

thf(2954,plain,
    ! [SV749: $i,SV654: $i,SV177: $i,SV403: $i] :
      ( ( ( ~ ( subset @ SV403 @ ( setminus @ SV177 @ SV654 ) ) )
        = $true )
      | ( ( ~ ( in @ SV749 @ SV654 )
          | ~ ( in @ SV749 @ SV403 ) )
        = $true )
      | ( ( in @ SV749 @ SV177 )
        = $false )
      | ( ( in @ SV654 @ ( powerset @ SV177 ) )
        = $false )
      | ( ( in @ SV403 @ ( powerset @ SV177 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2807]) ).

thf(2955,plain,
    ! [SV404: $i,SV178: $i,SV733: $i,SV616: $i,SV549: $i > $i > $o] :
      ( ( ( SV549 @ SV616 @ SV733 )
        = $false )
      | ( ( in @ ( kpair @ SV616 @ SV733 )
          @ ( dpsetconstr @ SV178 @ SV404
            @ ^ [SY2978: $i,SY2979: $i] : ( SV549 @ SY2978 @ SY2979 ) ) )
        = $true )
      | ( ( in @ SV733 @ SV404 )
        = $false )
      | ( ( in @ SV616 @ SV178 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2808]) ).

thf(2956,plain,
    ! [SV185: $i,SV554: $i,SV700: $i,SV411: $i,SV755: $i] :
      ( ( ( in @ SV755 @ SV411 )
        = $false )
      | ( ( ~ ( in @ ( kpair @ SV700 @ SV755 ) @ SV554 )
          | ( ( ap @ SV185 @ SV411 @ SV554 @ SV700 )
            = SV755 ) )
        = $true )
      | ( ( in @ SV700 @ SV185 )
        = $false )
      | ( ( func @ SV185 @ SV411 @ SV554 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2809]) ).

thf(2957,plain,
    ! [SV190: $i,SV416: $i,SV558: $i,SV701: $i] :
      ( ( ( ~ ( in @ ( sK70_SY3128 @ SV701 @ SV558 @ SV416 @ SV190 ) @ SV190 )
          | ( ( ap @ SV190 @ SV416 @ SV558 @ ( sK70_SY3128 @ SV701 @ SV558 @ SV416 @ SV190 ) )
            = ( ap @ SV190 @ SV416 @ SV701 @ ( sK70_SY3128 @ SV701 @ SV558 @ SV416 @ SV190 ) ) ) )
        = $false )
      | ( ( SV558 = SV701 )
        = $true )
      | ( ( func @ SV190 @ SV416 @ SV701 )
        = $false )
      | ( ( func @ SV190 @ SV416 @ SV558 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2812]) ).

thf(2958,plain,
    ! [SV750: $i,SV657: $i,SV417: $i,SV191: $i,SV768: $i] :
      ( ( ( ~ ( in @ SV768 @ SV191 )
          | ~ ( in @ SV768 @ ( binintersect @ SV417 @ SV657 ) )
          | ( in @ SV768 @ ( binunion @ SV417 @ SV750 ) ) )
        = $true )
      | ( ( in @ SV750 @ ( powerset @ SV191 ) )
        = $false )
      | ( ( in @ SV657 @ ( powerset @ SV191 ) )
        = $false )
      | ( ( in @ SV417 @ ( powerset @ SV191 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2813]) ).

thf(2959,plain,
    ! [SV419: $i,SV702: $i,SV193: $i,SV658: $i] :
      ( ( ( ~ ( in @ SV658 @ SV193 )
          | ( in @ SV702 @ SV419 ) )
        = $true )
      | ( ( SV658 = SV702 )
        = $false )
      | ( ( SV193 = SV419 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2814]) ).

thf(2960,plain,
    ! [SV193: $i,SV658: $i,SV419: $i,SV702: $i] :
      ( ( ( ~ ( in @ SV702 @ SV419 )
          | ( in @ SV658 @ SV193 ) )
        = $true )
      | ( ( SV658 = SV702 )
        = $false )
      | ( ( SV193 = SV419 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2815]) ).

thf(2961,plain,
    ! [SV198: $i,SV567: $i,SV710: $i,SV424: $i,SV756: $i] :
      ( ( ( in @ SV756 @ SV424 )
        = $false )
      | ( ( ~ ( in @ ( kpair @ SV710 @ SV756 ) @ SV567 )
          | ( ( ap @ SV198 @ SV424 @ SV567 @ SV710 )
            = SV756 ) )
        = $true )
      | ( ( in @ SV710 @ SV198 )
        = $false )
      | ( ( in @ SV567 @ ( funcSet @ SV198 @ SV424 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2816]) ).

thf(2962,plain,
    ! [SV426: $i > $o,SV200: $i,SV761: $i] :
      ( ( ( ~ ( ~ ( in @ SV761 @ SV200 )
              | ~ ( SV426 @ SV761 ) ) )
        = $false )
      | ( ( in @ ( sK16_SY2777 @ SV426 @ SV200 ) @ SV200 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2817]) ).

thf(2963,plain,
    ! [SV426: $i > $o,SV200: $i,SV762: $i] :
      ( ( ( ~ ( ~ ( in @ SV762 @ SV200 )
              | ~ ( SV426 @ SV762 ) ) )
        = $false )
      | ( ( SV426 @ ( sK16_SY2777 @ SV426 @ SV200 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2818]) ).

thf(2964,plain,
    ! [SV205: $i,SV430: $i] :
      ( ( ( ~ ( in @ SV430 @ ( sK49_SY2781 @ SV205 @ SV430 ) )
          | ~ ( in @ ( sK49_SY2781 @ SV205 @ SV430 ) @ SV205 ) )
        = $false )
      | ( ( in @ SV430 @ ( setunion @ SV205 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2819]) ).

thf(2965,plain,
    ! [SV205: $i,SV757: $i,SV430: $i] :
      ( ( ( ~ ( in @ SV430 @ SV757 )
          | ~ ( in @ SV757 @ SV205 ) )
        = $true )
      | ( ( in @ SV430 @ ( setunion @ SV205 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2820]) ).

thf(2966,plain,
    ! [SV712: $o,SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | SV712 ) )
        = $true )
      | ( SV712 = $true )
      | ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2821]) ).

thf(2967,plain,
    ! [SV712: $o,SV206: $i,SV431: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV431 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | SV712 )
          | SV712 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2822]) ).

thf(2968,plain,
    ! [SV712: $o,SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | SV712 ) )
        = $true )
      | ( SV712 = $true )
      | ( SV712 = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2823]) ).

thf(2969,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | $true ) )
        = $true )
      | ( $true = $true )
      | ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2824]) ).

thf(2970,plain,
    ! [SV206: $i,SV431: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV431 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | $true )
          | $true )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2825]) ).

thf(2971,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | $true ) )
        = $true )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2826]) ).

thf(2972,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | $false ) )
        = $true )
      | ( $false = $true )
      | ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2827]) ).

thf(2973,plain,
    ! [SV206: $i,SV431: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV431 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | $false )
          | $false )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2828]) ).

thf(2974,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | $false ) )
        = $true )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2829]) ).

thf(2975,plain,
    ! [SV209: $i,SV434: $i,SV659: $i > $o,SV713: $i > $o] :
      ( ( ( in @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) @ SV209 )
        = $true )
      | ( ( ( dsetconstr @ SV209
            @ ^ [SY3097: $i] : ( SV659 @ SY3097 ) )
          = ( dsetconstr @ SV434
            @ ^ [SY3136: $i] : ( SV713 @ SY3136 ) ) )
        = $true )
      | ( ( SV209 = SV434 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2832]) ).

thf(2976,plain,
    ! [SV434: $i,SV713: $i > $o,SV659: $i > $o,SV209: $i] :
      ( ( ( ~ ( in @ ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) @ SV434 )
          | ( ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 )
           != ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) )
          | ~ ( ~ ( ~ ( SV659 @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) )
                  | ( SV713 @ ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) ) )
              | ~ ( ~ ( SV713 @ ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) )
                  | ( SV659 @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) ) ) ) )
        = $false )
      | ( ( ( dsetconstr @ SV209
            @ ^ [SY3097: $i] : ( SV659 @ SY3097 ) )
          = ( dsetconstr @ SV434
            @ ^ [SY3136: $i] : ( SV713 @ SY3136 ) ) )
        = $true )
      | ( ( SV209 = SV434 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2833]) ).

thf(2977,plain,
    ! [SV210: $i,SV714: $o,SV435: $i,SV571: $i] :
      ( ( ( ~ ( ~ ( in @ SV571 @ SV435 )
              | SV714 ) )
        = $true )
      | ( SV714 = $true )
      | ( ( SV571 = SV210 )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2834]) ).

thf(2978,plain,
    ! [SV210: $i,SV714: $o,SV435: $i,SV571: $i] :
      ( ( ( ~ ( in @ SV571 @ SV435 )
          | SV714 )
        = $false )
      | ( SV714 = $true )
      | ( SV714 = $false )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2835]) ).

thf(2979,plain,
    ! [SV210: $i,SV435: $i,SV571: $i] :
      ( ( ( ~ ( ~ ( in @ SV571 @ SV435 )
              | $true ) )
        = $true )
      | ( $true = $true )
      | ( ( SV571 = SV210 )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2836]) ).

thf(2980,plain,
    ! [SV210: $i,SV435: $i,SV571: $i] :
      ( ( ( ~ ( in @ SV571 @ SV435 )
          | $true )
        = $false )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2837]) ).

thf(2981,plain,
    ! [SV210: $i,SV435: $i,SV571: $i] :
      ( ( ( ~ ( ~ ( in @ SV571 @ SV435 )
              | $false ) )
        = $true )
      | ( $false = $true )
      | ( ( SV571 = SV210 )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2838]) ).

thf(2982,plain,
    ! [SV210: $i,SV435: $i,SV571: $i] :
      ( ( ( ~ ( in @ SV571 @ SV435 )
          | $false )
        = $false )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2839]) ).

thf(2983,plain,
    ! [SV660: $i,SV211: $i > $o] :
      ( ( ( ~ ( SV211 @ ( sK72_SY3099 @ SV660 @ SV211 ) )
          | ( SV660
            = ( sK72_SY3099 @ SV660 @ SV211 ) ) )
        = $false )
      | ( ( SV211 @ SV660 )
        = $false )
      | ( ( ~ ! [SY2378: $i] :
                ~ ~ ( ~ ( SV211 @ SY2378 )
                    | ~ ! [SY2379: $i] :
                          ( ~ ( SV211 @ SY2379 )
                          | ( SY2378 = SY2379 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2840]) ).

thf(2984,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ~ ! [SY2388: $i] :
                  ~ ~ ( ~ ( SV214 @ SY2388 )
                      | ~ ! [SY2389: $i] :
                            ( ~ ( SV214 @ SY2389 )
                            | ( SY2388 = SY2389 ) ) )
          | ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2841]) ).

thf(2985,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ~ ! [SY2803: $i] :
                  ~ ~ ( ~ ( SV438 @ SY2803 )
                      | ~ ! [SY2804: $i] :
                            ( ~ ( SV438 @ SY2804 )
                            | ( SY2803 = SY2804 ) ) )
          | ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2842]) ).

thf(2986,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) ) )
        = $false )
      | ( ( ~ ( ~ ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
              | ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ~ ! [SY2388: $i] :
                          ~ ~ ( ~ ( SV214 @ SY2388 )
                              | ~ ! [SY2389: $i] :
                                    ( ~ ( SV214 @ SY2389 )
                                    | ( SY2388 = SY2389 ) ) )
                  | ~ ! [SY2801: $i] :
                        ~ ~ ( ~ ( SV438 @ SY2801 )
                            | ~ ! [SY2802: $i] :
                                  ( ~ ( SV438 @ SY2802 )
                                  | ( SY2801 = SY2802 ) ) ) )
              | ~ ( ~ ~ ! [SY2803: $i] :
                          ~ ~ ( ~ ( SV438 @ SY2803 )
                              | ~ ! [SY2804: $i] :
                                    ( ~ ( SV438 @ SY2804 )
                                    | ( SY2803 = SY2804 ) ) )
                  | ~ ! [SY2394: $i] :
                        ~ ~ ( ~ ( SV214 @ SY2394 )
                            | ~ ! [SY2395: $i] :
                                  ( ~ ( SV214 @ SY2395 )
                                  | ( SY2394 = SY2395 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2843]) ).

thf(2987,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( ~ ( ~ ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
              | ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ~ ! [SY2388: $i] :
                          ~ ~ ( ~ ( SV214 @ SY2388 )
                              | ~ ! [SY2389: $i] :
                                    ( ~ ( SV214 @ SY2389 )
                                    | ( SY2388 = SY2389 ) ) )
                  | ~ ! [SY2801: $i] :
                        ~ ~ ( ~ ( SV438 @ SY2801 )
                            | ~ ! [SY2802: $i] :
                                  ( ~ ( SV438 @ SY2802 )
                                  | ( SY2801 = SY2802 ) ) ) )
              | ~ ( ~ ~ ! [SY2803: $i] :
                          ~ ~ ( ~ ( SV438 @ SY2803 )
                              | ~ ! [SY2804: $i] :
                                    ( ~ ( SV438 @ SY2804 )
                                    | ( SY2803 = SY2804 ) ) )
                  | ~ ! [SY2394: $i] :
                        ~ ~ ( ~ ( SV214 @ SY2394 )
                            | ~ ! [SY2395: $i] :
                                  ( ~ ( SV214 @ SY2395 )
                                  | ( SY2394 = SY2395 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2843]) ).

thf(2988,plain,
    ! [SV216: $i,SV440: $i > $o,SV573: $i] :
      ( ( ( ~ ( in @ ( sK56_SY3006 @ SV573 @ SV440 @ SV216 ) @ SV216 ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV216
            @ ^ [SY2811: $i] : ( SV440 @ SY2811 ) ) )
        = $true )
      | ( ( SV440 @ SV573 )
        = $false )
      | ( ( in @ SV573 @ SV216 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2846]) ).

thf(2989,plain,
    ! [SV216: $i,SV573: $i,SV440: $i > $o] :
      ( ( ( ~ ( SV440 @ ( sK56_SY3006 @ SV573 @ SV440 @ SV216 ) )
          | ( ( sK56_SY3006 @ SV573 @ SV440 @ SV216 )
            = SV573 ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV216
            @ ^ [SY2811: $i] : ( SV440 @ SY2811 ) ) )
        = $true )
      | ( ( SV440 @ SV573 )
        = $false )
      | ( ( in @ SV573 @ SV216 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2846]) ).

thf(2990,plain,
    ! [SV221: $i,SV445: $i,SV579: $i,SV721: $i] :
      ( ( ( ~ ( in @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ SV221 )
          | ! [SY3182: $i] :
              ( ~ ( in @ SY3182 @ SV445 )
              | ~ ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ SY3182 ) @ SV579 )
              | ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ SY3182 ) @ SV721 ) ) )
        = $false )
      | ( ( ~ ! [SY3142: $i] :
                ( ~ ( in @ SY3142 @ SV221 )
                | ! [SY3143: $i] :
                    ( ~ ( in @ SY3143 @ SV445 )
                    | ~ ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV721 )
                    | ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV579 ) ) )
          | ( SV579 = SV721 ) )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2850]) ).

thf(2991,plain,
    ! [SV751: $i,SV663: $i,SV451: $i,SV228: $i,SV769: $i] :
      ( ( ( ~ ( in @ SV769 @ SV228 )
          | ~ ( in @ SV769 @ ( binintersect @ SV451 @ SV663 ) )
          | ( in @ SV769 @ ( binunion @ SV663 @ SV751 ) ) )
        = $true )
      | ( ( in @ SV751 @ ( powerset @ SV228 ) )
        = $false )
      | ( ( in @ SV663 @ ( powerset @ SV228 ) )
        = $false )
      | ( ( in @ SV451 @ ( powerset @ SV228 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2853]) ).

thf(2992,plain,
    ! [SV723: $i,SV583: $i,SV230: $i,SV453: $o] :
      ( ( SV453 = $true )
      | ( ( ( dsetconstr @ SV230
            @ ^ [SY3145: $i] :
                ( ~ ( ~ SV453
                    | ( SY3145 != SV583 ) )
                | ~ ( ~ ~ SV453
                    | ( SY3145 != SV723 ) ) ) )
          = ( setadjoin @ SV723 @ emptyset ) )
        = $true )
      | ( ( in @ SV723 @ SV230 )
        = $false )
      | ( ( in @ SV583 @ SV230 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2854]) ).

thf(2993,plain,
    ! [SV724: $i,SV584: $i,SV230: $i] :
      ( ( $true = $true )
      | ( ( ( dsetconstr @ SV230
            @ ^ [SY3146: $i] :
                ( ~ ( ~ $true
                    | ( SY3146 != SV584 ) )
                | ~ ( ~ ~ $true
                    | ( SY3146 != SV724 ) ) ) )
          = ( setadjoin @ SV724 @ emptyset ) )
        = $true )
      | ( ( in @ SV724 @ SV230 )
        = $false )
      | ( ( in @ SV584 @ SV230 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2855]) ).

thf(2994,plain,
    ! [SV725: $i,SV585: $i,SV230: $i] :
      ( ( $false = $true )
      | ( ( ( dsetconstr @ SV230
            @ ^ [SY3147: $i] :
                ( ~ ( ~ $false
                    | ( SY3147 != SV585 ) )
                | ~ ( ~ ~ $false
                    | ( SY3147 != SV725 ) ) ) )
          = ( setadjoin @ SV725 @ emptyset ) )
        = $true )
      | ( ( in @ SV725 @ SV230 )
        = $false )
      | ( ( in @ SV585 @ SV230 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2856]) ).

thf(2995,plain,
    ! [SV231: $i,SV454: $i,SV664: $i] :
      ( ( ( ~ ( in @ ( sK57_SY3103 @ SV664 @ SV454 @ SV231 ) @ SV231 ) )
        = $false )
      | ( ( in @ SV454 @ ( powerset @ SV664 ) )
        = $true )
      | ( ( in @ SV664 @ ( powerset @ SV231 ) )
        = $false )
      | ( ( in @ SV454 @ ( powerset @ SV231 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2857]) ).

thf(2996,plain,
    ! [SV231: $i,SV454: $i,SV664: $i] :
      ( ( ( ~ ( in @ ( sK57_SY3103 @ SV664 @ SV454 @ SV231 ) @ SV454 )
          | ( in @ ( sK57_SY3103 @ SV664 @ SV454 @ SV231 ) @ SV664 ) )
        = $false )
      | ( ( in @ SV454 @ ( powerset @ SV664 ) )
        = $true )
      | ( ( in @ SV664 @ ( powerset @ SV231 ) )
        = $false )
      | ( ( in @ SV454 @ ( powerset @ SV231 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2857]) ).

thf(2997,plain,
    ! [SV243: $i,SV466: $i,SV665: $i] :
      ( ( ( ~ ( in @ ( sK58_SY3104 @ SV665 @ SV466 @ SV243 ) @ SV243 ) )
        = $false )
      | ( ( subset @ SV466 @ SV665 )
        = $true )
      | ( ( in @ SV665 @ ( powerset @ SV243 ) )
        = $false )
      | ( ( in @ SV466 @ ( powerset @ SV243 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2858]) ).

thf(2998,plain,
    ! [SV243: $i,SV466: $i,SV665: $i] :
      ( ( ( ~ ( in @ ( sK58_SY3104 @ SV665 @ SV466 @ SV243 ) @ SV466 )
          | ( in @ ( sK58_SY3104 @ SV665 @ SV466 @ SV243 ) @ SV665 ) )
        = $false )
      | ( ( subset @ SV466 @ SV665 )
        = $true )
      | ( ( in @ SV665 @ ( powerset @ SV243 ) )
        = $false )
      | ( ( in @ SV466 @ ( powerset @ SV243 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2858]) ).

thf(2999,plain,
    ! [SV594: $i > $i,SV467: $i,SV244: $i,SV758: $i] :
      ( ( ( in @ SV758 @ SV244 )
        = $false )
      | ( ( ( ap @ SV244 @ SV467
            @ ( lam @ SV244 @ SV467
              @ ^ [SY3033: $i] : ( SV594 @ SY3033 ) )
            @ SV758 )
          = ( SV594 @ SV758 ) )
        = $true )
      | ( ( in @ ( sK29_SY3031 @ SV467 @ SV594 @ SV244 ) @ SV244 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2859]) ).

thf(3000,plain,
    ! [SV666: $i,SV469: $i,SV246: $i,SV753: $i] :
      ( ( ( ~ ( in @ SV753 @ ( setminus @ SV246 @ SV469 ) ) )
        = $true )
      | ( ( ~ ( in @ SV753 @ ( binintersect @ SV469 @ SV666 ) ) )
        = $true )
      | ( ( in @ SV753 @ SV246 )
        = $false )
      | ( ( in @ SV666 @ ( powerset @ SV246 ) )
        = $false )
      | ( ( in @ SV469 @ ( powerset @ SV246 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2861]) ).

thf(3001,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ~ ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) ) )
        = $false )
      | ( ( ~ ( ( ( sK37_SY3106 @ SV667 @ SV253 )
               != SV667 )
              | ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2491: $i] :
                ~ ~ ( ~ ( SV253 @ SY2491 )
                    | ~ ! [SY2492: $i] :
                          ( ~ ( SV253 @ SY2492 )
                          | ( SY2491 = SY2492 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2862]) ).

thf(3002,plain,
    ! [SV253: $i > $o,SV667: $i] :
      ( ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $false )
      | ( ( ~ ( ( ( sK37_SY3106 @ SV667 @ SV253 )
               != SV667 )
              | ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2491: $i] :
                ~ ~ ( ~ ( SV253 @ SY2491 )
                    | ~ ! [SY2492: $i] :
                          ( ~ ( SV253 @ SY2492 )
                          | ( SY2491 = SY2492 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2862]) ).

thf(3003,plain,
    ! [SV475: $i,SV255: $i,SV668: $o] :
      ( ( ( in @ ( sK41_SY3107 @ SV668 @ SV255 @ SV475 ) @ SV255 )
        = $true )
      | ( SV668 = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2864]) ).

thf(3004,plain,
    ! [SV475: $i,SV255: $i] :
      ( ( ( in @ ( sK42_SX0 @ SV255 @ SV475 ) @ SV255 )
        = $true )
      | ( $true = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2867]) ).

thf(3005,plain,
    ! [SV475: $i,SV255: $i] :
      ( ( ( in @ ( sK43_SX0 @ SV255 @ SV475 ) @ SV255 )
        = $true )
      | ( $false = $true )
      | ( ( in @ SV475 @ ( setunion @ SV255 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2870]) ).

thf(3006,plain,
    ! [SV281: $i > $o,SV35: $i,SV770: $i] :
      ( ( ( ~ ( in @ SV770 @ SV35 )
          | ~ ( SV281 @ SV770 ) )
        = $true )
      | ( ( in @ ( sK30_SY2514 @ SV281 @ SV35 ) @ SV35 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2872]) ).

thf(3007,plain,
    ! [SV281: $i > $o,SV35: $i,SV771: $i] :
      ( ( ( ~ ( in @ SV771 @ SV35 )
          | ~ ( SV281 @ SV771 ) )
        = $true )
      | ( ( SV281 @ ( sK30_SY2514 @ SV281 @ SV35 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2873]) ).

thf(3008,plain,
    ! [SV36: $i,SV734: $i,SV619: $i,SV282: $i] :
      ( ( ( subset @ SV282 @ SV619 )
        = $false )
      | ( ( ~ ~ ( in @ SV734 @ SV619 )
          | ~ ( in @ SV734 @ SV282 ) )
        = $true )
      | ( ( in @ SV734 @ SV36 )
        = $false )
      | ( ( in @ SV619 @ ( powerset @ SV36 ) )
        = $false )
      | ( ( in @ SV282 @ ( powerset @ SV36 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2874]) ).

thf(3009,plain,
    ! [SV620: $i,SV37: $i > $o] :
      ( ( ( ~ ( SV37 @ ( sK59_SY3056 @ SV620 @ SV37 ) ) )
        = $false )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( ~ ! [SY1897: $i] :
                ~ ! [SY1898: $i] :
                    ~ ( ~ ( ~ ( SV37 @ SY1898 )
                          | ( SY1898 = SY1897 ) )
                      | ~ ( ( SY1898 != SY1897 )
                          | ( SV37 @ SY1898 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2875]) ).

thf(3010,plain,
    ! [SV37: $i > $o,SV620: $i] :
      ( ( ( SV620
          = ( sK59_SY3056 @ SV620 @ SV37 ) )
        = $false )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( ~ ! [SY1897: $i] :
                ~ ! [SY1898: $i] :
                    ~ ( ~ ( ~ ( SV37 @ SY1898 )
                          | ( SY1898 = SY1897 ) )
                      | ~ ( ( SY1898 != SY1897 )
                          | ( SV37 @ SY1898 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2875]) ).

thf(3011,plain,
    ! [SV621: $i,SV41: $i > $o] :
      ( ( ( ~ ( SV41 @ ( sK60_SY3057 @ SV621 @ SV41 ) ) )
        = $false )
      | ( ( SV41 @ SV621 )
        = $false )
      | ( ( ! [SY1909: $i,SY1910: $i] :
              ( ~ ( SV41 @ SY1909 )
              | ~ ( SV41 @ SY1910 )
              | ( SY1909 = SY1910 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2879]) ).

thf(3012,plain,
    ! [SV41: $i > $o,SV621: $i] :
      ( ( ( SV621
          = ( sK60_SY3057 @ SV621 @ SV41 ) )
        = $false )
      | ( ( SV41 @ SV621 )
        = $false )
      | ( ( ! [SY1909: $i,SY1910: $i] :
              ( ~ ( SV41 @ SY1909 )
              | ~ ( SV41 @ SY1910 )
              | ( SY1909 = SY1910 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2879]) ).

thf(3013,plain,
    ! [SV622: $i,SV43: $i > $o] :
      ( ( ( ~ ( SV43 @ ( sK61_SY3058 @ SV622 @ SV43 ) ) )
        = $false )
      | ( ( SV43 @ SV622 )
        = $false )
      | ( ( ! [SY1916: $i,SY1917: $i] :
              ( ~ ( SV43 @ SY1916 )
              | ~ ( SV43 @ SY1917 )
              | ( SY1916 = SY1917 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2880]) ).

thf(3014,plain,
    ! [SV43: $i > $o,SV622: $i] :
      ( ( ( SV622
          = ( sK61_SY3058 @ SV622 @ SV43 ) )
        = $false )
      | ( ( SV43 @ SV622 )
        = $false )
      | ( ( ! [SY1916: $i,SY1917: $i] :
              ( ~ ( SV43 @ SY1916 )
              | ~ ( SV43 @ SY1917 )
              | ( SY1916 = SY1917 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2880]) ).

thf(3015,plain,
    ! [SV623: $i,SV286: $i,SV44: $i,SV736: $i] :
      ( ( ( in @ SV736 @ ( setminus @ SV44 @ ( binunion @ SV286 @ SV623 ) ) )
        = $false )
      | ( ( ~ ( in @ SV736 @ SV286 ) )
        = $true )
      | ( ( in @ SV736 @ SV44 )
        = $false )
      | ( ( in @ SV623 @ ( powerset @ SV44 ) )
        = $false )
      | ( ( in @ SV286 @ ( powerset @ SV44 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2881]) ).

thf(3016,plain,
    ! [SV46: $i,SV673: $i,SV287: $i > $o] :
      ( ( ( SV287 @ SV673 )
        = $true )
      | ( ( in @ SV673 @ SV46 )
        = $false )
      | ( ( ~ ! [SY2528: $i] :
                ( ~ ( in @ SY2528 @ SV46 )
                | ( SV287 @ SY2528 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2882]) ).

thf(3017,plain,
    ! [SV624: $i,SV48: $i > $o] :
      ( ( ( ~ ( SV48 @ ( sK62_SY3060 @ SV624 @ SV48 ) ) )
        = $false )
      | ( ( SV48 @ SV624 )
        = $false )
      | ( ( ~ ! [SY1928: $i] :
                ~ ~ ( ~ ( SV48 @ SY1928 )
                    | ~ ! [SY1929: $i] :
                          ( ~ ( SV48 @ SY1929 )
                          | ( SY1928 = SY1929 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2883]) ).

thf(3018,plain,
    ! [SV48: $i > $o,SV624: $i] :
      ( ( ( SV624
          = ( sK62_SY3060 @ SV624 @ SV48 ) )
        = $false )
      | ( ( SV48 @ SV624 )
        = $false )
      | ( ( ~ ! [SY1928: $i] :
                ~ ~ ( ~ ( SV48 @ SY1928 )
                    | ~ ! [SY1929: $i] :
                          ( ~ ( SV48 @ SY1929 )
                          | ( SY1928 = SY1929 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2883]) ).

thf(3019,plain,
    ! [SV51: $i,SV291: $i] :
      ( ( ( ~ ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV291 ) )
        = $false )
      | ( ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV51 )
        = $true )
      | ( ( SV51 = SV291 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2884]) ).

thf(3020,plain,
    ! [SV51: $i,SV291: $i] :
      ( ( ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV51 )
        = $false )
      | ( ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV51 )
        = $true )
      | ( ( SV51 = SV291 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2884]) ).

thf(3021,plain,
    ! [SV51: $i,SV291: $i] :
      ( ( ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV291 )
        = $true )
      | ( ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV291 )
        = $false )
      | ( ( SV51 = SV291 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2885]) ).

thf(3022,plain,
    ! [SV292: $i > $o,SV52: $i,SV772: $i] :
      ( ( ( ~ ( in @ SV772 @ SV52 )
          | ~ ( SV292 @ SV772 ) )
        = $true )
      | ( ( in @ ( sK31_SY2534 @ SV292 @ SV52 ) @ SV52 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2887]) ).

thf(3023,plain,
    ! [SV292: $i > $o,SV52: $i,SV773: $i] :
      ( ( ( ~ ( in @ SV773 @ SV52 )
          | ~ ( SV292 @ SV773 ) )
        = $true )
      | ( ( SV292 @ ( sK31_SY2534 @ SV292 @ SV52 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2888]) ).

thf(3024,plain,
    ! [SV63: $i,SV302: $i,SV676: $i > $o,SV496: $i,SV774: $i] :
      ( ( ( ~ ( in @ SV774 @ SV496 )
          | ( SV676 @ SV774 ) )
        = $true )
      | ( ( in @ ( sK44_SY3111 @ SV676 @ SV496 @ SV302 @ SV63 ) @ SV63 )
        = $true )
      | ( ( subset @ SV496 @ ( cartprod @ SV63 @ SV302 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2889]) ).

thf(3025,plain,
    ! [SV302: $i,SV676: $i > $o,SV496: $i,SV63: $i] :
      ( ( ( ~ ( in @ ( sK63_SY3167 @ SV63 @ SV496 @ SV676 @ SV302 ) @ SV302 ) )
        = $false )
      | ( ( ! [SY3113: $i] :
              ( ~ ( in @ SY3113 @ SV496 )
              | ( SV676 @ SY3113 ) ) )
        = $true )
      | ( ( subset @ SV496 @ ( cartprod @ SV63 @ SV302 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2890]) ).

thf(3026,plain,
    ! [SV63: $i,SV302: $i,SV496: $i,SV676: $i > $o] :
      ( ( ( ~ ( in @ ( kpair @ ( sK44_SY3111 @ SV676 @ SV496 @ SV302 @ SV63 ) @ ( sK63_SY3167 @ SV63 @ SV496 @ SV676 @ SV302 ) ) @ SV496 )
          | ( SV676 @ ( kpair @ ( sK44_SY3111 @ SV676 @ SV496 @ SV302 @ SV63 ) @ ( sK63_SY3167 @ SV63 @ SV496 @ SV676 @ SV302 ) ) ) )
        = $false )
      | ( ( ! [SY3113: $i] :
              ( ~ ( in @ SY3113 @ SV496 )
              | ( SV676 @ SY3113 ) ) )
        = $true )
      | ( ( subset @ SV496 @ ( cartprod @ SV63 @ SV302 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2890]) ).

thf(3027,plain,
    ! [SV73: $i,SV311: $i,SV502: $i,SV681: $i] :
      ( ( ( ~ ( in @ ( sK64_SY3118 @ SV681 @ SV502 @ SV311 @ SV73 ) @ SV73 ) )
        = $false )
      | ( ( SV502 = SV681 )
        = $true )
      | ( ( in @ SV681 @ ( funcSet @ SV73 @ SV311 ) )
        = $false )
      | ( ( in @ SV502 @ ( funcSet @ SV73 @ SV311 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2891]) ).

thf(3028,plain,
    ! [SV681: $i,SV502: $i,SV311: $i,SV73: $i] :
      ( ( ( ( ap @ SV73 @ SV311 @ SV502 @ ( sK64_SY3118 @ SV681 @ SV502 @ SV311 @ SV73 ) )
          = ( ap @ SV73 @ SV311 @ SV681 @ ( sK64_SY3118 @ SV681 @ SV502 @ SV311 @ SV73 ) ) )
        = $false )
      | ( ( SV502 = SV681 )
        = $true )
      | ( ( in @ SV681 @ ( funcSet @ SV73 @ SV311 ) )
        = $false )
      | ( ( in @ SV502 @ ( funcSet @ SV73 @ SV311 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2891]) ).

thf(3029,plain,
    ! [SV737: $i,SV627: $i,SV314: $i,SV76: $i,SV763: $i] :
      ( ( ( ~ ( in @ SV763 @ SV76 ) )
        = $true )
      | ( ( ~ ( in @ SV763 @ ( binintersect @ SV314 @ SV627 ) )
          | ( in @ SV763 @ ( binintersect @ ( binunion @ SV314 @ SV737 ) @ ( binunion @ SV627 @ SV737 ) ) ) )
        = $true )
      | ( ( in @ SV737 @ ( powerset @ SV76 ) )
        = $false )
      | ( ( in @ SV627 @ ( powerset @ SV76 ) )
        = $false )
      | ( ( in @ SV314 @ ( powerset @ SV76 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2892]) ).

thf(3030,plain,
    ! [SV315: $i > $o,SV775: $i,SV77: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV77 @ SV775 )
                | ~ ! [SY3183: $i] :
                      ( ~ ( SV77 @ SY3183 )
                      | ( SV775 = SY3183 ) ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2893]) ).

thf(3031,plain,
    ! [SV315: $i > $o,SV77: $i > $o] :
      ( ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( ~ ( ~ ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
              | ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2001: $i] :
                  ~ ~ ( ~ ( SV77 @ SY2001 )
                      | ~ ! [SY2002: $i] :
                            ( ~ ( SV77 @ SY2002 )
                            | ( SY2001 = SY2002 ) ) )
          | ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2894]) ).

thf(3032,plain,
    ! [SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
          | ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( ~ ~ ! [SY2001: $i] :
                  ~ ~ ( ~ ( SV77 @ SY2001 )
                      | ~ ! [SY2002: $i] :
                            ( ~ ( SV77 @ SY2002 )
                            | ( SY2001 = SY2002 ) ) )
          | ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2895]) ).

thf(3033,plain,
    ! [SV80: $i,SV318: $i,SV628: $i] :
      ( ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV80 )
        = $true )
      | ( ( ~ ! [SY3067: $i] :
                ( ~ ( in @ SY3067 @ SV80 )
                | ~ ( in @ SY3067 @ SV628 )
                | ( in @ SY3067 @ SV318 ) )
          | ( SV318 = SV628 ) )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2896]) ).

thf(3034,plain,
    ! [SV80: $i,SV318: $i,SV628: $i] :
      ( ( ( ~ ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV318 ) )
        = $false )
      | ( ( ~ ! [SY3067: $i] :
                ( ~ ( in @ SY3067 @ SV80 )
                | ~ ( in @ SY3067 @ SV628 )
                | ( in @ SY3067 @ SV318 ) )
          | ( SV318 = SV628 ) )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2897]) ).

thf(3035,plain,
    ! [SV80: $i,SV318: $i,SV628: $i] :
      ( ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV628 )
        = $false )
      | ( ( ~ ! [SY3067: $i] :
                ( ~ ( in @ SY3067 @ SV80 )
                | ~ ( in @ SY3067 @ SV628 )
                | ( in @ SY3067 @ SV318 ) )
          | ( SV318 = SV628 ) )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2897]) ).

thf(3036,plain,
    ! [SV319: $i,SV81: $i] :
      ( ( ( in @ ( sK52_SY2586 @ SV81 @ SV319 ) @ SV319 )
        = $true )
      | ( ( SV81 = SV319 )
        = $true )
      | ( ( in @ ( sK8_SY2585 @ SV319 @ SV81 ) @ SV81 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2898]) ).

thf(3037,plain,
    ! [SV84: $i,SV321: $i > $o,SV682: $i] :
      ( ( ( ~ ( in @ ( sK53_SY2593 @ SV682 @ SV321 @ SV84 ) @ SV84 )
          | ~ ~ ( SV321 @ ( sK53_SY2593 @ SV682 @ SV321 @ SV84 ) ) )
        = $false )
      | ( ( SV321 @ SV682 )
        = $true )
      | ( ( in @ SV682 @ SV84 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2902]) ).

thf(3038,plain,
    ! [SV85: $i,SV609: $o,SV322: $i,SV507: $i] :
      ( ( ( ~ ( in @ SV507 @ SV322 )
          | SV609 )
        = $false )
      | ( SV609 = $true )
      | ( ( in @ SV507 @ SV85 )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2903]) ).

thf(3039,plain,
    ! [SV85: $i,SV609: $o,SV322: $i,SV507: $i] :
      ( ( ( ~ ( in @ SV507 @ SV322 ) )
        = $false )
      | ( SV609 = $true )
      | ( SV609 = $false )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2904]) ).

thf(3040,plain,
    ! [SV322: $i,SV85: $i,SV507: $i,SV609: $o] :
      ( ( SV609 = $false )
      | ( SV609 = $true )
      | ( SV609 = $false )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2904]) ).

thf(3041,plain,
    ! [SV85: $i,SV322: $i,SV507: $i] :
      ( ( ( ~ ( in @ SV507 @ SV322 )
          | $true )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV507 @ SV85 )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2905]) ).

thf(3042,plain,
    ! [SV85: $i,SV322: $i,SV507: $i] :
      ( ( ( ~ ( in @ SV507 @ SV322 ) )
        = $false )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2906]) ).

thf(3043,plain,
    ! [SV322: $i,SV85: $i,SV507: $i] :
      ( ( $true = $false )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2906]) ).

thf(3044,plain,
    ! [SV85: $i,SV322: $i,SV507: $i] :
      ( ( ( ~ ( in @ SV507 @ SV322 )
          | $false )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV507 @ SV85 )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2907]) ).

thf(3045,plain,
    ! [SV85: $i,SV322: $i,SV507: $i] :
      ( ( ( ~ ( in @ SV507 @ SV322 ) )
        = $false )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2908]) ).

thf(3046,plain,
    ! [SV322: $i,SV85: $i,SV507: $i] :
      ( ( $false = $false )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2908]) ).

thf(3047,plain,
    ! [SV87: $i] :
      ( ( ( ~ ( in @ ( sK39_SY2033 @ SV87 ) @ omega ) )
        = $false )
      | ( ( in @ emptyset @ SV87 )
        = $false )
      | ( ( ! [SY2034: $i] :
              ( ~ ( in @ SY2034 @ omega )
              | ( in @ SY2034 @ SV87 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2909]) ).

thf(3048,plain,
    ! [SV87: $i] :
      ( ( ( ~ ( in @ ( sK39_SY2033 @ SV87 ) @ SV87 ) )
        = $false )
      | ( ( in @ emptyset @ SV87 )
        = $false )
      | ( ( ! [SY2034: $i] :
              ( ~ ( in @ SY2034 @ omega )
              | ( in @ SY2034 @ SV87 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2909]) ).

thf(3049,plain,
    ! [SV87: $i,SV759: $i] :
      ( ( ( in @ SV759 @ omega )
        = $false )
      | ( ( in @ SV759 @ SV87 )
        = $true )
      | ( ( in @ emptyset @ SV87 )
        = $false )
      | ( ( in @ ( setadjoin @ ( sK39_SY2033 @ SV87 ) @ ( sK39_SY2033 @ SV87 ) ) @ SV87 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2910]) ).

thf(3050,plain,
    ! [SV324: $i,SV629: $i,SV88: $i,SV760: $i] :
      ( ( ( in @ SV760 @ SV88 )
        = $false )
      | ( ( ~ ( in @ SV760 @ SV629 )
          | ( in @ SV760 @ ( setminus @ SV88 @ SV324 ) ) )
        = $true )
      | ( ( subset @ SV324 @ ( setminus @ SV88 @ SV629 ) )
        = $false )
      | ( ( in @ SV629 @ ( powerset @ SV88 ) )
        = $false )
      | ( ( in @ SV324 @ ( powerset @ SV88 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2911]) ).

thf(3051,plain,
    ! [SV683: $i,SV325: $i > $o,SV89: $i] :
      ( ( ( ( dsetconstr @ SV89
            @ ^ [SY2603: $i] : ( SV325 @ SY2603 ) )
         != emptyset )
        = $true )
      | ( $false = $true )
      | ( ( in @ SV683 @ SV89 )
        = $false )
      | ( ( SV325 @ SV683 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2912]) ).

thf(3052,plain,
    ! [SV96: $i,SV332: $i,SV512: $i,SV685: $i] :
      ( ( ( ~ ( in @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) @ SV96 ) )
        = $false )
      | ( ( ! [SY3120: $i] :
              ( ~ ( in @ SY3120 @ SV96 )
              | ! [SY3121: $i] :
                  ( ~ ( in @ SY3121 @ SV332 )
                  | ~ ( in @ ( kpair @ SY3120 @ SY3121 ) @ SV685 )
                  | ( in @ ( kpair @ SY3120 @ SY3121 ) @ SV512 ) ) ) )
        = $true )
      | ( ( func @ SV96 @ SV332 @ SV685 )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV512 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2913]) ).

thf(3053,plain,
    ! [SV685: $i,SV512: $i,SV332: $i,SV96: $i] :
      ( ( ( ( ap @ SV96 @ SV332 @ SV512 @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) )
          = ( ap @ SV96 @ SV332 @ SV685 @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) ) )
        = $false )
      | ( ( ! [SY3120: $i] :
              ( ~ ( in @ SY3120 @ SV96 )
              | ! [SY3121: $i] :
                  ( ~ ( in @ SY3121 @ SV332 )
                  | ~ ( in @ ( kpair @ SY3120 @ SY3121 ) @ SV685 )
                  | ( in @ ( kpair @ SY3120 @ SY3121 ) @ SV512 ) ) ) )
        = $true )
      | ( ( func @ SV96 @ SV332 @ SV685 )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV512 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2913]) ).

thf(3054,plain,
    ! [SV98: $i,SV513: $i,SV333: $i] :
      ( ( ( ! [SY3150: $i] :
              ~ ~ ( ~ ( in @ SY3150 @ SV333 )
                  | ( SV513
                   != ( kpair @ ( sK33_SY2921 @ SV513 @ SV333 @ SV98 ) @ SY3150 ) ) ) )
        = $false )
      | ( ( in @ SV513 @ ( cartprod @ SV98 @ SV333 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2915]) ).

thf(3055,plain,
    ! [SV99: $i,SV738: $i,SV633: $i,SV334: $i] :
      ( ( ( in @ SV334 @ ( powerset @ SV633 ) )
        = $false )
      | ( ( ~ ( in @ SV738 @ SV334 )
          | ( in @ SV738 @ SV633 ) )
        = $true )
      | ( ( in @ SV738 @ SV99 )
        = $false )
      | ( ( in @ SV633 @ ( powerset @ SV99 ) )
        = $false )
      | ( ( in @ SV334 @ ( powerset @ SV99 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2916]) ).

thf(3056,plain,
    ! [SV336: $i > $o,SV102: $i,SV764: $i] :
      ( ( ( ~ ( ~ ( in @ SV764 @ SV102 )
              | ~ ( SV336 @ SV764 ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( in @ ( sK11_SY2627 @ SV336 @ SV102 ) @ SV102 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2917]) ).

thf(3057,plain,
    ! [SV336: $i > $o,SV102: $i] :
      ( ( ( ! [SY2629: $i] :
              ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                  | ~ ( SV336 @ SY2629 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( in @ ( sK34_SY3074 @ SV336 @ SV102 ) @ SV102 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2918]) ).

thf(3058,plain,
    ! [SV336: $i > $o,SV102: $i] :
      ( ( ( ~ ! [SY2629: $i] :
                ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                    | ~ ( SV336 @ SY2629 ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( SV336 @ ( sK11_SY2627 @ SV336 @ SV102 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2919]) ).

thf(3059,plain,
    ! [SV336: $i > $o,SV102: $i] :
      ( ( ( ~ ~ ! [SY2629: $i] :
                  ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                      | ~ ( SV336 @ SY2629 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( SV336 @ ( sK34_SY3074 @ SV336 @ SV102 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2920]) ).

thf(3060,plain,
    ! [SV336: $i > $o,SV102: $i] :
      ( ( ( ~ ! [SY2629: $i] :
                ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                    | ~ ( SV336 @ SY2629 ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( ( sK11_SY2627 @ SV336 @ SV102 )
          = ( sK34_SY3074 @ SV336 @ SV102 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2921]) ).

thf(3061,plain,
    ! [SV109: $i] :
      ( ( ~ ! [SY2932: $i] :
              ( ~ ( in @ SY2932 @ ( sK3_SY2100 @ SV109 ) )
              | ! [SY2102: $i] :
                  ( ~ ( in @ SY2102 @ SY2932 )
                  | ( in @ SY2102 @ SV109 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2922]) ).

thf(3062,plain,
    ! [SV109: $i] :
      ( ( ~ ! [SY2934: $i,SY2935: $i] :
              ( ~ ~ ( ~ ( in @ SY2934 @ SV109 )
                    | ~ ( in @ SY2935 @ SV109 ) )
              | ~ ! [SY2936: $i] :
                    ( ~ ( in @ SY2936 @ ( sK3_SY2100 @ SV109 ) )
                    | ~ ( ~ ( ~ ( in @ SY2934 @ SY2936 )
                            | ( in @ SY2935 @ SY2936 ) )
                        | ~ ( ~ ( in @ SY2935 @ SY2936 )
                            | ( in @ SY2934 @ SY2936 ) ) ) )
              | ( SY2934 = SY2935 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2922]) ).

thf(3063,plain,
    ! [SV776: $i,SV109: $i,SV765: $i] :
      ( ( ~ ~ ( ~ ( in @ SV765 @ ( sK3_SY2100 @ SV109 ) )
              | ~ ( in @ SV776 @ ( sK3_SY2100 @ SV109 ) ) )
        | ! [SY3184: $i] :
            ( ~ ( in @ SY3184 @ SV765 )
            | ( in @ SY3184 @ SV776 ) )
        | ! [SY3185: $i] :
            ( ~ ( in @ SY3185 @ SV776 )
            | ( in @ SY3185 @ SV765 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2923]) ).

thf(3064,plain,
    ! [SV109: $i,SV739: $i] :
      ( ( ( ~ ! [SY3154: $i] :
                ( ~ ( in @ SY3154 @ SV739 )
                | ( in @ SY3154 @ SV109 ) ) )
        = $true )
      | ( ( ~ ~ ! [SY3155: $i] :
                  ~ ( in @ SY3155 @ SV739 ) )
        = $true )
      | ( ( ~ ! [SY3156: $i] :
                ~ ~ ! [SY3157: $i] :
                      ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3156 @ ( sK3_SY2100 @ SV109 ) )
                                      | ~ ( in @ SY3157 @ SV739 ) )
                                | ~ ~ ~ ! [SY3158: $i] :
                                          ~ ~ ( ~ ( in @ SY3158 @ SY3156 )
                                              | ~ ( in @ SY3158 @ SV739 ) ) )
                          | ~ ! [SY2947: $i] :
                                ( ~ ( in @ SY2947 @ ( sK3_SY2100 @ SV109 ) )
                                | ! [SX6: $i] :
                                    ( ~ ( in @ SX6 @ SY2947 )
                                    | ( in @ SX6 @ SY3156 ) )
                                | ( in @ SY3157 @ SY2947 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2924]) ).

thf(3065,plain,
    ! [SV110: $i,SV635: $i] :
      ( ( ( in @ ( sK40_SY2119 @ SV635 @ SV110 ) @ SV110 )
        = $true )
      | ( ( in @ SV635 @ SV110 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2925]) ).

thf(3066,plain,
    ! [SV110: $i,SV635: $i] :
      ( ( ( ~ ~ ! [SY3161: $i] :
                  ~ ~ ( ~ ( in @ SY3161 @ ( sK40_SY2119 @ SV635 @ SV110 ) )
                      | ~ ( in @ SY3161 @ SV110 ) ) )
        = $true )
      | ( ( in @ SV635 @ SV110 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2926]) ).

thf(3067,plain,
    ! [SV636: $i,SV112: $i > $o] :
      ( ( ( ~ ( SV112 @ ( sK66_SY3077 @ SV636 @ SV112 ) ) )
        = $false )
      | ( ( SV112 @ SV636 )
        = $false )
      | ( ( ~ ! [SY2125: $i] :
                ~ ( SV112 @ SY2125 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2927]) ).

thf(3068,plain,
    ! [SV112: $i > $o,SV636: $i] :
      ( ( ( SV636
          = ( sK66_SY3077 @ SV636 @ SV112 ) )
        = $false )
      | ( ( SV112 @ SV636 )
        = $false )
      | ( ( ~ ! [SY2125: $i] :
                ~ ( SV112 @ SY2125 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2927]) ).

thf(3069,plain,
    ! [SV116: $i,SV637: $i,SV346: $i,SV740: $i] :
      ( ( ( ~ ( in @ SV740 @ ( binunion @ SV346 @ SV637 ) ) )
        = $false )
      | ( ( ~ ( in @ SV740 @ SV346 ) )
        = $true )
      | ( ( in @ SV740 @ SV116 )
        = $false )
      | ( ( in @ SV637 @ ( powerset @ SV116 ) )
        = $false )
      | ( ( in @ SV346 @ ( powerset @ SV116 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2930]) ).

thf(3070,plain,
    ! [SV353: $i > $o,SV125: $i,SV766: $i] :
      ( ( ( ~ ( ~ ( in @ SV766 @ SV125 )
              | ~ ( SV353 @ SV766 ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( in @ ( sK12_SY2657 @ SV353 @ SV125 ) @ SV125 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2934]) ).

thf(3071,plain,
    ! [SV353: $i > $o,SV125: $i] :
      ( ( ( ! [SY2659: $i] :
              ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                  | ~ ( SV353 @ SY2659 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( in @ ( sK36_SY3079 @ SV353 @ SV125 ) @ SV125 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2935]) ).

thf(3072,plain,
    ! [SV353: $i > $o,SV125: $i] :
      ( ( ( ~ ! [SY2659: $i] :
                ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                    | ~ ( SV353 @ SY2659 ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( SV353 @ ( sK12_SY2657 @ SV353 @ SV125 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2936]) ).

thf(3073,plain,
    ! [SV353: $i > $o,SV125: $i] :
      ( ( ( ~ ~ ! [SY2659: $i] :
                  ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                      | ~ ( SV353 @ SY2659 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( SV353 @ ( sK36_SY3079 @ SV353 @ SV125 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2937]) ).

thf(3074,plain,
    ! [SV353: $i > $o,SV125: $i] :
      ( ( ( ~ ! [SY2659: $i] :
                ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                    | ~ ( SV353 @ SY2659 ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( ( sK12_SY2657 @ SV353 @ SV125 )
          = ( sK36_SY3079 @ SV353 @ SV125 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2938]) ).

thf(3075,plain,
    ! [SV135: $i,SV363: $i,SV690: $i > $o,SV529: $i,SV777: $i] :
      ( ( ( ~ ( in @ SV777 @ SV529 )
          | ( SV690 @ SV777 ) )
        = $true )
      | ( ( in @ ( sK46_SY3122 @ SV690 @ SV529 @ SV363 @ SV135 ) @ SV135 )
        = $true )
      | ( ( subset @ SV529 @ ( cartprod @ SV135 @ SV363 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2939]) ).

thf(3076,plain,
    ! [SV363: $i,SV690: $i > $o,SV529: $i,SV135: $i] :
      ( ( ( ~ ( in @ ( sK67_SY3168 @ SV135 @ SV529 @ SV690 @ SV363 ) @ SV363 ) )
        = $false )
      | ( ( ! [SY3124: $i] :
              ( ~ ( in @ SY3124 @ SV529 )
              | ( SV690 @ SY3124 ) ) )
        = $true )
      | ( ( subset @ SV529 @ ( cartprod @ SV135 @ SV363 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2940]) ).

thf(3077,plain,
    ! [SV135: $i,SV363: $i,SV529: $i,SV690: $i > $o] :
      ( ( ( ~ ( in @ ( kpair @ ( sK46_SY3122 @ SV690 @ SV529 @ SV363 @ SV135 ) @ ( sK67_SY3168 @ SV135 @ SV529 @ SV690 @ SV363 ) ) @ SV529 )
          | ( SV690 @ ( kpair @ ( sK46_SY3122 @ SV690 @ SV529 @ SV363 @ SV135 ) @ ( sK67_SY3168 @ SV135 @ SV529 @ SV690 @ SV363 ) ) ) )
        = $false )
      | ( ( ! [SY3124: $i] :
              ( ~ ( in @ SY3124 @ SV529 )
              | ( SV690 @ SY3124 ) ) )
        = $true )
      | ( ( subset @ SV529 @ ( cartprod @ SV135 @ SV363 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2940]) ).

thf(3078,plain,
    ! [SV137: $i,SV365: $i,SV643: $i,SV741: $i] :
      ( ( ( ~ ( in @ SV741 @ SV643 ) )
        = $false )
      | ( ( ~ ( in @ SV741 @ ( binintersect @ SV365 @ SV643 ) ) )
        = $true )
      | ( ( in @ SV741 @ SV137 )
        = $false )
      | ( ( in @ SV643 @ ( powerset @ SV137 ) )
        = $false )
      | ( ( in @ SV365 @ ( powerset @ SV137 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2941]) ).

thf(3079,plain,
    ! [SV142: $i,SV742: $i,SV644: $i,SV372: $i > $o] :
      ( ( ( SV372 @ SV644 )
        = $false )
      | ( ( ~ ( SV372 @ SV742 )
          | ( SV644 = SV742 ) )
        = $true )
      | ( ( in @ SV742 @ SV142 )
        = $false )
      | ( ( in @ SV644 @ SV142 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV142
            @ ^ [SY2680: $i] : ( SV372 @ SY2680 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2942]) ).

thf(3080,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV767: $i] :
      ( ( ( ~ ( ~ ( in @ SV767 @ ( sK47_SY2690 @ SV147 @ SV377 ) )
              | ~ ! [SY3179: $i] :
                    ~ ~ ( ~ ( in @ SY3179 @ SV377 )
                        | ~ ( SV147 @ SY3179 @ SV767 ) ) )
          | ~ ( ~ ~ ! [SY3180: $i] :
                      ~ ~ ( ~ ( in @ SY3180 @ SV377 )
                          | ~ ( SV147 @ SY3180 @ SV767 ) )
              | ( in @ SV767 @ ( sK47_SY2690 @ SV147 @ SV377 ) ) ) )
        = $false )
      | ( ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2943]) ).

thf(3081,plain,
    ! [SV743: $i,SV377: $i,SV147: $i > $i > $o] :
      ( ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( ~ ! [SY3162: $i] :
                ( ~ ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SY3162 )
                | ( SV743 = SY3162 ) ) )
        = $true )
      | ( ( ~ ! [SY2690: $i] :
                ~ ! [SY2691: $i] :
                    ~ ( ~ ( ~ ( in @ SY2691 @ SY2690 )
                          | ~ ! [SY2692: $i] :
                                ~ ~ ( ~ ( in @ SY2692 @ SV377 )
                                    | ~ ( SV147 @ SY2692 @ SY2691 ) ) )
                      | ~ ( ~ ~ ! [SY2693: $i] :
                                  ~ ~ ( ~ ( in @ SY2693 @ SV377 )
                                      | ~ ( SV147 @ SY2693 @ SY2691 ) )
                          | ( in @ SY2691 @ SY2690 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2944]) ).

thf(3082,plain,
    ! [SV151: $i,SV645: $i,SV381: $i,SV744: $i] :
      ( ( ( ~ ( in @ SV744 @ ( binunion @ SV381 @ SV645 ) ) )
        = $false )
      | ( ( ~ ( in @ SV744 @ SV645 ) )
        = $true )
      | ( ( in @ SV744 @ SV151 )
        = $false )
      | ( ( in @ SV645 @ ( powerset @ SV151 ) )
        = $false )
      | ( ( in @ SV381 @ ( powerset @ SV151 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2945]) ).

thf(3083,plain,
    ! [SV156: $i,SV647: $i,SV385: $i,SV745: $i] :
      ( ( ( ~ ( in @ SV745 @ SV385 ) )
        = $false )
      | ( ( ~ ( in @ SV745 @ ( binintersect @ SV385 @ SV647 ) ) )
        = $true )
      | ( ( in @ SV745 @ SV156 )
        = $false )
      | ( ( in @ SV647 @ ( powerset @ SV156 ) )
        = $false )
      | ( ( in @ SV385 @ ( powerset @ SV156 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2946]) ).

thf(3084,plain,
    ! [SV648: $i,SV157: $i > $o] :
      ( ( ( ~ ( SV157 @ ( sK68_SY3087 @ SV648 @ SV157 ) ) )
        = $false )
      | ( ( SV157 @ SV648 )
        = $false )
      | ( ( SV157
          @ ( descr
            @ ^ [SY2227: $i] : ( SV157 @ SY2227 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2947]) ).

thf(3085,plain,
    ! [SV157: $i > $o,SV648: $i] :
      ( ( ( SV648
          = ( sK68_SY3087 @ SV648 @ SV157 ) )
        = $false )
      | ( ( SV157 @ SV648 )
        = $false )
      | ( ( SV157
          @ ( descr
            @ ^ [SY2227: $i] : ( SV157 @ SY2227 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2947]) ).

thf(3086,plain,
    ! [SV160: $i,SV388: $i > $o,SV694: $i] :
      ( ( ( ~ ( in @ ( sK54_SY2705 @ SV694 @ SV388 @ SV160 ) @ SV160 )
          | ~ ~ ( SV388 @ ( sK54_SY2705 @ SV694 @ SV388 @ SV160 ) ) )
        = $false )
      | ( ( SV388 @ SV694 )
        = $true )
      | ( ( in @ SV694 @ SV160 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2948]) ).

thf(3087,plain,
    ! [SV649: $i,SV389: $i,SV161: $i,SV746: $i] :
      ( ( ( in @ SV746 @ ( setminus @ SV161 @ SV389 ) )
        = $false )
      | ( ( in @ SV746 @ ( setminus @ SV161 @ ( binintersect @ SV389 @ SV649 ) ) )
        = $true )
      | ( ( in @ SV746 @ SV161 )
        = $false )
      | ( ( in @ SV649 @ ( powerset @ SV161 ) )
        = $false )
      | ( ( in @ SV389 @ ( powerset @ SV161 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2949]) ).

thf(3088,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( SV165 @ ( sK48_SY2242 @ SV651 @ SV165 ) )
        = $true )
      | ( ( ~ ! [SY2244: $i] :
                ~ ~ ( ~ ( SV165 @ SY2244 )
                    | ~ ! [SY2245: $i] :
                          ( ~ ( SV165 @ SY2245 )
                          | ( SY2244 = SY2245 ) ) ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2950]) ).

thf(3089,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( ~ ( SV165 @ ( sK55_SY3172 @ SV651 @ SV165 ) ) )
        = $false )
      | ( ( ~ ! [SY2244: $i] :
                ~ ~ ( ~ ( SV165 @ SY2244 )
                    | ~ ! [SY2245: $i] :
                          ( ~ ( SV165 @ SY2245 )
                          | ( SY2244 = SY2245 ) ) ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2951]) ).

thf(3090,plain,
    ! [SV165: $i > $o,SV651: $i] :
      ( ( ( ( sK48_SY2242 @ SV651 @ SV165 )
          = ( sK55_SY3172 @ SV651 @ SV165 ) )
        = $false )
      | ( ( ~ ! [SY2244: $i] :
                ~ ~ ( ~ ( SV165 @ SY2244 )
                    | ~ ! [SY2245: $i] :
                          ( ~ ( SV165 @ SY2245 )
                          | ( SY2244 = SY2245 ) ) ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2951]) ).

thf(3091,plain,
    ! [SV168: $i,SV395: $i,SV539: $i,SV695: $i] :
      ( ( ( ~ ( in @ ( sK69_SY3125 @ SV695 @ SV539 @ SV395 @ SV168 ) @ SV168 ) )
        = $false )
      | ( ( subset @ SV539 @ SV695 )
        = $true )
      | ( ( subset @ SV695 @ ( cartprod @ SV168 @ SV395 ) )
        = $false )
      | ( ( subset @ SV539 @ ( cartprod @ SV168 @ SV395 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2952]) ).

thf(3092,plain,
    ! [SV168: $i,SV539: $i,SV695: $i,SV395: $i] :
      ( ( ( ! [SY3181: $i] :
              ( ~ ( in @ SY3181 @ SV395 )
              | ~ ( in @ ( kpair @ ( sK69_SY3125 @ SV695 @ SV539 @ SV395 @ SV168 ) @ SY3181 ) @ SV539 )
              | ( in @ ( kpair @ ( sK69_SY3125 @ SV695 @ SV539 @ SV395 @ SV168 ) @ SY3181 ) @ SV695 ) ) )
        = $false )
      | ( ( subset @ SV539 @ SV695 )
        = $true )
      | ( ( subset @ SV695 @ ( cartprod @ SV168 @ SV395 ) )
        = $false )
      | ( ( subset @ SV539 @ ( cartprod @ SV168 @ SV395 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2952]) ).

thf(3093,plain,
    ! [SV749: $i,SV654: $i,SV177: $i,SV403: $i] :
      ( ( ( subset @ SV403 @ ( setminus @ SV177 @ SV654 ) )
        = $false )
      | ( ( ~ ( in @ SV749 @ SV654 )
          | ~ ( in @ SV749 @ SV403 ) )
        = $true )
      | ( ( in @ SV749 @ SV177 )
        = $false )
      | ( ( in @ SV654 @ ( powerset @ SV177 ) )
        = $false )
      | ( ( in @ SV403 @ ( powerset @ SV177 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2954]) ).

thf(3094,plain,
    ! [SV411: $i,SV185: $i,SV554: $i,SV755: $i,SV700: $i] :
      ( ( ( ~ ( in @ ( kpair @ SV700 @ SV755 ) @ SV554 ) )
        = $true )
      | ( ( ( ap @ SV185 @ SV411 @ SV554 @ SV700 )
          = SV755 )
        = $true )
      | ( ( in @ SV755 @ SV411 )
        = $false )
      | ( ( in @ SV700 @ SV185 )
        = $false )
      | ( ( func @ SV185 @ SV411 @ SV554 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2956]) ).

thf(3095,plain,
    ! [SV190: $i,SV416: $i,SV558: $i,SV701: $i] :
      ( ( ( ~ ( in @ ( sK70_SY3128 @ SV701 @ SV558 @ SV416 @ SV190 ) @ SV190 ) )
        = $false )
      | ( ( SV558 = SV701 )
        = $true )
      | ( ( func @ SV190 @ SV416 @ SV701 )
        = $false )
      | ( ( func @ SV190 @ SV416 @ SV558 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2957]) ).

thf(3096,plain,
    ! [SV701: $i,SV558: $i,SV416: $i,SV190: $i] :
      ( ( ( ( ap @ SV190 @ SV416 @ SV558 @ ( sK70_SY3128 @ SV701 @ SV558 @ SV416 @ SV190 ) )
          = ( ap @ SV190 @ SV416 @ SV701 @ ( sK70_SY3128 @ SV701 @ SV558 @ SV416 @ SV190 ) ) )
        = $false )
      | ( ( SV558 = SV701 )
        = $true )
      | ( ( func @ SV190 @ SV416 @ SV701 )
        = $false )
      | ( ( func @ SV190 @ SV416 @ SV558 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2957]) ).

thf(3097,plain,
    ! [SV750: $i,SV657: $i,SV417: $i,SV191: $i,SV768: $i] :
      ( ( ( ~ ( in @ SV768 @ SV191 ) )
        = $true )
      | ( ( ~ ( in @ SV768 @ ( binintersect @ SV417 @ SV657 ) )
          | ( in @ SV768 @ ( binunion @ SV417 @ SV750 ) ) )
        = $true )
      | ( ( in @ SV750 @ ( powerset @ SV191 ) )
        = $false )
      | ( ( in @ SV657 @ ( powerset @ SV191 ) )
        = $false )
      | ( ( in @ SV417 @ ( powerset @ SV191 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2958]) ).

thf(3098,plain,
    ! [SV419: $i,SV702: $i,SV193: $i,SV658: $i] :
      ( ( ( ~ ( in @ SV658 @ SV193 ) )
        = $true )
      | ( ( in @ SV702 @ SV419 )
        = $true )
      | ( ( SV658 = SV702 )
        = $false )
      | ( ( SV193 = SV419 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2959]) ).

thf(3099,plain,
    ! [SV193: $i,SV658: $i,SV419: $i,SV702: $i] :
      ( ( ( ~ ( in @ SV702 @ SV419 ) )
        = $true )
      | ( ( in @ SV658 @ SV193 )
        = $true )
      | ( ( SV658 = SV702 )
        = $false )
      | ( ( SV193 = SV419 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2960]) ).

thf(3100,plain,
    ! [SV424: $i,SV198: $i,SV567: $i,SV756: $i,SV710: $i] :
      ( ( ( ~ ( in @ ( kpair @ SV710 @ SV756 ) @ SV567 ) )
        = $true )
      | ( ( ( ap @ SV198 @ SV424 @ SV567 @ SV710 )
          = SV756 )
        = $true )
      | ( ( in @ SV756 @ SV424 )
        = $false )
      | ( ( in @ SV710 @ SV198 )
        = $false )
      | ( ( in @ SV567 @ ( funcSet @ SV198 @ SV424 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2961]) ).

thf(3101,plain,
    ! [SV426: $i > $o,SV200: $i,SV761: $i] :
      ( ( ( ~ ( in @ SV761 @ SV200 )
          | ~ ( SV426 @ SV761 ) )
        = $true )
      | ( ( in @ ( sK16_SY2777 @ SV426 @ SV200 ) @ SV200 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2962]) ).

thf(3102,plain,
    ! [SV426: $i > $o,SV200: $i,SV762: $i] :
      ( ( ( ~ ( in @ SV762 @ SV200 )
          | ~ ( SV426 @ SV762 ) )
        = $true )
      | ( ( SV426 @ ( sK16_SY2777 @ SV426 @ SV200 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2963]) ).

thf(3103,plain,
    ! [SV205: $i,SV430: $i] :
      ( ( ( ~ ( in @ SV430 @ ( sK49_SY2781 @ SV205 @ SV430 ) ) )
        = $false )
      | ( ( in @ SV430 @ ( setunion @ SV205 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2964]) ).

thf(3104,plain,
    ! [SV430: $i,SV205: $i] :
      ( ( ( ~ ( in @ ( sK49_SY2781 @ SV205 @ SV430 ) @ SV205 ) )
        = $false )
      | ( ( in @ SV430 @ ( setunion @ SV205 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2964]) ).

thf(3105,plain,
    ! [SV205: $i,SV757: $i,SV430: $i] :
      ( ( ( ~ ( in @ SV430 @ SV757 ) )
        = $true )
      | ( ( ~ ( in @ SV757 @ SV205 ) )
        = $true )
      | ( ( in @ SV430 @ ( setunion @ SV205 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2965]) ).

thf(3106,plain,
    ! [SV712: $o,SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ~ ( in @ SV570 @ SV206 )
          | ~ ( in @ SV570 @ SV431 )
          | SV712 )
        = $false )
      | ( SV712 = $true )
      | ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2966]) ).

thf(3107,plain,
    ! [SV712: $o,SV206: $i,SV431: $i,SV570: $i] :
      ( ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | SV712 )
          | SV712 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2967]) ).

thf(3108,plain,
    ! [SV712: $o,SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ~ ( in @ SV570 @ SV206 )
          | ~ ( in @ SV570 @ SV431 )
          | SV712 )
        = $false )
      | ( SV712 = $true )
      | ( SV712 = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2968]) ).

thf(3109,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ~ ( in @ SV570 @ SV206 )
          | ~ ( in @ SV570 @ SV431 )
          | $true )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2969]) ).

thf(3110,plain,
    ! [SV206: $i,SV431: $i,SV570: $i] :
      ( ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | $true )
          | $true )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2970]) ).

thf(3111,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ~ ( in @ SV570 @ SV206 )
          | ~ ( in @ SV570 @ SV431 )
          | $true )
        = $false )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2971]) ).

thf(3112,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ~ ( in @ SV570 @ SV206 )
          | ~ ( in @ SV570 @ SV431 )
          | $false )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2972]) ).

thf(3113,plain,
    ! [SV206: $i,SV431: $i,SV570: $i] :
      ( ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | $false )
          | $false )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2973]) ).

thf(3114,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ~ ( in @ SV570 @ SV206 )
          | ~ ( in @ SV570 @ SV431 )
          | $false )
        = $false )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2974]) ).

thf(3115,plain,
    ! [SV434: $i,SV713: $i > $o,SV659: $i > $o,SV209: $i] :
      ( ( ( ~ ( in @ ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) @ SV434 ) )
        = $false )
      | ( ( ( dsetconstr @ SV209
            @ ^ [SY3097: $i] : ( SV659 @ SY3097 ) )
          = ( dsetconstr @ SV434
            @ ^ [SY3136: $i] : ( SV713 @ SY3136 ) ) )
        = $true )
      | ( ( SV209 = SV434 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2976]) ).

thf(3116,plain,
    ! [SV209: $i,SV434: $i,SV659: $i > $o,SV713: $i > $o] :
      ( ( ( ( ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 )
           != ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) )
          | ~ ( ~ ( ~ ( SV659 @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) )
                  | ( SV713 @ ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) ) )
              | ~ ( ~ ( SV713 @ ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) )
                  | ( SV659 @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) ) ) ) )
        = $false )
      | ( ( ( dsetconstr @ SV209
            @ ^ [SY3097: $i] : ( SV659 @ SY3097 ) )
          = ( dsetconstr @ SV434
            @ ^ [SY3136: $i] : ( SV713 @ SY3136 ) ) )
        = $true )
      | ( ( SV209 = SV434 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2976]) ).

thf(3117,plain,
    ! [SV210: $i,SV714: $o,SV435: $i,SV571: $i] :
      ( ( ( ~ ( in @ SV571 @ SV435 )
          | SV714 )
        = $false )
      | ( SV714 = $true )
      | ( ( SV571 = SV210 )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2977]) ).

thf(3118,plain,
    ! [SV210: $i,SV714: $o,SV435: $i,SV571: $i] :
      ( ( ( ~ ( in @ SV571 @ SV435 ) )
        = $false )
      | ( SV714 = $true )
      | ( SV714 = $false )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2978]) ).

thf(3119,plain,
    ! [SV435: $i,SV210: $i,SV571: $i,SV714: $o] :
      ( ( SV714 = $false )
      | ( SV714 = $true )
      | ( SV714 = $false )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2978]) ).

thf(3120,plain,
    ! [SV210: $i,SV435: $i,SV571: $i] :
      ( ( ( ~ ( in @ SV571 @ SV435 )
          | $true )
        = $false )
      | ( $true = $true )
      | ( ( SV571 = SV210 )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2979]) ).

thf(3121,plain,
    ! [SV210: $i,SV435: $i,SV571: $i] :
      ( ( ( ~ ( in @ SV571 @ SV435 ) )
        = $false )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2980]) ).

thf(3122,plain,
    ! [SV435: $i,SV210: $i,SV571: $i] :
      ( ( $true = $false )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2980]) ).

thf(3123,plain,
    ! [SV210: $i,SV435: $i,SV571: $i] :
      ( ( ( ~ ( in @ SV571 @ SV435 )
          | $false )
        = $false )
      | ( $false = $true )
      | ( ( SV571 = SV210 )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2981]) ).

thf(3124,plain,
    ! [SV210: $i,SV435: $i,SV571: $i] :
      ( ( ( ~ ( in @ SV571 @ SV435 ) )
        = $false )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2982]) ).

thf(3125,plain,
    ! [SV435: $i,SV210: $i,SV571: $i] :
      ( ( $false = $false )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2982]) ).

thf(3126,plain,
    ! [SV660: $i,SV211: $i > $o] :
      ( ( ( ~ ( SV211 @ ( sK72_SY3099 @ SV660 @ SV211 ) ) )
        = $false )
      | ( ( SV211 @ SV660 )
        = $false )
      | ( ( ~ ! [SY2378: $i] :
                ~ ~ ( ~ ( SV211 @ SY2378 )
                    | ~ ! [SY2379: $i] :
                          ( ~ ( SV211 @ SY2379 )
                          | ( SY2378 = SY2379 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2983]) ).

thf(3127,plain,
    ! [SV211: $i > $o,SV660: $i] :
      ( ( ( SV660
          = ( sK72_SY3099 @ SV660 @ SV211 ) )
        = $false )
      | ( ( SV211 @ SV660 )
        = $false )
      | ( ( ~ ! [SY2378: $i] :
                ~ ~ ( ~ ( SV211 @ SY2378 )
                    | ~ ! [SY2379: $i] :
                          ( ~ ( SV211 @ SY2379 )
                          | ( SY2378 = SY2379 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2983]) ).

thf(3128,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ~ ! [SY2388: $i] :
                  ~ ~ ( ~ ( SV214 @ SY2388 )
                      | ~ ! [SY2389: $i] :
                            ( ~ ( SV214 @ SY2389 )
                            | ( SY2388 = SY2389 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2984]) ).

thf(3129,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ~ ! [SY2803: $i] :
                  ~ ~ ( ~ ( SV438 @ SY2803 )
                      | ~ ! [SY2804: $i] :
                            ( ~ ( SV438 @ SY2804 )
                            | ( SY2803 = SY2804 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2985]) ).

thf(3130,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( ~ ( ~ ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
              | ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ~ ! [SY2388: $i] :
                          ~ ~ ( ~ ( SV214 @ SY2388 )
                              | ~ ! [SY2389: $i] :
                                    ( ~ ( SV214 @ SY2389 )
                                    | ( SY2388 = SY2389 ) ) )
                  | ~ ! [SY2801: $i] :
                        ~ ~ ( ~ ( SV438 @ SY2801 )
                            | ~ ! [SY2802: $i] :
                                  ( ~ ( SV438 @ SY2802 )
                                  | ( SY2801 = SY2802 ) ) ) )
              | ~ ( ~ ~ ! [SY2803: $i] :
                          ~ ~ ( ~ ( SV438 @ SY2803 )
                              | ~ ! [SY2804: $i] :
                                    ( ~ ( SV438 @ SY2804 )
                                    | ( SY2803 = SY2804 ) ) )
                  | ~ ! [SY2394: $i] :
                        ~ ~ ( ~ ( SV214 @ SY2394 )
                            | ~ ! [SY2395: $i] :
                                  ( ~ ( SV214 @ SY2395 )
                                  | ( SY2394 = SY2395 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2986]) ).

thf(3131,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
          | ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( ~ ( ~ ( ~ ~ ! [SY2388: $i] :
                          ~ ~ ( ~ ( SV214 @ SY2388 )
                              | ~ ! [SY2389: $i] :
                                    ( ~ ( SV214 @ SY2389 )
                                    | ( SY2388 = SY2389 ) ) )
                  | ~ ! [SY2801: $i] :
                        ~ ~ ( ~ ( SV438 @ SY2801 )
                            | ~ ! [SY2802: $i] :
                                  ( ~ ( SV438 @ SY2802 )
                                  | ( SY2801 = SY2802 ) ) ) )
              | ~ ( ~ ~ ! [SY2803: $i] :
                          ~ ~ ( ~ ( SV438 @ SY2803 )
                              | ~ ! [SY2804: $i] :
                                    ( ~ ( SV438 @ SY2804 )
                                    | ( SY2803 = SY2804 ) ) )
                  | ~ ! [SY2394: $i] :
                        ~ ~ ( ~ ( SV214 @ SY2394 )
                            | ~ ! [SY2395: $i] :
                                  ( ~ ( SV214 @ SY2395 )
                                  | ( SY2394 = SY2395 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2987]) ).

thf(3132,plain,
    ! [SV216: $i,SV440: $i > $o,SV573: $i] :
      ( ( ( in @ ( sK56_SY3006 @ SV573 @ SV440 @ SV216 ) @ SV216 )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV216
            @ ^ [SY2811: $i] : ( SV440 @ SY2811 ) ) )
        = $true )
      | ( ( SV440 @ SV573 )
        = $false )
      | ( ( in @ SV573 @ SV216 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2988]) ).

thf(3133,plain,
    ! [SV216: $i,SV573: $i,SV440: $i > $o] :
      ( ( ( ~ ( SV440 @ ( sK56_SY3006 @ SV573 @ SV440 @ SV216 ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV216
            @ ^ [SY2811: $i] : ( SV440 @ SY2811 ) ) )
        = $true )
      | ( ( SV440 @ SV573 )
        = $false )
      | ( ( in @ SV573 @ SV216 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2989]) ).

thf(3134,plain,
    ! [SV216: $i,SV440: $i > $o,SV573: $i] :
      ( ( ( ( sK56_SY3006 @ SV573 @ SV440 @ SV216 )
          = SV573 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV216
            @ ^ [SY2811: $i] : ( SV440 @ SY2811 ) ) )
        = $true )
      | ( ( SV440 @ SV573 )
        = $false )
      | ( ( in @ SV573 @ SV216 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2989]) ).

thf(3135,plain,
    ! [SV221: $i,SV445: $i,SV579: $i,SV721: $i] :
      ( ( ( ~ ( in @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ SV221 ) )
        = $false )
      | ( ( ~ ! [SY3142: $i] :
                ( ~ ( in @ SY3142 @ SV221 )
                | ! [SY3143: $i] :
                    ( ~ ( in @ SY3143 @ SV445 )
                    | ~ ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV721 )
                    | ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV579 ) ) )
          | ( SV579 = SV721 ) )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2990]) ).

thf(3136,plain,
    ! [SV221: $i,SV579: $i,SV721: $i,SV445: $i] :
      ( ( ( ! [SY3182: $i] :
              ( ~ ( in @ SY3182 @ SV445 )
              | ~ ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ SY3182 ) @ SV579 )
              | ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ SY3182 ) @ SV721 ) ) )
        = $false )
      | ( ( ~ ! [SY3142: $i] :
                ( ~ ( in @ SY3142 @ SV221 )
                | ! [SY3143: $i] :
                    ( ~ ( in @ SY3143 @ SV445 )
                    | ~ ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV721 )
                    | ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV579 ) ) )
          | ( SV579 = SV721 ) )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2990]) ).

thf(3137,plain,
    ! [SV751: $i,SV663: $i,SV451: $i,SV228: $i,SV769: $i] :
      ( ( ( ~ ( in @ SV769 @ SV228 ) )
        = $true )
      | ( ( ~ ( in @ SV769 @ ( binintersect @ SV451 @ SV663 ) )
          | ( in @ SV769 @ ( binunion @ SV663 @ SV751 ) ) )
        = $true )
      | ( ( in @ SV751 @ ( powerset @ SV228 ) )
        = $false )
      | ( ( in @ SV663 @ ( powerset @ SV228 ) )
        = $false )
      | ( ( in @ SV451 @ ( powerset @ SV228 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2991]) ).

thf(3138,plain,
    ! [SV231: $i,SV454: $i,SV664: $i] :
      ( ( ( in @ ( sK57_SY3103 @ SV664 @ SV454 @ SV231 ) @ SV231 )
        = $true )
      | ( ( in @ SV454 @ ( powerset @ SV664 ) )
        = $true )
      | ( ( in @ SV664 @ ( powerset @ SV231 ) )
        = $false )
      | ( ( in @ SV454 @ ( powerset @ SV231 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2995]) ).

thf(3139,plain,
    ! [SV231: $i,SV454: $i,SV664: $i] :
      ( ( ( ~ ( in @ ( sK57_SY3103 @ SV664 @ SV454 @ SV231 ) @ SV454 ) )
        = $false )
      | ( ( in @ SV454 @ ( powerset @ SV664 ) )
        = $true )
      | ( ( in @ SV664 @ ( powerset @ SV231 ) )
        = $false )
      | ( ( in @ SV454 @ ( powerset @ SV231 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2996]) ).

thf(3140,plain,
    ! [SV231: $i,SV454: $i,SV664: $i] :
      ( ( ( in @ ( sK57_SY3103 @ SV664 @ SV454 @ SV231 ) @ SV664 )
        = $false )
      | ( ( in @ SV454 @ ( powerset @ SV664 ) )
        = $true )
      | ( ( in @ SV664 @ ( powerset @ SV231 ) )
        = $false )
      | ( ( in @ SV454 @ ( powerset @ SV231 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2996]) ).

thf(3141,plain,
    ! [SV243: $i,SV466: $i,SV665: $i] :
      ( ( ( in @ ( sK58_SY3104 @ SV665 @ SV466 @ SV243 ) @ SV243 )
        = $true )
      | ( ( subset @ SV466 @ SV665 )
        = $true )
      | ( ( in @ SV665 @ ( powerset @ SV243 ) )
        = $false )
      | ( ( in @ SV466 @ ( powerset @ SV243 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2997]) ).

thf(3142,plain,
    ! [SV243: $i,SV466: $i,SV665: $i] :
      ( ( ( ~ ( in @ ( sK58_SY3104 @ SV665 @ SV466 @ SV243 ) @ SV466 ) )
        = $false )
      | ( ( subset @ SV466 @ SV665 )
        = $true )
      | ( ( in @ SV665 @ ( powerset @ SV243 ) )
        = $false )
      | ( ( in @ SV466 @ ( powerset @ SV243 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2998]) ).

thf(3143,plain,
    ! [SV243: $i,SV466: $i,SV665: $i] :
      ( ( ( in @ ( sK58_SY3104 @ SV665 @ SV466 @ SV243 ) @ SV665 )
        = $false )
      | ( ( subset @ SV466 @ SV665 )
        = $true )
      | ( ( in @ SV665 @ ( powerset @ SV243 ) )
        = $false )
      | ( ( in @ SV466 @ ( powerset @ SV243 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2998]) ).

thf(3144,plain,
    ! [SV666: $i,SV469: $i,SV246: $i,SV753: $i] :
      ( ( ( in @ SV753 @ ( setminus @ SV246 @ SV469 ) )
        = $false )
      | ( ( ~ ( in @ SV753 @ ( binintersect @ SV469 @ SV666 ) ) )
        = $true )
      | ( ( in @ SV753 @ SV246 )
        = $false )
      | ( ( in @ SV666 @ ( powerset @ SV246 ) )
        = $false )
      | ( ( in @ SV469 @ ( powerset @ SV246 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3000]) ).

thf(3145,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $true )
      | ( ( ~ ( ( ( sK37_SY3106 @ SV667 @ SV253 )
               != SV667 )
              | ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2491: $i] :
                ~ ~ ( ~ ( SV253 @ SY2491 )
                    | ~ ! [SY2492: $i] :
                          ( ~ ( SV253 @ SY2492 )
                          | ( SY2491 = SY2492 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3001]) ).

thf(3146,plain,
    ! [SV253: $i > $o,SV667: $i] :
      ( ( ( ( ( sK37_SY3106 @ SV667 @ SV253 )
           != SV667 )
          | ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) ) )
        = $false )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $false )
      | ( ( ~ ! [SY2491: $i] :
                ~ ~ ( ~ ( SV253 @ SY2491 )
                    | ~ ! [SY2492: $i] :
                          ( ~ ( SV253 @ SY2492 )
                          | ( SY2491 = SY2492 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3002]) ).

thf(3147,plain,
    ! [SV281: $i > $o,SV35: $i,SV770: $i] :
      ( ( ( ~ ( in @ SV770 @ SV35 ) )
        = $true )
      | ( ( ~ ( SV281 @ SV770 ) )
        = $true )
      | ( ( in @ ( sK30_SY2514 @ SV281 @ SV35 ) @ SV35 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3006]) ).

thf(3148,plain,
    ! [SV281: $i > $o,SV35: $i,SV771: $i] :
      ( ( ( ~ ( in @ SV771 @ SV35 ) )
        = $true )
      | ( ( ~ ( SV281 @ SV771 ) )
        = $true )
      | ( ( SV281 @ ( sK30_SY2514 @ SV281 @ SV35 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3007]) ).

thf(3149,plain,
    ! [SV36: $i,SV282: $i,SV619: $i,SV734: $i] :
      ( ( ( ~ ~ ( in @ SV734 @ SV619 ) )
        = $true )
      | ( ( ~ ( in @ SV734 @ SV282 ) )
        = $true )
      | ( ( subset @ SV282 @ SV619 )
        = $false )
      | ( ( in @ SV734 @ SV36 )
        = $false )
      | ( ( in @ SV619 @ ( powerset @ SV36 ) )
        = $false )
      | ( ( in @ SV282 @ ( powerset @ SV36 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3008]) ).

thf(3150,plain,
    ! [SV620: $i,SV37: $i > $o] :
      ( ( ( SV37 @ ( sK59_SY3056 @ SV620 @ SV37 ) )
        = $true )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( ~ ! [SY1897: $i] :
                ~ ! [SY1898: $i] :
                    ~ ( ~ ( ~ ( SV37 @ SY1898 )
                          | ( SY1898 = SY1897 ) )
                      | ~ ( ( SY1898 != SY1897 )
                          | ( SV37 @ SY1898 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3009]) ).

thf(3151,plain,
    ! [SV620: $i,SV37: $i > $o] :
      ( ( ( ! [SY1897: $i] :
              ~ ! [SY1898: $i] :
                  ~ ( ~ ( ~ ( SV37 @ SY1898 )
                        | ( SY1898 = SY1897 ) )
                    | ~ ( ( SY1898 != SY1897 )
                        | ( SV37 @ SY1898 ) ) ) )
        = $false )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( SV620
          = ( sK59_SY3056 @ SV620 @ SV37 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3010]) ).

thf(3152,plain,
    ! [SV621: $i,SV41: $i > $o] :
      ( ( ( SV41 @ ( sK60_SY3057 @ SV621 @ SV41 ) )
        = $true )
      | ( ( SV41 @ SV621 )
        = $false )
      | ( ( ! [SY1909: $i,SY1910: $i] :
              ( ~ ( SV41 @ SY1909 )
              | ~ ( SV41 @ SY1910 )
              | ( SY1909 = SY1910 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3011]) ).

thf(3153,plain,
    ! [SV621: $i,SV778: $i,SV41: $i > $o] :
      ( ( ( ! [SY3186: $i] :
              ( ~ ( SV41 @ SV778 )
              | ~ ( SV41 @ SY3186 )
              | ( SV778 = SY3186 ) ) )
        = $true )
      | ( ( SV41 @ SV621 )
        = $false )
      | ( ( SV621
          = ( sK60_SY3057 @ SV621 @ SV41 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3012]) ).

thf(3154,plain,
    ! [SV622: $i,SV43: $i > $o] :
      ( ( ( SV43 @ ( sK61_SY3058 @ SV622 @ SV43 ) )
        = $true )
      | ( ( SV43 @ SV622 )
        = $false )
      | ( ( ! [SY1916: $i,SY1917: $i] :
              ( ~ ( SV43 @ SY1916 )
              | ~ ( SV43 @ SY1917 )
              | ( SY1916 = SY1917 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3013]) ).

thf(3155,plain,
    ! [SV622: $i,SV779: $i,SV43: $i > $o] :
      ( ( ( ! [SY3187: $i] :
              ( ~ ( SV43 @ SV779 )
              | ~ ( SV43 @ SY3187 )
              | ( SV779 = SY3187 ) ) )
        = $true )
      | ( ( SV43 @ SV622 )
        = $false )
      | ( ( SV622
          = ( sK61_SY3058 @ SV622 @ SV43 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3014]) ).

thf(3156,plain,
    ! [SV623: $i,SV44: $i,SV286: $i,SV736: $i] :
      ( ( ( in @ SV736 @ SV286 )
        = $false )
      | ( ( in @ SV736 @ ( setminus @ SV44 @ ( binunion @ SV286 @ SV623 ) ) )
        = $false )
      | ( ( in @ SV736 @ SV44 )
        = $false )
      | ( ( in @ SV623 @ ( powerset @ SV44 ) )
        = $false )
      | ( ( in @ SV286 @ ( powerset @ SV44 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3015]) ).

thf(3157,plain,
    ! [SV673: $i,SV287: $i > $o,SV46: $i] :
      ( ( ( ! [SY2528: $i] :
              ( ~ ( in @ SY2528 @ SV46 )
              | ( SV287 @ SY2528 ) ) )
        = $false )
      | ( ( in @ SV673 @ SV46 )
        = $false )
      | ( ( SV287 @ SV673 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3016]) ).

thf(3158,plain,
    ! [SV624: $i,SV48: $i > $o] :
      ( ( ( SV48 @ ( sK62_SY3060 @ SV624 @ SV48 ) )
        = $true )
      | ( ( SV48 @ SV624 )
        = $false )
      | ( ( ~ ! [SY1928: $i] :
                ~ ~ ( ~ ( SV48 @ SY1928 )
                    | ~ ! [SY1929: $i] :
                          ( ~ ( SV48 @ SY1929 )
                          | ( SY1928 = SY1929 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3017]) ).

thf(3159,plain,
    ! [SV624: $i,SV48: $i > $o] :
      ( ( ( ! [SY1928: $i] :
              ~ ~ ( ~ ( SV48 @ SY1928 )
                  | ~ ! [SY1929: $i] :
                        ( ~ ( SV48 @ SY1929 )
                        | ( SY1928 = SY1929 ) ) ) )
        = $false )
      | ( ( SV48 @ SV624 )
        = $false )
      | ( ( SV624
          = ( sK62_SY3060 @ SV624 @ SV48 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3018]) ).

thf(3160,plain,
    ! [SV51: $i,SV291: $i] :
      ( ( ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV291 )
        = $true )
      | ( ( in @ ( sK6_SY2533 @ SV291 @ SV51 ) @ SV51 )
        = $true )
      | ( ( SV51 = SV291 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3019]) ).

thf(3161,plain,
    ! [SV292: $i > $o,SV52: $i,SV772: $i] :
      ( ( ( ~ ( in @ SV772 @ SV52 ) )
        = $true )
      | ( ( ~ ( SV292 @ SV772 ) )
        = $true )
      | ( ( in @ ( sK31_SY2534 @ SV292 @ SV52 ) @ SV52 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3022]) ).

thf(3162,plain,
    ! [SV292: $i > $o,SV52: $i,SV773: $i] :
      ( ( ( ~ ( in @ SV773 @ SV52 ) )
        = $true )
      | ( ( ~ ( SV292 @ SV773 ) )
        = $true )
      | ( ( SV292 @ ( sK31_SY2534 @ SV292 @ SV52 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3023]) ).

thf(3163,plain,
    ! [SV63: $i,SV302: $i,SV676: $i > $o,SV496: $i,SV774: $i] :
      ( ( ( ~ ( in @ SV774 @ SV496 ) )
        = $true )
      | ( ( SV676 @ SV774 )
        = $true )
      | ( ( in @ ( sK44_SY3111 @ SV676 @ SV496 @ SV302 @ SV63 ) @ SV63 )
        = $true )
      | ( ( subset @ SV496 @ ( cartprod @ SV63 @ SV302 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3024]) ).

thf(3164,plain,
    ! [SV302: $i,SV676: $i > $o,SV496: $i,SV63: $i] :
      ( ( ( in @ ( sK63_SY3167 @ SV63 @ SV496 @ SV676 @ SV302 ) @ SV302 )
        = $true )
      | ( ( ! [SY3113: $i] :
              ( ~ ( in @ SY3113 @ SV496 )
              | ( SV676 @ SY3113 ) ) )
        = $true )
      | ( ( subset @ SV496 @ ( cartprod @ SV63 @ SV302 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3025]) ).

thf(3165,plain,
    ! [SV63: $i,SV302: $i,SV496: $i,SV676: $i > $o] :
      ( ( ( ~ ( in @ ( kpair @ ( sK44_SY3111 @ SV676 @ SV496 @ SV302 @ SV63 ) @ ( sK63_SY3167 @ SV63 @ SV496 @ SV676 @ SV302 ) ) @ SV496 ) )
        = $false )
      | ( ( ! [SY3113: $i] :
              ( ~ ( in @ SY3113 @ SV496 )
              | ( SV676 @ SY3113 ) ) )
        = $true )
      | ( ( subset @ SV496 @ ( cartprod @ SV63 @ SV302 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3026]) ).

thf(3166,plain,
    ! [SV63: $i,SV302: $i,SV496: $i,SV676: $i > $o] :
      ( ( ( SV676 @ ( kpair @ ( sK44_SY3111 @ SV676 @ SV496 @ SV302 @ SV63 ) @ ( sK63_SY3167 @ SV63 @ SV496 @ SV676 @ SV302 ) ) )
        = $false )
      | ( ( ! [SY3113: $i] :
              ( ~ ( in @ SY3113 @ SV496 )
              | ( SV676 @ SY3113 ) ) )
        = $true )
      | ( ( subset @ SV496 @ ( cartprod @ SV63 @ SV302 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3026]) ).

thf(3167,plain,
    ! [SV73: $i,SV311: $i,SV502: $i,SV681: $i] :
      ( ( ( in @ ( sK64_SY3118 @ SV681 @ SV502 @ SV311 @ SV73 ) @ SV73 )
        = $true )
      | ( ( SV502 = SV681 )
        = $true )
      | ( ( in @ SV681 @ ( funcSet @ SV73 @ SV311 ) )
        = $false )
      | ( ( in @ SV502 @ ( funcSet @ SV73 @ SV311 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3027]) ).

thf(3168,plain,
    ! [SV737: $i,SV627: $i,SV314: $i,SV76: $i,SV763: $i] :
      ( ( ( in @ SV763 @ SV76 )
        = $false )
      | ( ( ~ ( in @ SV763 @ ( binintersect @ SV314 @ SV627 ) )
          | ( in @ SV763 @ ( binintersect @ ( binunion @ SV314 @ SV737 ) @ ( binunion @ SV627 @ SV737 ) ) ) )
        = $true )
      | ( ( in @ SV737 @ ( powerset @ SV76 ) )
        = $false )
      | ( ( in @ SV627 @ ( powerset @ SV76 ) )
        = $false )
      | ( ( in @ SV314 @ ( powerset @ SV76 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3029]) ).

thf(3169,plain,
    ! [SV315: $i > $o,SV775: $i,SV77: $i > $o] :
      ( ( ( ~ ( ~ ( SV77 @ SV775 )
              | ~ ! [SY3183: $i] :
                    ( ~ ( SV77 @ SY3183 )
                    | ( SV775 = SY3183 ) ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3030]) ).

thf(3170,plain,
    ! [SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
          | ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( ~ ~ ! [SY2001: $i] :
                  ~ ~ ( ~ ( SV77 @ SY2001 )
                      | ~ ! [SY2002: $i] :
                            ( ~ ( SV77 @ SY2002 )
                            | ( SY2001 = SY2002 ) ) )
          | ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3031]) ).

thf(3171,plain,
    ! [SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( ~ ~ ! [SY2001: $i] :
                  ~ ~ ( ~ ( SV77 @ SY2001 )
                      | ~ ! [SY2002: $i] :
                            ( ~ ( SV77 @ SY2002 )
                            | ( SY2001 = SY2002 ) ) )
          | ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3032]) ).

thf(3172,plain,
    ! [SV315: $i > $o,SV77: $i > $o] :
      ( ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( ~ ~ ! [SY2001: $i] :
                  ~ ~ ( ~ ( SV77 @ SY2001 )
                      | ~ ! [SY2002: $i] :
                            ( ~ ( SV77 @ SY2002 )
                            | ( SY2001 = SY2002 ) ) )
          | ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3032]) ).

thf(3173,plain,
    ! [SV318: $i,SV628: $i,SV80: $i] :
      ( ( ( ~ ! [SY3067: $i] :
                ( ~ ( in @ SY3067 @ SV80 )
                | ~ ( in @ SY3067 @ SV628 )
                | ( in @ SY3067 @ SV318 ) ) )
        = $true )
      | ( ( SV318 = SV628 )
        = $true )
      | ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV80 )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3033]) ).

thf(3174,plain,
    ! [SV80: $i,SV318: $i,SV628: $i] :
      ( ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV318 )
        = $true )
      | ( ( ~ ! [SY3067: $i] :
                ( ~ ( in @ SY3067 @ SV80 )
                | ~ ( in @ SY3067 @ SV628 )
                | ( in @ SY3067 @ SV318 ) )
          | ( SV318 = SV628 ) )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3034]) ).

thf(3175,plain,
    ! [SV318: $i,SV628: $i,SV80: $i] :
      ( ( ( ~ ! [SY3067: $i] :
                ( ~ ( in @ SY3067 @ SV80 )
                | ~ ( in @ SY3067 @ SV628 )
                | ( in @ SY3067 @ SV318 ) ) )
        = $true )
      | ( ( SV318 = SV628 )
        = $true )
      | ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV628 )
        = $false )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3035]) ).

thf(3176,plain,
    ! [SV84: $i,SV321: $i > $o,SV682: $i] :
      ( ( ( ~ ( in @ ( sK53_SY2593 @ SV682 @ SV321 @ SV84 ) @ SV84 ) )
        = $false )
      | ( ( SV321 @ SV682 )
        = $true )
      | ( ( in @ SV682 @ SV84 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3037]) ).

thf(3177,plain,
    ! [SV84: $i,SV682: $i,SV321: $i > $o] :
      ( ( ( ~ ~ ( SV321 @ ( sK53_SY2593 @ SV682 @ SV321 @ SV84 ) ) )
        = $false )
      | ( ( SV321 @ SV682 )
        = $true )
      | ( ( in @ SV682 @ SV84 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3037]) ).

thf(3178,plain,
    ! [SV85: $i,SV609: $o,SV322: $i,SV507: $i] :
      ( ( ( ~ ( in @ SV507 @ SV322 ) )
        = $false )
      | ( SV609 = $true )
      | ( ( in @ SV507 @ SV85 )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3038]) ).

thf(3179,plain,
    ! [SV322: $i,SV85: $i,SV507: $i,SV609: $o] :
      ( ( SV609 = $false )
      | ( SV609 = $true )
      | ( ( in @ SV507 @ SV85 )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3038]) ).

thf(3180,plain,
    ! [SV85: $i,SV609: $o,SV322: $i,SV507: $i] :
      ( ( ( in @ SV507 @ SV322 )
        = $true )
      | ( SV609 = $true )
      | ( SV609 = $false )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3039]) ).

thf(3181,plain,
    ! [SV85: $i,SV322: $i,SV507: $i] :
      ( ( ( ~ ( in @ SV507 @ SV322 ) )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV507 @ SV85 )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3041]) ).

thf(3182,plain,
    ! [SV322: $i,SV85: $i,SV507: $i] :
      ( ( $true = $false )
      | ( $true = $true )
      | ( ( in @ SV507 @ SV85 )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3041]) ).

thf(3183,plain,
    ! [SV85: $i,SV322: $i,SV507: $i] :
      ( ( ( in @ SV507 @ SV322 )
        = $true )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3042]) ).

thf(3184,plain,
    ! [SV85: $i,SV322: $i,SV507: $i] :
      ( ( ( ~ ( in @ SV507 @ SV322 ) )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV507 @ SV85 )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3044]) ).

thf(3185,plain,
    ! [SV322: $i,SV85: $i,SV507: $i] :
      ( ( $false = $false )
      | ( $false = $true )
      | ( ( in @ SV507 @ SV85 )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3044]) ).

thf(3186,plain,
    ! [SV85: $i,SV322: $i,SV507: $i] :
      ( ( ( in @ SV507 @ SV322 )
        = $true )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3045]) ).

thf(3187,plain,
    ! [SV87: $i] :
      ( ( ( in @ ( sK39_SY2033 @ SV87 ) @ omega )
        = $true )
      | ( ( in @ emptyset @ SV87 )
        = $false )
      | ( ( ! [SY2034: $i] :
              ( ~ ( in @ SY2034 @ omega )
              | ( in @ SY2034 @ SV87 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3047]) ).

thf(3188,plain,
    ! [SV87: $i] :
      ( ( ( in @ ( sK39_SY2033 @ SV87 ) @ SV87 )
        = $true )
      | ( ( in @ emptyset @ SV87 )
        = $false )
      | ( ( ! [SY2034: $i] :
              ( ~ ( in @ SY2034 @ omega )
              | ( in @ SY2034 @ SV87 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3048]) ).

thf(3189,plain,
    ! [SV324: $i,SV88: $i,SV629: $i,SV760: $i] :
      ( ( ( ~ ( in @ SV760 @ SV629 ) )
        = $true )
      | ( ( in @ SV760 @ ( setminus @ SV88 @ SV324 ) )
        = $true )
      | ( ( in @ SV760 @ SV88 )
        = $false )
      | ( ( subset @ SV324 @ ( setminus @ SV88 @ SV629 ) )
        = $false )
      | ( ( in @ SV629 @ ( powerset @ SV88 ) )
        = $false )
      | ( ( in @ SV324 @ ( powerset @ SV88 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3050]) ).

thf(3190,plain,
    ! [SV683: $i,SV325: $i > $o,SV89: $i] :
      ( ( ( ( dsetconstr @ SV89
            @ ^ [SY2603: $i] : ( SV325 @ SY2603 ) )
          = emptyset )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV683 @ SV89 )
        = $false )
      | ( ( SV325 @ SV683 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3051]) ).

thf(3191,plain,
    ! [SV96: $i,SV332: $i,SV512: $i,SV685: $i] :
      ( ( ( in @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) @ SV96 )
        = $true )
      | ( ( ! [SY3120: $i] :
              ( ~ ( in @ SY3120 @ SV96 )
              | ! [SY3121: $i] :
                  ( ~ ( in @ SY3121 @ SV332 )
                  | ~ ( in @ ( kpair @ SY3120 @ SY3121 ) @ SV685 )
                  | ( in @ ( kpair @ SY3120 @ SY3121 ) @ SV512 ) ) ) )
        = $true )
      | ( ( func @ SV96 @ SV332 @ SV685 )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV512 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3052]) ).

thf(3192,plain,
    ! [SV512: $i,SV685: $i,SV332: $i,SV96: $i,SV780: $i] :
      ( ( ( ~ ( in @ SV780 @ SV96 )
          | ! [SY3188: $i] :
              ( ~ ( in @ SY3188 @ SV332 )
              | ~ ( in @ ( kpair @ SV780 @ SY3188 ) @ SV685 )
              | ( in @ ( kpair @ SV780 @ SY3188 ) @ SV512 ) ) )
        = $true )
      | ( ( ( ap @ SV96 @ SV332 @ SV512 @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) )
          = ( ap @ SV96 @ SV332 @ SV685 @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) ) )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV685 )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV512 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3053]) ).

thf(3193,plain,
    ! [SV333: $i,SV513: $i,SV98: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK74_SY3150 @ SV98 @ SV513 @ SV333 ) @ SV333 )
                | ( SV513
                 != ( kpair @ ( sK33_SY2921 @ SV513 @ SV333 @ SV98 ) @ ( sK74_SY3150 @ SV98 @ SV513 @ SV333 ) ) ) ) )
        = $false )
      | ( ( in @ SV513 @ ( cartprod @ SV98 @ SV333 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3054]) ).

thf(3194,plain,
    ! [SV99: $i,SV633: $i,SV334: $i,SV738: $i] :
      ( ( ( ~ ( in @ SV738 @ SV334 ) )
        = $true )
      | ( ( in @ SV738 @ SV633 )
        = $true )
      | ( ( in @ SV334 @ ( powerset @ SV633 ) )
        = $false )
      | ( ( in @ SV738 @ SV99 )
        = $false )
      | ( ( in @ SV633 @ ( powerset @ SV99 ) )
        = $false )
      | ( ( in @ SV334 @ ( powerset @ SV99 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3055]) ).

thf(3195,plain,
    ! [SV336: $i > $o,SV102: $i,SV764: $i] :
      ( ( ( ~ ( in @ SV764 @ SV102 )
          | ~ ( SV336 @ SV764 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( in @ ( sK11_SY2627 @ SV336 @ SV102 ) @ SV102 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3056]) ).

thf(3196,plain,
    ! [SV336: $i > $o,SV102: $i,SV781: $i] :
      ( ( ( ~ ~ ( ~ ( in @ SV781 @ SV102 )
                | ~ ( SV336 @ SV781 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( in @ ( sK34_SY3074 @ SV336 @ SV102 ) @ SV102 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3057]) ).

thf(3197,plain,
    ! [SV336: $i > $o,SV102: $i] :
      ( ( ( ! [SY2629: $i] :
              ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                  | ~ ( SV336 @ SY2629 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( SV336 @ ( sK11_SY2627 @ SV336 @ SV102 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3058]) ).

thf(3198,plain,
    ! [SV336: $i > $o,SV102: $i] :
      ( ( ( ~ ! [SY2629: $i] :
                ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                    | ~ ( SV336 @ SY2629 ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( SV336 @ ( sK34_SY3074 @ SV336 @ SV102 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3059]) ).

thf(3199,plain,
    ! [SV336: $i > $o,SV102: $i] :
      ( ( ( ! [SY2629: $i] :
              ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                  | ~ ( SV336 @ SY2629 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( ( sK11_SY2627 @ SV336 @ SV102 )
          = ( sK34_SY3074 @ SV336 @ SV102 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3060]) ).

thf(3200,plain,
    ! [SV109: $i] :
      ( ( ! [SY2932: $i] :
            ( ~ ( in @ SY2932 @ ( sK3_SY2100 @ SV109 ) )
            | ! [SY2102: $i] :
                ( ~ ( in @ SY2102 @ SY2932 )
                | ( in @ SY2102 @ SV109 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3061]) ).

thf(3201,plain,
    ! [SV109: $i] :
      ( ( ! [SY2934: $i,SY2935: $i] :
            ( ~ ~ ( ~ ( in @ SY2934 @ SV109 )
                  | ~ ( in @ SY2935 @ SV109 ) )
            | ~ ! [SY2936: $i] :
                  ( ~ ( in @ SY2936 @ ( sK3_SY2100 @ SV109 ) )
                  | ~ ( ~ ( ~ ( in @ SY2934 @ SY2936 )
                          | ( in @ SY2935 @ SY2936 ) )
                      | ~ ( ~ ( in @ SY2935 @ SY2936 )
                          | ( in @ SY2934 @ SY2936 ) ) ) )
            | ( SY2934 = SY2935 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[3062]) ).

thf(3202,plain,
    ! [SV776: $i,SV109: $i,SV765: $i] :
      ( ( ( ~ ~ ( ~ ( in @ SV765 @ ( sK3_SY2100 @ SV109 ) )
                | ~ ( in @ SV776 @ ( sK3_SY2100 @ SV109 ) ) ) )
        = $true )
      | ( ( ! [SY3184: $i] :
              ( ~ ( in @ SY3184 @ SV765 )
              | ( in @ SY3184 @ SV776 ) )
          | ! [SY3185: $i] :
              ( ~ ( in @ SY3185 @ SV776 )
              | ( in @ SY3185 @ SV765 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3063]) ).

thf(3203,plain,
    ! [SV109: $i,SV739: $i] :
      ( ( ( ! [SY3154: $i] :
              ( ~ ( in @ SY3154 @ SV739 )
              | ( in @ SY3154 @ SV109 ) ) )
        = $false )
      | ( ( ~ ~ ! [SY3155: $i] :
                  ~ ( in @ SY3155 @ SV739 ) )
        = $true )
      | ( ( ~ ! [SY3156: $i] :
                ~ ~ ! [SY3157: $i] :
                      ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3156 @ ( sK3_SY2100 @ SV109 ) )
                                      | ~ ( in @ SY3157 @ SV739 ) )
                                | ~ ~ ~ ! [SY3158: $i] :
                                          ~ ~ ( ~ ( in @ SY3158 @ SY3156 )
                                              | ~ ( in @ SY3158 @ SV739 ) ) )
                          | ~ ! [SY2947: $i] :
                                ( ~ ( in @ SY2947 @ ( sK3_SY2100 @ SV109 ) )
                                | ! [SX6: $i] :
                                    ( ~ ( in @ SX6 @ SY2947 )
                                    | ( in @ SX6 @ SY3156 ) )
                                | ( in @ SY3157 @ SY2947 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3064]) ).

thf(3204,plain,
    ! [SV110: $i,SV635: $i] :
      ( ( ( ~ ! [SY3161: $i] :
                ~ ~ ( ~ ( in @ SY3161 @ ( sK40_SY2119 @ SV635 @ SV110 ) )
                    | ~ ( in @ SY3161 @ SV110 ) ) )
        = $false )
      | ( ( in @ SV635 @ SV110 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3066]) ).

thf(3205,plain,
    ! [SV636: $i,SV112: $i > $o] :
      ( ( ( SV112 @ ( sK66_SY3077 @ SV636 @ SV112 ) )
        = $true )
      | ( ( SV112 @ SV636 )
        = $false )
      | ( ( ~ ! [SY2125: $i] :
                ~ ( SV112 @ SY2125 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3067]) ).

thf(3206,plain,
    ! [SV636: $i,SV112: $i > $o] :
      ( ( ( ! [SY2125: $i] :
              ~ ( SV112 @ SY2125 ) )
        = $false )
      | ( ( SV112 @ SV636 )
        = $false )
      | ( ( SV636
          = ( sK66_SY3077 @ SV636 @ SV112 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3068]) ).

thf(3207,plain,
    ! [SV116: $i,SV637: $i,SV346: $i,SV740: $i] :
      ( ( ( in @ SV740 @ ( binunion @ SV346 @ SV637 ) )
        = $true )
      | ( ( ~ ( in @ SV740 @ SV346 ) )
        = $true )
      | ( ( in @ SV740 @ SV116 )
        = $false )
      | ( ( in @ SV637 @ ( powerset @ SV116 ) )
        = $false )
      | ( ( in @ SV346 @ ( powerset @ SV116 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3069]) ).

thf(3208,plain,
    ! [SV353: $i > $o,SV125: $i,SV766: $i] :
      ( ( ( ~ ( in @ SV766 @ SV125 )
          | ~ ( SV353 @ SV766 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( in @ ( sK12_SY2657 @ SV353 @ SV125 ) @ SV125 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3070]) ).

thf(3209,plain,
    ! [SV353: $i > $o,SV125: $i,SV782: $i] :
      ( ( ( ~ ~ ( ~ ( in @ SV782 @ SV125 )
                | ~ ( SV353 @ SV782 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( in @ ( sK36_SY3079 @ SV353 @ SV125 ) @ SV125 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3071]) ).

thf(3210,plain,
    ! [SV353: $i > $o,SV125: $i] :
      ( ( ( ! [SY2659: $i] :
              ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                  | ~ ( SV353 @ SY2659 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( SV353 @ ( sK12_SY2657 @ SV353 @ SV125 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3072]) ).

thf(3211,plain,
    ! [SV353: $i > $o,SV125: $i] :
      ( ( ( ~ ! [SY2659: $i] :
                ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                    | ~ ( SV353 @ SY2659 ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( SV353 @ ( sK36_SY3079 @ SV353 @ SV125 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3073]) ).

thf(3212,plain,
    ! [SV353: $i > $o,SV125: $i] :
      ( ( ( ! [SY2659: $i] :
              ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                  | ~ ( SV353 @ SY2659 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( ( sK12_SY2657 @ SV353 @ SV125 )
          = ( sK36_SY3079 @ SV353 @ SV125 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3074]) ).

thf(3213,plain,
    ! [SV135: $i,SV363: $i,SV690: $i > $o,SV529: $i,SV777: $i] :
      ( ( ( ~ ( in @ SV777 @ SV529 ) )
        = $true )
      | ( ( SV690 @ SV777 )
        = $true )
      | ( ( in @ ( sK46_SY3122 @ SV690 @ SV529 @ SV363 @ SV135 ) @ SV135 )
        = $true )
      | ( ( subset @ SV529 @ ( cartprod @ SV135 @ SV363 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3075]) ).

thf(3214,plain,
    ! [SV363: $i,SV690: $i > $o,SV529: $i,SV135: $i] :
      ( ( ( in @ ( sK67_SY3168 @ SV135 @ SV529 @ SV690 @ SV363 ) @ SV363 )
        = $true )
      | ( ( ! [SY3124: $i] :
              ( ~ ( in @ SY3124 @ SV529 )
              | ( SV690 @ SY3124 ) ) )
        = $true )
      | ( ( subset @ SV529 @ ( cartprod @ SV135 @ SV363 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3076]) ).

thf(3215,plain,
    ! [SV135: $i,SV363: $i,SV529: $i,SV690: $i > $o] :
      ( ( ( ~ ( in @ ( kpair @ ( sK46_SY3122 @ SV690 @ SV529 @ SV363 @ SV135 ) @ ( sK67_SY3168 @ SV135 @ SV529 @ SV690 @ SV363 ) ) @ SV529 ) )
        = $false )
      | ( ( ! [SY3124: $i] :
              ( ~ ( in @ SY3124 @ SV529 )
              | ( SV690 @ SY3124 ) ) )
        = $true )
      | ( ( subset @ SV529 @ ( cartprod @ SV135 @ SV363 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3077]) ).

thf(3216,plain,
    ! [SV135: $i,SV363: $i,SV529: $i,SV690: $i > $o] :
      ( ( ( SV690 @ ( kpair @ ( sK46_SY3122 @ SV690 @ SV529 @ SV363 @ SV135 ) @ ( sK67_SY3168 @ SV135 @ SV529 @ SV690 @ SV363 ) ) )
        = $false )
      | ( ( ! [SY3124: $i] :
              ( ~ ( in @ SY3124 @ SV529 )
              | ( SV690 @ SY3124 ) ) )
        = $true )
      | ( ( subset @ SV529 @ ( cartprod @ SV135 @ SV363 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3077]) ).

thf(3217,plain,
    ! [SV137: $i,SV365: $i,SV643: $i,SV741: $i] :
      ( ( ( in @ SV741 @ SV643 )
        = $true )
      | ( ( ~ ( in @ SV741 @ ( binintersect @ SV365 @ SV643 ) ) )
        = $true )
      | ( ( in @ SV741 @ SV137 )
        = $false )
      | ( ( in @ SV643 @ ( powerset @ SV137 ) )
        = $false )
      | ( ( in @ SV365 @ ( powerset @ SV137 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3078]) ).

thf(3218,plain,
    ! [SV142: $i,SV644: $i,SV742: $i,SV372: $i > $o] :
      ( ( ( ~ ( SV372 @ SV742 ) )
        = $true )
      | ( ( SV644 = SV742 )
        = $true )
      | ( ( SV372 @ SV644 )
        = $false )
      | ( ( in @ SV742 @ SV142 )
        = $false )
      | ( ( in @ SV644 @ SV142 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV142
            @ ^ [SY2680: $i] : ( SV372 @ SY2680 ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3079]) ).

thf(3219,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV767: $i] :
      ( ( ( ~ ( ~ ( in @ SV767 @ ( sK47_SY2690 @ SV147 @ SV377 ) )
              | ~ ! [SY3179: $i] :
                    ~ ~ ( ~ ( in @ SY3179 @ SV377 )
                        | ~ ( SV147 @ SY3179 @ SV767 ) ) ) )
        = $false )
      | ( ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3080]) ).

thf(3220,plain,
    ! [SV767: $i,SV147: $i > $i > $o,SV377: $i] :
      ( ( ( ~ ( ~ ~ ! [SY3180: $i] :
                      ~ ~ ( ~ ( in @ SY3180 @ SV377 )
                          | ~ ( SV147 @ SY3180 @ SV767 ) )
              | ( in @ SV767 @ ( sK47_SY2690 @ SV147 @ SV377 ) ) ) )
        = $false )
      | ( ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3080]) ).

thf(3221,plain,
    ! [SV743: $i,SV377: $i,SV147: $i > $i > $o] :
      ( ( ( ! [SY3162: $i] :
              ( ~ ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SY3162 )
              | ( SV743 = SY3162 ) ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( ~ ! [SY2690: $i] :
                ~ ! [SY2691: $i] :
                    ~ ( ~ ( ~ ( in @ SY2691 @ SY2690 )
                          | ~ ! [SY2692: $i] :
                                ~ ~ ( ~ ( in @ SY2692 @ SV377 )
                                    | ~ ( SV147 @ SY2692 @ SY2691 ) ) )
                      | ~ ( ~ ~ ! [SY2693: $i] :
                                  ~ ~ ( ~ ( in @ SY2693 @ SV377 )
                                      | ~ ( SV147 @ SY2693 @ SY2691 ) )
                          | ( in @ SY2691 @ SY2690 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3081]) ).

thf(3222,plain,
    ! [SV151: $i,SV645: $i,SV381: $i,SV744: $i] :
      ( ( ( in @ SV744 @ ( binunion @ SV381 @ SV645 ) )
        = $true )
      | ( ( ~ ( in @ SV744 @ SV645 ) )
        = $true )
      | ( ( in @ SV744 @ SV151 )
        = $false )
      | ( ( in @ SV645 @ ( powerset @ SV151 ) )
        = $false )
      | ( ( in @ SV381 @ ( powerset @ SV151 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3082]) ).

thf(3223,plain,
    ! [SV156: $i,SV647: $i,SV385: $i,SV745: $i] :
      ( ( ( in @ SV745 @ SV385 )
        = $true )
      | ( ( ~ ( in @ SV745 @ ( binintersect @ SV385 @ SV647 ) ) )
        = $true )
      | ( ( in @ SV745 @ SV156 )
        = $false )
      | ( ( in @ SV647 @ ( powerset @ SV156 ) )
        = $false )
      | ( ( in @ SV385 @ ( powerset @ SV156 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3083]) ).

thf(3224,plain,
    ! [SV648: $i,SV157: $i > $o] :
      ( ( ( SV157 @ ( sK68_SY3087 @ SV648 @ SV157 ) )
        = $true )
      | ( ( SV157 @ SV648 )
        = $false )
      | ( ( SV157
          @ ( descr
            @ ^ [SY2227: $i] : ( SV157 @ SY2227 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3084]) ).

thf(3225,plain,
    ! [SV160: $i,SV388: $i > $o,SV694: $i] :
      ( ( ( ~ ( in @ ( sK54_SY2705 @ SV694 @ SV388 @ SV160 ) @ SV160 ) )
        = $false )
      | ( ( SV388 @ SV694 )
        = $true )
      | ( ( in @ SV694 @ SV160 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3086]) ).

thf(3226,plain,
    ! [SV160: $i,SV694: $i,SV388: $i > $o] :
      ( ( ( ~ ~ ( SV388 @ ( sK54_SY2705 @ SV694 @ SV388 @ SV160 ) ) )
        = $false )
      | ( ( SV388 @ SV694 )
        = $true )
      | ( ( in @ SV694 @ SV160 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3086]) ).

thf(3227,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( ! [SY2244: $i] :
              ~ ~ ( ~ ( SV165 @ SY2244 )
                  | ~ ! [SY2245: $i] :
                        ( ~ ( SV165 @ SY2245 )
                        | ( SY2244 = SY2245 ) ) ) )
        = $false )
      | ( ( SV165 @ ( sK48_SY2242 @ SV651 @ SV165 ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3088]) ).

thf(3228,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( SV165 @ ( sK55_SY3172 @ SV651 @ SV165 ) )
        = $true )
      | ( ( ~ ! [SY2244: $i] :
                ~ ~ ( ~ ( SV165 @ SY2244 )
                    | ~ ! [SY2245: $i] :
                          ( ~ ( SV165 @ SY2245 )
                          | ( SY2244 = SY2245 ) ) ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3089]) ).

thf(3229,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( ! [SY2244: $i] :
              ~ ~ ( ~ ( SV165 @ SY2244 )
                  | ~ ! [SY2245: $i] :
                        ( ~ ( SV165 @ SY2245 )
                        | ( SY2244 = SY2245 ) ) ) )
        = $false )
      | ( ( ( sK48_SY2242 @ SV651 @ SV165 )
          = ( sK55_SY3172 @ SV651 @ SV165 ) )
        = $false )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3090]) ).

thf(3230,plain,
    ! [SV168: $i,SV395: $i,SV539: $i,SV695: $i] :
      ( ( ( in @ ( sK69_SY3125 @ SV695 @ SV539 @ SV395 @ SV168 ) @ SV168 )
        = $true )
      | ( ( subset @ SV539 @ SV695 )
        = $true )
      | ( ( subset @ SV695 @ ( cartprod @ SV168 @ SV395 ) )
        = $false )
      | ( ( subset @ SV539 @ ( cartprod @ SV168 @ SV395 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3091]) ).

thf(3231,plain,
    ! [SV395: $i,SV695: $i,SV539: $i,SV168: $i] :
      ( ( ( ~ ( in @ ( sK75_SY3181 @ SV168 @ SV539 @ SV695 @ SV395 ) @ SV395 )
          | ~ ( in @ ( kpair @ ( sK69_SY3125 @ SV695 @ SV539 @ SV395 @ SV168 ) @ ( sK75_SY3181 @ SV168 @ SV539 @ SV695 @ SV395 ) ) @ SV539 )
          | ( in @ ( kpair @ ( sK69_SY3125 @ SV695 @ SV539 @ SV395 @ SV168 ) @ ( sK75_SY3181 @ SV168 @ SV539 @ SV695 @ SV395 ) ) @ SV695 ) )
        = $false )
      | ( ( subset @ SV539 @ SV695 )
        = $true )
      | ( ( subset @ SV695 @ ( cartprod @ SV168 @ SV395 ) )
        = $false )
      | ( ( subset @ SV539 @ ( cartprod @ SV168 @ SV395 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3092]) ).

thf(3232,plain,
    ! [SV177: $i,SV403: $i,SV654: $i,SV749: $i] :
      ( ( ( ~ ( in @ SV749 @ SV654 ) )
        = $true )
      | ( ( ~ ( in @ SV749 @ SV403 ) )
        = $true )
      | ( ( subset @ SV403 @ ( setminus @ SV177 @ SV654 ) )
        = $false )
      | ( ( in @ SV749 @ SV177 )
        = $false )
      | ( ( in @ SV654 @ ( powerset @ SV177 ) )
        = $false )
      | ( ( in @ SV403 @ ( powerset @ SV177 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3093]) ).

thf(3233,plain,
    ! [SV411: $i,SV185: $i,SV554: $i,SV755: $i,SV700: $i] :
      ( ( ( in @ ( kpair @ SV700 @ SV755 ) @ SV554 )
        = $false )
      | ( ( ( ap @ SV185 @ SV411 @ SV554 @ SV700 )
          = SV755 )
        = $true )
      | ( ( in @ SV755 @ SV411 )
        = $false )
      | ( ( in @ SV700 @ SV185 )
        = $false )
      | ( ( func @ SV185 @ SV411 @ SV554 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3094]) ).

thf(3234,plain,
    ! [SV190: $i,SV416: $i,SV558: $i,SV701: $i] :
      ( ( ( in @ ( sK70_SY3128 @ SV701 @ SV558 @ SV416 @ SV190 ) @ SV190 )
        = $true )
      | ( ( SV558 = SV701 )
        = $true )
      | ( ( func @ SV190 @ SV416 @ SV701 )
        = $false )
      | ( ( func @ SV190 @ SV416 @ SV558 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3095]) ).

thf(3235,plain,
    ! [SV750: $i,SV657: $i,SV417: $i,SV191: $i,SV768: $i] :
      ( ( ( in @ SV768 @ SV191 )
        = $false )
      | ( ( ~ ( in @ SV768 @ ( binintersect @ SV417 @ SV657 ) )
          | ( in @ SV768 @ ( binunion @ SV417 @ SV750 ) ) )
        = $true )
      | ( ( in @ SV750 @ ( powerset @ SV191 ) )
        = $false )
      | ( ( in @ SV657 @ ( powerset @ SV191 ) )
        = $false )
      | ( ( in @ SV417 @ ( powerset @ SV191 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3097]) ).

thf(3236,plain,
    ! [SV419: $i,SV702: $i,SV193: $i,SV658: $i] :
      ( ( ( in @ SV658 @ SV193 )
        = $false )
      | ( ( in @ SV702 @ SV419 )
        = $true )
      | ( ( SV658 = SV702 )
        = $false )
      | ( ( SV193 = SV419 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3098]) ).

thf(3237,plain,
    ! [SV193: $i,SV658: $i,SV419: $i,SV702: $i] :
      ( ( ( in @ SV702 @ SV419 )
        = $false )
      | ( ( in @ SV658 @ SV193 )
        = $true )
      | ( ( SV658 = SV702 )
        = $false )
      | ( ( SV193 = SV419 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3099]) ).

thf(3238,plain,
    ! [SV424: $i,SV198: $i,SV567: $i,SV756: $i,SV710: $i] :
      ( ( ( in @ ( kpair @ SV710 @ SV756 ) @ SV567 )
        = $false )
      | ( ( ( ap @ SV198 @ SV424 @ SV567 @ SV710 )
          = SV756 )
        = $true )
      | ( ( in @ SV756 @ SV424 )
        = $false )
      | ( ( in @ SV710 @ SV198 )
        = $false )
      | ( ( in @ SV567 @ ( funcSet @ SV198 @ SV424 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3100]) ).

thf(3239,plain,
    ! [SV426: $i > $o,SV200: $i,SV761: $i] :
      ( ( ( ~ ( in @ SV761 @ SV200 ) )
        = $true )
      | ( ( ~ ( SV426 @ SV761 ) )
        = $true )
      | ( ( in @ ( sK16_SY2777 @ SV426 @ SV200 ) @ SV200 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3101]) ).

thf(3240,plain,
    ! [SV426: $i > $o,SV200: $i,SV762: $i] :
      ( ( ( ~ ( in @ SV762 @ SV200 ) )
        = $true )
      | ( ( ~ ( SV426 @ SV762 ) )
        = $true )
      | ( ( SV426 @ ( sK16_SY2777 @ SV426 @ SV200 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3102]) ).

thf(3241,plain,
    ! [SV205: $i,SV430: $i] :
      ( ( ( in @ SV430 @ ( sK49_SY2781 @ SV205 @ SV430 ) )
        = $true )
      | ( ( in @ SV430 @ ( setunion @ SV205 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3103]) ).

thf(3242,plain,
    ! [SV430: $i,SV205: $i] :
      ( ( ( in @ ( sK49_SY2781 @ SV205 @ SV430 ) @ SV205 )
        = $true )
      | ( ( in @ SV430 @ ( setunion @ SV205 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3104]) ).

thf(3243,plain,
    ! [SV205: $i,SV757: $i,SV430: $i] :
      ( ( ( in @ SV430 @ SV757 )
        = $false )
      | ( ( ~ ( in @ SV757 @ SV205 ) )
        = $true )
      | ( ( in @ SV430 @ ( setunion @ SV205 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3105]) ).

thf(3244,plain,
    ! [SV431: $i,SV712: $o,SV206: $i,SV570: $i] :
      ( ( ( ~ ~ ( in @ SV570 @ SV206 ) )
        = $false )
      | ( SV712 = $true )
      | ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3106]) ).

thf(3245,plain,
    ! [SV206: $i,SV712: $o,SV431: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV431 )
          | SV712 )
        = $false )
      | ( SV712 = $true )
      | ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3106]) ).

thf(3246,plain,
    ! [SV712: $o,SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | SV712 ) )
        = $true )
      | ( SV712 = $true )
      | ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3107]) ).

thf(3247,plain,
    ! [SV431: $i,SV712: $o,SV206: $i,SV570: $i] :
      ( ( ( ~ ~ ( in @ SV570 @ SV206 ) )
        = $false )
      | ( SV712 = $true )
      | ( SV712 = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3108]) ).

thf(3248,plain,
    ! [SV206: $i,SV712: $o,SV431: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV431 )
          | SV712 )
        = $false )
      | ( SV712 = $true )
      | ( SV712 = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3108]) ).

thf(3249,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ~ ( in @ SV570 @ SV206 ) )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3109]) ).

thf(3250,plain,
    ! [SV206: $i,SV431: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV431 )
          | $true )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3109]) ).

thf(3251,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | $true ) )
        = $true )
      | ( $true = $true )
      | ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3110]) ).

thf(3252,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ~ ( in @ SV570 @ SV206 ) )
        = $false )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3111]) ).

thf(3253,plain,
    ! [SV206: $i,SV431: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV431 )
          | $true )
        = $false )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3111]) ).

thf(3254,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ~ ( in @ SV570 @ SV206 ) )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3112]) ).

thf(3255,plain,
    ! [SV206: $i,SV431: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV431 )
          | $false )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3112]) ).

thf(3256,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ( ~ ~ ( in @ SV570 @ SV206 )
              | ~ ( in @ SV570 @ SV431 )
              | $false ) )
        = $true )
      | ( $false = $true )
      | ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3113]) ).

thf(3257,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ~ ( in @ SV570 @ SV206 ) )
        = $false )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3114]) ).

thf(3258,plain,
    ! [SV206: $i,SV431: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV431 )
          | $false )
        = $false )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3114]) ).

thf(3259,plain,
    ! [SV434: $i,SV713: $i > $o,SV659: $i > $o,SV209: $i] :
      ( ( ( in @ ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) @ SV434 )
        = $true )
      | ( ( ( dsetconstr @ SV209
            @ ^ [SY3097: $i] : ( SV659 @ SY3097 ) )
          = ( dsetconstr @ SV434
            @ ^ [SY3136: $i] : ( SV713 @ SY3136 ) ) )
        = $true )
      | ( ( SV209 = SV434 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3115]) ).

thf(3260,plain,
    ! [SV209: $i,SV434: $i,SV659: $i > $o,SV713: $i > $o] :
      ( ( ( ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 )
         != ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) )
        = $false )
      | ( ( ( dsetconstr @ SV209
            @ ^ [SY3097: $i] : ( SV659 @ SY3097 ) )
          = ( dsetconstr @ SV434
            @ ^ [SY3136: $i] : ( SV713 @ SY3136 ) ) )
        = $true )
      | ( ( SV209 = SV434 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3116]) ).

thf(3261,plain,
    ! [SV209: $i,SV434: $i,SV713: $i > $o,SV659: $i > $o] :
      ( ( ( ~ ( ~ ( ~ ( SV659 @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) )
                  | ( SV713 @ ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) ) )
              | ~ ( ~ ( SV713 @ ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) )
                  | ( SV659 @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) ) ) ) )
        = $false )
      | ( ( ( dsetconstr @ SV209
            @ ^ [SY3097: $i] : ( SV659 @ SY3097 ) )
          = ( dsetconstr @ SV434
            @ ^ [SY3136: $i] : ( SV713 @ SY3136 ) ) )
        = $true )
      | ( ( SV209 = SV434 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3116]) ).

thf(3262,plain,
    ! [SV210: $i,SV714: $o,SV435: $i,SV571: $i] :
      ( ( ( ~ ( in @ SV571 @ SV435 ) )
        = $false )
      | ( SV714 = $true )
      | ( ( SV571 = SV210 )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3117]) ).

thf(3263,plain,
    ! [SV435: $i,SV210: $i,SV571: $i,SV714: $o] :
      ( ( SV714 = $false )
      | ( SV714 = $true )
      | ( ( SV571 = SV210 )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3117]) ).

thf(3264,plain,
    ! [SV210: $i,SV714: $o,SV435: $i,SV571: $i] :
      ( ( ( in @ SV571 @ SV435 )
        = $true )
      | ( SV714 = $true )
      | ( SV714 = $false )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3118]) ).

thf(3265,plain,
    ! [SV210: $i,SV435: $i,SV571: $i] :
      ( ( ( ~ ( in @ SV571 @ SV435 ) )
        = $false )
      | ( $true = $true )
      | ( ( SV571 = SV210 )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3120]) ).

thf(3266,plain,
    ! [SV435: $i,SV210: $i,SV571: $i] :
      ( ( $true = $false )
      | ( $true = $true )
      | ( ( SV571 = SV210 )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3120]) ).

thf(3267,plain,
    ! [SV210: $i,SV435: $i,SV571: $i] :
      ( ( ( in @ SV571 @ SV435 )
        = $true )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3121]) ).

thf(3268,plain,
    ! [SV210: $i,SV435: $i,SV571: $i] :
      ( ( ( ~ ( in @ SV571 @ SV435 ) )
        = $false )
      | ( $false = $true )
      | ( ( SV571 = SV210 )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3123]) ).

thf(3269,plain,
    ! [SV435: $i,SV210: $i,SV571: $i] :
      ( ( $false = $false )
      | ( $false = $true )
      | ( ( SV571 = SV210 )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3123]) ).

thf(3270,plain,
    ! [SV210: $i,SV435: $i,SV571: $i] :
      ( ( ( in @ SV571 @ SV435 )
        = $true )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3124]) ).

thf(3271,plain,
    ! [SV660: $i,SV211: $i > $o] :
      ( ( ( SV211 @ ( sK72_SY3099 @ SV660 @ SV211 ) )
        = $true )
      | ( ( SV211 @ SV660 )
        = $false )
      | ( ( ~ ! [SY2378: $i] :
                ~ ~ ( ~ ( SV211 @ SY2378 )
                    | ~ ! [SY2379: $i] :
                          ( ~ ( SV211 @ SY2379 )
                          | ( SY2378 = SY2379 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3126]) ).

thf(3272,plain,
    ! [SV660: $i,SV211: $i > $o] :
      ( ( ( ! [SY2378: $i] :
              ~ ~ ( ~ ( SV211 @ SY2378 )
                  | ~ ! [SY2379: $i] :
                        ( ~ ( SV211 @ SY2379 )
                        | ( SY2378 = SY2379 ) ) ) )
        = $false )
      | ( ( SV211 @ SV660 )
        = $false )
      | ( ( SV660
          = ( sK72_SY3099 @ SV660 @ SV211 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3127]) ).

thf(3273,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ! [SY2388: $i] :
                ~ ~ ( ~ ( SV214 @ SY2388 )
                    | ~ ! [SY2389: $i] :
                          ( ~ ( SV214 @ SY2389 )
                          | ( SY2388 = SY2389 ) ) ) )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3128]) ).

thf(3274,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ! [SY2803: $i] :
                ~ ~ ( ~ ( SV438 @ SY2803 )
                    | ~ ! [SY2804: $i] :
                          ( ~ ( SV438 @ SY2804 )
                          | ( SY2803 = SY2804 ) ) ) )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3129]) ).

thf(3275,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
          | ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ~ ! [SY2388: $i] :
                          ~ ~ ( ~ ( SV214 @ SY2388 )
                              | ~ ! [SY2389: $i] :
                                    ( ~ ( SV214 @ SY2389 )
                                    | ( SY2388 = SY2389 ) ) )
                  | ~ ! [SY2801: $i] :
                        ~ ~ ( ~ ( SV438 @ SY2801 )
                            | ~ ! [SY2802: $i] :
                                  ( ~ ( SV438 @ SY2802 )
                                  | ( SY2801 = SY2802 ) ) ) )
              | ~ ( ~ ~ ! [SY2803: $i] :
                          ~ ~ ( ~ ( SV438 @ SY2803 )
                              | ~ ! [SY2804: $i] :
                                    ( ~ ( SV438 @ SY2804 )
                                    | ( SY2803 = SY2804 ) ) )
                  | ~ ! [SY2394: $i] :
                        ~ ~ ( ~ ( SV214 @ SY2394 )
                            | ~ ! [SY2395: $i] :
                                  ( ~ ( SV214 @ SY2395 )
                                  | ( SY2394 = SY2395 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3130]) ).

thf(3276,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( ~ ( ~ ( ~ ~ ! [SY2388: $i] :
                          ~ ~ ( ~ ( SV214 @ SY2388 )
                              | ~ ! [SY2389: $i] :
                                    ( ~ ( SV214 @ SY2389 )
                                    | ( SY2388 = SY2389 ) ) )
                  | ~ ! [SY2801: $i] :
                        ~ ~ ( ~ ( SV438 @ SY2801 )
                            | ~ ! [SY2802: $i] :
                                  ( ~ ( SV438 @ SY2802 )
                                  | ( SY2801 = SY2802 ) ) ) )
              | ~ ( ~ ~ ! [SY2803: $i] :
                          ~ ~ ( ~ ( SV438 @ SY2803 )
                              | ~ ! [SY2804: $i] :
                                    ( ~ ( SV438 @ SY2804 )
                                    | ( SY2803 = SY2804 ) ) )
                  | ~ ! [SY2394: $i] :
                        ~ ~ ( ~ ( SV214 @ SY2394 )
                            | ~ ! [SY2395: $i] :
                                  ( ~ ( SV214 @ SY2395 )
                                  | ( SY2394 = SY2395 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3131]) ).

thf(3277,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( ~ ( ~ ( ~ ~ ! [SY2388: $i] :
                          ~ ~ ( ~ ( SV214 @ SY2388 )
                              | ~ ! [SY2389: $i] :
                                    ( ~ ( SV214 @ SY2389 )
                                    | ( SY2388 = SY2389 ) ) )
                  | ~ ! [SY2801: $i] :
                        ~ ~ ( ~ ( SV438 @ SY2801 )
                            | ~ ! [SY2802: $i] :
                                  ( ~ ( SV438 @ SY2802 )
                                  | ( SY2801 = SY2802 ) ) ) )
              | ~ ( ~ ~ ! [SY2803: $i] :
                          ~ ~ ( ~ ( SV438 @ SY2803 )
                              | ~ ! [SY2804: $i] :
                                    ( ~ ( SV438 @ SY2804 )
                                    | ( SY2803 = SY2804 ) ) )
                  | ~ ! [SY2394: $i] :
                        ~ ~ ( ~ ( SV214 @ SY2394 )
                            | ~ ! [SY2395: $i] :
                                  ( ~ ( SV214 @ SY2395 )
                                  | ( SY2394 = SY2395 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3131]) ).

thf(3278,plain,
    ! [SV216: $i,SV573: $i,SV440: $i > $o] :
      ( ( ( SV440 @ ( sK56_SY3006 @ SV573 @ SV440 @ SV216 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV216
            @ ^ [SY2811: $i] : ( SV440 @ SY2811 ) ) )
        = $true )
      | ( ( SV440 @ SV573 )
        = $false )
      | ( ( in @ SV573 @ SV216 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3133]) ).

thf(3279,plain,
    ! [SV221: $i,SV445: $i,SV579: $i,SV721: $i] :
      ( ( ( in @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ SV221 )
        = $true )
      | ( ( ~ ! [SY3142: $i] :
                ( ~ ( in @ SY3142 @ SV221 )
                | ! [SY3143: $i] :
                    ( ~ ( in @ SY3143 @ SV445 )
                    | ~ ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV721 )
                    | ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV579 ) ) )
          | ( SV579 = SV721 ) )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3135]) ).

thf(3280,plain,
    ! [SV445: $i,SV721: $i,SV579: $i,SV221: $i] :
      ( ( ( ~ ( in @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) @ SV445 )
          | ~ ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV579 )
          | ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV721 ) )
        = $false )
      | ( ( ~ ! [SY3142: $i] :
                ( ~ ( in @ SY3142 @ SV221 )
                | ! [SY3143: $i] :
                    ( ~ ( in @ SY3143 @ SV445 )
                    | ~ ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV721 )
                    | ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV579 ) ) )
          | ( SV579 = SV721 ) )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3136]) ).

thf(3281,plain,
    ! [SV751: $i,SV663: $i,SV451: $i,SV228: $i,SV769: $i] :
      ( ( ( in @ SV769 @ SV228 )
        = $false )
      | ( ( ~ ( in @ SV769 @ ( binintersect @ SV451 @ SV663 ) )
          | ( in @ SV769 @ ( binunion @ SV663 @ SV751 ) ) )
        = $true )
      | ( ( in @ SV751 @ ( powerset @ SV228 ) )
        = $false )
      | ( ( in @ SV663 @ ( powerset @ SV228 ) )
        = $false )
      | ( ( in @ SV451 @ ( powerset @ SV228 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3137]) ).

thf(3282,plain,
    ! [SV231: $i,SV454: $i,SV664: $i] :
      ( ( ( in @ ( sK57_SY3103 @ SV664 @ SV454 @ SV231 ) @ SV454 )
        = $true )
      | ( ( in @ SV454 @ ( powerset @ SV664 ) )
        = $true )
      | ( ( in @ SV664 @ ( powerset @ SV231 ) )
        = $false )
      | ( ( in @ SV454 @ ( powerset @ SV231 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3139]) ).

thf(3283,plain,
    ! [SV243: $i,SV466: $i,SV665: $i] :
      ( ( ( in @ ( sK58_SY3104 @ SV665 @ SV466 @ SV243 ) @ SV466 )
        = $true )
      | ( ( subset @ SV466 @ SV665 )
        = $true )
      | ( ( in @ SV665 @ ( powerset @ SV243 ) )
        = $false )
      | ( ( in @ SV466 @ ( powerset @ SV243 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3142]) ).

thf(3284,plain,
    ! [SV246: $i,SV666: $i,SV469: $i,SV753: $i] :
      ( ( ( in @ SV753 @ ( binintersect @ SV469 @ SV666 ) )
        = $false )
      | ( ( in @ SV753 @ ( setminus @ SV246 @ SV469 ) )
        = $false )
      | ( ( in @ SV753 @ SV246 )
        = $false )
      | ( ( in @ SV666 @ ( powerset @ SV246 ) )
        = $false )
      | ( ( in @ SV469 @ ( powerset @ SV246 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3144]) ).

thf(3285,plain,
    ! [SV253: $i > $o,SV667: $i] :
      ( ( ( ( ( sK37_SY3106 @ SV667 @ SV253 )
           != SV667 )
          | ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) ) )
        = $false )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $true )
      | ( ( ~ ! [SY2491: $i] :
                ~ ~ ( ~ ( SV253 @ SY2491 )
                    | ~ ! [SY2492: $i] :
                          ( ~ ( SV253 @ SY2492 )
                          | ( SY2491 = SY2492 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3145]) ).

thf(3286,plain,
    ! [SV253: $i > $o,SV667: $i] :
      ( ( ( ( sK37_SY3106 @ SV667 @ SV253 )
         != SV667 )
        = $false )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $false )
      | ( ( ~ ! [SY2491: $i] :
                ~ ~ ( ~ ( SV253 @ SY2491 )
                    | ~ ! [SY2492: $i] :
                          ( ~ ( SV253 @ SY2492 )
                          | ( SY2491 = SY2492 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3146]) ).

thf(3287,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $false )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $false )
      | ( ( ~ ! [SY2491: $i] :
                ~ ~ ( ~ ( SV253 @ SY2491 )
                    | ~ ! [SY2492: $i] :
                          ( ~ ( SV253 @ SY2492 )
                          | ( SY2491 = SY2492 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3146]) ).

thf(3288,plain,
    ! [SV281: $i > $o,SV35: $i,SV770: $i] :
      ( ( ( in @ SV770 @ SV35 )
        = $false )
      | ( ( ~ ( SV281 @ SV770 ) )
        = $true )
      | ( ( in @ ( sK30_SY2514 @ SV281 @ SV35 ) @ SV35 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3147]) ).

thf(3289,plain,
    ! [SV281: $i > $o,SV35: $i,SV771: $i] :
      ( ( ( in @ SV771 @ SV35 )
        = $false )
      | ( ( ~ ( SV281 @ SV771 ) )
        = $true )
      | ( ( SV281 @ ( sK30_SY2514 @ SV281 @ SV35 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3148]) ).

thf(3290,plain,
    ! [SV36: $i,SV282: $i,SV619: $i,SV734: $i] :
      ( ( ( ~ ( in @ SV734 @ SV619 ) )
        = $false )
      | ( ( ~ ( in @ SV734 @ SV282 ) )
        = $true )
      | ( ( subset @ SV282 @ SV619 )
        = $false )
      | ( ( in @ SV734 @ SV36 )
        = $false )
      | ( ( in @ SV619 @ ( powerset @ SV36 ) )
        = $false )
      | ( ( in @ SV282 @ ( powerset @ SV36 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3149]) ).

thf(3291,plain,
    ! [SV620: $i,SV37: $i > $o] :
      ( ( ( ! [SY1897: $i] :
              ~ ! [SY1898: $i] :
                  ~ ( ~ ( ~ ( SV37 @ SY1898 )
                        | ( SY1898 = SY1897 ) )
                    | ~ ( ( SY1898 != SY1897 )
                        | ( SV37 @ SY1898 ) ) ) )
        = $false )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( SV37 @ ( sK59_SY3056 @ SV620 @ SV37 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3150]) ).

thf(3292,plain,
    ! [SV620: $i,SV37: $i > $o] :
      ( ( ( ~ ! [SY3189: $i] :
                ~ ( ~ ( ~ ( SV37 @ SY3189 )
                      | ( SY3189
                        = ( sK77_SY1897 @ SV620 @ SV37 ) ) )
                  | ~ ( ( SY3189
                       != ( sK77_SY1897 @ SV620 @ SV37 ) )
                      | ( SV37 @ SY3189 ) ) ) )
        = $false )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( SV620
          = ( sK59_SY3056 @ SV620 @ SV37 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3151]) ).

thf(3293,plain,
    ! [SV621: $i,SV783: $i,SV41: $i > $o] :
      ( ( ( ! [SY3190: $i] :
              ( ~ ( SV41 @ SV783 )
              | ~ ( SV41 @ SY3190 )
              | ( SV783 = SY3190 ) ) )
        = $true )
      | ( ( SV41 @ SV621 )
        = $false )
      | ( ( SV41 @ ( sK60_SY3057 @ SV621 @ SV41 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3152]) ).

thf(3294,plain,
    ! [SV621: $i,SV784: $i,SV778: $i,SV41: $i > $o] :
      ( ( ( ~ ( SV41 @ SV778 )
          | ~ ( SV41 @ SV784 )
          | ( SV778 = SV784 ) )
        = $true )
      | ( ( SV41 @ SV621 )
        = $false )
      | ( ( SV621
          = ( sK60_SY3057 @ SV621 @ SV41 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3153]) ).

thf(3295,plain,
    ! [SV622: $i,SV785: $i,SV43: $i > $o] :
      ( ( ( ! [SY3191: $i] :
              ( ~ ( SV43 @ SV785 )
              | ~ ( SV43 @ SY3191 )
              | ( SV785 = SY3191 ) ) )
        = $true )
      | ( ( SV43 @ SV622 )
        = $false )
      | ( ( SV43 @ ( sK61_SY3058 @ SV622 @ SV43 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3154]) ).

thf(3296,plain,
    ! [SV622: $i,SV786: $i,SV779: $i,SV43: $i > $o] :
      ( ( ( ~ ( SV43 @ SV779 )
          | ~ ( SV43 @ SV786 )
          | ( SV779 = SV786 ) )
        = $true )
      | ( ( SV43 @ SV622 )
        = $false )
      | ( ( SV622
          = ( sK61_SY3058 @ SV622 @ SV43 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3155]) ).

thf(3297,plain,
    ! [SV46: $i,SV287: $i > $o,SV673: $i] :
      ( ( ( ~ ( in @ ( sK78_SY2528 @ SV673 @ SV287 @ SV46 ) @ SV46 )
          | ( SV287 @ ( sK78_SY2528 @ SV673 @ SV287 @ SV46 ) ) )
        = $false )
      | ( ( in @ SV673 @ SV46 )
        = $false )
      | ( ( SV287 @ SV673 )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[3157]) ).

thf(3298,plain,
    ! [SV624: $i,SV48: $i > $o] :
      ( ( ( ! [SY1928: $i] :
              ~ ~ ( ~ ( SV48 @ SY1928 )
                  | ~ ! [SY1929: $i] :
                        ( ~ ( SV48 @ SY1929 )
                        | ( SY1928 = SY1929 ) ) ) )
        = $false )
      | ( ( SV48 @ SV624 )
        = $false )
      | ( ( SV48 @ ( sK62_SY3060 @ SV624 @ SV48 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3158]) ).

thf(3299,plain,
    ! [SV624: $i,SV48: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV48 @ ( sK79_SY1928 @ SV624 @ SV48 ) )
                | ~ ! [SY3192: $i] :
                      ( ~ ( SV48 @ SY3192 )
                      | ( ( sK79_SY1928 @ SV624 @ SV48 )
                        = SY3192 ) ) ) )
        = $false )
      | ( ( SV48 @ SV624 )
        = $false )
      | ( ( SV624
          = ( sK62_SY3060 @ SV624 @ SV48 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3159]) ).

thf(3300,plain,
    ! [SV292: $i > $o,SV52: $i,SV772: $i] :
      ( ( ( in @ SV772 @ SV52 )
        = $false )
      | ( ( ~ ( SV292 @ SV772 ) )
        = $true )
      | ( ( in @ ( sK31_SY2534 @ SV292 @ SV52 ) @ SV52 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3161]) ).

thf(3301,plain,
    ! [SV292: $i > $o,SV52: $i,SV773: $i] :
      ( ( ( in @ SV773 @ SV52 )
        = $false )
      | ( ( ~ ( SV292 @ SV773 ) )
        = $true )
      | ( ( SV292 @ ( sK31_SY2534 @ SV292 @ SV52 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3162]) ).

thf(3302,plain,
    ! [SV63: $i,SV302: $i,SV676: $i > $o,SV496: $i,SV774: $i] :
      ( ( ( in @ SV774 @ SV496 )
        = $false )
      | ( ( SV676 @ SV774 )
        = $true )
      | ( ( in @ ( sK44_SY3111 @ SV676 @ SV496 @ SV302 @ SV63 ) @ SV63 )
        = $true )
      | ( ( subset @ SV496 @ ( cartprod @ SV63 @ SV302 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3163]) ).

thf(3303,plain,
    ! [SV302: $i,SV63: $i,SV676: $i > $o,SV496: $i,SV787: $i] :
      ( ( ( ~ ( in @ SV787 @ SV496 )
          | ( SV676 @ SV787 ) )
        = $true )
      | ( ( in @ ( sK63_SY3167 @ SV63 @ SV496 @ SV676 @ SV302 ) @ SV302 )
        = $true )
      | ( ( subset @ SV496 @ ( cartprod @ SV63 @ SV302 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3164]) ).

thf(3304,plain,
    ! [SV63: $i,SV302: $i,SV496: $i,SV676: $i > $o] :
      ( ( ( in @ ( kpair @ ( sK44_SY3111 @ SV676 @ SV496 @ SV302 @ SV63 ) @ ( sK63_SY3167 @ SV63 @ SV496 @ SV676 @ SV302 ) ) @ SV496 )
        = $true )
      | ( ( ! [SY3113: $i] :
              ( ~ ( in @ SY3113 @ SV496 )
              | ( SV676 @ SY3113 ) ) )
        = $true )
      | ( ( subset @ SV496 @ ( cartprod @ SV63 @ SV302 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3165]) ).

thf(3305,plain,
    ! [SV63: $i,SV302: $i,SV676: $i > $o,SV496: $i,SV788: $i] :
      ( ( ( ~ ( in @ SV788 @ SV496 )
          | ( SV676 @ SV788 ) )
        = $true )
      | ( ( SV676 @ ( kpair @ ( sK44_SY3111 @ SV676 @ SV496 @ SV302 @ SV63 ) @ ( sK63_SY3167 @ SV63 @ SV496 @ SV676 @ SV302 ) ) )
        = $false )
      | ( ( subset @ SV496 @ ( cartprod @ SV63 @ SV302 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3166]) ).

thf(3306,plain,
    ! [SV76: $i,SV737: $i,SV627: $i,SV314: $i,SV763: $i] :
      ( ( ( ~ ( in @ SV763 @ ( binintersect @ SV314 @ SV627 ) ) )
        = $true )
      | ( ( in @ SV763 @ ( binintersect @ ( binunion @ SV314 @ SV737 ) @ ( binunion @ SV627 @ SV737 ) ) )
        = $true )
      | ( ( in @ SV763 @ SV76 )
        = $false )
      | ( ( in @ SV737 @ ( powerset @ SV76 ) )
        = $false )
      | ( ( in @ SV627 @ ( powerset @ SV76 ) )
        = $false )
      | ( ( in @ SV314 @ ( powerset @ SV76 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3168]) ).

thf(3307,plain,
    ! [SV315: $i > $o,SV775: $i,SV77: $i > $o] :
      ( ( ( ~ ( SV77 @ SV775 )
          | ~ ! [SY3183: $i] :
                ( ~ ( SV77 @ SY3183 )
                | ( SV775 = SY3183 ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3169]) ).

thf(3308,plain,
    ! [SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( ~ ~ ! [SY2001: $i] :
                  ~ ~ ( ~ ( SV77 @ SY2001 )
                      | ~ ! [SY2002: $i] :
                            ( ~ ( SV77 @ SY2002 )
                            | ( SY2001 = SY2002 ) ) )
          | ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3170]) ).

thf(3309,plain,
    ! [SV315: $i > $o,SV77: $i > $o] :
      ( ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( ~ ~ ! [SY2001: $i] :
                  ~ ~ ( ~ ( SV77 @ SY2001 )
                      | ~ ! [SY2002: $i] :
                            ( ~ ( SV77 @ SY2002 )
                            | ( SY2001 = SY2002 ) ) )
          | ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3170]) ).

thf(3310,plain,
    ! [SV77: $i > $o,SV315: $i > $o] :
      ( ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( ~ ~ ! [SY2001: $i] :
                  ~ ~ ( ~ ( SV77 @ SY2001 )
                      | ~ ! [SY2002: $i] :
                            ( ~ ( SV77 @ SY2002 )
                            | ( SY2001 = SY2002 ) ) )
          | ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3171]) ).

thf(3311,plain,
    ! [SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ~ ~ ! [SY2001: $i] :
                  ~ ~ ( ~ ( SV77 @ SY2001 )
                      | ~ ! [SY2002: $i] :
                            ( ~ ( SV77 @ SY2002 )
                            | ( SY2001 = SY2002 ) ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3172]) ).

thf(3312,plain,
    ! [SV318: $i,SV628: $i,SV80: $i] :
      ( ( ( ! [SY3067: $i] :
              ( ~ ( in @ SY3067 @ SV80 )
              | ~ ( in @ SY3067 @ SV628 )
              | ( in @ SY3067 @ SV318 ) ) )
        = $false )
      | ( ( SV318 = SV628 )
        = $true )
      | ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV80 )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3173]) ).

thf(3313,plain,
    ! [SV318: $i,SV628: $i,SV80: $i] :
      ( ( ( ~ ! [SY3067: $i] :
                ( ~ ( in @ SY3067 @ SV80 )
                | ~ ( in @ SY3067 @ SV628 )
                | ( in @ SY3067 @ SV318 ) ) )
        = $true )
      | ( ( SV318 = SV628 )
        = $true )
      | ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV318 )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3174]) ).

thf(3314,plain,
    ! [SV318: $i,SV628: $i,SV80: $i] :
      ( ( ( ! [SY3067: $i] :
              ( ~ ( in @ SY3067 @ SV80 )
              | ~ ( in @ SY3067 @ SV628 )
              | ( in @ SY3067 @ SV318 ) ) )
        = $false )
      | ( ( SV318 = SV628 )
        = $true )
      | ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV628 )
        = $false )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3175]) ).

thf(3315,plain,
    ! [SV84: $i,SV321: $i > $o,SV682: $i] :
      ( ( ( in @ ( sK53_SY2593 @ SV682 @ SV321 @ SV84 ) @ SV84 )
        = $true )
      | ( ( SV321 @ SV682 )
        = $true )
      | ( ( in @ SV682 @ SV84 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3176]) ).

thf(3316,plain,
    ! [SV84: $i,SV682: $i,SV321: $i > $o] :
      ( ( ( ~ ( SV321 @ ( sK53_SY2593 @ SV682 @ SV321 @ SV84 ) ) )
        = $true )
      | ( ( SV321 @ SV682 )
        = $true )
      | ( ( in @ SV682 @ SV84 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3177]) ).

thf(3317,plain,
    ! [SV85: $i,SV609: $o,SV322: $i,SV507: $i] :
      ( ( ( in @ SV507 @ SV322 )
        = $true )
      | ( SV609 = $true )
      | ( ( in @ SV507 @ SV85 )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3178]) ).

thf(3318,plain,
    ! [SV85: $i,SV322: $i,SV507: $i] :
      ( ( ( in @ SV507 @ SV322 )
        = $true )
      | ( $true = $true )
      | ( ( in @ SV507 @ SV85 )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3181]) ).

thf(3319,plain,
    ! [SV85: $i,SV322: $i,SV507: $i] :
      ( ( ( in @ SV507 @ SV322 )
        = $true )
      | ( $false = $true )
      | ( ( in @ SV507 @ SV85 )
        = $true )
      | ( ( in @ SV507 @ ( binunion @ SV85 @ SV322 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3184]) ).

thf(3320,plain,
    ! [SV87: $i,SV789: $i] :
      ( ( ( ~ ( in @ SV789 @ omega )
          | ( in @ SV789 @ SV87 ) )
        = $true )
      | ( ( in @ emptyset @ SV87 )
        = $false )
      | ( ( in @ ( sK39_SY2033 @ SV87 ) @ omega )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3187]) ).

thf(3321,plain,
    ! [SV87: $i,SV790: $i] :
      ( ( ( ~ ( in @ SV790 @ omega )
          | ( in @ SV790 @ SV87 ) )
        = $true )
      | ( ( in @ emptyset @ SV87 )
        = $false )
      | ( ( in @ ( sK39_SY2033 @ SV87 ) @ SV87 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3188]) ).

thf(3322,plain,
    ! [SV324: $i,SV88: $i,SV629: $i,SV760: $i] :
      ( ( ( in @ SV760 @ SV629 )
        = $false )
      | ( ( in @ SV760 @ ( setminus @ SV88 @ SV324 ) )
        = $true )
      | ( ( in @ SV760 @ SV88 )
        = $false )
      | ( ( subset @ SV324 @ ( setminus @ SV88 @ SV629 ) )
        = $false )
      | ( ( in @ SV629 @ ( powerset @ SV88 ) )
        = $false )
      | ( ( in @ SV324 @ ( powerset @ SV88 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3189]) ).

thf(3323,plain,
    ! [SV512: $i,SV685: $i,SV332: $i,SV96: $i,SV791: $i] :
      ( ( ( ~ ( in @ SV791 @ SV96 )
          | ! [SY3193: $i] :
              ( ~ ( in @ SY3193 @ SV332 )
              | ~ ( in @ ( kpair @ SV791 @ SY3193 ) @ SV685 )
              | ( in @ ( kpair @ SV791 @ SY3193 ) @ SV512 ) ) )
        = $true )
      | ( ( in @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) @ SV96 )
        = $true )
      | ( ( func @ SV96 @ SV332 @ SV685 )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV512 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3191]) ).

thf(3324,plain,
    ! [SV512: $i,SV685: $i,SV332: $i,SV96: $i,SV780: $i] :
      ( ( ( ~ ( in @ SV780 @ SV96 ) )
        = $true )
      | ( ( ! [SY3188: $i] :
              ( ~ ( in @ SY3188 @ SV332 )
              | ~ ( in @ ( kpair @ SV780 @ SY3188 ) @ SV685 )
              | ( in @ ( kpair @ SV780 @ SY3188 ) @ SV512 ) ) )
        = $true )
      | ( ( ( ap @ SV96 @ SV332 @ SV512 @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) )
          = ( ap @ SV96 @ SV332 @ SV685 @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) ) )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV685 )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV512 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3192]) ).

thf(3325,plain,
    ! [SV333: $i,SV513: $i,SV98: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK74_SY3150 @ SV98 @ SV513 @ SV333 ) @ SV333 )
              | ( SV513
               != ( kpair @ ( sK33_SY2921 @ SV513 @ SV333 @ SV98 ) @ ( sK74_SY3150 @ SV98 @ SV513 @ SV333 ) ) ) ) )
        = $true )
      | ( ( in @ SV513 @ ( cartprod @ SV98 @ SV333 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3193]) ).

thf(3326,plain,
    ! [SV99: $i,SV633: $i,SV334: $i,SV738: $i] :
      ( ( ( in @ SV738 @ SV334 )
        = $false )
      | ( ( in @ SV738 @ SV633 )
        = $true )
      | ( ( in @ SV334 @ ( powerset @ SV633 ) )
        = $false )
      | ( ( in @ SV738 @ SV99 )
        = $false )
      | ( ( in @ SV633 @ ( powerset @ SV99 ) )
        = $false )
      | ( ( in @ SV334 @ ( powerset @ SV99 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3194]) ).

thf(3327,plain,
    ! [SV336: $i > $o,SV102: $i,SV764: $i] :
      ( ( ( ~ ( in @ SV764 @ SV102 ) )
        = $true )
      | ( ( ~ ( SV336 @ SV764 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( in @ ( sK11_SY2627 @ SV336 @ SV102 ) @ SV102 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3195]) ).

thf(3328,plain,
    ! [SV336: $i > $o,SV102: $i,SV781: $i] :
      ( ( ( ~ ( ~ ( in @ SV781 @ SV102 )
              | ~ ( SV336 @ SV781 ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( in @ ( sK34_SY3074 @ SV336 @ SV102 ) @ SV102 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3196]) ).

thf(3329,plain,
    ! [SV336: $i > $o,SV102: $i,SV792: $i] :
      ( ( ( ~ ~ ( ~ ( in @ SV792 @ SV102 )
                | ~ ( SV336 @ SV792 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( SV336 @ ( sK11_SY2627 @ SV336 @ SV102 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3197]) ).

thf(3330,plain,
    ! [SV336: $i > $o,SV102: $i] :
      ( ( ( ! [SY2629: $i] :
              ~ ~ ( ~ ( in @ SY2629 @ SV102 )
                  | ~ ( SV336 @ SY2629 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( SV336 @ ( sK34_SY3074 @ SV336 @ SV102 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3198]) ).

thf(3331,plain,
    ! [SV336: $i > $o,SV102: $i,SV793: $i] :
      ( ( ( ~ ~ ( ~ ( in @ SV793 @ SV102 )
                | ~ ( SV336 @ SV793 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( ( sK11_SY2627 @ SV336 @ SV102 )
          = ( sK34_SY3074 @ SV336 @ SV102 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3199]) ).

thf(3332,plain,
    ! [SV109: $i,SV794: $i] :
      ( ( ~ ( in @ SV794 @ ( sK3_SY2100 @ SV109 ) )
        | ! [SY3194: $i] :
            ( ~ ( in @ SY3194 @ SV794 )
            | ( in @ SY3194 @ SV109 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3200]) ).

thf(3333,plain,
    ! [SV109: $i,SV795: $i] :
      ( ( ! [SY3195: $i] :
            ( ~ ~ ( ~ ( in @ SV795 @ SV109 )
                  | ~ ( in @ SY3195 @ SV109 ) )
            | ~ ! [SY3196: $i] :
                  ( ~ ( in @ SY3196 @ ( sK3_SY2100 @ SV109 ) )
                  | ~ ( ~ ( ~ ( in @ SV795 @ SY3196 )
                          | ( in @ SY3195 @ SY3196 ) )
                      | ~ ( ~ ( in @ SY3195 @ SY3196 )
                          | ( in @ SV795 @ SY3196 ) ) ) )
            | ( SV795 = SY3195 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3201]) ).

thf(3334,plain,
    ! [SV776: $i,SV109: $i,SV765: $i] :
      ( ( ( ~ ( ~ ( in @ SV765 @ ( sK3_SY2100 @ SV109 ) )
              | ~ ( in @ SV776 @ ( sK3_SY2100 @ SV109 ) ) ) )
        = $false )
      | ( ( ! [SY3184: $i] :
              ( ~ ( in @ SY3184 @ SV765 )
              | ( in @ SY3184 @ SV776 ) )
          | ! [SY3185: $i] :
              ( ~ ( in @ SY3185 @ SV776 )
              | ( in @ SY3185 @ SV765 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3202]) ).

thf(3335,plain,
    ! [SV739: $i,SV109: $i] :
      ( ( ( ~ ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
          | ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 ) )
        = $false )
      | ( ( ~ ~ ! [SY3155: $i] :
                  ~ ( in @ SY3155 @ SV739 ) )
        = $true )
      | ( ( ~ ! [SY3156: $i] :
                ~ ~ ! [SY3157: $i] :
                      ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3156 @ ( sK3_SY2100 @ SV109 ) )
                                      | ~ ( in @ SY3157 @ SV739 ) )
                                | ~ ~ ~ ! [SY3158: $i] :
                                          ~ ~ ( ~ ( in @ SY3158 @ SY3156 )
                                              | ~ ( in @ SY3158 @ SV739 ) ) )
                          | ~ ! [SY2947: $i] :
                                ( ~ ( in @ SY2947 @ ( sK3_SY2100 @ SV109 ) )
                                | ! [SX6: $i] :
                                    ( ~ ( in @ SX6 @ SY2947 )
                                    | ( in @ SX6 @ SY3156 ) )
                                | ( in @ SY3157 @ SY2947 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[3203]) ).

thf(3336,plain,
    ! [SV110: $i,SV635: $i] :
      ( ( ( ! [SY3161: $i] :
              ~ ~ ( ~ ( in @ SY3161 @ ( sK40_SY2119 @ SV635 @ SV110 ) )
                  | ~ ( in @ SY3161 @ SV110 ) ) )
        = $true )
      | ( ( in @ SV635 @ SV110 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3204]) ).

thf(3337,plain,
    ! [SV636: $i,SV112: $i > $o] :
      ( ( ( ! [SY2125: $i] :
              ~ ( SV112 @ SY2125 ) )
        = $false )
      | ( ( SV112 @ SV636 )
        = $false )
      | ( ( SV112 @ ( sK66_SY3077 @ SV636 @ SV112 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3205]) ).

thf(3338,plain,
    ! [SV636: $i,SV112: $i > $o] :
      ( ( ( ~ ( SV112 @ ( sK81_SY2125 @ SV636 @ SV112 ) ) )
        = $false )
      | ( ( SV112 @ SV636 )
        = $false )
      | ( ( SV636
          = ( sK66_SY3077 @ SV636 @ SV112 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3206]) ).

thf(3339,plain,
    ! [SV116: $i,SV637: $i,SV346: $i,SV740: $i] :
      ( ( ( in @ SV740 @ SV346 )
        = $false )
      | ( ( in @ SV740 @ ( binunion @ SV346 @ SV637 ) )
        = $true )
      | ( ( in @ SV740 @ SV116 )
        = $false )
      | ( ( in @ SV637 @ ( powerset @ SV116 ) )
        = $false )
      | ( ( in @ SV346 @ ( powerset @ SV116 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3207]) ).

thf(3340,plain,
    ! [SV353: $i > $o,SV125: $i,SV766: $i] :
      ( ( ( ~ ( in @ SV766 @ SV125 ) )
        = $true )
      | ( ( ~ ( SV353 @ SV766 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( in @ ( sK12_SY2657 @ SV353 @ SV125 ) @ SV125 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3208]) ).

thf(3341,plain,
    ! [SV353: $i > $o,SV125: $i,SV782: $i] :
      ( ( ( ~ ( ~ ( in @ SV782 @ SV125 )
              | ~ ( SV353 @ SV782 ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( in @ ( sK36_SY3079 @ SV353 @ SV125 ) @ SV125 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3209]) ).

thf(3342,plain,
    ! [SV353: $i > $o,SV125: $i,SV796: $i] :
      ( ( ( ~ ~ ( ~ ( in @ SV796 @ SV125 )
                | ~ ( SV353 @ SV796 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( SV353 @ ( sK12_SY2657 @ SV353 @ SV125 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3210]) ).

thf(3343,plain,
    ! [SV353: $i > $o,SV125: $i] :
      ( ( ( ! [SY2659: $i] :
              ~ ~ ( ~ ( in @ SY2659 @ SV125 )
                  | ~ ( SV353 @ SY2659 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( SV353 @ ( sK36_SY3079 @ SV353 @ SV125 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3211]) ).

thf(3344,plain,
    ! [SV353: $i > $o,SV125: $i,SV797: $i] :
      ( ( ( ~ ~ ( ~ ( in @ SV797 @ SV125 )
                | ~ ( SV353 @ SV797 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( ( sK12_SY2657 @ SV353 @ SV125 )
          = ( sK36_SY3079 @ SV353 @ SV125 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3212]) ).

thf(3345,plain,
    ! [SV135: $i,SV363: $i,SV690: $i > $o,SV529: $i,SV777: $i] :
      ( ( ( in @ SV777 @ SV529 )
        = $false )
      | ( ( SV690 @ SV777 )
        = $true )
      | ( ( in @ ( sK46_SY3122 @ SV690 @ SV529 @ SV363 @ SV135 ) @ SV135 )
        = $true )
      | ( ( subset @ SV529 @ ( cartprod @ SV135 @ SV363 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3213]) ).

thf(3346,plain,
    ! [SV363: $i,SV135: $i,SV690: $i > $o,SV529: $i,SV798: $i] :
      ( ( ( ~ ( in @ SV798 @ SV529 )
          | ( SV690 @ SV798 ) )
        = $true )
      | ( ( in @ ( sK67_SY3168 @ SV135 @ SV529 @ SV690 @ SV363 ) @ SV363 )
        = $true )
      | ( ( subset @ SV529 @ ( cartprod @ SV135 @ SV363 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3214]) ).

thf(3347,plain,
    ! [SV135: $i,SV363: $i,SV529: $i,SV690: $i > $o] :
      ( ( ( in @ ( kpair @ ( sK46_SY3122 @ SV690 @ SV529 @ SV363 @ SV135 ) @ ( sK67_SY3168 @ SV135 @ SV529 @ SV690 @ SV363 ) ) @ SV529 )
        = $true )
      | ( ( ! [SY3124: $i] :
              ( ~ ( in @ SY3124 @ SV529 )
              | ( SV690 @ SY3124 ) ) )
        = $true )
      | ( ( subset @ SV529 @ ( cartprod @ SV135 @ SV363 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3215]) ).

thf(3348,plain,
    ! [SV135: $i,SV363: $i,SV690: $i > $o,SV529: $i,SV799: $i] :
      ( ( ( ~ ( in @ SV799 @ SV529 )
          | ( SV690 @ SV799 ) )
        = $true )
      | ( ( SV690 @ ( kpair @ ( sK46_SY3122 @ SV690 @ SV529 @ SV363 @ SV135 ) @ ( sK67_SY3168 @ SV135 @ SV529 @ SV690 @ SV363 ) ) )
        = $false )
      | ( ( subset @ SV529 @ ( cartprod @ SV135 @ SV363 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3216]) ).

thf(3349,plain,
    ! [SV137: $i,SV643: $i,SV365: $i,SV741: $i] :
      ( ( ( in @ SV741 @ ( binintersect @ SV365 @ SV643 ) )
        = $false )
      | ( ( in @ SV741 @ SV643 )
        = $true )
      | ( ( in @ SV741 @ SV137 )
        = $false )
      | ( ( in @ SV643 @ ( powerset @ SV137 ) )
        = $false )
      | ( ( in @ SV365 @ ( powerset @ SV137 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3217]) ).

thf(3350,plain,
    ! [SV142: $i,SV644: $i,SV742: $i,SV372: $i > $o] :
      ( ( ( SV372 @ SV742 )
        = $false )
      | ( ( SV644 = SV742 )
        = $true )
      | ( ( SV372 @ SV644 )
        = $false )
      | ( ( in @ SV742 @ SV142 )
        = $false )
      | ( ( in @ SV644 @ SV142 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV142
            @ ^ [SY2680: $i] : ( SV372 @ SY2680 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3218]) ).

thf(3351,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV767: $i] :
      ( ( ( ~ ( in @ SV767 @ ( sK47_SY2690 @ SV147 @ SV377 ) )
          | ~ ! [SY3179: $i] :
                ~ ~ ( ~ ( in @ SY3179 @ SV377 )
                    | ~ ( SV147 @ SY3179 @ SV767 ) ) )
        = $true )
      | ( ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3219]) ).

thf(3352,plain,
    ! [SV767: $i,SV147: $i > $i > $o,SV377: $i] :
      ( ( ( ~ ~ ! [SY3180: $i] :
                  ~ ~ ( ~ ( in @ SY3180 @ SV377 )
                      | ~ ( SV147 @ SY3180 @ SV767 ) )
          | ( in @ SV767 @ ( sK47_SY2690 @ SV147 @ SV377 ) ) )
        = $true )
      | ( ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3220]) ).

thf(3353,plain,
    ! [SV743: $i,SV377: $i,SV147: $i > $i > $o] :
      ( ( ( ~ ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
          | ( SV743
            = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( ~ ! [SY2690: $i] :
                ~ ! [SY2691: $i] :
                    ~ ( ~ ( ~ ( in @ SY2691 @ SY2690 )
                          | ~ ! [SY2692: $i] :
                                ~ ~ ( ~ ( in @ SY2692 @ SV377 )
                                    | ~ ( SV147 @ SY2692 @ SY2691 ) ) )
                      | ~ ( ~ ~ ! [SY2693: $i] :
                                  ~ ~ ( ~ ( in @ SY2693 @ SV377 )
                                      | ~ ( SV147 @ SY2693 @ SY2691 ) )
                          | ( in @ SY2691 @ SY2690 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[3221]) ).

thf(3354,plain,
    ! [SV151: $i,SV381: $i,SV645: $i,SV744: $i] :
      ( ( ( in @ SV744 @ SV645 )
        = $false )
      | ( ( in @ SV744 @ ( binunion @ SV381 @ SV645 ) )
        = $true )
      | ( ( in @ SV744 @ SV151 )
        = $false )
      | ( ( in @ SV645 @ ( powerset @ SV151 ) )
        = $false )
      | ( ( in @ SV381 @ ( powerset @ SV151 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3222]) ).

thf(3355,plain,
    ! [SV156: $i,SV647: $i,SV385: $i,SV745: $i] :
      ( ( ( in @ SV745 @ ( binintersect @ SV385 @ SV647 ) )
        = $false )
      | ( ( in @ SV745 @ SV385 )
        = $true )
      | ( ( in @ SV745 @ SV156 )
        = $false )
      | ( ( in @ SV647 @ ( powerset @ SV156 ) )
        = $false )
      | ( ( in @ SV385 @ ( powerset @ SV156 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3223]) ).

thf(3356,plain,
    ! [SV160: $i,SV388: $i > $o,SV694: $i] :
      ( ( ( in @ ( sK54_SY2705 @ SV694 @ SV388 @ SV160 ) @ SV160 )
        = $true )
      | ( ( SV388 @ SV694 )
        = $true )
      | ( ( in @ SV694 @ SV160 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3225]) ).

thf(3357,plain,
    ! [SV160: $i,SV694: $i,SV388: $i > $o] :
      ( ( ( ~ ( SV388 @ ( sK54_SY2705 @ SV694 @ SV388 @ SV160 ) ) )
        = $true )
      | ( ( SV388 @ SV694 )
        = $true )
      | ( ( in @ SV694 @ SV160 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3226]) ).

thf(3358,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV165 @ ( sK83_SY2244 @ SV651 @ SV165 ) )
                | ~ ! [SY3197: $i] :
                      ( ~ ( SV165 @ SY3197 )
                      | ( ( sK83_SY2244 @ SV651 @ SV165 )
                        = SY3197 ) ) ) )
        = $false )
      | ( ( SV165 @ ( sK48_SY2242 @ SV651 @ SV165 ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3227]) ).

thf(3359,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( ! [SY2244: $i] :
              ~ ~ ( ~ ( SV165 @ SY2244 )
                  | ~ ! [SY2245: $i] :
                        ( ~ ( SV165 @ SY2245 )
                        | ( SY2244 = SY2245 ) ) ) )
        = $false )
      | ( ( SV165 @ ( sK55_SY3172 @ SV651 @ SV165 ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3228]) ).

thf(3360,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV165 @ ( sK84_SY2244 @ SV651 @ SV165 ) )
                | ~ ! [SY3198: $i] :
                      ( ~ ( SV165 @ SY3198 )
                      | ( ( sK84_SY2244 @ SV651 @ SV165 )
                        = SY3198 ) ) ) )
        = $false )
      | ( ( ( sK48_SY2242 @ SV651 @ SV165 )
          = ( sK55_SY3172 @ SV651 @ SV165 ) )
        = $false )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3229]) ).

thf(3361,plain,
    ! [SV395: $i,SV695: $i,SV539: $i,SV168: $i] :
      ( ( ( ~ ( in @ ( sK75_SY3181 @ SV168 @ SV539 @ SV695 @ SV395 ) @ SV395 ) )
        = $false )
      | ( ( subset @ SV539 @ SV695 )
        = $true )
      | ( ( subset @ SV695 @ ( cartprod @ SV168 @ SV395 ) )
        = $false )
      | ( ( subset @ SV539 @ ( cartprod @ SV168 @ SV395 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3231]) ).

thf(3362,plain,
    ! [SV168: $i,SV395: $i,SV539: $i,SV695: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK69_SY3125 @ SV695 @ SV539 @ SV395 @ SV168 ) @ ( sK75_SY3181 @ SV168 @ SV539 @ SV695 @ SV395 ) ) @ SV539 )
          | ( in @ ( kpair @ ( sK69_SY3125 @ SV695 @ SV539 @ SV395 @ SV168 ) @ ( sK75_SY3181 @ SV168 @ SV539 @ SV695 @ SV395 ) ) @ SV695 ) )
        = $false )
      | ( ( subset @ SV539 @ SV695 )
        = $true )
      | ( ( subset @ SV695 @ ( cartprod @ SV168 @ SV395 ) )
        = $false )
      | ( ( subset @ SV539 @ ( cartprod @ SV168 @ SV395 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3231]) ).

thf(3363,plain,
    ! [SV177: $i,SV403: $i,SV654: $i,SV749: $i] :
      ( ( ( in @ SV749 @ SV654 )
        = $false )
      | ( ( ~ ( in @ SV749 @ SV403 ) )
        = $true )
      | ( ( subset @ SV403 @ ( setminus @ SV177 @ SV654 ) )
        = $false )
      | ( ( in @ SV749 @ SV177 )
        = $false )
      | ( ( in @ SV654 @ ( powerset @ SV177 ) )
        = $false )
      | ( ( in @ SV403 @ ( powerset @ SV177 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3232]) ).

thf(3364,plain,
    ! [SV191: $i,SV750: $i,SV657: $i,SV417: $i,SV768: $i] :
      ( ( ( ~ ( in @ SV768 @ ( binintersect @ SV417 @ SV657 ) ) )
        = $true )
      | ( ( in @ SV768 @ ( binunion @ SV417 @ SV750 ) )
        = $true )
      | ( ( in @ SV768 @ SV191 )
        = $false )
      | ( ( in @ SV750 @ ( powerset @ SV191 ) )
        = $false )
      | ( ( in @ SV657 @ ( powerset @ SV191 ) )
        = $false )
      | ( ( in @ SV417 @ ( powerset @ SV191 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3235]) ).

thf(3365,plain,
    ! [SV426: $i > $o,SV200: $i,SV761: $i] :
      ( ( ( in @ SV761 @ SV200 )
        = $false )
      | ( ( ~ ( SV426 @ SV761 ) )
        = $true )
      | ( ( in @ ( sK16_SY2777 @ SV426 @ SV200 ) @ SV200 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3239]) ).

thf(3366,plain,
    ! [SV426: $i > $o,SV200: $i,SV762: $i] :
      ( ( ( in @ SV762 @ SV200 )
        = $false )
      | ( ( ~ ( SV426 @ SV762 ) )
        = $true )
      | ( ( SV426 @ ( sK16_SY2777 @ SV426 @ SV200 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3240]) ).

thf(3367,plain,
    ! [SV430: $i,SV205: $i,SV757: $i] :
      ( ( ( in @ SV757 @ SV205 )
        = $false )
      | ( ( in @ SV430 @ SV757 )
        = $false )
      | ( ( in @ SV430 @ ( setunion @ SV205 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3243]) ).

thf(3368,plain,
    ! [SV431: $i,SV712: $o,SV206: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV206 ) )
        = $true )
      | ( SV712 = $true )
      | ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3244]) ).

thf(3369,plain,
    ! [SV206: $i,SV712: $o,SV431: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV431 ) )
        = $false )
      | ( SV712 = $true )
      | ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3245]) ).

thf(3370,plain,
    ! [SV431: $i,SV206: $i,SV570: $i,SV712: $o] :
      ( ( SV712 = $false )
      | ( SV712 = $true )
      | ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3245]) ).

thf(3371,plain,
    ! [SV712: $o,SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ~ ( in @ SV570 @ SV206 )
          | ~ ( in @ SV570 @ SV431 )
          | SV712 )
        = $false )
      | ( SV712 = $true )
      | ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3246]) ).

thf(3372,plain,
    ! [SV431: $i,SV712: $o,SV206: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV206 ) )
        = $true )
      | ( SV712 = $true )
      | ( SV712 = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3247]) ).

thf(3373,plain,
    ! [SV206: $i,SV712: $o,SV431: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV431 ) )
        = $false )
      | ( SV712 = $true )
      | ( SV712 = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3248]) ).

thf(3374,plain,
    ! [SV431: $i,SV206: $i,SV570: $i,SV712: $o] :
      ( ( SV712 = $false )
      | ( SV712 = $true )
      | ( SV712 = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3248]) ).

thf(3375,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV206 ) )
        = $true )
      | ( $true = $true )
      | ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3249]) ).

thf(3376,plain,
    ! [SV206: $i,SV431: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV431 ) )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3250]) ).

thf(3377,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( $true = $false )
      | ( $true = $true )
      | ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3250]) ).

thf(3378,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ~ ( in @ SV570 @ SV206 )
          | ~ ( in @ SV570 @ SV431 )
          | $true )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3251]) ).

thf(3379,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV206 ) )
        = $true )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3252]) ).

thf(3380,plain,
    ! [SV206: $i,SV431: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV431 ) )
        = $false )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3253]) ).

thf(3381,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( $true = $false )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3253]) ).

thf(3382,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV206 ) )
        = $true )
      | ( $false = $true )
      | ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3254]) ).

thf(3383,plain,
    ! [SV206: $i,SV431: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV431 ) )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3255]) ).

thf(3384,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( $false = $false )
      | ( $false = $true )
      | ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3255]) ).

thf(3385,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ~ ( in @ SV570 @ SV206 )
          | ~ ( in @ SV570 @ SV431 )
          | $false )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3256]) ).

thf(3386,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV206 ) )
        = $true )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3257]) ).

thf(3387,plain,
    ! [SV206: $i,SV431: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV431 ) )
        = $false )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3258]) ).

thf(3388,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( $false = $false )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3258]) ).

thf(3389,plain,
    ! [SV209: $i,SV434: $i,SV659: $i > $o,SV713: $i > $o] :
      ( ( ( ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 )
          = ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) )
        = $true )
      | ( ( ( dsetconstr @ SV209
            @ ^ [SY3097: $i] : ( SV659 @ SY3097 ) )
          = ( dsetconstr @ SV434
            @ ^ [SY3136: $i] : ( SV713 @ SY3136 ) ) )
        = $true )
      | ( ( SV209 = SV434 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3260]) ).

thf(3390,plain,
    ! [SV209: $i,SV434: $i,SV713: $i > $o,SV659: $i > $o] :
      ( ( ( ~ ( ~ ( SV659 @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) )
              | ( SV713 @ ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) ) )
          | ~ ( ~ ( SV713 @ ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) )
              | ( SV659 @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) ) ) )
        = $true )
      | ( ( ( dsetconstr @ SV209
            @ ^ [SY3097: $i] : ( SV659 @ SY3097 ) )
          = ( dsetconstr @ SV434
            @ ^ [SY3136: $i] : ( SV713 @ SY3136 ) ) )
        = $true )
      | ( ( SV209 = SV434 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3261]) ).

thf(3391,plain,
    ! [SV210: $i,SV714: $o,SV435: $i,SV571: $i] :
      ( ( ( in @ SV571 @ SV435 )
        = $true )
      | ( SV714 = $true )
      | ( ( SV571 = SV210 )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3262]) ).

thf(3392,plain,
    ! [SV210: $i,SV435: $i,SV571: $i] :
      ( ( ( in @ SV571 @ SV435 )
        = $true )
      | ( $true = $true )
      | ( ( SV571 = SV210 )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3265]) ).

thf(3393,plain,
    ! [SV210: $i,SV435: $i,SV571: $i] :
      ( ( ( in @ SV571 @ SV435 )
        = $true )
      | ( $false = $true )
      | ( ( SV571 = SV210 )
        = $true )
      | ( ( in @ SV571 @ ( setadjoin @ SV210 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3268]) ).

thf(3394,plain,
    ! [SV660: $i,SV211: $i > $o] :
      ( ( ( ! [SY2378: $i] :
              ~ ~ ( ~ ( SV211 @ SY2378 )
                  | ~ ! [SY2379: $i] :
                        ( ~ ( SV211 @ SY2379 )
                        | ( SY2378 = SY2379 ) ) ) )
        = $false )
      | ( ( SV211 @ SV660 )
        = $false )
      | ( ( SV211 @ ( sK72_SY3099 @ SV660 @ SV211 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3271]) ).

thf(3395,plain,
    ! [SV660: $i,SV211: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV211 @ ( sK85_SY2378 @ SV660 @ SV211 ) )
                | ~ ! [SY3199: $i] :
                      ( ~ ( SV211 @ SY3199 )
                      | ( ( sK85_SY2378 @ SV660 @ SV211 )
                        = SY3199 ) ) ) )
        = $false )
      | ( ( SV211 @ SV660 )
        = $false )
      | ( ( SV660
          = ( sK72_SY3099 @ SV660 @ SV211 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3272]) ).

thf(3396,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ! [SY2388: $i] :
              ~ ~ ( ~ ( SV214 @ SY2388 )
                  | ~ ! [SY2389: $i] :
                        ( ~ ( SV214 @ SY2389 )
                        | ( SY2388 = SY2389 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3273]) ).

thf(3397,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ! [SY2803: $i] :
              ~ ~ ( ~ ( SV438 @ SY2803 )
                  | ~ ! [SY2804: $i] :
                        ( ~ ( SV438 @ SY2804 )
                        | ( SY2803 = SY2804 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3274]) ).

thf(3398,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ~ ! [SY2388: $i] :
                          ~ ~ ( ~ ( SV214 @ SY2388 )
                              | ~ ! [SY2389: $i] :
                                    ( ~ ( SV214 @ SY2389 )
                                    | ( SY2388 = SY2389 ) ) )
                  | ~ ! [SY2801: $i] :
                        ~ ~ ( ~ ( SV438 @ SY2801 )
                            | ~ ! [SY2802: $i] :
                                  ( ~ ( SV438 @ SY2802 )
                                  | ( SY2801 = SY2802 ) ) ) )
              | ~ ( ~ ~ ! [SY2803: $i] :
                          ~ ~ ( ~ ( SV438 @ SY2803 )
                              | ~ ! [SY2804: $i] :
                                    ( ~ ( SV438 @ SY2804 )
                                    | ( SY2803 = SY2804 ) ) )
                  | ~ ! [SY2394: $i] :
                        ~ ~ ( ~ ( SV214 @ SY2394 )
                            | ~ ! [SY2395: $i] :
                                  ( ~ ( SV214 @ SY2395 )
                                  | ( SY2394 = SY2395 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3275]) ).

thf(3399,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ~ ! [SY2388: $i] :
                          ~ ~ ( ~ ( SV214 @ SY2388 )
                              | ~ ! [SY2389: $i] :
                                    ( ~ ( SV214 @ SY2389 )
                                    | ( SY2388 = SY2389 ) ) )
                  | ~ ! [SY2801: $i] :
                        ~ ~ ( ~ ( SV438 @ SY2801 )
                            | ~ ! [SY2802: $i] :
                                  ( ~ ( SV438 @ SY2802 )
                                  | ( SY2801 = SY2802 ) ) ) )
              | ~ ( ~ ~ ! [SY2803: $i] :
                          ~ ~ ( ~ ( SV438 @ SY2803 )
                              | ~ ! [SY2804: $i] :
                                    ( ~ ( SV438 @ SY2804 )
                                    | ( SY2803 = SY2804 ) ) )
                  | ~ ! [SY2394: $i] :
                        ~ ~ ( ~ ( SV214 @ SY2394 )
                            | ~ ! [SY2395: $i] :
                                  ( ~ ( SV214 @ SY2395 )
                                  | ( SY2394 = SY2395 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3275]) ).

thf(3400,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( ~ ( ~ ( ~ ~ ! [SY2388: $i] :
                          ~ ~ ( ~ ( SV214 @ SY2388 )
                              | ~ ! [SY2389: $i] :
                                    ( ~ ( SV214 @ SY2389 )
                                    | ( SY2388 = SY2389 ) ) )
                  | ~ ! [SY2801: $i] :
                        ~ ~ ( ~ ( SV438 @ SY2801 )
                            | ~ ! [SY2802: $i] :
                                  ( ~ ( SV438 @ SY2802 )
                                  | ( SY2801 = SY2802 ) ) ) )
              | ~ ( ~ ~ ! [SY2803: $i] :
                          ~ ~ ( ~ ( SV438 @ SY2803 )
                              | ~ ! [SY2804: $i] :
                                    ( ~ ( SV438 @ SY2804 )
                                    | ( SY2803 = SY2804 ) ) )
                  | ~ ! [SY2394: $i] :
                        ~ ~ ( ~ ( SV214 @ SY2394 )
                            | ~ ! [SY2395: $i] :
                                  ( ~ ( SV214 @ SY2395 )
                                  | ( SY2394 = SY2395 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3276]) ).

thf(3401,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ( ~ ~ ! [SY2388: $i] :
                      ~ ~ ( ~ ( SV214 @ SY2388 )
                          | ~ ! [SY2389: $i] :
                                ( ~ ( SV214 @ SY2389 )
                                | ( SY2388 = SY2389 ) ) )
              | ~ ! [SY2801: $i] :
                    ~ ~ ( ~ ( SV438 @ SY2801 )
                        | ~ ! [SY2802: $i] :
                              ( ~ ( SV438 @ SY2802 )
                              | ( SY2801 = SY2802 ) ) ) )
          | ~ ( ~ ~ ! [SY2803: $i] :
                      ~ ~ ( ~ ( SV438 @ SY2803 )
                          | ~ ! [SY2804: $i] :
                                ( ~ ( SV438 @ SY2804 )
                                | ( SY2803 = SY2804 ) ) )
              | ~ ! [SY2394: $i] :
                    ~ ~ ( ~ ( SV214 @ SY2394 )
                        | ~ ! [SY2395: $i] :
                              ( ~ ( SV214 @ SY2395 )
                              | ( SY2394 = SY2395 ) ) ) ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3277]) ).

thf(3402,plain,
    ! [SV579: $i,SV721: $i,SV445: $i,SV221: $i] :
      ( ( ( ~ ! [SY3142: $i] :
                ( ~ ( in @ SY3142 @ SV221 )
                | ! [SY3143: $i] :
                    ( ~ ( in @ SY3143 @ SV445 )
                    | ~ ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV721 )
                    | ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV579 ) ) ) )
        = $true )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ SV221 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3279]) ).

thf(3403,plain,
    ! [SV445: $i,SV721: $i,SV579: $i,SV221: $i] :
      ( ( ( ~ ( in @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) @ SV445 ) )
        = $false )
      | ( ( ~ ! [SY3142: $i] :
                ( ~ ( in @ SY3142 @ SV221 )
                | ! [SY3143: $i] :
                    ( ~ ( in @ SY3143 @ SV445 )
                    | ~ ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV721 )
                    | ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV579 ) ) )
          | ( SV579 = SV721 ) )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3280]) ).

thf(3404,plain,
    ! [SV221: $i,SV445: $i,SV579: $i,SV721: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV579 )
          | ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV721 ) )
        = $false )
      | ( ( ~ ! [SY3142: $i] :
                ( ~ ( in @ SY3142 @ SV221 )
                | ! [SY3143: $i] :
                    ( ~ ( in @ SY3143 @ SV445 )
                    | ~ ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV721 )
                    | ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV579 ) ) )
          | ( SV579 = SV721 ) )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3280]) ).

thf(3405,plain,
    ! [SV228: $i,SV751: $i,SV663: $i,SV451: $i,SV769: $i] :
      ( ( ( ~ ( in @ SV769 @ ( binintersect @ SV451 @ SV663 ) ) )
        = $true )
      | ( ( in @ SV769 @ ( binunion @ SV663 @ SV751 ) )
        = $true )
      | ( ( in @ SV769 @ SV228 )
        = $false )
      | ( ( in @ SV751 @ ( powerset @ SV228 ) )
        = $false )
      | ( ( in @ SV663 @ ( powerset @ SV228 ) )
        = $false )
      | ( ( in @ SV451 @ ( powerset @ SV228 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3281]) ).

thf(3406,plain,
    ! [SV253: $i > $o,SV667: $i] :
      ( ( ( ( sK37_SY3106 @ SV667 @ SV253 )
         != SV667 )
        = $false )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $true )
      | ( ( ~ ! [SY2491: $i] :
                ~ ~ ( ~ ( SV253 @ SY2491 )
                    | ~ ! [SY2492: $i] :
                          ( ~ ( SV253 @ SY2492 )
                          | ( SY2491 = SY2492 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3285]) ).

thf(3407,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $false )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $true )
      | ( ( ~ ! [SY2491: $i] :
                ~ ~ ( ~ ( SV253 @ SY2491 )
                    | ~ ! [SY2492: $i] :
                          ( ~ ( SV253 @ SY2492 )
                          | ( SY2491 = SY2492 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3285]) ).

thf(3408,plain,
    ! [SV253: $i > $o,SV667: $i] :
      ( ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $true )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $false )
      | ( ( ~ ! [SY2491: $i] :
                ~ ~ ( ~ ( SV253 @ SY2491 )
                    | ~ ! [SY2492: $i] :
                          ( ~ ( SV253 @ SY2492 )
                          | ( SY2491 = SY2492 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3286]) ).

thf(3409,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ! [SY2491: $i] :
              ~ ~ ( ~ ( SV253 @ SY2491 )
                  | ~ ! [SY2492: $i] :
                        ( ~ ( SV253 @ SY2492 )
                        | ( SY2491 = SY2492 ) ) ) )
        = $false )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $false )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3287]) ).

thf(3410,plain,
    ! [SV35: $i,SV770: $i,SV281: $i > $o] :
      ( ( ( SV281 @ SV770 )
        = $false )
      | ( ( in @ SV770 @ SV35 )
        = $false )
      | ( ( in @ ( sK30_SY2514 @ SV281 @ SV35 ) @ SV35 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3288]) ).

thf(3411,plain,
    ! [SV35: $i,SV771: $i,SV281: $i > $o] :
      ( ( ( SV281 @ SV771 )
        = $false )
      | ( ( in @ SV771 @ SV35 )
        = $false )
      | ( ( SV281 @ ( sK30_SY2514 @ SV281 @ SV35 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3289]) ).

thf(3412,plain,
    ! [SV36: $i,SV282: $i,SV619: $i,SV734: $i] :
      ( ( ( in @ SV734 @ SV619 )
        = $true )
      | ( ( ~ ( in @ SV734 @ SV282 ) )
        = $true )
      | ( ( subset @ SV282 @ SV619 )
        = $false )
      | ( ( in @ SV734 @ SV36 )
        = $false )
      | ( ( in @ SV619 @ ( powerset @ SV36 ) )
        = $false )
      | ( ( in @ SV282 @ ( powerset @ SV36 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3290]) ).

thf(3413,plain,
    ! [SV620: $i,SV37: $i > $o] :
      ( ( ( ~ ! [SY3200: $i] :
                ~ ( ~ ( ~ ( SV37 @ SY3200 )
                      | ( SY3200
                        = ( sK86_SY1897 @ SV620 @ SV37 ) ) )
                  | ~ ( ( SY3200
                       != ( sK86_SY1897 @ SV620 @ SV37 ) )
                      | ( SV37 @ SY3200 ) ) ) )
        = $false )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( SV37 @ ( sK59_SY3056 @ SV620 @ SV37 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[3291]) ).

thf(3414,plain,
    ! [SV620: $i,SV37: $i > $o] :
      ( ( ( ! [SY3189: $i] :
              ~ ( ~ ( ~ ( SV37 @ SY3189 )
                    | ( SY3189
                      = ( sK77_SY1897 @ SV620 @ SV37 ) ) )
                | ~ ( ( SY3189
                     != ( sK77_SY1897 @ SV620 @ SV37 ) )
                    | ( SV37 @ SY3189 ) ) ) )
        = $true )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( SV620
          = ( sK59_SY3056 @ SV620 @ SV37 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3292]) ).

thf(3415,plain,
    ! [SV621: $i,SV800: $i,SV783: $i,SV41: $i > $o] :
      ( ( ( ~ ( SV41 @ SV783 )
          | ~ ( SV41 @ SV800 )
          | ( SV783 = SV800 ) )
        = $true )
      | ( ( SV41 @ SV621 )
        = $false )
      | ( ( SV41 @ ( sK60_SY3057 @ SV621 @ SV41 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3293]) ).

thf(3416,plain,
    ! [SV621: $i,SV784: $i,SV778: $i,SV41: $i > $o] :
      ( ( ( ~ ( SV41 @ SV778 ) )
        = $true )
      | ( ( ~ ( SV41 @ SV784 )
          | ( SV778 = SV784 ) )
        = $true )
      | ( ( SV41 @ SV621 )
        = $false )
      | ( ( SV621
          = ( sK60_SY3057 @ SV621 @ SV41 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3294]) ).

thf(3417,plain,
    ! [SV622: $i,SV801: $i,SV785: $i,SV43: $i > $o] :
      ( ( ( ~ ( SV43 @ SV785 )
          | ~ ( SV43 @ SV801 )
          | ( SV785 = SV801 ) )
        = $true )
      | ( ( SV43 @ SV622 )
        = $false )
      | ( ( SV43 @ ( sK61_SY3058 @ SV622 @ SV43 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3295]) ).

thf(3418,plain,
    ! [SV622: $i,SV786: $i,SV779: $i,SV43: $i > $o] :
      ( ( ( ~ ( SV43 @ SV779 ) )
        = $true )
      | ( ( ~ ( SV43 @ SV786 )
          | ( SV779 = SV786 ) )
        = $true )
      | ( ( SV43 @ SV622 )
        = $false )
      | ( ( SV622
          = ( sK61_SY3058 @ SV622 @ SV43 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3296]) ).

thf(3419,plain,
    ! [SV46: $i,SV287: $i > $o,SV673: $i] :
      ( ( ( ~ ( in @ ( sK78_SY2528 @ SV673 @ SV287 @ SV46 ) @ SV46 ) )
        = $false )
      | ( ( in @ SV673 @ SV46 )
        = $false )
      | ( ( SV287 @ SV673 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3297]) ).

thf(3420,plain,
    ! [SV46: $i,SV673: $i,SV287: $i > $o] :
      ( ( ( SV287 @ ( sK78_SY2528 @ SV673 @ SV287 @ SV46 ) )
        = $false )
      | ( ( in @ SV673 @ SV46 )
        = $false )
      | ( ( SV287 @ SV673 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3297]) ).

thf(3421,plain,
    ! [SV624: $i,SV48: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV48 @ ( sK87_SY1928 @ SV624 @ SV48 ) )
                | ~ ! [SY3201: $i] :
                      ( ~ ( SV48 @ SY3201 )
                      | ( ( sK87_SY1928 @ SV624 @ SV48 )
                        = SY3201 ) ) ) )
        = $false )
      | ( ( SV48 @ SV624 )
        = $false )
      | ( ( SV48 @ ( sK62_SY3060 @ SV624 @ SV48 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[3298]) ).

thf(3422,plain,
    ! [SV624: $i,SV48: $i > $o] :
      ( ( ( ~ ( ~ ( SV48 @ ( sK79_SY1928 @ SV624 @ SV48 ) )
              | ~ ! [SY3192: $i] :
                    ( ~ ( SV48 @ SY3192 )
                    | ( ( sK79_SY1928 @ SV624 @ SV48 )
                      = SY3192 ) ) ) )
        = $true )
      | ( ( SV48 @ SV624 )
        = $false )
      | ( ( SV624
          = ( sK62_SY3060 @ SV624 @ SV48 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3299]) ).

thf(3423,plain,
    ! [SV52: $i,SV772: $i,SV292: $i > $o] :
      ( ( ( SV292 @ SV772 )
        = $false )
      | ( ( in @ SV772 @ SV52 )
        = $false )
      | ( ( in @ ( sK31_SY2534 @ SV292 @ SV52 ) @ SV52 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3300]) ).

thf(3424,plain,
    ! [SV52: $i,SV773: $i,SV292: $i > $o] :
      ( ( ( SV292 @ SV773 )
        = $false )
      | ( ( in @ SV773 @ SV52 )
        = $false )
      | ( ( SV292 @ ( sK31_SY2534 @ SV292 @ SV52 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3301]) ).

thf(3425,plain,
    ! [SV302: $i,SV63: $i,SV676: $i > $o,SV496: $i,SV787: $i] :
      ( ( ( ~ ( in @ SV787 @ SV496 ) )
        = $true )
      | ( ( SV676 @ SV787 )
        = $true )
      | ( ( in @ ( sK63_SY3167 @ SV63 @ SV496 @ SV676 @ SV302 ) @ SV302 )
        = $true )
      | ( ( subset @ SV496 @ ( cartprod @ SV63 @ SV302 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3303]) ).

thf(3426,plain,
    ! [SV63: $i,SV302: $i,SV676: $i > $o,SV496: $i,SV802: $i] :
      ( ( ( ~ ( in @ SV802 @ SV496 )
          | ( SV676 @ SV802 ) )
        = $true )
      | ( ( in @ ( kpair @ ( sK44_SY3111 @ SV676 @ SV496 @ SV302 @ SV63 ) @ ( sK63_SY3167 @ SV63 @ SV496 @ SV676 @ SV302 ) ) @ SV496 )
        = $true )
      | ( ( subset @ SV496 @ ( cartprod @ SV63 @ SV302 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3304]) ).

thf(3427,plain,
    ! [SV63: $i,SV302: $i,SV676: $i > $o,SV496: $i,SV788: $i] :
      ( ( ( ~ ( in @ SV788 @ SV496 ) )
        = $true )
      | ( ( SV676 @ SV788 )
        = $true )
      | ( ( SV676 @ ( kpair @ ( sK44_SY3111 @ SV676 @ SV496 @ SV302 @ SV63 ) @ ( sK63_SY3167 @ SV63 @ SV496 @ SV676 @ SV302 ) ) )
        = $false )
      | ( ( subset @ SV496 @ ( cartprod @ SV63 @ SV302 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3305]) ).

thf(3428,plain,
    ! [SV76: $i,SV737: $i,SV627: $i,SV314: $i,SV763: $i] :
      ( ( ( in @ SV763 @ ( binintersect @ SV314 @ SV627 ) )
        = $false )
      | ( ( in @ SV763 @ ( binintersect @ ( binunion @ SV314 @ SV737 ) @ ( binunion @ SV627 @ SV737 ) ) )
        = $true )
      | ( ( in @ SV763 @ SV76 )
        = $false )
      | ( ( in @ SV737 @ ( powerset @ SV76 ) )
        = $false )
      | ( ( in @ SV627 @ ( powerset @ SV76 ) )
        = $false )
      | ( ( in @ SV314 @ ( powerset @ SV76 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3306]) ).

thf(3429,plain,
    ! [SV315: $i > $o,SV775: $i,SV77: $i > $o] :
      ( ( ( ~ ( SV77 @ SV775 ) )
        = $true )
      | ( ( ~ ! [SY3183: $i] :
                ( ~ ( SV77 @ SY3183 )
                | ( SV775 = SY3183 ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3307]) ).

thf(3430,plain,
    ! [SV77: $i > $o,SV315: $i > $o] :
      ( ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( ~ ~ ! [SY2001: $i] :
                  ~ ~ ( ~ ( SV77 @ SY2001 )
                      | ~ ! [SY2002: $i] :
                            ( ~ ( SV77 @ SY2002 )
                            | ( SY2001 = SY2002 ) ) )
          | ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3308]) ).

thf(3431,plain,
    ! [SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ~ ~ ! [SY2001: $i] :
                  ~ ~ ( ~ ( SV77 @ SY2001 )
                      | ~ ! [SY2002: $i] :
                            ( ~ ( SV77 @ SY2002 )
                            | ( SY2001 = SY2002 ) ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3309]) ).

thf(3432,plain,
    ! [SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ~ ~ ! [SY2001: $i] :
                  ~ ~ ( ~ ( SV77 @ SY2001 )
                      | ~ ! [SY2002: $i] :
                            ( ~ ( SV77 @ SY2002 )
                            | ( SY2001 = SY2002 ) ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3310]) ).

thf(3433,plain,
    ! [SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ~ ! [SY2001: $i] :
                ~ ~ ( ~ ( SV77 @ SY2001 )
                    | ~ ! [SY2002: $i] :
                          ( ~ ( SV77 @ SY2002 )
                          | ( SY2001 = SY2002 ) ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3311]) ).

thf(3434,plain,
    ! [SV80: $i,SV628: $i,SV318: $i] :
      ( ( ( ~ ( in @ ( sK88_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV80 )
          | ~ ( in @ ( sK88_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV628 )
          | ( in @ ( sK88_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV318 ) )
        = $false )
      | ( ( SV318 = SV628 )
        = $true )
      | ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV80 )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3312]) ).

thf(3435,plain,
    ! [SV318: $i,SV628: $i,SV80: $i] :
      ( ( ( ! [SY3067: $i] :
              ( ~ ( in @ SY3067 @ SV80 )
              | ~ ( in @ SY3067 @ SV628 )
              | ( in @ SY3067 @ SV318 ) ) )
        = $false )
      | ( ( SV318 = SV628 )
        = $true )
      | ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV318 )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3313]) ).

thf(3436,plain,
    ! [SV80: $i,SV628: $i,SV318: $i] :
      ( ( ( ~ ( in @ ( sK89_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV80 )
          | ~ ( in @ ( sK89_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV628 )
          | ( in @ ( sK89_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV318 ) )
        = $false )
      | ( ( SV318 = SV628 )
        = $true )
      | ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV628 )
        = $false )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3314]) ).

thf(3437,plain,
    ! [SV84: $i,SV682: $i,SV321: $i > $o] :
      ( ( ( SV321 @ ( sK53_SY2593 @ SV682 @ SV321 @ SV84 ) )
        = $false )
      | ( ( SV321 @ SV682 )
        = $true )
      | ( ( in @ SV682 @ SV84 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3316]) ).

thf(3438,plain,
    ! [SV87: $i,SV789: $i] :
      ( ( ( ~ ( in @ SV789 @ omega ) )
        = $true )
      | ( ( in @ SV789 @ SV87 )
        = $true )
      | ( ( in @ emptyset @ SV87 )
        = $false )
      | ( ( in @ ( sK39_SY2033 @ SV87 ) @ omega )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3320]) ).

thf(3439,plain,
    ! [SV87: $i,SV790: $i] :
      ( ( ( ~ ( in @ SV790 @ omega ) )
        = $true )
      | ( ( in @ SV790 @ SV87 )
        = $true )
      | ( ( in @ emptyset @ SV87 )
        = $false )
      | ( ( in @ ( sK39_SY2033 @ SV87 ) @ SV87 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3321]) ).

thf(3440,plain,
    ! [SV512: $i,SV685: $i,SV332: $i,SV96: $i,SV791: $i] :
      ( ( ( ~ ( in @ SV791 @ SV96 ) )
        = $true )
      | ( ( ! [SY3193: $i] :
              ( ~ ( in @ SY3193 @ SV332 )
              | ~ ( in @ ( kpair @ SV791 @ SY3193 ) @ SV685 )
              | ( in @ ( kpair @ SV791 @ SY3193 ) @ SV512 ) ) )
        = $true )
      | ( ( in @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) @ SV96 )
        = $true )
      | ( ( func @ SV96 @ SV332 @ SV685 )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV512 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3323]) ).

thf(3441,plain,
    ! [SV512: $i,SV685: $i,SV332: $i,SV96: $i,SV780: $i] :
      ( ( ( in @ SV780 @ SV96 )
        = $false )
      | ( ( ! [SY3188: $i] :
              ( ~ ( in @ SY3188 @ SV332 )
              | ~ ( in @ ( kpair @ SV780 @ SY3188 ) @ SV685 )
              | ( in @ ( kpair @ SV780 @ SY3188 ) @ SV512 ) ) )
        = $true )
      | ( ( ( ap @ SV96 @ SV332 @ SV512 @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) )
          = ( ap @ SV96 @ SV332 @ SV685 @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) ) )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV685 )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV512 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3324]) ).

thf(3442,plain,
    ! [SV333: $i,SV513: $i,SV98: $i] :
      ( ( ( ~ ( in @ ( sK74_SY3150 @ SV98 @ SV513 @ SV333 ) @ SV333 )
          | ( SV513
           != ( kpair @ ( sK33_SY2921 @ SV513 @ SV333 @ SV98 ) @ ( sK74_SY3150 @ SV98 @ SV513 @ SV333 ) ) ) )
        = $false )
      | ( ( in @ SV513 @ ( cartprod @ SV98 @ SV333 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3325]) ).

thf(3443,plain,
    ! [SV336: $i > $o,SV102: $i,SV764: $i] :
      ( ( ( in @ SV764 @ SV102 )
        = $false )
      | ( ( ~ ( SV336 @ SV764 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( in @ ( sK11_SY2627 @ SV336 @ SV102 ) @ SV102 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3327]) ).

thf(3444,plain,
    ! [SV336: $i > $o,SV102: $i,SV781: $i] :
      ( ( ( ~ ( in @ SV781 @ SV102 )
          | ~ ( SV336 @ SV781 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( in @ ( sK34_SY3074 @ SV336 @ SV102 ) @ SV102 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3328]) ).

thf(3445,plain,
    ! [SV336: $i > $o,SV102: $i,SV792: $i] :
      ( ( ( ~ ( ~ ( in @ SV792 @ SV102 )
              | ~ ( SV336 @ SV792 ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( SV336 @ ( sK11_SY2627 @ SV336 @ SV102 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3329]) ).

thf(3446,plain,
    ! [SV336: $i > $o,SV102: $i,SV803: $i] :
      ( ( ( ~ ~ ( ~ ( in @ SV803 @ SV102 )
                | ~ ( SV336 @ SV803 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( SV336 @ ( sK34_SY3074 @ SV336 @ SV102 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3330]) ).

thf(3447,plain,
    ! [SV336: $i > $o,SV102: $i,SV793: $i] :
      ( ( ( ~ ( ~ ( in @ SV793 @ SV102 )
              | ~ ( SV336 @ SV793 ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( ( sK11_SY2627 @ SV336 @ SV102 )
          = ( sK34_SY3074 @ SV336 @ SV102 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3331]) ).

thf(3448,plain,
    ! [SV109: $i,SV794: $i] :
      ( ( ( ~ ( in @ SV794 @ ( sK3_SY2100 @ SV109 ) ) )
        = $true )
      | ( ( ! [SY3194: $i] :
              ( ~ ( in @ SY3194 @ SV794 )
              | ( in @ SY3194 @ SV109 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3332]) ).

thf(3449,plain,
    ! [SV804: $i,SV109: $i,SV795: $i] :
      ( ( ~ ~ ( ~ ( in @ SV795 @ SV109 )
              | ~ ( in @ SV804 @ SV109 ) )
        | ~ ! [SY3202: $i] :
              ( ~ ( in @ SY3202 @ ( sK3_SY2100 @ SV109 ) )
              | ~ ( ~ ( ~ ( in @ SV795 @ SY3202 )
                      | ( in @ SV804 @ SY3202 ) )
                  | ~ ( ~ ( in @ SV804 @ SY3202 )
                      | ( in @ SV795 @ SY3202 ) ) ) )
        | ( SV795 = SV804 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3333]) ).

thf(3450,plain,
    ! [SV776: $i,SV109: $i,SV765: $i] :
      ( ( ( ~ ( in @ SV765 @ ( sK3_SY2100 @ SV109 ) )
          | ~ ( in @ SV776 @ ( sK3_SY2100 @ SV109 ) ) )
        = $true )
      | ( ( ! [SY3184: $i] :
              ( ~ ( in @ SY3184 @ SV765 )
              | ( in @ SY3184 @ SV776 ) )
          | ! [SY3185: $i] :
              ( ~ ( in @ SY3185 @ SV776 )
              | ( in @ SY3185 @ SV765 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3334]) ).

thf(3451,plain,
    ! [SV739: $i,SV109: $i] :
      ( ( ( ~ ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 ) )
        = $false )
      | ( ( ~ ~ ! [SY3155: $i] :
                  ~ ( in @ SY3155 @ SV739 ) )
        = $true )
      | ( ( ~ ! [SY3156: $i] :
                ~ ~ ! [SY3157: $i] :
                      ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3156 @ ( sK3_SY2100 @ SV109 ) )
                                      | ~ ( in @ SY3157 @ SV739 ) )
                                | ~ ~ ~ ! [SY3158: $i] :
                                          ~ ~ ( ~ ( in @ SY3158 @ SY3156 )
                                              | ~ ( in @ SY3158 @ SV739 ) ) )
                          | ~ ! [SY2947: $i] :
                                ( ~ ( in @ SY2947 @ ( sK3_SY2100 @ SV109 ) )
                                | ! [SX6: $i] :
                                    ( ~ ( in @ SX6 @ SY2947 )
                                    | ( in @ SX6 @ SY3156 ) )
                                | ( in @ SY3157 @ SY2947 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3335]) ).

thf(3452,plain,
    ! [SV739: $i,SV109: $i] :
      ( ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( ~ ~ ! [SY3155: $i] :
                  ~ ( in @ SY3155 @ SV739 ) )
        = $true )
      | ( ( ~ ! [SY3156: $i] :
                ~ ~ ! [SY3157: $i] :
                      ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3156 @ ( sK3_SY2100 @ SV109 ) )
                                      | ~ ( in @ SY3157 @ SV739 ) )
                                | ~ ~ ~ ! [SY3158: $i] :
                                          ~ ~ ( ~ ( in @ SY3158 @ SY3156 )
                                              | ~ ( in @ SY3158 @ SV739 ) ) )
                          | ~ ! [SY2947: $i] :
                                ( ~ ( in @ SY2947 @ ( sK3_SY2100 @ SV109 ) )
                                | ! [SX6: $i] :
                                    ( ~ ( in @ SX6 @ SY2947 )
                                    | ( in @ SX6 @ SY3156 ) )
                                | ( in @ SY3157 @ SY2947 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3335]) ).

thf(3453,plain,
    ! [SV110: $i,SV635: $i,SV805: $i] :
      ( ( ( ~ ~ ( ~ ( in @ SV805 @ ( sK40_SY2119 @ SV635 @ SV110 ) )
                | ~ ( in @ SV805 @ SV110 ) ) )
        = $true )
      | ( ( in @ SV635 @ SV110 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3336]) ).

thf(3454,plain,
    ! [SV636: $i,SV112: $i > $o] :
      ( ( ( ~ ( SV112 @ ( sK90_SY2125 @ SV636 @ SV112 ) ) )
        = $false )
      | ( ( SV112 @ SV636 )
        = $false )
      | ( ( SV112 @ ( sK66_SY3077 @ SV636 @ SV112 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[3337]) ).

thf(3455,plain,
    ! [SV636: $i,SV112: $i > $o] :
      ( ( ( SV112 @ ( sK81_SY2125 @ SV636 @ SV112 ) )
        = $true )
      | ( ( SV112 @ SV636 )
        = $false )
      | ( ( SV636
          = ( sK66_SY3077 @ SV636 @ SV112 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3338]) ).

thf(3456,plain,
    ! [SV353: $i > $o,SV125: $i,SV766: $i] :
      ( ( ( in @ SV766 @ SV125 )
        = $false )
      | ( ( ~ ( SV353 @ SV766 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( in @ ( sK12_SY2657 @ SV353 @ SV125 ) @ SV125 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3340]) ).

thf(3457,plain,
    ! [SV353: $i > $o,SV125: $i,SV782: $i] :
      ( ( ( ~ ( in @ SV782 @ SV125 )
          | ~ ( SV353 @ SV782 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( in @ ( sK36_SY3079 @ SV353 @ SV125 ) @ SV125 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3341]) ).

thf(3458,plain,
    ! [SV353: $i > $o,SV125: $i,SV796: $i] :
      ( ( ( ~ ( ~ ( in @ SV796 @ SV125 )
              | ~ ( SV353 @ SV796 ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( SV353 @ ( sK12_SY2657 @ SV353 @ SV125 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3342]) ).

thf(3459,plain,
    ! [SV353: $i > $o,SV125: $i,SV806: $i] :
      ( ( ( ~ ~ ( ~ ( in @ SV806 @ SV125 )
                | ~ ( SV353 @ SV806 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( SV353 @ ( sK36_SY3079 @ SV353 @ SV125 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3343]) ).

thf(3460,plain,
    ! [SV353: $i > $o,SV125: $i,SV797: $i] :
      ( ( ( ~ ( ~ ( in @ SV797 @ SV125 )
              | ~ ( SV353 @ SV797 ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( ( sK12_SY2657 @ SV353 @ SV125 )
          = ( sK36_SY3079 @ SV353 @ SV125 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3344]) ).

thf(3461,plain,
    ! [SV363: $i,SV135: $i,SV690: $i > $o,SV529: $i,SV798: $i] :
      ( ( ( ~ ( in @ SV798 @ SV529 ) )
        = $true )
      | ( ( SV690 @ SV798 )
        = $true )
      | ( ( in @ ( sK67_SY3168 @ SV135 @ SV529 @ SV690 @ SV363 ) @ SV363 )
        = $true )
      | ( ( subset @ SV529 @ ( cartprod @ SV135 @ SV363 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3346]) ).

thf(3462,plain,
    ! [SV135: $i,SV363: $i,SV690: $i > $o,SV529: $i,SV807: $i] :
      ( ( ( ~ ( in @ SV807 @ SV529 )
          | ( SV690 @ SV807 ) )
        = $true )
      | ( ( in @ ( kpair @ ( sK46_SY3122 @ SV690 @ SV529 @ SV363 @ SV135 ) @ ( sK67_SY3168 @ SV135 @ SV529 @ SV690 @ SV363 ) ) @ SV529 )
        = $true )
      | ( ( subset @ SV529 @ ( cartprod @ SV135 @ SV363 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3347]) ).

thf(3463,plain,
    ! [SV135: $i,SV363: $i,SV690: $i > $o,SV529: $i,SV799: $i] :
      ( ( ( ~ ( in @ SV799 @ SV529 ) )
        = $true )
      | ( ( SV690 @ SV799 )
        = $true )
      | ( ( SV690 @ ( kpair @ ( sK46_SY3122 @ SV690 @ SV529 @ SV363 @ SV135 ) @ ( sK67_SY3168 @ SV135 @ SV529 @ SV690 @ SV363 ) ) )
        = $false )
      | ( ( subset @ SV529 @ ( cartprod @ SV135 @ SV363 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3348]) ).

thf(3464,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV767: $i] :
      ( ( ( ~ ( in @ SV767 @ ( sK47_SY2690 @ SV147 @ SV377 ) ) )
        = $true )
      | ( ( ~ ! [SY3179: $i] :
                ~ ~ ( ~ ( in @ SY3179 @ SV377 )
                    | ~ ( SV147 @ SY3179 @ SV767 ) ) )
        = $true )
      | ( ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3351]) ).

thf(3465,plain,
    ! [SV767: $i,SV147: $i > $i > $o,SV377: $i] :
      ( ( ( ~ ~ ! [SY3180: $i] :
                  ~ ~ ( ~ ( in @ SY3180 @ SV377 )
                      | ~ ( SV147 @ SY3180 @ SV767 ) ) )
        = $true )
      | ( ( in @ SV767 @ ( sK47_SY2690 @ SV147 @ SV377 ) )
        = $true )
      | ( ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3352]) ).

thf(3466,plain,
    ! [SV743: $i,SV377: $i,SV147: $i > $i > $o] :
      ( ( ( ~ ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( ~ ! [SY2690: $i] :
                ~ ! [SY2691: $i] :
                    ~ ( ~ ( ~ ( in @ SY2691 @ SY2690 )
                          | ~ ! [SY2692: $i] :
                                ~ ~ ( ~ ( in @ SY2692 @ SV377 )
                                    | ~ ( SV147 @ SY2692 @ SY2691 ) ) )
                      | ~ ( ~ ~ ! [SY2693: $i] :
                                  ~ ~ ( ~ ( in @ SY2693 @ SV377 )
                                      | ~ ( SV147 @ SY2693 @ SY2691 ) )
                          | ( in @ SY2691 @ SY2690 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3353]) ).

thf(3467,plain,
    ! [SV147: $i > $i > $o,SV377: $i,SV743: $i] :
      ( ( ( SV743
          = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( ~ ! [SY2690: $i] :
                ~ ! [SY2691: $i] :
                    ~ ( ~ ( ~ ( in @ SY2691 @ SY2690 )
                          | ~ ! [SY2692: $i] :
                                ~ ~ ( ~ ( in @ SY2692 @ SV377 )
                                    | ~ ( SV147 @ SY2692 @ SY2691 ) ) )
                      | ~ ( ~ ~ ! [SY2693: $i] :
                                  ~ ~ ( ~ ( in @ SY2693 @ SV377 )
                                      | ~ ( SV147 @ SY2693 @ SY2691 ) )
                          | ( in @ SY2691 @ SY2690 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3353]) ).

thf(3468,plain,
    ! [SV160: $i,SV694: $i,SV388: $i > $o] :
      ( ( ( SV388 @ ( sK54_SY2705 @ SV694 @ SV388 @ SV160 ) )
        = $false )
      | ( ( SV388 @ SV694 )
        = $true )
      | ( ( in @ SV694 @ SV160 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3357]) ).

thf(3469,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( ~ ( ~ ( SV165 @ ( sK83_SY2244 @ SV651 @ SV165 ) )
              | ~ ! [SY3197: $i] :
                    ( ~ ( SV165 @ SY3197 )
                    | ( ( sK83_SY2244 @ SV651 @ SV165 )
                      = SY3197 ) ) ) )
        = $true )
      | ( ( SV165 @ ( sK48_SY2242 @ SV651 @ SV165 ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3358]) ).

thf(3470,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV165 @ ( sK91_SY2244 @ SV651 @ SV165 ) )
                | ~ ! [SY3203: $i] :
                      ( ~ ( SV165 @ SY3203 )
                      | ( ( sK91_SY2244 @ SV651 @ SV165 )
                        = SY3203 ) ) ) )
        = $false )
      | ( ( SV165 @ ( sK55_SY3172 @ SV651 @ SV165 ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3359]) ).

thf(3471,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( ~ ( ~ ( SV165 @ ( sK84_SY2244 @ SV651 @ SV165 ) )
              | ~ ! [SY3198: $i] :
                    ( ~ ( SV165 @ SY3198 )
                    | ( ( sK84_SY2244 @ SV651 @ SV165 )
                      = SY3198 ) ) ) )
        = $true )
      | ( ( ( sK48_SY2242 @ SV651 @ SV165 )
          = ( sK55_SY3172 @ SV651 @ SV165 ) )
        = $false )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3360]) ).

thf(3472,plain,
    ! [SV395: $i,SV695: $i,SV539: $i,SV168: $i] :
      ( ( ( in @ ( sK75_SY3181 @ SV168 @ SV539 @ SV695 @ SV395 ) @ SV395 )
        = $true )
      | ( ( subset @ SV539 @ SV695 )
        = $true )
      | ( ( subset @ SV695 @ ( cartprod @ SV168 @ SV395 ) )
        = $false )
      | ( ( subset @ SV539 @ ( cartprod @ SV168 @ SV395 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3361]) ).

thf(3473,plain,
    ! [SV168: $i,SV395: $i,SV539: $i,SV695: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK69_SY3125 @ SV695 @ SV539 @ SV395 @ SV168 ) @ ( sK75_SY3181 @ SV168 @ SV539 @ SV695 @ SV395 ) ) @ SV539 ) )
        = $false )
      | ( ( subset @ SV539 @ SV695 )
        = $true )
      | ( ( subset @ SV695 @ ( cartprod @ SV168 @ SV395 ) )
        = $false )
      | ( ( subset @ SV539 @ ( cartprod @ SV168 @ SV395 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3362]) ).

thf(3474,plain,
    ! [SV168: $i,SV395: $i,SV539: $i,SV695: $i] :
      ( ( ( in @ ( kpair @ ( sK69_SY3125 @ SV695 @ SV539 @ SV395 @ SV168 ) @ ( sK75_SY3181 @ SV168 @ SV539 @ SV695 @ SV395 ) ) @ SV695 )
        = $false )
      | ( ( subset @ SV539 @ SV695 )
        = $true )
      | ( ( subset @ SV695 @ ( cartprod @ SV168 @ SV395 ) )
        = $false )
      | ( ( subset @ SV539 @ ( cartprod @ SV168 @ SV395 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3362]) ).

thf(3475,plain,
    ! [SV177: $i,SV654: $i,SV403: $i,SV749: $i] :
      ( ( ( in @ SV749 @ SV403 )
        = $false )
      | ( ( in @ SV749 @ SV654 )
        = $false )
      | ( ( subset @ SV403 @ ( setminus @ SV177 @ SV654 ) )
        = $false )
      | ( ( in @ SV749 @ SV177 )
        = $false )
      | ( ( in @ SV654 @ ( powerset @ SV177 ) )
        = $false )
      | ( ( in @ SV403 @ ( powerset @ SV177 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3363]) ).

thf(3476,plain,
    ! [SV191: $i,SV750: $i,SV657: $i,SV417: $i,SV768: $i] :
      ( ( ( in @ SV768 @ ( binintersect @ SV417 @ SV657 ) )
        = $false )
      | ( ( in @ SV768 @ ( binunion @ SV417 @ SV750 ) )
        = $true )
      | ( ( in @ SV768 @ SV191 )
        = $false )
      | ( ( in @ SV750 @ ( powerset @ SV191 ) )
        = $false )
      | ( ( in @ SV657 @ ( powerset @ SV191 ) )
        = $false )
      | ( ( in @ SV417 @ ( powerset @ SV191 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3364]) ).

thf(3477,plain,
    ! [SV200: $i,SV761: $i,SV426: $i > $o] :
      ( ( ( SV426 @ SV761 )
        = $false )
      | ( ( in @ SV761 @ SV200 )
        = $false )
      | ( ( in @ ( sK16_SY2777 @ SV426 @ SV200 ) @ SV200 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3365]) ).

thf(3478,plain,
    ! [SV200: $i,SV762: $i,SV426: $i > $o] :
      ( ( ( SV426 @ SV762 )
        = $false )
      | ( ( in @ SV762 @ SV200 )
        = $false )
      | ( ( SV426 @ ( sK16_SY2777 @ SV426 @ SV200 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3366]) ).

thf(3479,plain,
    ! [SV431: $i,SV712: $o,SV206: $i,SV570: $i] :
      ( ( ( in @ SV570 @ SV206 )
        = $false )
      | ( SV712 = $true )
      | ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3368]) ).

thf(3480,plain,
    ! [SV206: $i,SV712: $o,SV431: $i,SV570: $i] :
      ( ( ( in @ SV570 @ SV431 )
        = $true )
      | ( SV712 = $true )
      | ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3369]) ).

thf(3481,plain,
    ! [SV431: $i,SV712: $o,SV206: $i,SV570: $i] :
      ( ( ( ~ ~ ( in @ SV570 @ SV206 ) )
        = $false )
      | ( SV712 = $true )
      | ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3371]) ).

thf(3482,plain,
    ! [SV206: $i,SV712: $o,SV431: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV431 )
          | SV712 )
        = $false )
      | ( SV712 = $true )
      | ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3371]) ).

thf(3483,plain,
    ! [SV431: $i,SV712: $o,SV206: $i,SV570: $i] :
      ( ( ( in @ SV570 @ SV206 )
        = $false )
      | ( SV712 = $true )
      | ( SV712 = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3372]) ).

thf(3484,plain,
    ! [SV206: $i,SV712: $o,SV431: $i,SV570: $i] :
      ( ( ( in @ SV570 @ SV431 )
        = $true )
      | ( SV712 = $true )
      | ( SV712 = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3373]) ).

thf(3485,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( in @ SV570 @ SV206 )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3375]) ).

thf(3486,plain,
    ! [SV206: $i,SV431: $i,SV570: $i] :
      ( ( ( in @ SV570 @ SV431 )
        = $true )
      | ( $true = $true )
      | ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3376]) ).

thf(3487,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ~ ( in @ SV570 @ SV206 ) )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3378]) ).

thf(3488,plain,
    ! [SV206: $i,SV431: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV431 )
          | $true )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3378]) ).

thf(3489,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( in @ SV570 @ SV206 )
        = $false )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3379]) ).

thf(3490,plain,
    ! [SV206: $i,SV431: $i,SV570: $i] :
      ( ( ( in @ SV570 @ SV431 )
        = $true )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3380]) ).

thf(3491,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( in @ SV570 @ SV206 )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3382]) ).

thf(3492,plain,
    ! [SV206: $i,SV431: $i,SV570: $i] :
      ( ( ( in @ SV570 @ SV431 )
        = $true )
      | ( $false = $true )
      | ( ( in @ SV570 @ SV206 )
        = $true )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3383]) ).

thf(3493,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ~ ( in @ SV570 @ SV206 ) )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3385]) ).

thf(3494,plain,
    ! [SV206: $i,SV431: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV431 )
          | $false )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3385]) ).

thf(3495,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( in @ SV570 @ SV206 )
        = $false )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3386]) ).

thf(3496,plain,
    ! [SV206: $i,SV431: $i,SV570: $i] :
      ( ( ( in @ SV570 @ SV431 )
        = $true )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3387]) ).

thf(3497,plain,
    ! [SV209: $i,SV434: $i,SV713: $i > $o,SV659: $i > $o] :
      ( ( ( ~ ( ~ ( SV659 @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) )
              | ( SV713 @ ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( SV713 @ ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) )
              | ( SV659 @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) ) ) )
        = $true )
      | ( ( ( dsetconstr @ SV209
            @ ^ [SY3097: $i] : ( SV659 @ SY3097 ) )
          = ( dsetconstr @ SV434
            @ ^ [SY3136: $i] : ( SV713 @ SY3136 ) ) )
        = $true )
      | ( ( SV209 = SV434 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3390]) ).

thf(3498,plain,
    ! [SV660: $i,SV211: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV211 @ ( sK92_SY2378 @ SV660 @ SV211 ) )
                | ~ ! [SY3204: $i] :
                      ( ~ ( SV211 @ SY3204 )
                      | ( ( sK92_SY2378 @ SV660 @ SV211 )
                        = SY3204 ) ) ) )
        = $false )
      | ( ( SV211 @ SV660 )
        = $false )
      | ( ( SV211 @ ( sK72_SY3099 @ SV660 @ SV211 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[3394]) ).

thf(3499,plain,
    ! [SV660: $i,SV211: $i > $o] :
      ( ( ( ~ ( ~ ( SV211 @ ( sK85_SY2378 @ SV660 @ SV211 ) )
              | ~ ! [SY3199: $i] :
                    ( ~ ( SV211 @ SY3199 )
                    | ( ( sK85_SY2378 @ SV660 @ SV211 )
                      = SY3199 ) ) ) )
        = $true )
      | ( ( SV211 @ SV660 )
        = $false )
      | ( ( SV660
          = ( sK72_SY3099 @ SV660 @ SV211 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3395]) ).

thf(3500,plain,
    ! [SV438: $i > $o,SV808: $i,SV214: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV214 @ SV808 )
                | ~ ! [SY3205: $i] :
                      ( ~ ( SV214 @ SY3205 )
                      | ( SV808 = SY3205 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3396]) ).

thf(3501,plain,
    ! [SV214: $i > $o,SV809: $i,SV438: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV438 @ SV809 )
                | ~ ! [SY3206: $i] :
                      ( ~ ( SV438 @ SY3206 )
                      | ( SV809 = SY3206 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3397]) ).

thf(3502,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ~ ! [SY2388: $i] :
                          ~ ~ ( ~ ( SV214 @ SY2388 )
                              | ~ ! [SY2389: $i] :
                                    ( ~ ( SV214 @ SY2389 )
                                    | ( SY2388 = SY2389 ) ) )
                  | ~ ! [SY2801: $i] :
                        ~ ~ ( ~ ( SV438 @ SY2801 )
                            | ~ ! [SY2802: $i] :
                                  ( ~ ( SV438 @ SY2802 )
                                  | ( SY2801 = SY2802 ) ) ) )
              | ~ ( ~ ~ ! [SY2803: $i] :
                          ~ ~ ( ~ ( SV438 @ SY2803 )
                              | ~ ! [SY2804: $i] :
                                    ( ~ ( SV438 @ SY2804 )
                                    | ( SY2803 = SY2804 ) ) )
                  | ~ ! [SY2394: $i] :
                        ~ ~ ( ~ ( SV214 @ SY2394 )
                            | ~ ! [SY2395: $i] :
                                  ( ~ ( SV214 @ SY2395 )
                                  | ( SY2394 = SY2395 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3398]) ).

thf(3503,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ( ~ ~ ! [SY2388: $i] :
                      ~ ~ ( ~ ( SV214 @ SY2388 )
                          | ~ ! [SY2389: $i] :
                                ( ~ ( SV214 @ SY2389 )
                                | ( SY2388 = SY2389 ) ) )
              | ~ ! [SY2801: $i] :
                    ~ ~ ( ~ ( SV438 @ SY2801 )
                        | ~ ! [SY2802: $i] :
                              ( ~ ( SV438 @ SY2802 )
                              | ( SY2801 = SY2802 ) ) ) )
          | ~ ( ~ ~ ! [SY2803: $i] :
                      ~ ~ ( ~ ( SV438 @ SY2803 )
                          | ~ ! [SY2804: $i] :
                                ( ~ ( SV438 @ SY2804 )
                                | ( SY2803 = SY2804 ) ) )
              | ~ ! [SY2394: $i] :
                    ~ ~ ( ~ ( SV214 @ SY2394 )
                        | ~ ! [SY2395: $i] :
                              ( ~ ( SV214 @ SY2395 )
                              | ( SY2394 = SY2395 ) ) ) ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3399]) ).

thf(3504,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ( ~ ~ ! [SY2388: $i] :
                      ~ ~ ( ~ ( SV214 @ SY2388 )
                          | ~ ! [SY2389: $i] :
                                ( ~ ( SV214 @ SY2389 )
                                | ( SY2388 = SY2389 ) ) )
              | ~ ! [SY2801: $i] :
                    ~ ~ ( ~ ( SV438 @ SY2801 )
                        | ~ ! [SY2802: $i] :
                              ( ~ ( SV438 @ SY2802 )
                              | ( SY2801 = SY2802 ) ) ) )
          | ~ ( ~ ~ ! [SY2803: $i] :
                      ~ ~ ( ~ ( SV438 @ SY2803 )
                          | ~ ! [SY2804: $i] :
                                ( ~ ( SV438 @ SY2804 )
                                | ( SY2803 = SY2804 ) ) )
              | ~ ! [SY2394: $i] :
                    ~ ~ ( ~ ( SV214 @ SY2394 )
                        | ~ ! [SY2395: $i] :
                              ( ~ ( SV214 @ SY2395 )
                              | ( SY2394 = SY2395 ) ) ) ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3400]) ).

thf(3505,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ( ~ ~ ! [SY2388: $i] :
                      ~ ~ ( ~ ( SV214 @ SY2388 )
                          | ~ ! [SY2389: $i] :
                                ( ~ ( SV214 @ SY2389 )
                                | ( SY2388 = SY2389 ) ) )
              | ~ ! [SY2801: $i] :
                    ~ ~ ( ~ ( SV438 @ SY2801 )
                        | ~ ! [SY2802: $i] :
                              ( ~ ( SV438 @ SY2802 )
                              | ( SY2801 = SY2802 ) ) ) ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3401]) ).

thf(3506,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ( ~ ~ ! [SY2803: $i] :
                      ~ ~ ( ~ ( SV438 @ SY2803 )
                          | ~ ! [SY2804: $i] :
                                ( ~ ( SV438 @ SY2804 )
                                | ( SY2803 = SY2804 ) ) )
              | ~ ! [SY2394: $i] :
                    ~ ~ ( ~ ( SV214 @ SY2394 )
                        | ~ ! [SY2395: $i] :
                              ( ~ ( SV214 @ SY2395 )
                              | ( SY2394 = SY2395 ) ) ) ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3401]) ).

thf(3507,plain,
    ! [SV579: $i,SV721: $i,SV445: $i,SV221: $i] :
      ( ( ( ! [SY3142: $i] :
              ( ~ ( in @ SY3142 @ SV221 )
              | ! [SY3143: $i] :
                  ( ~ ( in @ SY3143 @ SV445 )
                  | ~ ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV721 )
                  | ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV579 ) ) ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ SV221 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3402]) ).

thf(3508,plain,
    ! [SV445: $i,SV721: $i,SV579: $i,SV221: $i] :
      ( ( ( in @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) @ SV445 )
        = $true )
      | ( ( ~ ! [SY3142: $i] :
                ( ~ ( in @ SY3142 @ SV221 )
                | ! [SY3143: $i] :
                    ( ~ ( in @ SY3143 @ SV445 )
                    | ~ ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV721 )
                    | ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV579 ) ) )
          | ( SV579 = SV721 ) )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3403]) ).

thf(3509,plain,
    ! [SV221: $i,SV445: $i,SV579: $i,SV721: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV579 ) )
        = $false )
      | ( ( ~ ! [SY3142: $i] :
                ( ~ ( in @ SY3142 @ SV221 )
                | ! [SY3143: $i] :
                    ( ~ ( in @ SY3143 @ SV445 )
                    | ~ ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV721 )
                    | ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV579 ) ) )
          | ( SV579 = SV721 ) )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3404]) ).

thf(3510,plain,
    ! [SV221: $i,SV445: $i,SV579: $i,SV721: $i] :
      ( ( ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV721 )
        = $false )
      | ( ( ~ ! [SY3142: $i] :
                ( ~ ( in @ SY3142 @ SV221 )
                | ! [SY3143: $i] :
                    ( ~ ( in @ SY3143 @ SV445 )
                    | ~ ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV721 )
                    | ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV579 ) ) )
          | ( SV579 = SV721 ) )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3404]) ).

thf(3511,plain,
    ! [SV228: $i,SV751: $i,SV663: $i,SV451: $i,SV769: $i] :
      ( ( ( in @ SV769 @ ( binintersect @ SV451 @ SV663 ) )
        = $false )
      | ( ( in @ SV769 @ ( binunion @ SV663 @ SV751 ) )
        = $true )
      | ( ( in @ SV769 @ SV228 )
        = $false )
      | ( ( in @ SV751 @ ( powerset @ SV228 ) )
        = $false )
      | ( ( in @ SV663 @ ( powerset @ SV228 ) )
        = $false )
      | ( ( in @ SV451 @ ( powerset @ SV228 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3405]) ).

thf(3512,plain,
    ! [SV253: $i > $o,SV667: $i] :
      ( ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $true )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $true )
      | ( ( ~ ! [SY2491: $i] :
                ~ ~ ( ~ ( SV253 @ SY2491 )
                    | ~ ! [SY2492: $i] :
                          ( ~ ( SV253 @ SY2492 )
                          | ( SY2491 = SY2492 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3406]) ).

thf(3513,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ! [SY2491: $i] :
              ~ ~ ( ~ ( SV253 @ SY2491 )
                  | ~ ! [SY2492: $i] :
                        ( ~ ( SV253 @ SY2492 )
                        | ( SY2491 = SY2492 ) ) ) )
        = $false )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $true )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3407]) ).

thf(3514,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ! [SY2491: $i] :
              ~ ~ ( ~ ( SV253 @ SY2491 )
                  | ~ ! [SY2492: $i] :
                        ( ~ ( SV253 @ SY2492 )
                        | ( SY2491 = SY2492 ) ) ) )
        = $false )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $false )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3408]) ).

thf(3515,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV253 @ ( sK93_SY2491 @ SV667 @ SV253 ) )
                | ~ ! [SY3207: $i] :
                      ( ~ ( SV253 @ SY3207 )
                      | ( ( sK93_SY2491 @ SV667 @ SV253 )
                        = SY3207 ) ) ) )
        = $false )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $false )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3409]) ).

thf(3516,plain,
    ! [SV36: $i,SV619: $i,SV282: $i,SV734: $i] :
      ( ( ( in @ SV734 @ SV282 )
        = $false )
      | ( ( in @ SV734 @ SV619 )
        = $true )
      | ( ( subset @ SV282 @ SV619 )
        = $false )
      | ( ( in @ SV734 @ SV36 )
        = $false )
      | ( ( in @ SV619 @ ( powerset @ SV36 ) )
        = $false )
      | ( ( in @ SV282 @ ( powerset @ SV36 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3412]) ).

thf(3517,plain,
    ! [SV620: $i,SV37: $i > $o] :
      ( ( ( ! [SY3200: $i] :
              ~ ( ~ ( ~ ( SV37 @ SY3200 )
                    | ( SY3200
                      = ( sK86_SY1897 @ SV620 @ SV37 ) ) )
                | ~ ( ( SY3200
                     != ( sK86_SY1897 @ SV620 @ SV37 ) )
                    | ( SV37 @ SY3200 ) ) ) )
        = $true )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( SV37 @ ( sK59_SY3056 @ SV620 @ SV37 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3413]) ).

thf(3518,plain,
    ! [SV620: $i,SV810: $i,SV37: $i > $o] :
      ( ( ( ~ ( ~ ( ~ ( SV37 @ SV810 )
                  | ( SV810
                    = ( sK77_SY1897 @ SV620 @ SV37 ) ) )
              | ~ ( ( SV810
                   != ( sK77_SY1897 @ SV620 @ SV37 ) )
                  | ( SV37 @ SV810 ) ) ) )
        = $true )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( SV620
          = ( sK59_SY3056 @ SV620 @ SV37 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3414]) ).

thf(3519,plain,
    ! [SV621: $i,SV800: $i,SV783: $i,SV41: $i > $o] :
      ( ( ( ~ ( SV41 @ SV783 ) )
        = $true )
      | ( ( ~ ( SV41 @ SV800 )
          | ( SV783 = SV800 ) )
        = $true )
      | ( ( SV41 @ SV621 )
        = $false )
      | ( ( SV41 @ ( sK60_SY3057 @ SV621 @ SV41 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3415]) ).

thf(3520,plain,
    ! [SV621: $i,SV784: $i,SV778: $i,SV41: $i > $o] :
      ( ( ( SV41 @ SV778 )
        = $false )
      | ( ( ~ ( SV41 @ SV784 )
          | ( SV778 = SV784 ) )
        = $true )
      | ( ( SV41 @ SV621 )
        = $false )
      | ( ( SV621
          = ( sK60_SY3057 @ SV621 @ SV41 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3416]) ).

thf(3521,plain,
    ! [SV622: $i,SV801: $i,SV785: $i,SV43: $i > $o] :
      ( ( ( ~ ( SV43 @ SV785 ) )
        = $true )
      | ( ( ~ ( SV43 @ SV801 )
          | ( SV785 = SV801 ) )
        = $true )
      | ( ( SV43 @ SV622 )
        = $false )
      | ( ( SV43 @ ( sK61_SY3058 @ SV622 @ SV43 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3417]) ).

thf(3522,plain,
    ! [SV622: $i,SV786: $i,SV779: $i,SV43: $i > $o] :
      ( ( ( SV43 @ SV779 )
        = $false )
      | ( ( ~ ( SV43 @ SV786 )
          | ( SV779 = SV786 ) )
        = $true )
      | ( ( SV43 @ SV622 )
        = $false )
      | ( ( SV622
          = ( sK61_SY3058 @ SV622 @ SV43 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3418]) ).

thf(3523,plain,
    ! [SV46: $i,SV287: $i > $o,SV673: $i] :
      ( ( ( in @ ( sK78_SY2528 @ SV673 @ SV287 @ SV46 ) @ SV46 )
        = $true )
      | ( ( in @ SV673 @ SV46 )
        = $false )
      | ( ( SV287 @ SV673 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3419]) ).

thf(3524,plain,
    ! [SV624: $i,SV48: $i > $o] :
      ( ( ( ~ ( ~ ( SV48 @ ( sK87_SY1928 @ SV624 @ SV48 ) )
              | ~ ! [SY3201: $i] :
                    ( ~ ( SV48 @ SY3201 )
                    | ( ( sK87_SY1928 @ SV624 @ SV48 )
                      = SY3201 ) ) ) )
        = $true )
      | ( ( SV48 @ SV624 )
        = $false )
      | ( ( SV48 @ ( sK62_SY3060 @ SV624 @ SV48 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3421]) ).

thf(3525,plain,
    ! [SV624: $i,SV48: $i > $o] :
      ( ( ( ~ ( SV48 @ ( sK79_SY1928 @ SV624 @ SV48 ) )
          | ~ ! [SY3192: $i] :
                ( ~ ( SV48 @ SY3192 )
                | ( ( sK79_SY1928 @ SV624 @ SV48 )
                  = SY3192 ) ) )
        = $false )
      | ( ( SV48 @ SV624 )
        = $false )
      | ( ( SV624
          = ( sK62_SY3060 @ SV624 @ SV48 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3422]) ).

thf(3526,plain,
    ! [SV302: $i,SV63: $i,SV676: $i > $o,SV496: $i,SV787: $i] :
      ( ( ( in @ SV787 @ SV496 )
        = $false )
      | ( ( SV676 @ SV787 )
        = $true )
      | ( ( in @ ( sK63_SY3167 @ SV63 @ SV496 @ SV676 @ SV302 ) @ SV302 )
        = $true )
      | ( ( subset @ SV496 @ ( cartprod @ SV63 @ SV302 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3425]) ).

thf(3527,plain,
    ! [SV63: $i,SV302: $i,SV676: $i > $o,SV496: $i,SV802: $i] :
      ( ( ( ~ ( in @ SV802 @ SV496 ) )
        = $true )
      | ( ( SV676 @ SV802 )
        = $true )
      | ( ( in @ ( kpair @ ( sK44_SY3111 @ SV676 @ SV496 @ SV302 @ SV63 ) @ ( sK63_SY3167 @ SV63 @ SV496 @ SV676 @ SV302 ) ) @ SV496 )
        = $true )
      | ( ( subset @ SV496 @ ( cartprod @ SV63 @ SV302 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3426]) ).

thf(3528,plain,
    ! [SV63: $i,SV302: $i,SV676: $i > $o,SV496: $i,SV788: $i] :
      ( ( ( in @ SV788 @ SV496 )
        = $false )
      | ( ( SV676 @ SV788 )
        = $true )
      | ( ( SV676 @ ( kpair @ ( sK44_SY3111 @ SV676 @ SV496 @ SV302 @ SV63 ) @ ( sK63_SY3167 @ SV63 @ SV496 @ SV676 @ SV302 ) ) )
        = $false )
      | ( ( subset @ SV496 @ ( cartprod @ SV63 @ SV302 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3427]) ).

thf(3529,plain,
    ! [SV315: $i > $o,SV775: $i,SV77: $i > $o] :
      ( ( ( SV77 @ SV775 )
        = $false )
      | ( ( ~ ! [SY3183: $i] :
                ( ~ ( SV77 @ SY3183 )
                | ( SV775 = SY3183 ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3429]) ).

thf(3530,plain,
    ! [SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ~ ~ ! [SY2001: $i] :
                  ~ ~ ( ~ ( SV77 @ SY2001 )
                      | ~ ! [SY2002: $i] :
                            ( ~ ( SV77 @ SY2002 )
                            | ( SY2001 = SY2002 ) ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3430]) ).

thf(3531,plain,
    ! [SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ~ ! [SY2001: $i] :
                ~ ~ ( ~ ( SV77 @ SY2001 )
                    | ~ ! [SY2002: $i] :
                          ( ~ ( SV77 @ SY2002 )
                          | ( SY2001 = SY2002 ) ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3431]) ).

thf(3532,plain,
    ! [SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ~ ! [SY2001: $i] :
                ~ ~ ( ~ ( SV77 @ SY2001 )
                    | ~ ! [SY2002: $i] :
                          ( ~ ( SV77 @ SY2002 )
                          | ( SY2001 = SY2002 ) ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3432]) ).

thf(3533,plain,
    ! [SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ! [SY2001: $i] :
              ~ ~ ( ~ ( SV77 @ SY2001 )
                  | ~ ! [SY2002: $i] :
                        ( ~ ( SV77 @ SY2002 )
                        | ( SY2001 = SY2002 ) ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3433]) ).

thf(3534,plain,
    ! [SV80: $i,SV628: $i,SV318: $i] :
      ( ( ( ~ ( in @ ( sK88_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV80 ) )
        = $false )
      | ( ( SV318 = SV628 )
        = $true )
      | ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV80 )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3434]) ).

thf(3535,plain,
    ! [SV80: $i,SV628: $i,SV318: $i] :
      ( ( ( ~ ( in @ ( sK88_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV628 )
          | ( in @ ( sK88_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV318 ) )
        = $false )
      | ( ( SV318 = SV628 )
        = $true )
      | ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV80 )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3434]) ).

thf(3536,plain,
    ! [SV80: $i,SV628: $i,SV318: $i] :
      ( ( ( ~ ( in @ ( sK94_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV80 )
          | ~ ( in @ ( sK94_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV628 )
          | ( in @ ( sK94_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV318 ) )
        = $false )
      | ( ( SV318 = SV628 )
        = $true )
      | ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV318 )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3435]) ).

thf(3537,plain,
    ! [SV80: $i,SV628: $i,SV318: $i] :
      ( ( ( ~ ( in @ ( sK89_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV80 ) )
        = $false )
      | ( ( SV318 = SV628 )
        = $true )
      | ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV628 )
        = $false )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3436]) ).

thf(3538,plain,
    ! [SV80: $i,SV628: $i,SV318: $i] :
      ( ( ( ~ ( in @ ( sK89_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV628 )
          | ( in @ ( sK89_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV318 ) )
        = $false )
      | ( ( SV318 = SV628 )
        = $true )
      | ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV628 )
        = $false )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3436]) ).

thf(3539,plain,
    ! [SV87: $i,SV789: $i] :
      ( ( ( in @ SV789 @ omega )
        = $false )
      | ( ( in @ SV789 @ SV87 )
        = $true )
      | ( ( in @ emptyset @ SV87 )
        = $false )
      | ( ( in @ ( sK39_SY2033 @ SV87 ) @ omega )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3438]) ).

thf(3540,plain,
    ! [SV87: $i,SV790: $i] :
      ( ( ( in @ SV790 @ omega )
        = $false )
      | ( ( in @ SV790 @ SV87 )
        = $true )
      | ( ( in @ emptyset @ SV87 )
        = $false )
      | ( ( in @ ( sK39_SY2033 @ SV87 ) @ SV87 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3439]) ).

thf(3541,plain,
    ! [SV512: $i,SV685: $i,SV332: $i,SV96: $i,SV791: $i] :
      ( ( ( in @ SV791 @ SV96 )
        = $false )
      | ( ( ! [SY3193: $i] :
              ( ~ ( in @ SY3193 @ SV332 )
              | ~ ( in @ ( kpair @ SV791 @ SY3193 ) @ SV685 )
              | ( in @ ( kpair @ SV791 @ SY3193 ) @ SV512 ) ) )
        = $true )
      | ( ( in @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) @ SV96 )
        = $true )
      | ( ( func @ SV96 @ SV332 @ SV685 )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV512 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3440]) ).

thf(3542,plain,
    ! [SV96: $i,SV512: $i,SV685: $i,SV780: $i,SV332: $i,SV811: $i] :
      ( ( ( ~ ( in @ SV811 @ SV332 )
          | ~ ( in @ ( kpair @ SV780 @ SV811 ) @ SV685 )
          | ( in @ ( kpair @ SV780 @ SV811 ) @ SV512 ) )
        = $true )
      | ( ( in @ SV780 @ SV96 )
        = $false )
      | ( ( ( ap @ SV96 @ SV332 @ SV512 @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) )
          = ( ap @ SV96 @ SV332 @ SV685 @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) ) )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV685 )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV512 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3441]) ).

thf(3543,plain,
    ! [SV333: $i,SV513: $i,SV98: $i] :
      ( ( ( ~ ( in @ ( sK74_SY3150 @ SV98 @ SV513 @ SV333 ) @ SV333 ) )
        = $false )
      | ( ( in @ SV513 @ ( cartprod @ SV98 @ SV333 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3442]) ).

thf(3544,plain,
    ! [SV98: $i,SV333: $i,SV513: $i] :
      ( ( ( SV513
         != ( kpair @ ( sK33_SY2921 @ SV513 @ SV333 @ SV98 ) @ ( sK74_SY3150 @ SV98 @ SV513 @ SV333 ) ) )
        = $false )
      | ( ( in @ SV513 @ ( cartprod @ SV98 @ SV333 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3442]) ).

thf(3545,plain,
    ! [SV102: $i,SV764: $i,SV336: $i > $o] :
      ( ( ( SV336 @ SV764 )
        = $false )
      | ( ( in @ SV764 @ SV102 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( in @ ( sK11_SY2627 @ SV336 @ SV102 ) @ SV102 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3443]) ).

thf(3546,plain,
    ! [SV336: $i > $o,SV102: $i,SV781: $i] :
      ( ( ( ~ ( in @ SV781 @ SV102 ) )
        = $true )
      | ( ( ~ ( SV336 @ SV781 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( in @ ( sK34_SY3074 @ SV336 @ SV102 ) @ SV102 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3444]) ).

thf(3547,plain,
    ! [SV336: $i > $o,SV102: $i,SV792: $i] :
      ( ( ( ~ ( in @ SV792 @ SV102 )
          | ~ ( SV336 @ SV792 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( SV336 @ ( sK11_SY2627 @ SV336 @ SV102 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3445]) ).

thf(3548,plain,
    ! [SV336: $i > $o,SV102: $i,SV803: $i] :
      ( ( ( ~ ( ~ ( in @ SV803 @ SV102 )
              | ~ ( SV336 @ SV803 ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( SV336 @ ( sK34_SY3074 @ SV336 @ SV102 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3446]) ).

thf(3549,plain,
    ! [SV336: $i > $o,SV102: $i,SV793: $i] :
      ( ( ( ~ ( in @ SV793 @ SV102 )
          | ~ ( SV336 @ SV793 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( ( sK11_SY2627 @ SV336 @ SV102 )
          = ( sK34_SY3074 @ SV336 @ SV102 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3447]) ).

thf(3550,plain,
    ! [SV109: $i,SV794: $i] :
      ( ( ( in @ SV794 @ ( sK3_SY2100 @ SV109 ) )
        = $false )
      | ( ( ! [SY3194: $i] :
              ( ~ ( in @ SY3194 @ SV794 )
              | ( in @ SY3194 @ SV109 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3448]) ).

thf(3551,plain,
    ! [SV804: $i,SV109: $i,SV795: $i] :
      ( ( ( ~ ~ ( ~ ( in @ SV795 @ SV109 )
                | ~ ( in @ SV804 @ SV109 ) ) )
        = $true )
      | ( ( ~ ! [SY3202: $i] :
                ( ~ ( in @ SY3202 @ ( sK3_SY2100 @ SV109 ) )
                | ~ ( ~ ( ~ ( in @ SV795 @ SY3202 )
                        | ( in @ SV804 @ SY3202 ) )
                    | ~ ( ~ ( in @ SV804 @ SY3202 )
                        | ( in @ SV795 @ SY3202 ) ) ) )
          | ( SV795 = SV804 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3449]) ).

thf(3552,plain,
    ! [SV776: $i,SV109: $i,SV765: $i] :
      ( ( ( ~ ( in @ SV765 @ ( sK3_SY2100 @ SV109 ) ) )
        = $true )
      | ( ( ~ ( in @ SV776 @ ( sK3_SY2100 @ SV109 ) ) )
        = $true )
      | ( ( ! [SY3184: $i] :
              ( ~ ( in @ SY3184 @ SV765 )
              | ( in @ SY3184 @ SV776 ) )
          | ! [SY3185: $i] :
              ( ~ ( in @ SY3185 @ SV776 )
              | ( in @ SY3185 @ SV765 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3450]) ).

thf(3553,plain,
    ! [SV739: $i,SV109: $i] :
      ( ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( ~ ~ ! [SY3155: $i] :
                  ~ ( in @ SY3155 @ SV739 ) )
        = $true )
      | ( ( ~ ! [SY3156: $i] :
                ~ ~ ! [SY3157: $i] :
                      ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3156 @ ( sK3_SY2100 @ SV109 ) )
                                      | ~ ( in @ SY3157 @ SV739 ) )
                                | ~ ~ ~ ! [SY3158: $i] :
                                          ~ ~ ( ~ ( in @ SY3158 @ SY3156 )
                                              | ~ ( in @ SY3158 @ SV739 ) ) )
                          | ~ ! [SY2947: $i] :
                                ( ~ ( in @ SY2947 @ ( sK3_SY2100 @ SV109 ) )
                                | ! [SX6: $i] :
                                    ( ~ ( in @ SX6 @ SY2947 )
                                    | ( in @ SX6 @ SY3156 ) )
                                | ( in @ SY3157 @ SY2947 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3451]) ).

thf(3554,plain,
    ! [SV109: $i,SV739: $i] :
      ( ( ( ~ ! [SY3155: $i] :
                ~ ( in @ SY3155 @ SV739 ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( ~ ! [SY3156: $i] :
                ~ ~ ! [SY3157: $i] :
                      ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3156 @ ( sK3_SY2100 @ SV109 ) )
                                      | ~ ( in @ SY3157 @ SV739 ) )
                                | ~ ~ ~ ! [SY3158: $i] :
                                          ~ ~ ( ~ ( in @ SY3158 @ SY3156 )
                                              | ~ ( in @ SY3158 @ SV739 ) ) )
                          | ~ ! [SY2947: $i] :
                                ( ~ ( in @ SY2947 @ ( sK3_SY2100 @ SV109 ) )
                                | ! [SX6: $i] :
                                    ( ~ ( in @ SX6 @ SY2947 )
                                    | ( in @ SX6 @ SY3156 ) )
                                | ( in @ SY3157 @ SY2947 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3452]) ).

thf(3555,plain,
    ! [SV110: $i,SV635: $i,SV805: $i] :
      ( ( ( ~ ( ~ ( in @ SV805 @ ( sK40_SY2119 @ SV635 @ SV110 ) )
              | ~ ( in @ SV805 @ SV110 ) ) )
        = $false )
      | ( ( in @ SV635 @ SV110 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3453]) ).

thf(3556,plain,
    ! [SV636: $i,SV112: $i > $o] :
      ( ( ( SV112 @ ( sK90_SY2125 @ SV636 @ SV112 ) )
        = $true )
      | ( ( SV112 @ SV636 )
        = $false )
      | ( ( SV112 @ ( sK66_SY3077 @ SV636 @ SV112 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3454]) ).

thf(3557,plain,
    ! [SV125: $i,SV766: $i,SV353: $i > $o] :
      ( ( ( SV353 @ SV766 )
        = $false )
      | ( ( in @ SV766 @ SV125 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( in @ ( sK12_SY2657 @ SV353 @ SV125 ) @ SV125 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3456]) ).

thf(3558,plain,
    ! [SV353: $i > $o,SV125: $i,SV782: $i] :
      ( ( ( ~ ( in @ SV782 @ SV125 ) )
        = $true )
      | ( ( ~ ( SV353 @ SV782 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( in @ ( sK36_SY3079 @ SV353 @ SV125 ) @ SV125 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3457]) ).

thf(3559,plain,
    ! [SV353: $i > $o,SV125: $i,SV796: $i] :
      ( ( ( ~ ( in @ SV796 @ SV125 )
          | ~ ( SV353 @ SV796 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( SV353 @ ( sK12_SY2657 @ SV353 @ SV125 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3458]) ).

thf(3560,plain,
    ! [SV353: $i > $o,SV125: $i,SV806: $i] :
      ( ( ( ~ ( ~ ( in @ SV806 @ SV125 )
              | ~ ( SV353 @ SV806 ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( SV353 @ ( sK36_SY3079 @ SV353 @ SV125 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3459]) ).

thf(3561,plain,
    ! [SV353: $i > $o,SV125: $i,SV797: $i] :
      ( ( ( ~ ( in @ SV797 @ SV125 )
          | ~ ( SV353 @ SV797 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( ( sK12_SY2657 @ SV353 @ SV125 )
          = ( sK36_SY3079 @ SV353 @ SV125 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3460]) ).

thf(3562,plain,
    ! [SV363: $i,SV135: $i,SV690: $i > $o,SV529: $i,SV798: $i] :
      ( ( ( in @ SV798 @ SV529 )
        = $false )
      | ( ( SV690 @ SV798 )
        = $true )
      | ( ( in @ ( sK67_SY3168 @ SV135 @ SV529 @ SV690 @ SV363 ) @ SV363 )
        = $true )
      | ( ( subset @ SV529 @ ( cartprod @ SV135 @ SV363 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3461]) ).

thf(3563,plain,
    ! [SV135: $i,SV363: $i,SV690: $i > $o,SV529: $i,SV807: $i] :
      ( ( ( ~ ( in @ SV807 @ SV529 ) )
        = $true )
      | ( ( SV690 @ SV807 )
        = $true )
      | ( ( in @ ( kpair @ ( sK46_SY3122 @ SV690 @ SV529 @ SV363 @ SV135 ) @ ( sK67_SY3168 @ SV135 @ SV529 @ SV690 @ SV363 ) ) @ SV529 )
        = $true )
      | ( ( subset @ SV529 @ ( cartprod @ SV135 @ SV363 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3462]) ).

thf(3564,plain,
    ! [SV135: $i,SV363: $i,SV690: $i > $o,SV529: $i,SV799: $i] :
      ( ( ( in @ SV799 @ SV529 )
        = $false )
      | ( ( SV690 @ SV799 )
        = $true )
      | ( ( SV690 @ ( kpair @ ( sK46_SY3122 @ SV690 @ SV529 @ SV363 @ SV135 ) @ ( sK67_SY3168 @ SV135 @ SV529 @ SV690 @ SV363 ) ) )
        = $false )
      | ( ( subset @ SV529 @ ( cartprod @ SV135 @ SV363 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3463]) ).

thf(3565,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV767: $i] :
      ( ( ( in @ SV767 @ ( sK47_SY2690 @ SV147 @ SV377 ) )
        = $false )
      | ( ( ~ ! [SY3179: $i] :
                ~ ~ ( ~ ( in @ SY3179 @ SV377 )
                    | ~ ( SV147 @ SY3179 @ SV767 ) ) )
        = $true )
      | ( ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3464]) ).

thf(3566,plain,
    ! [SV767: $i,SV147: $i > $i > $o,SV377: $i] :
      ( ( ( ~ ! [SY3180: $i] :
                ~ ~ ( ~ ( in @ SY3180 @ SV377 )
                    | ~ ( SV147 @ SY3180 @ SV767 ) ) )
        = $false )
      | ( ( in @ SV767 @ ( sK47_SY2690 @ SV147 @ SV377 ) )
        = $true )
      | ( ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3465]) ).

thf(3567,plain,
    ! [SV743: $i,SV377: $i,SV147: $i > $i > $o] :
      ( ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( ~ ! [SY2690: $i] :
                ~ ! [SY2691: $i] :
                    ~ ( ~ ( ~ ( in @ SY2691 @ SY2690 )
                          | ~ ! [SY2692: $i] :
                                ~ ~ ( ~ ( in @ SY2692 @ SV377 )
                                    | ~ ( SV147 @ SY2692 @ SY2691 ) ) )
                      | ~ ( ~ ~ ! [SY2693: $i] :
                                  ~ ~ ( ~ ( in @ SY2693 @ SV377 )
                                      | ~ ( SV147 @ SY2693 @ SY2691 ) )
                          | ( in @ SY2691 @ SY2690 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3466]) ).

thf(3568,plain,
    ! [SV743: $i,SV147: $i > $i > $o,SV377: $i] :
      ( ( ( ! [SY2690: $i] :
              ~ ! [SY2691: $i] :
                  ~ ( ~ ( ~ ( in @ SY2691 @ SY2690 )
                        | ~ ! [SY2692: $i] :
                              ~ ~ ( ~ ( in @ SY2692 @ SV377 )
                                  | ~ ( SV147 @ SY2692 @ SY2691 ) ) )
                    | ~ ( ~ ~ ! [SY2693: $i] :
                                ~ ~ ( ~ ( in @ SY2693 @ SV377 )
                                    | ~ ( SV147 @ SY2693 @ SY2691 ) )
                        | ( in @ SY2691 @ SY2690 ) ) ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV743
          = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3467]) ).

thf(3569,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( ~ ( SV165 @ ( sK83_SY2244 @ SV651 @ SV165 ) )
          | ~ ! [SY3197: $i] :
                ( ~ ( SV165 @ SY3197 )
                | ( ( sK83_SY2244 @ SV651 @ SV165 )
                  = SY3197 ) ) )
        = $false )
      | ( ( SV165 @ ( sK48_SY2242 @ SV651 @ SV165 ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3469]) ).

thf(3570,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( ~ ( ~ ( SV165 @ ( sK91_SY2244 @ SV651 @ SV165 ) )
              | ~ ! [SY3203: $i] :
                    ( ~ ( SV165 @ SY3203 )
                    | ( ( sK91_SY2244 @ SV651 @ SV165 )
                      = SY3203 ) ) ) )
        = $true )
      | ( ( SV165 @ ( sK55_SY3172 @ SV651 @ SV165 ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3470]) ).

thf(3571,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( ~ ( SV165 @ ( sK84_SY2244 @ SV651 @ SV165 ) )
          | ~ ! [SY3198: $i] :
                ( ~ ( SV165 @ SY3198 )
                | ( ( sK84_SY2244 @ SV651 @ SV165 )
                  = SY3198 ) ) )
        = $false )
      | ( ( ( sK48_SY2242 @ SV651 @ SV165 )
          = ( sK55_SY3172 @ SV651 @ SV165 ) )
        = $false )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3471]) ).

thf(3572,plain,
    ! [SV168: $i,SV395: $i,SV539: $i,SV695: $i] :
      ( ( ( in @ ( kpair @ ( sK69_SY3125 @ SV695 @ SV539 @ SV395 @ SV168 ) @ ( sK75_SY3181 @ SV168 @ SV539 @ SV695 @ SV395 ) ) @ SV539 )
        = $true )
      | ( ( subset @ SV539 @ SV695 )
        = $true )
      | ( ( subset @ SV695 @ ( cartprod @ SV168 @ SV395 ) )
        = $false )
      | ( ( subset @ SV539 @ ( cartprod @ SV168 @ SV395 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3473]) ).

thf(3573,plain,
    ! [SV431: $i,SV712: $o,SV206: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV206 ) )
        = $true )
      | ( SV712 = $true )
      | ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3481]) ).

thf(3574,plain,
    ! [SV206: $i,SV712: $o,SV431: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV431 ) )
        = $false )
      | ( SV712 = $true )
      | ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3482]) ).

thf(3575,plain,
    ! [SV206: $i,SV431: $i,SV570: $i,SV712: $o] :
      ( ( SV712 = $false )
      | ( SV712 = $true )
      | ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3482]) ).

thf(3576,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV206 ) )
        = $true )
      | ( $true = $true )
      | ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3487]) ).

thf(3577,plain,
    ! [SV206: $i,SV431: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV431 ) )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3488]) ).

thf(3578,plain,
    ! [SV206: $i,SV431: $i,SV570: $i] :
      ( ( $true = $false )
      | ( $true = $true )
      | ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3488]) ).

thf(3579,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV206 ) )
        = $true )
      | ( $false = $true )
      | ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3493]) ).

thf(3580,plain,
    ! [SV206: $i,SV431: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV431 ) )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3494]) ).

thf(3581,plain,
    ! [SV206: $i,SV431: $i,SV570: $i] :
      ( ( $false = $false )
      | ( $false = $true )
      | ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3494]) ).

thf(3582,plain,
    ! [SV209: $i,SV434: $i,SV713: $i > $o,SV659: $i > $o] :
      ( ( ( ~ ( SV659 @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) )
          | ( SV713 @ ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) ) )
        = $false )
      | ( ( ~ ( ~ ( SV713 @ ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) )
              | ( SV659 @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) ) ) )
        = $true )
      | ( ( ( dsetconstr @ SV209
            @ ^ [SY3097: $i] : ( SV659 @ SY3097 ) )
          = ( dsetconstr @ SV434
            @ ^ [SY3136: $i] : ( SV713 @ SY3136 ) ) )
        = $true )
      | ( ( SV209 = SV434 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3497]) ).

thf(3583,plain,
    ! [SV660: $i,SV211: $i > $o] :
      ( ( ( ~ ( ~ ( SV211 @ ( sK92_SY2378 @ SV660 @ SV211 ) )
              | ~ ! [SY3204: $i] :
                    ( ~ ( SV211 @ SY3204 )
                    | ( ( sK92_SY2378 @ SV660 @ SV211 )
                      = SY3204 ) ) ) )
        = $true )
      | ( ( SV211 @ SV660 )
        = $false )
      | ( ( SV211 @ ( sK72_SY3099 @ SV660 @ SV211 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3498]) ).

thf(3584,plain,
    ! [SV660: $i,SV211: $i > $o] :
      ( ( ( ~ ( SV211 @ ( sK85_SY2378 @ SV660 @ SV211 ) )
          | ~ ! [SY3199: $i] :
                ( ~ ( SV211 @ SY3199 )
                | ( ( sK85_SY2378 @ SV660 @ SV211 )
                  = SY3199 ) ) )
        = $false )
      | ( ( SV211 @ SV660 )
        = $false )
      | ( ( SV660
          = ( sK72_SY3099 @ SV660 @ SV211 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3499]) ).

thf(3585,plain,
    ! [SV438: $i > $o,SV808: $i,SV214: $i > $o] :
      ( ( ( ~ ( ~ ( SV214 @ SV808 )
              | ~ ! [SY3205: $i] :
                    ( ~ ( SV214 @ SY3205 )
                    | ( SV808 = SY3205 ) ) ) )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3500]) ).

thf(3586,plain,
    ! [SV214: $i > $o,SV809: $i,SV438: $i > $o] :
      ( ( ( ~ ( ~ ( SV438 @ SV809 )
              | ~ ! [SY3206: $i] :
                    ( ~ ( SV438 @ SY3206 )
                    | ( SV809 = SY3206 ) ) ) )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3501]) ).

thf(3587,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ( ~ ~ ! [SY2388: $i] :
                      ~ ~ ( ~ ( SV214 @ SY2388 )
                          | ~ ! [SY2389: $i] :
                                ( ~ ( SV214 @ SY2389 )
                                | ( SY2388 = SY2389 ) ) )
              | ~ ! [SY2801: $i] :
                    ~ ~ ( ~ ( SV438 @ SY2801 )
                        | ~ ! [SY2802: $i] :
                              ( ~ ( SV438 @ SY2802 )
                              | ( SY2801 = SY2802 ) ) ) )
          | ~ ( ~ ~ ! [SY2803: $i] :
                      ~ ~ ( ~ ( SV438 @ SY2803 )
                          | ~ ! [SY2804: $i] :
                                ( ~ ( SV438 @ SY2804 )
                                | ( SY2803 = SY2804 ) ) )
              | ~ ! [SY2394: $i] :
                    ~ ~ ( ~ ( SV214 @ SY2394 )
                        | ~ ! [SY2395: $i] :
                              ( ~ ( SV214 @ SY2395 )
                              | ( SY2394 = SY2395 ) ) ) ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3502]) ).

thf(3588,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ( ~ ~ ! [SY2388: $i] :
                      ~ ~ ( ~ ( SV214 @ SY2388 )
                          | ~ ! [SY2389: $i] :
                                ( ~ ( SV214 @ SY2389 )
                                | ( SY2388 = SY2389 ) ) )
              | ~ ! [SY2801: $i] :
                    ~ ~ ( ~ ( SV438 @ SY2801 )
                        | ~ ! [SY2802: $i] :
                              ( ~ ( SV438 @ SY2802 )
                              | ( SY2801 = SY2802 ) ) ) ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3503]) ).

thf(3589,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ( ~ ~ ! [SY2803: $i] :
                      ~ ~ ( ~ ( SV438 @ SY2803 )
                          | ~ ! [SY2804: $i] :
                                ( ~ ( SV438 @ SY2804 )
                                | ( SY2803 = SY2804 ) ) )
              | ~ ! [SY2394: $i] :
                    ~ ~ ( ~ ( SV214 @ SY2394 )
                        | ~ ! [SY2395: $i] :
                              ( ~ ( SV214 @ SY2395 )
                              | ( SY2394 = SY2395 ) ) ) ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3503]) ).

thf(3590,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ( ~ ~ ! [SY2388: $i] :
                      ~ ~ ( ~ ( SV214 @ SY2388 )
                          | ~ ! [SY2389: $i] :
                                ( ~ ( SV214 @ SY2389 )
                                | ( SY2388 = SY2389 ) ) )
              | ~ ! [SY2801: $i] :
                    ~ ~ ( ~ ( SV438 @ SY2801 )
                        | ~ ! [SY2802: $i] :
                              ( ~ ( SV438 @ SY2802 )
                              | ( SY2801 = SY2802 ) ) ) ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3504]) ).

thf(3591,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ( ~ ~ ! [SY2803: $i] :
                      ~ ~ ( ~ ( SV438 @ SY2803 )
                          | ~ ! [SY2804: $i] :
                                ( ~ ( SV438 @ SY2804 )
                                | ( SY2803 = SY2804 ) ) )
              | ~ ! [SY2394: $i] :
                    ~ ~ ( ~ ( SV214 @ SY2394 )
                        | ~ ! [SY2395: $i] :
                              ( ~ ( SV214 @ SY2395 )
                              | ( SY2394 = SY2395 ) ) ) ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3504]) ).

thf(3592,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ~ ! [SY2388: $i] :
                  ~ ~ ( ~ ( SV214 @ SY2388 )
                      | ~ ! [SY2389: $i] :
                            ( ~ ( SV214 @ SY2389 )
                            | ( SY2388 = SY2389 ) ) )
          | ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3505]) ).

thf(3593,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ~ ! [SY2803: $i] :
                  ~ ~ ( ~ ( SV438 @ SY2803 )
                      | ~ ! [SY2804: $i] :
                            ( ~ ( SV438 @ SY2804 )
                            | ( SY2803 = SY2804 ) ) )
          | ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3506]) ).

thf(3594,plain,
    ! [SV221: $i,SV445: $i,SV721: $i,SV579: $i] :
      ( ( ( ~ ( in @ ( sK95_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ SV221 )
          | ! [SY3208: $i] :
              ( ~ ( in @ SY3208 @ SV445 )
              | ~ ( in @ ( kpair @ ( sK95_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ SY3208 ) @ SV721 )
              | ( in @ ( kpair @ ( sK95_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ SY3208 ) @ SV579 ) ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ SV221 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3507]) ).

thf(3595,plain,
    ! [SV579: $i,SV721: $i,SV445: $i,SV221: $i] :
      ( ( ( ~ ! [SY3142: $i] :
                ( ~ ( in @ SY3142 @ SV221 )
                | ! [SY3143: $i] :
                    ( ~ ( in @ SY3143 @ SV445 )
                    | ~ ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV721 )
                    | ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV579 ) ) ) )
        = $true )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) @ SV445 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3508]) ).

thf(3596,plain,
    ! [SV221: $i,SV445: $i,SV579: $i,SV721: $i] :
      ( ( ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV579 )
        = $true )
      | ( ( ~ ! [SY3142: $i] :
                ( ~ ( in @ SY3142 @ SV221 )
                | ! [SY3143: $i] :
                    ( ~ ( in @ SY3143 @ SV445 )
                    | ~ ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV721 )
                    | ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV579 ) ) )
          | ( SV579 = SV721 ) )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3509]) ).

thf(3597,plain,
    ! [SV579: $i,SV721: $i,SV445: $i,SV221: $i] :
      ( ( ( ~ ! [SY3142: $i] :
                ( ~ ( in @ SY3142 @ SV221 )
                | ! [SY3143: $i] :
                    ( ~ ( in @ SY3143 @ SV445 )
                    | ~ ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV721 )
                    | ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV579 ) ) ) )
        = $true )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV721 )
        = $false )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3510]) ).

thf(3598,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ! [SY2491: $i] :
              ~ ~ ( ~ ( SV253 @ SY2491 )
                  | ~ ! [SY2492: $i] :
                        ( ~ ( SV253 @ SY2492 )
                        | ( SY2491 = SY2492 ) ) ) )
        = $false )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $true )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3512]) ).

thf(3599,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV253 @ ( sK96_SY2491 @ SV667 @ SV253 ) )
                | ~ ! [SY3209: $i] :
                      ( ~ ( SV253 @ SY3209 )
                      | ( ( sK96_SY2491 @ SV667 @ SV253 )
                        = SY3209 ) ) ) )
        = $false )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $true )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3513]) ).

thf(3600,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV253 @ ( sK97_SY2491 @ SV667 @ SV253 ) )
                | ~ ! [SY3210: $i] :
                      ( ~ ( SV253 @ SY3210 )
                      | ( ( sK97_SY2491 @ SV667 @ SV253 )
                        = SY3210 ) ) ) )
        = $false )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $false )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[3514]) ).

thf(3601,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ~ ( ~ ( SV253 @ ( sK93_SY2491 @ SV667 @ SV253 ) )
              | ~ ! [SY3207: $i] :
                    ( ~ ( SV253 @ SY3207 )
                    | ( ( sK93_SY2491 @ SV667 @ SV253 )
                      = SY3207 ) ) ) )
        = $true )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $false )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3515]) ).

thf(3602,plain,
    ! [SV620: $i,SV812: $i,SV37: $i > $o] :
      ( ( ( ~ ( ~ ( ~ ( SV37 @ SV812 )
                  | ( SV812
                    = ( sK86_SY1897 @ SV620 @ SV37 ) ) )
              | ~ ( ( SV812
                   != ( sK86_SY1897 @ SV620 @ SV37 ) )
                  | ( SV37 @ SV812 ) ) ) )
        = $true )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( SV37 @ ( sK59_SY3056 @ SV620 @ SV37 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3517]) ).

thf(3603,plain,
    ! [SV620: $i,SV810: $i,SV37: $i > $o] :
      ( ( ( ~ ( ~ ( SV37 @ SV810 )
              | ( SV810
                = ( sK77_SY1897 @ SV620 @ SV37 ) ) )
          | ~ ( ( SV810
               != ( sK77_SY1897 @ SV620 @ SV37 ) )
              | ( SV37 @ SV810 ) ) )
        = $false )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( SV620
          = ( sK59_SY3056 @ SV620 @ SV37 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3518]) ).

thf(3604,plain,
    ! [SV621: $i,SV800: $i,SV783: $i,SV41: $i > $o] :
      ( ( ( SV41 @ SV783 )
        = $false )
      | ( ( ~ ( SV41 @ SV800 )
          | ( SV783 = SV800 ) )
        = $true )
      | ( ( SV41 @ SV621 )
        = $false )
      | ( ( SV41 @ ( sK60_SY3057 @ SV621 @ SV41 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3519]) ).

thf(3605,plain,
    ! [SV621: $i,SV778: $i,SV784: $i,SV41: $i > $o] :
      ( ( ( ~ ( SV41 @ SV784 ) )
        = $true )
      | ( ( SV778 = SV784 )
        = $true )
      | ( ( SV41 @ SV778 )
        = $false )
      | ( ( SV41 @ SV621 )
        = $false )
      | ( ( SV621
          = ( sK60_SY3057 @ SV621 @ SV41 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3520]) ).

thf(3606,plain,
    ! [SV622: $i,SV801: $i,SV785: $i,SV43: $i > $o] :
      ( ( ( SV43 @ SV785 )
        = $false )
      | ( ( ~ ( SV43 @ SV801 )
          | ( SV785 = SV801 ) )
        = $true )
      | ( ( SV43 @ SV622 )
        = $false )
      | ( ( SV43 @ ( sK61_SY3058 @ SV622 @ SV43 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3521]) ).

thf(3607,plain,
    ! [SV622: $i,SV779: $i,SV786: $i,SV43: $i > $o] :
      ( ( ( ~ ( SV43 @ SV786 ) )
        = $true )
      | ( ( SV779 = SV786 )
        = $true )
      | ( ( SV43 @ SV779 )
        = $false )
      | ( ( SV43 @ SV622 )
        = $false )
      | ( ( SV622
          = ( sK61_SY3058 @ SV622 @ SV43 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3522]) ).

thf(3608,plain,
    ! [SV624: $i,SV48: $i > $o] :
      ( ( ( ~ ( SV48 @ ( sK87_SY1928 @ SV624 @ SV48 ) )
          | ~ ! [SY3201: $i] :
                ( ~ ( SV48 @ SY3201 )
                | ( ( sK87_SY1928 @ SV624 @ SV48 )
                  = SY3201 ) ) )
        = $false )
      | ( ( SV48 @ SV624 )
        = $false )
      | ( ( SV48 @ ( sK62_SY3060 @ SV624 @ SV48 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3524]) ).

thf(3609,plain,
    ! [SV624: $i,SV48: $i > $o] :
      ( ( ( ~ ( SV48 @ ( sK79_SY1928 @ SV624 @ SV48 ) ) )
        = $false )
      | ( ( SV48 @ SV624 )
        = $false )
      | ( ( SV624
          = ( sK62_SY3060 @ SV624 @ SV48 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3525]) ).

thf(3610,plain,
    ! [SV624: $i,SV48: $i > $o] :
      ( ( ( ~ ! [SY3192: $i] :
                ( ~ ( SV48 @ SY3192 )
                | ( ( sK79_SY1928 @ SV624 @ SV48 )
                  = SY3192 ) ) )
        = $false )
      | ( ( SV48 @ SV624 )
        = $false )
      | ( ( SV624
          = ( sK62_SY3060 @ SV624 @ SV48 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3525]) ).

thf(3611,plain,
    ! [SV63: $i,SV302: $i,SV676: $i > $o,SV496: $i,SV802: $i] :
      ( ( ( in @ SV802 @ SV496 )
        = $false )
      | ( ( SV676 @ SV802 )
        = $true )
      | ( ( in @ ( kpair @ ( sK44_SY3111 @ SV676 @ SV496 @ SV302 @ SV63 ) @ ( sK63_SY3167 @ SV63 @ SV496 @ SV676 @ SV302 ) ) @ SV496 )
        = $true )
      | ( ( subset @ SV496 @ ( cartprod @ SV63 @ SV302 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3527]) ).

thf(3612,plain,
    ! [SV315: $i > $o,SV775: $i,SV77: $i > $o] :
      ( ( ( ! [SY3183: $i] :
              ( ~ ( SV77 @ SY3183 )
              | ( SV775 = SY3183 ) ) )
        = $false )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3529]) ).

thf(3613,plain,
    ! [SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ~ ! [SY2001: $i] :
                ~ ~ ( ~ ( SV77 @ SY2001 )
                    | ~ ! [SY2002: $i] :
                          ( ~ ( SV77 @ SY2002 )
                          | ( SY2001 = SY2002 ) ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3530]) ).

thf(3614,plain,
    ! [SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ! [SY2001: $i] :
              ~ ~ ( ~ ( SV77 @ SY2001 )
                  | ~ ! [SY2002: $i] :
                        ( ~ ( SV77 @ SY2002 )
                        | ( SY2001 = SY2002 ) ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3531]) ).

thf(3615,plain,
    ! [SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ! [SY2001: $i] :
              ~ ~ ( ~ ( SV77 @ SY2001 )
                  | ~ ! [SY2002: $i] :
                        ( ~ ( SV77 @ SY2002 )
                        | ( SY2001 = SY2002 ) ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3532]) ).

thf(3616,plain,
    ! [SV315: $i > $o,SV813: $i,SV77: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV77 @ SV813 )
                | ~ ! [SY3211: $i] :
                      ( ~ ( SV77 @ SY3211 )
                      | ( SV813 = SY3211 ) ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3533]) ).

thf(3617,plain,
    ! [SV80: $i,SV628: $i,SV318: $i] :
      ( ( ( in @ ( sK88_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV80 )
        = $true )
      | ( ( SV318 = SV628 )
        = $true )
      | ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV80 )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3534]) ).

thf(3618,plain,
    ! [SV80: $i,SV628: $i,SV318: $i] :
      ( ( ( ~ ( in @ ( sK88_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV628 ) )
        = $false )
      | ( ( SV318 = SV628 )
        = $true )
      | ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV80 )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3535]) ).

thf(3619,plain,
    ! [SV80: $i,SV628: $i,SV318: $i] :
      ( ( ( in @ ( sK88_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV318 )
        = $false )
      | ( ( SV318 = SV628 )
        = $true )
      | ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV80 )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3535]) ).

thf(3620,plain,
    ! [SV80: $i,SV628: $i,SV318: $i] :
      ( ( ( ~ ( in @ ( sK94_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV80 ) )
        = $false )
      | ( ( SV318 = SV628 )
        = $true )
      | ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV318 )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3536]) ).

thf(3621,plain,
    ! [SV80: $i,SV628: $i,SV318: $i] :
      ( ( ( ~ ( in @ ( sK94_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV628 )
          | ( in @ ( sK94_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV318 ) )
        = $false )
      | ( ( SV318 = SV628 )
        = $true )
      | ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV318 )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3536]) ).

thf(3622,plain,
    ! [SV80: $i,SV628: $i,SV318: $i] :
      ( ( ( in @ ( sK89_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV80 )
        = $true )
      | ( ( SV318 = SV628 )
        = $true )
      | ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV628 )
        = $false )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3537]) ).

thf(3623,plain,
    ! [SV80: $i,SV628: $i,SV318: $i] :
      ( ( ( ~ ( in @ ( sK89_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV628 ) )
        = $false )
      | ( ( SV318 = SV628 )
        = $true )
      | ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV628 )
        = $false )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3538]) ).

thf(3624,plain,
    ! [SV80: $i,SV628: $i,SV318: $i] :
      ( ( ( in @ ( sK89_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV318 )
        = $false )
      | ( ( SV318 = SV628 )
        = $true )
      | ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV628 )
        = $false )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3538]) ).

thf(3625,plain,
    ! [SV96: $i,SV512: $i,SV685: $i,SV791: $i,SV332: $i,SV814: $i] :
      ( ( ( ~ ( in @ SV814 @ SV332 )
          | ~ ( in @ ( kpair @ SV791 @ SV814 ) @ SV685 )
          | ( in @ ( kpair @ SV791 @ SV814 ) @ SV512 ) )
        = $true )
      | ( ( in @ SV791 @ SV96 )
        = $false )
      | ( ( in @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) @ SV96 )
        = $true )
      | ( ( func @ SV96 @ SV332 @ SV685 )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV512 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3541]) ).

thf(3626,plain,
    ! [SV96: $i,SV512: $i,SV685: $i,SV780: $i,SV332: $i,SV811: $i] :
      ( ( ( ~ ( in @ SV811 @ SV332 ) )
        = $true )
      | ( ( ~ ( in @ ( kpair @ SV780 @ SV811 ) @ SV685 )
          | ( in @ ( kpair @ SV780 @ SV811 ) @ SV512 ) )
        = $true )
      | ( ( in @ SV780 @ SV96 )
        = $false )
      | ( ( ( ap @ SV96 @ SV332 @ SV512 @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) )
          = ( ap @ SV96 @ SV332 @ SV685 @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) ) )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV685 )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV512 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3542]) ).

thf(3627,plain,
    ! [SV333: $i,SV513: $i,SV98: $i] :
      ( ( ( in @ ( sK74_SY3150 @ SV98 @ SV513 @ SV333 ) @ SV333 )
        = $true )
      | ( ( in @ SV513 @ ( cartprod @ SV98 @ SV333 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3543]) ).

thf(3628,plain,
    ! [SV98: $i,SV333: $i,SV513: $i] :
      ( ( ( SV513
          = ( kpair @ ( sK33_SY2921 @ SV513 @ SV333 @ SV98 ) @ ( sK74_SY3150 @ SV98 @ SV513 @ SV333 ) ) )
        = $true )
      | ( ( in @ SV513 @ ( cartprod @ SV98 @ SV333 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3544]) ).

thf(3629,plain,
    ! [SV336: $i > $o,SV102: $i,SV781: $i] :
      ( ( ( in @ SV781 @ SV102 )
        = $false )
      | ( ( ~ ( SV336 @ SV781 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( in @ ( sK34_SY3074 @ SV336 @ SV102 ) @ SV102 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3546]) ).

thf(3630,plain,
    ! [SV336: $i > $o,SV102: $i,SV792: $i] :
      ( ( ( ~ ( in @ SV792 @ SV102 ) )
        = $true )
      | ( ( ~ ( SV336 @ SV792 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( SV336 @ ( sK11_SY2627 @ SV336 @ SV102 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3547]) ).

thf(3631,plain,
    ! [SV336: $i > $o,SV102: $i,SV803: $i] :
      ( ( ( ~ ( in @ SV803 @ SV102 )
          | ~ ( SV336 @ SV803 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( SV336 @ ( sK34_SY3074 @ SV336 @ SV102 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3548]) ).

thf(3632,plain,
    ! [SV336: $i > $o,SV102: $i,SV793: $i] :
      ( ( ( ~ ( in @ SV793 @ SV102 ) )
        = $true )
      | ( ( ~ ( SV336 @ SV793 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( ( sK11_SY2627 @ SV336 @ SV102 )
          = ( sK34_SY3074 @ SV336 @ SV102 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3549]) ).

thf(3633,plain,
    ! [SV109: $i,SV794: $i,SV815: $i] :
      ( ( ( ~ ( in @ SV815 @ SV794 )
          | ( in @ SV815 @ SV109 ) )
        = $true )
      | ( ( in @ SV794 @ ( sK3_SY2100 @ SV109 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3550]) ).

thf(3634,plain,
    ! [SV804: $i,SV109: $i,SV795: $i] :
      ( ( ( ~ ( ~ ( in @ SV795 @ SV109 )
              | ~ ( in @ SV804 @ SV109 ) ) )
        = $false )
      | ( ( ~ ! [SY3202: $i] :
                ( ~ ( in @ SY3202 @ ( sK3_SY2100 @ SV109 ) )
                | ~ ( ~ ( ~ ( in @ SV795 @ SY3202 )
                        | ( in @ SV804 @ SY3202 ) )
                    | ~ ( ~ ( in @ SV804 @ SY3202 )
                        | ( in @ SV795 @ SY3202 ) ) ) )
          | ( SV795 = SV804 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3551]) ).

thf(3635,plain,
    ! [SV776: $i,SV109: $i,SV765: $i] :
      ( ( ( in @ SV765 @ ( sK3_SY2100 @ SV109 ) )
        = $false )
      | ( ( ~ ( in @ SV776 @ ( sK3_SY2100 @ SV109 ) ) )
        = $true )
      | ( ( ! [SY3184: $i] :
              ( ~ ( in @ SY3184 @ SV765 )
              | ( in @ SY3184 @ SV776 ) )
          | ! [SY3185: $i] :
              ( ~ ( in @ SY3185 @ SV776 )
              | ( in @ SY3185 @ SV765 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3552]) ).

thf(3636,plain,
    ! [SV109: $i,SV739: $i] :
      ( ( ( ~ ! [SY3155: $i] :
                ~ ( in @ SY3155 @ SV739 ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( ~ ! [SY3156: $i] :
                ~ ~ ! [SY3157: $i] :
                      ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3156 @ ( sK3_SY2100 @ SV109 ) )
                                      | ~ ( in @ SY3157 @ SV739 ) )
                                | ~ ~ ~ ! [SY3158: $i] :
                                          ~ ~ ( ~ ( in @ SY3158 @ SY3156 )
                                              | ~ ( in @ SY3158 @ SV739 ) ) )
                          | ~ ! [SY2947: $i] :
                                ( ~ ( in @ SY2947 @ ( sK3_SY2100 @ SV109 ) )
                                | ! [SX6: $i] :
                                    ( ~ ( in @ SX6 @ SY2947 )
                                    | ( in @ SX6 @ SY3156 ) )
                                | ( in @ SY3157 @ SY2947 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3553]) ).

thf(3637,plain,
    ! [SV109: $i,SV739: $i] :
      ( ( ( ! [SY3155: $i] :
              ~ ( in @ SY3155 @ SV739 ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( ~ ! [SY3156: $i] :
                ~ ~ ! [SY3157: $i] :
                      ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3156 @ ( sK3_SY2100 @ SV109 ) )
                                      | ~ ( in @ SY3157 @ SV739 ) )
                                | ~ ~ ~ ! [SY3158: $i] :
                                          ~ ~ ( ~ ( in @ SY3158 @ SY3156 )
                                              | ~ ( in @ SY3158 @ SV739 ) ) )
                          | ~ ! [SY2947: $i] :
                                ( ~ ( in @ SY2947 @ ( sK3_SY2100 @ SV109 ) )
                                | ! [SX6: $i] :
                                    ( ~ ( in @ SX6 @ SY2947 )
                                    | ( in @ SX6 @ SY3156 ) )
                                | ( in @ SY3157 @ SY2947 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3554]) ).

thf(3638,plain,
    ! [SV110: $i,SV635: $i,SV805: $i] :
      ( ( ( ~ ( in @ SV805 @ ( sK40_SY2119 @ SV635 @ SV110 ) )
          | ~ ( in @ SV805 @ SV110 ) )
        = $true )
      | ( ( in @ SV635 @ SV110 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3555]) ).

thf(3639,plain,
    ! [SV353: $i > $o,SV125: $i,SV782: $i] :
      ( ( ( in @ SV782 @ SV125 )
        = $false )
      | ( ( ~ ( SV353 @ SV782 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( in @ ( sK36_SY3079 @ SV353 @ SV125 ) @ SV125 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3558]) ).

thf(3640,plain,
    ! [SV353: $i > $o,SV125: $i,SV796: $i] :
      ( ( ( ~ ( in @ SV796 @ SV125 ) )
        = $true )
      | ( ( ~ ( SV353 @ SV796 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( SV353 @ ( sK12_SY2657 @ SV353 @ SV125 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3559]) ).

thf(3641,plain,
    ! [SV353: $i > $o,SV125: $i,SV806: $i] :
      ( ( ( ~ ( in @ SV806 @ SV125 )
          | ~ ( SV353 @ SV806 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( SV353 @ ( sK36_SY3079 @ SV353 @ SV125 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3560]) ).

thf(3642,plain,
    ! [SV353: $i > $o,SV125: $i,SV797: $i] :
      ( ( ( ~ ( in @ SV797 @ SV125 ) )
        = $true )
      | ( ( ~ ( SV353 @ SV797 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( ( sK12_SY2657 @ SV353 @ SV125 )
          = ( sK36_SY3079 @ SV353 @ SV125 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3561]) ).

thf(3643,plain,
    ! [SV135: $i,SV363: $i,SV690: $i > $o,SV529: $i,SV807: $i] :
      ( ( ( in @ SV807 @ SV529 )
        = $false )
      | ( ( SV690 @ SV807 )
        = $true )
      | ( ( in @ ( kpair @ ( sK46_SY3122 @ SV690 @ SV529 @ SV363 @ SV135 ) @ ( sK67_SY3168 @ SV135 @ SV529 @ SV690 @ SV363 ) ) @ SV529 )
        = $true )
      | ( ( subset @ SV529 @ ( cartprod @ SV135 @ SV363 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3563]) ).

thf(3644,plain,
    ! [SV767: $i,SV147: $i > $i > $o,SV377: $i] :
      ( ( ( ! [SY3179: $i] :
              ~ ~ ( ~ ( in @ SY3179 @ SV377 )
                  | ~ ( SV147 @ SY3179 @ SV767 ) ) )
        = $false )
      | ( ( in @ SV767 @ ( sK47_SY2690 @ SV147 @ SV377 ) )
        = $false )
      | ( ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3565]) ).

thf(3645,plain,
    ! [SV767: $i,SV147: $i > $i > $o,SV377: $i] :
      ( ( ( ! [SY3180: $i] :
              ~ ~ ( ~ ( in @ SY3180 @ SV377 )
                  | ~ ( SV147 @ SY3180 @ SV767 ) ) )
        = $true )
      | ( ( in @ SV767 @ ( sK47_SY2690 @ SV147 @ SV377 ) )
        = $true )
      | ( ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3566]) ).

thf(3646,plain,
    ! [SV743: $i,SV147: $i > $i > $o,SV377: $i] :
      ( ( ( ! [SY2690: $i] :
              ~ ! [SY2691: $i] :
                  ~ ( ~ ( ~ ( in @ SY2691 @ SY2690 )
                        | ~ ! [SY2692: $i] :
                              ~ ~ ( ~ ( in @ SY2692 @ SV377 )
                                  | ~ ( SV147 @ SY2692 @ SY2691 ) ) )
                    | ~ ( ~ ~ ! [SY2693: $i] :
                                ~ ~ ( ~ ( in @ SY2693 @ SV377 )
                                    | ~ ( SV147 @ SY2693 @ SY2691 ) )
                        | ( in @ SY2691 @ SY2690 ) ) ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3567]) ).

thf(3647,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV743: $i] :
      ( ( ( ~ ! [SY3212: $i] :
                ~ ( ~ ( ~ ( in @ SY3212 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) )
                      | ~ ! [SY2692: $i] :
                            ~ ~ ( ~ ( in @ SY2692 @ SV377 )
                                | ~ ( SV147 @ SY2692 @ SY3212 ) ) )
                  | ~ ( ~ ~ ! [SY2693: $i] :
                              ~ ~ ( ~ ( in @ SY2693 @ SV377 )
                                  | ~ ( SV147 @ SY2693 @ SY3212 ) )
                      | ( in @ SY3212 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) ) ) ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV743
          = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3568]) ).

thf(3648,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( ~ ( SV165 @ ( sK83_SY2244 @ SV651 @ SV165 ) ) )
        = $false )
      | ( ( SV165 @ ( sK48_SY2242 @ SV651 @ SV165 ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3569]) ).

thf(3649,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( ~ ! [SY3197: $i] :
                ( ~ ( SV165 @ SY3197 )
                | ( ( sK83_SY2244 @ SV651 @ SV165 )
                  = SY3197 ) ) )
        = $false )
      | ( ( SV165 @ ( sK48_SY2242 @ SV651 @ SV165 ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3569]) ).

thf(3650,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( ~ ( SV165 @ ( sK91_SY2244 @ SV651 @ SV165 ) )
          | ~ ! [SY3203: $i] :
                ( ~ ( SV165 @ SY3203 )
                | ( ( sK91_SY2244 @ SV651 @ SV165 )
                  = SY3203 ) ) )
        = $false )
      | ( ( SV165 @ ( sK55_SY3172 @ SV651 @ SV165 ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3570]) ).

thf(3651,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( ~ ( SV165 @ ( sK84_SY2244 @ SV651 @ SV165 ) ) )
        = $false )
      | ( ( ( sK48_SY2242 @ SV651 @ SV165 )
          = ( sK55_SY3172 @ SV651 @ SV165 ) )
        = $false )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3571]) ).

thf(3652,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( ~ ! [SY3198: $i] :
                ( ~ ( SV165 @ SY3198 )
                | ( ( sK84_SY2244 @ SV651 @ SV165 )
                  = SY3198 ) ) )
        = $false )
      | ( ( ( sK48_SY2242 @ SV651 @ SV165 )
          = ( sK55_SY3172 @ SV651 @ SV165 ) )
        = $false )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3571]) ).

thf(3653,plain,
    ! [SV431: $i,SV712: $o,SV206: $i,SV570: $i] :
      ( ( ( in @ SV570 @ SV206 )
        = $false )
      | ( SV712 = $true )
      | ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3573]) ).

thf(3654,plain,
    ! [SV206: $i,SV712: $o,SV431: $i,SV570: $i] :
      ( ( ( in @ SV570 @ SV431 )
        = $true )
      | ( SV712 = $true )
      | ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3574]) ).

thf(3655,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( in @ SV570 @ SV206 )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3576]) ).

thf(3656,plain,
    ! [SV206: $i,SV431: $i,SV570: $i] :
      ( ( ( in @ SV570 @ SV431 )
        = $true )
      | ( $true = $true )
      | ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3577]) ).

thf(3657,plain,
    ! [SV431: $i,SV206: $i,SV570: $i] :
      ( ( ( in @ SV570 @ SV206 )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3579]) ).

thf(3658,plain,
    ! [SV206: $i,SV431: $i,SV570: $i] :
      ( ( ( in @ SV570 @ SV431 )
        = $true )
      | ( $false = $true )
      | ( ( in @ SV570 @ SV431 )
        = $false )
      | ( ( in @ SV570 @ ( symdiff @ SV206 @ SV431 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3580]) ).

thf(3659,plain,
    ! [SV209: $i,SV434: $i,SV713: $i > $o,SV659: $i > $o] :
      ( ( ( ~ ( SV659 @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) ) )
        = $false )
      | ( ( ~ ( ~ ( SV713 @ ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) )
              | ( SV659 @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) ) ) )
        = $true )
      | ( ( ( dsetconstr @ SV209
            @ ^ [SY3097: $i] : ( SV659 @ SY3097 ) )
          = ( dsetconstr @ SV434
            @ ^ [SY3136: $i] : ( SV713 @ SY3136 ) ) )
        = $true )
      | ( ( SV209 = SV434 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3582]) ).

thf(3660,plain,
    ! [SV434: $i,SV659: $i > $o,SV209: $i,SV713: $i > $o] :
      ( ( ( SV713 @ ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) )
        = $false )
      | ( ( ~ ( ~ ( SV713 @ ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) )
              | ( SV659 @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) ) ) )
        = $true )
      | ( ( ( dsetconstr @ SV209
            @ ^ [SY3097: $i] : ( SV659 @ SY3097 ) )
          = ( dsetconstr @ SV434
            @ ^ [SY3136: $i] : ( SV713 @ SY3136 ) ) )
        = $true )
      | ( ( SV209 = SV434 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3582]) ).

thf(3661,plain,
    ! [SV660: $i,SV211: $i > $o] :
      ( ( ( ~ ( SV211 @ ( sK92_SY2378 @ SV660 @ SV211 ) )
          | ~ ! [SY3204: $i] :
                ( ~ ( SV211 @ SY3204 )
                | ( ( sK92_SY2378 @ SV660 @ SV211 )
                  = SY3204 ) ) )
        = $false )
      | ( ( SV211 @ SV660 )
        = $false )
      | ( ( SV211 @ ( sK72_SY3099 @ SV660 @ SV211 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3583]) ).

thf(3662,plain,
    ! [SV660: $i,SV211: $i > $o] :
      ( ( ( ~ ( SV211 @ ( sK85_SY2378 @ SV660 @ SV211 ) ) )
        = $false )
      | ( ( SV211 @ SV660 )
        = $false )
      | ( ( SV660
          = ( sK72_SY3099 @ SV660 @ SV211 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3584]) ).

thf(3663,plain,
    ! [SV660: $i,SV211: $i > $o] :
      ( ( ( ~ ! [SY3199: $i] :
                ( ~ ( SV211 @ SY3199 )
                | ( ( sK85_SY2378 @ SV660 @ SV211 )
                  = SY3199 ) ) )
        = $false )
      | ( ( SV211 @ SV660 )
        = $false )
      | ( ( SV660
          = ( sK72_SY3099 @ SV660 @ SV211 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3584]) ).

thf(3664,plain,
    ! [SV438: $i > $o,SV808: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV808 )
          | ~ ! [SY3205: $i] :
                ( ~ ( SV214 @ SY3205 )
                | ( SV808 = SY3205 ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3585]) ).

thf(3665,plain,
    ! [SV214: $i > $o,SV809: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV809 )
          | ~ ! [SY3206: $i] :
                ( ~ ( SV438 @ SY3206 )
                | ( SV809 = SY3206 ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3586]) ).

thf(3666,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ( ~ ~ ! [SY2388: $i] :
                      ~ ~ ( ~ ( SV214 @ SY2388 )
                          | ~ ! [SY2389: $i] :
                                ( ~ ( SV214 @ SY2389 )
                                | ( SY2388 = SY2389 ) ) )
              | ~ ! [SY2801: $i] :
                    ~ ~ ( ~ ( SV438 @ SY2801 )
                        | ~ ! [SY2802: $i] :
                              ( ~ ( SV438 @ SY2802 )
                              | ( SY2801 = SY2802 ) ) ) ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3587]) ).

thf(3667,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ( ~ ~ ! [SY2803: $i] :
                      ~ ~ ( ~ ( SV438 @ SY2803 )
                          | ~ ! [SY2804: $i] :
                                ( ~ ( SV438 @ SY2804 )
                                | ( SY2803 = SY2804 ) ) )
              | ~ ! [SY2394: $i] :
                    ~ ~ ( ~ ( SV214 @ SY2394 )
                        | ~ ! [SY2395: $i] :
                              ( ~ ( SV214 @ SY2395 )
                              | ( SY2394 = SY2395 ) ) ) ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3587]) ).

thf(3668,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ~ ! [SY2388: $i] :
                  ~ ~ ( ~ ( SV214 @ SY2388 )
                      | ~ ! [SY2389: $i] :
                            ( ~ ( SV214 @ SY2389 )
                            | ( SY2388 = SY2389 ) ) )
          | ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3588]) ).

thf(3669,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ~ ! [SY2803: $i] :
                  ~ ~ ( ~ ( SV438 @ SY2803 )
                      | ~ ! [SY2804: $i] :
                            ( ~ ( SV438 @ SY2804 )
                            | ( SY2803 = SY2804 ) ) )
          | ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3589]) ).

thf(3670,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ~ ! [SY2388: $i] :
                  ~ ~ ( ~ ( SV214 @ SY2388 )
                      | ~ ! [SY2389: $i] :
                            ( ~ ( SV214 @ SY2389 )
                            | ( SY2388 = SY2389 ) ) )
          | ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3590]) ).

thf(3671,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ~ ! [SY2803: $i] :
                  ~ ~ ( ~ ( SV438 @ SY2803 )
                      | ~ ! [SY2804: $i] :
                            ( ~ ( SV438 @ SY2804 )
                            | ( SY2803 = SY2804 ) ) )
          | ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3591]) ).

thf(3672,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ~ ! [SY2388: $i] :
                  ~ ~ ( ~ ( SV214 @ SY2388 )
                      | ~ ! [SY2389: $i] :
                            ( ~ ( SV214 @ SY2389 )
                            | ( SY2388 = SY2389 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3592]) ).

thf(3673,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ~ ! [SY2803: $i] :
                  ~ ~ ( ~ ( SV438 @ SY2803 )
                      | ~ ! [SY2804: $i] :
                            ( ~ ( SV438 @ SY2804 )
                            | ( SY2803 = SY2804 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3593]) ).

thf(3674,plain,
    ! [SV221: $i,SV445: $i,SV721: $i,SV579: $i] :
      ( ( ( ~ ( in @ ( sK95_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ SV221 ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ SV221 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3594]) ).

thf(3675,plain,
    ! [SV221: $i,SV721: $i,SV579: $i,SV445: $i] :
      ( ( ( ! [SY3208: $i] :
              ( ~ ( in @ SY3208 @ SV445 )
              | ~ ( in @ ( kpair @ ( sK95_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ SY3208 ) @ SV721 )
              | ( in @ ( kpair @ ( sK95_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ SY3208 ) @ SV579 ) ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ SV221 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3594]) ).

thf(3676,plain,
    ! [SV579: $i,SV721: $i,SV445: $i,SV221: $i] :
      ( ( ( ! [SY3142: $i] :
              ( ~ ( in @ SY3142 @ SV221 )
              | ! [SY3143: $i] :
                  ( ~ ( in @ SY3143 @ SV445 )
                  | ~ ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV721 )
                  | ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV579 ) ) ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) @ SV445 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3595]) ).

thf(3677,plain,
    ! [SV579: $i,SV721: $i,SV445: $i,SV221: $i] :
      ( ( ( ~ ! [SY3142: $i] :
                ( ~ ( in @ SY3142 @ SV221 )
                | ! [SY3143: $i] :
                    ( ~ ( in @ SY3143 @ SV445 )
                    | ~ ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV721 )
                    | ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV579 ) ) ) )
        = $true )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV579 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3596]) ).

thf(3678,plain,
    ! [SV579: $i,SV721: $i,SV445: $i,SV221: $i] :
      ( ( ( ! [SY3142: $i] :
              ( ~ ( in @ SY3142 @ SV221 )
              | ! [SY3143: $i] :
                  ( ~ ( in @ SY3143 @ SV445 )
                  | ~ ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV721 )
                  | ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV579 ) ) ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV721 )
        = $false )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3597]) ).

thf(3679,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV253 @ ( sK99_SY2491 @ SV667 @ SV253 ) )
                | ~ ! [SY3215: $i] :
                      ( ~ ( SV253 @ SY3215 )
                      | ( ( sK99_SY2491 @ SV667 @ SV253 )
                        = SY3215 ) ) ) )
        = $false )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $true )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[3598]) ).

thf(3680,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ~ ( ~ ( SV253 @ ( sK96_SY2491 @ SV667 @ SV253 ) )
              | ~ ! [SY3209: $i] :
                    ( ~ ( SV253 @ SY3209 )
                    | ( ( sK96_SY2491 @ SV667 @ SV253 )
                      = SY3209 ) ) ) )
        = $true )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $true )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3599]) ).

thf(3681,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ~ ( ~ ( SV253 @ ( sK97_SY2491 @ SV667 @ SV253 ) )
              | ~ ! [SY3210: $i] :
                    ( ~ ( SV253 @ SY3210 )
                    | ( ( sK97_SY2491 @ SV667 @ SV253 )
                      = SY3210 ) ) ) )
        = $true )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $false )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3600]) ).

thf(3682,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ~ ( SV253 @ ( sK93_SY2491 @ SV667 @ SV253 ) )
          | ~ ! [SY3207: $i] :
                ( ~ ( SV253 @ SY3207 )
                | ( ( sK93_SY2491 @ SV667 @ SV253 )
                  = SY3207 ) ) )
        = $false )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $false )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3601]) ).

thf(3683,plain,
    ! [SV620: $i,SV812: $i,SV37: $i > $o] :
      ( ( ( ~ ( ~ ( SV37 @ SV812 )
              | ( SV812
                = ( sK86_SY1897 @ SV620 @ SV37 ) ) )
          | ~ ( ( SV812
               != ( sK86_SY1897 @ SV620 @ SV37 ) )
              | ( SV37 @ SV812 ) ) )
        = $false )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( SV37 @ ( sK59_SY3056 @ SV620 @ SV37 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3602]) ).

thf(3684,plain,
    ! [SV620: $i,SV810: $i,SV37: $i > $o] :
      ( ( ( ~ ( ~ ( SV37 @ SV810 )
              | ( SV810
                = ( sK77_SY1897 @ SV620 @ SV37 ) ) ) )
        = $false )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( SV620
          = ( sK59_SY3056 @ SV620 @ SV37 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3603]) ).

thf(3685,plain,
    ! [SV37: $i > $o,SV620: $i,SV810: $i] :
      ( ( ( ~ ( ( SV810
               != ( sK77_SY1897 @ SV620 @ SV37 ) )
              | ( SV37 @ SV810 ) ) )
        = $false )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( SV620
          = ( sK59_SY3056 @ SV620 @ SV37 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3603]) ).

thf(3686,plain,
    ! [SV621: $i,SV783: $i,SV800: $i,SV41: $i > $o] :
      ( ( ( ~ ( SV41 @ SV800 ) )
        = $true )
      | ( ( SV783 = SV800 )
        = $true )
      | ( ( SV41 @ SV783 )
        = $false )
      | ( ( SV41 @ SV621 )
        = $false )
      | ( ( SV41 @ ( sK60_SY3057 @ SV621 @ SV41 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3604]) ).

thf(3687,plain,
    ! [SV621: $i,SV778: $i,SV784: $i,SV41: $i > $o] :
      ( ( ( SV41 @ SV784 )
        = $false )
      | ( ( SV778 = SV784 )
        = $true )
      | ( ( SV41 @ SV778 )
        = $false )
      | ( ( SV41 @ SV621 )
        = $false )
      | ( ( SV621
          = ( sK60_SY3057 @ SV621 @ SV41 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3605]) ).

thf(3688,plain,
    ! [SV622: $i,SV785: $i,SV801: $i,SV43: $i > $o] :
      ( ( ( ~ ( SV43 @ SV801 ) )
        = $true )
      | ( ( SV785 = SV801 )
        = $true )
      | ( ( SV43 @ SV785 )
        = $false )
      | ( ( SV43 @ SV622 )
        = $false )
      | ( ( SV43 @ ( sK61_SY3058 @ SV622 @ SV43 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3606]) ).

thf(3689,plain,
    ! [SV622: $i,SV779: $i,SV786: $i,SV43: $i > $o] :
      ( ( ( SV43 @ SV786 )
        = $false )
      | ( ( SV779 = SV786 )
        = $true )
      | ( ( SV43 @ SV779 )
        = $false )
      | ( ( SV43 @ SV622 )
        = $false )
      | ( ( SV622
          = ( sK61_SY3058 @ SV622 @ SV43 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3607]) ).

thf(3690,plain,
    ! [SV624: $i,SV48: $i > $o] :
      ( ( ( ~ ( SV48 @ ( sK87_SY1928 @ SV624 @ SV48 ) ) )
        = $false )
      | ( ( SV48 @ SV624 )
        = $false )
      | ( ( SV48 @ ( sK62_SY3060 @ SV624 @ SV48 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3608]) ).

thf(3691,plain,
    ! [SV624: $i,SV48: $i > $o] :
      ( ( ( ~ ! [SY3201: $i] :
                ( ~ ( SV48 @ SY3201 )
                | ( ( sK87_SY1928 @ SV624 @ SV48 )
                  = SY3201 ) ) )
        = $false )
      | ( ( SV48 @ SV624 )
        = $false )
      | ( ( SV48 @ ( sK62_SY3060 @ SV624 @ SV48 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3608]) ).

thf(3692,plain,
    ! [SV624: $i,SV48: $i > $o] :
      ( ( ( SV48 @ ( sK79_SY1928 @ SV624 @ SV48 ) )
        = $true )
      | ( ( SV48 @ SV624 )
        = $false )
      | ( ( SV624
          = ( sK62_SY3060 @ SV624 @ SV48 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3609]) ).

thf(3693,plain,
    ! [SV624: $i,SV48: $i > $o] :
      ( ( ( ! [SY3192: $i] :
              ( ~ ( SV48 @ SY3192 )
              | ( ( sK79_SY1928 @ SV624 @ SV48 )
                = SY3192 ) ) )
        = $true )
      | ( ( SV48 @ SV624 )
        = $false )
      | ( ( SV624
          = ( sK62_SY3060 @ SV624 @ SV48 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3610]) ).

thf(3694,plain,
    ! [SV775: $i,SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ~ ( SV77 @ ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) )
          | ( SV775
            = ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) ) )
        = $false )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[3612]) ).

thf(3695,plain,
    ! [SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ! [SY2001: $i] :
              ~ ~ ( ~ ( SV77 @ SY2001 )
                  | ~ ! [SY2002: $i] :
                        ( ~ ( SV77 @ SY2002 )
                        | ( SY2001 = SY2002 ) ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3613]) ).

thf(3696,plain,
    ! [SV315: $i > $o,SV816: $i,SV77: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV77 @ SV816 )
                | ~ ! [SY3216: $i] :
                      ( ~ ( SV77 @ SY3216 )
                      | ( SV816 = SY3216 ) ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3614]) ).

thf(3697,plain,
    ! [SV315: $i > $o,SV817: $i,SV77: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV77 @ SV817 )
                | ~ ! [SY3217: $i] :
                      ( ~ ( SV77 @ SY3217 )
                      | ( SV817 = SY3217 ) ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3615]) ).

thf(3698,plain,
    ! [SV315: $i > $o,SV813: $i,SV77: $i > $o] :
      ( ( ( ~ ( ~ ( SV77 @ SV813 )
              | ~ ! [SY3211: $i] :
                    ( ~ ( SV77 @ SY3211 )
                    | ( SV813 = SY3211 ) ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3616]) ).

thf(3699,plain,
    ! [SV80: $i,SV628: $i,SV318: $i] :
      ( ( ( in @ ( sK88_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV628 )
        = $true )
      | ( ( SV318 = SV628 )
        = $true )
      | ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV80 )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3618]) ).

thf(3700,plain,
    ! [SV80: $i,SV628: $i,SV318: $i] :
      ( ( ( in @ ( sK94_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV80 )
        = $true )
      | ( ( SV318 = SV628 )
        = $true )
      | ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV318 )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3620]) ).

thf(3701,plain,
    ! [SV80: $i,SV628: $i,SV318: $i] :
      ( ( ( ~ ( in @ ( sK94_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV628 ) )
        = $false )
      | ( ( SV318 = SV628 )
        = $true )
      | ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV318 )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3621]) ).

thf(3702,plain,
    ! [SV80: $i,SV628: $i,SV318: $i] :
      ( ( ( in @ ( sK94_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV318 )
        = $false )
      | ( ( SV318 = SV628 )
        = $true )
      | ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV318 )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3621]) ).

thf(3703,plain,
    ! [SV80: $i,SV628: $i,SV318: $i] :
      ( ( ( in @ ( sK89_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV628 )
        = $true )
      | ( ( SV318 = SV628 )
        = $true )
      | ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV628 )
        = $false )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3623]) ).

thf(3704,plain,
    ! [SV96: $i,SV512: $i,SV685: $i,SV791: $i,SV332: $i,SV814: $i] :
      ( ( ( ~ ( in @ SV814 @ SV332 ) )
        = $true )
      | ( ( ~ ( in @ ( kpair @ SV791 @ SV814 ) @ SV685 )
          | ( in @ ( kpair @ SV791 @ SV814 ) @ SV512 ) )
        = $true )
      | ( ( in @ SV791 @ SV96 )
        = $false )
      | ( ( in @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) @ SV96 )
        = $true )
      | ( ( func @ SV96 @ SV332 @ SV685 )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV512 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3625]) ).

thf(3705,plain,
    ! [SV96: $i,SV512: $i,SV685: $i,SV780: $i,SV332: $i,SV811: $i] :
      ( ( ( in @ SV811 @ SV332 )
        = $false )
      | ( ( ~ ( in @ ( kpair @ SV780 @ SV811 ) @ SV685 )
          | ( in @ ( kpair @ SV780 @ SV811 ) @ SV512 ) )
        = $true )
      | ( ( in @ SV780 @ SV96 )
        = $false )
      | ( ( ( ap @ SV96 @ SV332 @ SV512 @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) )
          = ( ap @ SV96 @ SV332 @ SV685 @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) ) )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV685 )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV512 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3626]) ).

thf(3706,plain,
    ! [SV102: $i,SV781: $i,SV336: $i > $o] :
      ( ( ( SV336 @ SV781 )
        = $false )
      | ( ( in @ SV781 @ SV102 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( in @ ( sK34_SY3074 @ SV336 @ SV102 ) @ SV102 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3629]) ).

thf(3707,plain,
    ! [SV336: $i > $o,SV102: $i,SV792: $i] :
      ( ( ( in @ SV792 @ SV102 )
        = $false )
      | ( ( ~ ( SV336 @ SV792 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( SV336 @ ( sK11_SY2627 @ SV336 @ SV102 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3630]) ).

thf(3708,plain,
    ! [SV336: $i > $o,SV102: $i,SV803: $i] :
      ( ( ( ~ ( in @ SV803 @ SV102 ) )
        = $true )
      | ( ( ~ ( SV336 @ SV803 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( SV336 @ ( sK34_SY3074 @ SV336 @ SV102 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3631]) ).

thf(3709,plain,
    ! [SV336: $i > $o,SV102: $i,SV793: $i] :
      ( ( ( in @ SV793 @ SV102 )
        = $false )
      | ( ( ~ ( SV336 @ SV793 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( ( sK11_SY2627 @ SV336 @ SV102 )
          = ( sK34_SY3074 @ SV336 @ SV102 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3632]) ).

thf(3710,plain,
    ! [SV109: $i,SV794: $i,SV815: $i] :
      ( ( ( ~ ( in @ SV815 @ SV794 ) )
        = $true )
      | ( ( in @ SV815 @ SV109 )
        = $true )
      | ( ( in @ SV794 @ ( sK3_SY2100 @ SV109 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3633]) ).

thf(3711,plain,
    ! [SV804: $i,SV109: $i,SV795: $i] :
      ( ( ( ~ ( in @ SV795 @ SV109 )
          | ~ ( in @ SV804 @ SV109 ) )
        = $true )
      | ( ( ~ ! [SY3202: $i] :
                ( ~ ( in @ SY3202 @ ( sK3_SY2100 @ SV109 ) )
                | ~ ( ~ ( ~ ( in @ SV795 @ SY3202 )
                        | ( in @ SV804 @ SY3202 ) )
                    | ~ ( ~ ( in @ SV804 @ SY3202 )
                        | ( in @ SV795 @ SY3202 ) ) ) )
          | ( SV795 = SV804 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3634]) ).

thf(3712,plain,
    ! [SV765: $i,SV109: $i,SV776: $i] :
      ( ( ( in @ SV776 @ ( sK3_SY2100 @ SV109 ) )
        = $false )
      | ( ( in @ SV765 @ ( sK3_SY2100 @ SV109 ) )
        = $false )
      | ( ( ! [SY3184: $i] :
              ( ~ ( in @ SY3184 @ SV765 )
              | ( in @ SY3184 @ SV776 ) )
          | ! [SY3185: $i] :
              ( ~ ( in @ SY3185 @ SV776 )
              | ( in @ SY3185 @ SV765 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3635]) ).

thf(3713,plain,
    ! [SV109: $i,SV739: $i] :
      ( ( ( ! [SY3155: $i] :
              ~ ( in @ SY3155 @ SV739 ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( ~ ! [SY3156: $i] :
                ~ ~ ! [SY3157: $i] :
                      ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3156 @ ( sK3_SY2100 @ SV109 ) )
                                      | ~ ( in @ SY3157 @ SV739 ) )
                                | ~ ~ ~ ! [SY3158: $i] :
                                          ~ ~ ( ~ ( in @ SY3158 @ SY3156 )
                                              | ~ ( in @ SY3158 @ SV739 ) ) )
                          | ~ ! [SY2947: $i] :
                                ( ~ ( in @ SY2947 @ ( sK3_SY2100 @ SV109 ) )
                                | ! [SX6: $i] :
                                    ( ~ ( in @ SX6 @ SY2947 )
                                    | ( in @ SX6 @ SY3156 ) )
                                | ( in @ SY3157 @ SY2947 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3636]) ).

thf(3714,plain,
    ! [SV109: $i,SV739: $i,SV818: $i] :
      ( ( ( ~ ( in @ SV818 @ SV739 ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( ~ ! [SY3156: $i] :
                ~ ~ ! [SY3157: $i] :
                      ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3156 @ ( sK3_SY2100 @ SV109 ) )
                                      | ~ ( in @ SY3157 @ SV739 ) )
                                | ~ ~ ~ ! [SY3158: $i] :
                                          ~ ~ ( ~ ( in @ SY3158 @ SY3156 )
                                              | ~ ( in @ SY3158 @ SV739 ) ) )
                          | ~ ! [SY2947: $i] :
                                ( ~ ( in @ SY2947 @ ( sK3_SY2100 @ SV109 ) )
                                | ! [SX6: $i] :
                                    ( ~ ( in @ SX6 @ SY2947 )
                                    | ( in @ SX6 @ SY3156 ) )
                                | ( in @ SY3157 @ SY2947 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3637]) ).

thf(3715,plain,
    ! [SV110: $i,SV635: $i,SV805: $i] :
      ( ( ( ~ ( in @ SV805 @ ( sK40_SY2119 @ SV635 @ SV110 ) ) )
        = $true )
      | ( ( ~ ( in @ SV805 @ SV110 ) )
        = $true )
      | ( ( in @ SV635 @ SV110 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3638]) ).

thf(3716,plain,
    ! [SV125: $i,SV782: $i,SV353: $i > $o] :
      ( ( ( SV353 @ SV782 )
        = $false )
      | ( ( in @ SV782 @ SV125 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( in @ ( sK36_SY3079 @ SV353 @ SV125 ) @ SV125 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3639]) ).

thf(3717,plain,
    ! [SV353: $i > $o,SV125: $i,SV796: $i] :
      ( ( ( in @ SV796 @ SV125 )
        = $false )
      | ( ( ~ ( SV353 @ SV796 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( SV353 @ ( sK12_SY2657 @ SV353 @ SV125 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3640]) ).

thf(3718,plain,
    ! [SV353: $i > $o,SV125: $i,SV806: $i] :
      ( ( ( ~ ( in @ SV806 @ SV125 ) )
        = $true )
      | ( ( ~ ( SV353 @ SV806 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( SV353 @ ( sK36_SY3079 @ SV353 @ SV125 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3641]) ).

thf(3719,plain,
    ! [SV353: $i > $o,SV125: $i,SV797: $i] :
      ( ( ( in @ SV797 @ SV125 )
        = $false )
      | ( ( ~ ( SV353 @ SV797 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( ( sK12_SY2657 @ SV353 @ SV125 )
          = ( sK36_SY3079 @ SV353 @ SV125 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3642]) ).

thf(3720,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV767: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK101_SY3179 @ SV767 @ SV147 @ SV377 ) @ SV377 )
                | ~ ( SV147 @ ( sK101_SY3179 @ SV767 @ SV147 @ SV377 ) @ SV767 ) ) )
        = $false )
      | ( ( in @ SV767 @ ( sK47_SY2690 @ SV147 @ SV377 ) )
        = $false )
      | ( ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[3644]) ).

thf(3721,plain,
    ! [SV767: $i,SV147: $i > $i > $o,SV377: $i,SV819: $i] :
      ( ( ( ~ ~ ( ~ ( in @ SV819 @ SV377 )
                | ~ ( SV147 @ SV819 @ SV767 ) ) )
        = $true )
      | ( ( in @ SV767 @ ( sK47_SY2690 @ SV147 @ SV377 ) )
        = $true )
      | ( ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3645]) ).

thf(3722,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV743: $i] :
      ( ( ( ~ ! [SY3218: $i] :
                ~ ( ~ ( ~ ( in @ SY3218 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) )
                      | ~ ! [SY2692: $i] :
                            ~ ~ ( ~ ( in @ SY2692 @ SV377 )
                                | ~ ( SV147 @ SY2692 @ SY3218 ) ) )
                  | ~ ( ~ ~ ! [SY2693: $i] :
                              ~ ~ ( ~ ( in @ SY2693 @ SV377 )
                                  | ~ ( SV147 @ SY2693 @ SY3218 ) )
                      | ( in @ SY3218 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) ) ) ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[3646]) ).

thf(3723,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV743: $i] :
      ( ( ( ! [SY3212: $i] :
              ~ ( ~ ( ~ ( in @ SY3212 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) )
                    | ~ ! [SY2692: $i] :
                          ~ ~ ( ~ ( in @ SY2692 @ SV377 )
                              | ~ ( SV147 @ SY2692 @ SY3212 ) ) )
                | ~ ( ~ ~ ! [SY2693: $i] :
                            ~ ~ ( ~ ( in @ SY2693 @ SV377 )
                                | ~ ( SV147 @ SY2693 @ SY3212 ) )
                    | ( in @ SY3212 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) ) ) ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV743
          = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3647]) ).

thf(3724,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( SV165 @ ( sK83_SY2244 @ SV651 @ SV165 ) )
        = $true )
      | ( ( SV165 @ ( sK48_SY2242 @ SV651 @ SV165 ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3648]) ).

thf(3725,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( ! [SY3197: $i] :
              ( ~ ( SV165 @ SY3197 )
              | ( ( sK83_SY2244 @ SV651 @ SV165 )
                = SY3197 ) ) )
        = $true )
      | ( ( SV165 @ ( sK48_SY2242 @ SV651 @ SV165 ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3649]) ).

thf(3726,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( ~ ( SV165 @ ( sK91_SY2244 @ SV651 @ SV165 ) ) )
        = $false )
      | ( ( SV165 @ ( sK55_SY3172 @ SV651 @ SV165 ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3650]) ).

thf(3727,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( ~ ! [SY3203: $i] :
                ( ~ ( SV165 @ SY3203 )
                | ( ( sK91_SY2244 @ SV651 @ SV165 )
                  = SY3203 ) ) )
        = $false )
      | ( ( SV165 @ ( sK55_SY3172 @ SV651 @ SV165 ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3650]) ).

thf(3728,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( SV165 @ ( sK84_SY2244 @ SV651 @ SV165 ) )
        = $true )
      | ( ( ( sK48_SY2242 @ SV651 @ SV165 )
          = ( sK55_SY3172 @ SV651 @ SV165 ) )
        = $false )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3651]) ).

thf(3729,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( ! [SY3198: $i] :
              ( ~ ( SV165 @ SY3198 )
              | ( ( sK84_SY2244 @ SV651 @ SV165 )
                = SY3198 ) ) )
        = $true )
      | ( ( ( sK48_SY2242 @ SV651 @ SV165 )
          = ( sK55_SY3172 @ SV651 @ SV165 ) )
        = $false )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3652]) ).

thf(3730,plain,
    ! [SV209: $i,SV434: $i,SV713: $i > $o,SV659: $i > $o] :
      ( ( ( SV659 @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) )
        = $true )
      | ( ( ~ ( ~ ( SV713 @ ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) )
              | ( SV659 @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) ) ) )
        = $true )
      | ( ( ( dsetconstr @ SV209
            @ ^ [SY3097: $i] : ( SV659 @ SY3097 ) )
          = ( dsetconstr @ SV434
            @ ^ [SY3136: $i] : ( SV713 @ SY3136 ) ) )
        = $true )
      | ( ( SV209 = SV434 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3659]) ).

thf(3731,plain,
    ! [SV434: $i,SV659: $i > $o,SV209: $i,SV713: $i > $o] :
      ( ( ( ~ ( SV713 @ ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) )
          | ( SV659 @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) ) )
        = $false )
      | ( ( SV713 @ ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) )
        = $false )
      | ( ( ( dsetconstr @ SV209
            @ ^ [SY3097: $i] : ( SV659 @ SY3097 ) )
          = ( dsetconstr @ SV434
            @ ^ [SY3136: $i] : ( SV713 @ SY3136 ) ) )
        = $true )
      | ( ( SV209 = SV434 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3660]) ).

thf(3732,plain,
    ! [SV660: $i,SV211: $i > $o] :
      ( ( ( ~ ( SV211 @ ( sK92_SY2378 @ SV660 @ SV211 ) ) )
        = $false )
      | ( ( SV211 @ SV660 )
        = $false )
      | ( ( SV211 @ ( sK72_SY3099 @ SV660 @ SV211 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3661]) ).

thf(3733,plain,
    ! [SV660: $i,SV211: $i > $o] :
      ( ( ( ~ ! [SY3204: $i] :
                ( ~ ( SV211 @ SY3204 )
                | ( ( sK92_SY2378 @ SV660 @ SV211 )
                  = SY3204 ) ) )
        = $false )
      | ( ( SV211 @ SV660 )
        = $false )
      | ( ( SV211 @ ( sK72_SY3099 @ SV660 @ SV211 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3661]) ).

thf(3734,plain,
    ! [SV660: $i,SV211: $i > $o] :
      ( ( ( SV211 @ ( sK85_SY2378 @ SV660 @ SV211 ) )
        = $true )
      | ( ( SV211 @ SV660 )
        = $false )
      | ( ( SV660
          = ( sK72_SY3099 @ SV660 @ SV211 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3662]) ).

thf(3735,plain,
    ! [SV660: $i,SV211: $i > $o] :
      ( ( ( ! [SY3199: $i] :
              ( ~ ( SV211 @ SY3199 )
              | ( ( sK85_SY2378 @ SV660 @ SV211 )
                = SY3199 ) ) )
        = $true )
      | ( ( SV211 @ SV660 )
        = $false )
      | ( ( SV660
          = ( sK72_SY3099 @ SV660 @ SV211 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3663]) ).

thf(3736,plain,
    ! [SV438: $i > $o,SV808: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV808 ) )
        = $true )
      | ( ( ~ ! [SY3205: $i] :
                ( ~ ( SV214 @ SY3205 )
                | ( SV808 = SY3205 ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3664]) ).

thf(3737,plain,
    ! [SV214: $i > $o,SV809: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV809 ) )
        = $true )
      | ( ( ~ ! [SY3206: $i] :
                ( ~ ( SV438 @ SY3206 )
                | ( SV809 = SY3206 ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3665]) ).

thf(3738,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ~ ! [SY2388: $i] :
                  ~ ~ ( ~ ( SV214 @ SY2388 )
                      | ~ ! [SY2389: $i] :
                            ( ~ ( SV214 @ SY2389 )
                            | ( SY2388 = SY2389 ) ) )
          | ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3666]) ).

thf(3739,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ~ ! [SY2803: $i] :
                  ~ ~ ( ~ ( SV438 @ SY2803 )
                      | ~ ! [SY2804: $i] :
                            ( ~ ( SV438 @ SY2804 )
                            | ( SY2803 = SY2804 ) ) )
          | ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3667]) ).

thf(3740,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ~ ! [SY2388: $i] :
                  ~ ~ ( ~ ( SV214 @ SY2388 )
                      | ~ ! [SY2389: $i] :
                            ( ~ ( SV214 @ SY2389 )
                            | ( SY2388 = SY2389 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3668]) ).

thf(3741,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ~ ! [SY2803: $i] :
                  ~ ~ ( ~ ( SV438 @ SY2803 )
                      | ~ ! [SY2804: $i] :
                            ( ~ ( SV438 @ SY2804 )
                            | ( SY2803 = SY2804 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3669]) ).

thf(3742,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ~ ! [SY2388: $i] :
                  ~ ~ ( ~ ( SV214 @ SY2388 )
                      | ~ ! [SY2389: $i] :
                            ( ~ ( SV214 @ SY2389 )
                            | ( SY2388 = SY2389 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3670]) ).

thf(3743,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ~ ! [SY2803: $i] :
                  ~ ~ ( ~ ( SV438 @ SY2803 )
                      | ~ ! [SY2804: $i] :
                            ( ~ ( SV438 @ SY2804 )
                            | ( SY2803 = SY2804 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3671]) ).

thf(3744,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ! [SY2388: $i] :
                ~ ~ ( ~ ( SV214 @ SY2388 )
                    | ~ ! [SY2389: $i] :
                          ( ~ ( SV214 @ SY2389 )
                          | ( SY2388 = SY2389 ) ) ) )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3672]) ).

thf(3745,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ! [SY2803: $i] :
                ~ ~ ( ~ ( SV438 @ SY2803 )
                    | ~ ! [SY2804: $i] :
                          ( ~ ( SV438 @ SY2804 )
                          | ( SY2803 = SY2804 ) ) ) )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3673]) ).

thf(3746,plain,
    ! [SV221: $i,SV445: $i,SV721: $i,SV579: $i] :
      ( ( ( in @ ( sK95_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ SV221 )
        = $true )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ SV221 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3674]) ).

thf(3747,plain,
    ! [SV445: $i,SV579: $i,SV721: $i,SV221: $i] :
      ( ( ( ~ ( in @ ( sK103_SY3208 @ SV221 @ SV721 @ SV579 @ SV445 ) @ SV445 )
          | ~ ( in @ ( kpair @ ( sK95_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ ( sK103_SY3208 @ SV221 @ SV721 @ SV579 @ SV445 ) ) @ SV721 )
          | ( in @ ( kpair @ ( sK95_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ ( sK103_SY3208 @ SV221 @ SV721 @ SV579 @ SV445 ) ) @ SV579 ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ SV221 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3675]) ).

thf(3748,plain,
    ! [SV221: $i,SV445: $i,SV721: $i,SV579: $i] :
      ( ( ( ~ ( in @ ( sK104_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ SV221 )
          | ! [SY3221: $i] :
              ( ~ ( in @ SY3221 @ SV445 )
              | ~ ( in @ ( kpair @ ( sK104_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ SY3221 ) @ SV721 )
              | ( in @ ( kpair @ ( sK104_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ SY3221 ) @ SV579 ) ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) @ SV445 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3676]) ).

thf(3749,plain,
    ! [SV579: $i,SV721: $i,SV445: $i,SV221: $i] :
      ( ( ( ! [SY3142: $i] :
              ( ~ ( in @ SY3142 @ SV221 )
              | ! [SY3143: $i] :
                  ( ~ ( in @ SY3143 @ SV445 )
                  | ~ ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV721 )
                  | ( in @ ( kpair @ SY3142 @ SY3143 ) @ SV579 ) ) ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV579 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3677]) ).

thf(3750,plain,
    ! [SV221: $i,SV445: $i,SV721: $i,SV579: $i] :
      ( ( ( ~ ( in @ ( sK105_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ SV221 )
          | ! [SY3222: $i] :
              ( ~ ( in @ SY3222 @ SV445 )
              | ~ ( in @ ( kpair @ ( sK105_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ SY3222 ) @ SV721 )
              | ( in @ ( kpair @ ( sK105_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ SY3222 ) @ SV579 ) ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV721 )
        = $false )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3678]) ).

thf(3751,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ~ ( ~ ( SV253 @ ( sK99_SY2491 @ SV667 @ SV253 ) )
              | ~ ! [SY3215: $i] :
                    ( ~ ( SV253 @ SY3215 )
                    | ( ( sK99_SY2491 @ SV667 @ SV253 )
                      = SY3215 ) ) ) )
        = $true )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $true )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3679]) ).

thf(3752,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ~ ( SV253 @ ( sK96_SY2491 @ SV667 @ SV253 ) )
          | ~ ! [SY3209: $i] :
                ( ~ ( SV253 @ SY3209 )
                | ( ( sK96_SY2491 @ SV667 @ SV253 )
                  = SY3209 ) ) )
        = $false )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $true )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3680]) ).

thf(3753,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ~ ( SV253 @ ( sK97_SY2491 @ SV667 @ SV253 ) )
          | ~ ! [SY3210: $i] :
                ( ~ ( SV253 @ SY3210 )
                | ( ( sK97_SY2491 @ SV667 @ SV253 )
                  = SY3210 ) ) )
        = $false )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $false )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3681]) ).

thf(3754,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ~ ( SV253 @ ( sK93_SY2491 @ SV667 @ SV253 ) ) )
        = $false )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $false )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3682]) ).

thf(3755,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ~ ! [SY3207: $i] :
                ( ~ ( SV253 @ SY3207 )
                | ( ( sK93_SY2491 @ SV667 @ SV253 )
                  = SY3207 ) ) )
        = $false )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $false )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3682]) ).

thf(3756,plain,
    ! [SV620: $i,SV812: $i,SV37: $i > $o] :
      ( ( ( ~ ( ~ ( SV37 @ SV812 )
              | ( SV812
                = ( sK86_SY1897 @ SV620 @ SV37 ) ) ) )
        = $false )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( SV37 @ ( sK59_SY3056 @ SV620 @ SV37 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3683]) ).

thf(3757,plain,
    ! [SV37: $i > $o,SV620: $i,SV812: $i] :
      ( ( ( ~ ( ( SV812
               != ( sK86_SY1897 @ SV620 @ SV37 ) )
              | ( SV37 @ SV812 ) ) )
        = $false )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( SV37 @ ( sK59_SY3056 @ SV620 @ SV37 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3683]) ).

thf(3758,plain,
    ! [SV620: $i,SV810: $i,SV37: $i > $o] :
      ( ( ( ~ ( SV37 @ SV810 )
          | ( SV810
            = ( sK77_SY1897 @ SV620 @ SV37 ) ) )
        = $true )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( SV620
          = ( sK59_SY3056 @ SV620 @ SV37 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3684]) ).

thf(3759,plain,
    ! [SV37: $i > $o,SV620: $i,SV810: $i] :
      ( ( ( ( SV810
           != ( sK77_SY1897 @ SV620 @ SV37 ) )
          | ( SV37 @ SV810 ) )
        = $true )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( SV620
          = ( sK59_SY3056 @ SV620 @ SV37 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3685]) ).

thf(3760,plain,
    ! [SV621: $i,SV783: $i,SV800: $i,SV41: $i > $o] :
      ( ( ( SV41 @ SV800 )
        = $false )
      | ( ( SV783 = SV800 )
        = $true )
      | ( ( SV41 @ SV783 )
        = $false )
      | ( ( SV41 @ SV621 )
        = $false )
      | ( ( SV41 @ ( sK60_SY3057 @ SV621 @ SV41 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3686]) ).

thf(3761,plain,
    ! [SV622: $i,SV785: $i,SV801: $i,SV43: $i > $o] :
      ( ( ( SV43 @ SV801 )
        = $false )
      | ( ( SV785 = SV801 )
        = $true )
      | ( ( SV43 @ SV785 )
        = $false )
      | ( ( SV43 @ SV622 )
        = $false )
      | ( ( SV43 @ ( sK61_SY3058 @ SV622 @ SV43 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3688]) ).

thf(3762,plain,
    ! [SV624: $i,SV48: $i > $o] :
      ( ( ( SV48 @ ( sK87_SY1928 @ SV624 @ SV48 ) )
        = $true )
      | ( ( SV48 @ SV624 )
        = $false )
      | ( ( SV48 @ ( sK62_SY3060 @ SV624 @ SV48 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3690]) ).

thf(3763,plain,
    ! [SV624: $i,SV48: $i > $o] :
      ( ( ( ! [SY3201: $i] :
              ( ~ ( SV48 @ SY3201 )
              | ( ( sK87_SY1928 @ SV624 @ SV48 )
                = SY3201 ) ) )
        = $true )
      | ( ( SV48 @ SV624 )
        = $false )
      | ( ( SV48 @ ( sK62_SY3060 @ SV624 @ SV48 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3691]) ).

thf(3764,plain,
    ! [SV624: $i,SV820: $i,SV48: $i > $o] :
      ( ( ( ~ ( SV48 @ SV820 )
          | ( ( sK79_SY1928 @ SV624 @ SV48 )
            = SV820 ) )
        = $true )
      | ( ( SV48 @ SV624 )
        = $false )
      | ( ( SV624
          = ( sK62_SY3060 @ SV624 @ SV48 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3693]) ).

thf(3765,plain,
    ! [SV775: $i,SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ~ ( SV77 @ ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) ) )
        = $false )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3694]) ).

thf(3766,plain,
    ! [SV77: $i > $o,SV315: $i > $o,SV775: $i] :
      ( ( ( SV775
          = ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) )
        = $false )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3694]) ).

thf(3767,plain,
    ! [SV315: $i > $o,SV821: $i,SV77: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV77 @ SV821 )
                | ~ ! [SY3223: $i] :
                      ( ~ ( SV77 @ SY3223 )
                      | ( SV821 = SY3223 ) ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3695]) ).

thf(3768,plain,
    ! [SV315: $i > $o,SV816: $i,SV77: $i > $o] :
      ( ( ( ~ ( ~ ( SV77 @ SV816 )
              | ~ ! [SY3216: $i] :
                    ( ~ ( SV77 @ SY3216 )
                    | ( SV816 = SY3216 ) ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3696]) ).

thf(3769,plain,
    ! [SV315: $i > $o,SV817: $i,SV77: $i > $o] :
      ( ( ( ~ ( ~ ( SV77 @ SV817 )
              | ~ ! [SY3217: $i] :
                    ( ~ ( SV77 @ SY3217 )
                    | ( SV817 = SY3217 ) ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3697]) ).

thf(3770,plain,
    ! [SV315: $i > $o,SV813: $i,SV77: $i > $o] :
      ( ( ( ~ ( SV77 @ SV813 )
          | ~ ! [SY3211: $i] :
                ( ~ ( SV77 @ SY3211 )
                | ( SV813 = SY3211 ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3698]) ).

thf(3771,plain,
    ! [SV80: $i,SV628: $i,SV318: $i] :
      ( ( ( in @ ( sK94_SY3067 @ SV318 @ SV628 @ SV80 ) @ SV628 )
        = $true )
      | ( ( SV318 = SV628 )
        = $true )
      | ( ( in @ ( sK51_SY3066 @ SV628 @ SV318 @ SV80 ) @ SV318 )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV80 ) )
        = $false )
      | ( ( in @ SV318 @ ( powerset @ SV80 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3701]) ).

thf(3772,plain,
    ! [SV96: $i,SV512: $i,SV685: $i,SV791: $i,SV332: $i,SV814: $i] :
      ( ( ( in @ SV814 @ SV332 )
        = $false )
      | ( ( ~ ( in @ ( kpair @ SV791 @ SV814 ) @ SV685 )
          | ( in @ ( kpair @ SV791 @ SV814 ) @ SV512 ) )
        = $true )
      | ( ( in @ SV791 @ SV96 )
        = $false )
      | ( ( in @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) @ SV96 )
        = $true )
      | ( ( func @ SV96 @ SV332 @ SV685 )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV512 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3704]) ).

thf(3773,plain,
    ! [SV96: $i,SV332: $i,SV512: $i,SV685: $i,SV811: $i,SV780: $i] :
      ( ( ( ~ ( in @ ( kpair @ SV780 @ SV811 ) @ SV685 ) )
        = $true )
      | ( ( in @ ( kpair @ SV780 @ SV811 ) @ SV512 )
        = $true )
      | ( ( in @ SV811 @ SV332 )
        = $false )
      | ( ( in @ SV780 @ SV96 )
        = $false )
      | ( ( ( ap @ SV96 @ SV332 @ SV512 @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) )
          = ( ap @ SV96 @ SV332 @ SV685 @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) ) )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV685 )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV512 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3705]) ).

thf(3774,plain,
    ! [SV102: $i,SV792: $i,SV336: $i > $o] :
      ( ( ( SV336 @ SV792 )
        = $false )
      | ( ( in @ SV792 @ SV102 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( SV336 @ ( sK11_SY2627 @ SV336 @ SV102 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3707]) ).

thf(3775,plain,
    ! [SV336: $i > $o,SV102: $i,SV803: $i] :
      ( ( ( in @ SV803 @ SV102 )
        = $false )
      | ( ( ~ ( SV336 @ SV803 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( SV336 @ ( sK34_SY3074 @ SV336 @ SV102 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3708]) ).

thf(3776,plain,
    ! [SV102: $i,SV793: $i,SV336: $i > $o] :
      ( ( ( SV336 @ SV793 )
        = $false )
      | ( ( in @ SV793 @ SV102 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( ( sK11_SY2627 @ SV336 @ SV102 )
          = ( sK34_SY3074 @ SV336 @ SV102 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3709]) ).

thf(3777,plain,
    ! [SV109: $i,SV794: $i,SV815: $i] :
      ( ( ( in @ SV815 @ SV794 )
        = $false )
      | ( ( in @ SV815 @ SV109 )
        = $true )
      | ( ( in @ SV794 @ ( sK3_SY2100 @ SV109 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3710]) ).

thf(3778,plain,
    ! [SV804: $i,SV109: $i,SV795: $i] :
      ( ( ( ~ ( in @ SV795 @ SV109 ) )
        = $true )
      | ( ( ~ ( in @ SV804 @ SV109 ) )
        = $true )
      | ( ( ~ ! [SY3202: $i] :
                ( ~ ( in @ SY3202 @ ( sK3_SY2100 @ SV109 ) )
                | ~ ( ~ ( ~ ( in @ SV795 @ SY3202 )
                        | ( in @ SV804 @ SY3202 ) )
                    | ~ ( ~ ( in @ SV804 @ SY3202 )
                        | ( in @ SV795 @ SY3202 ) ) ) )
          | ( SV795 = SV804 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3711]) ).

thf(3779,plain,
    ! [SV109: $i,SV776: $i,SV765: $i] :
      ( ( ( ! [SY3184: $i] :
              ( ~ ( in @ SY3184 @ SV765 )
              | ( in @ SY3184 @ SV776 ) ) )
        = $true )
      | ( ( ! [SY3185: $i] :
              ( ~ ( in @ SY3185 @ SV776 )
              | ( in @ SY3185 @ SV765 ) ) )
        = $true )
      | ( ( in @ SV765 @ ( sK3_SY2100 @ SV109 ) )
        = $false )
      | ( ( in @ SV776 @ ( sK3_SY2100 @ SV109 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3712]) ).

thf(3780,plain,
    ! [SV109: $i,SV739: $i,SV822: $i] :
      ( ( ( ~ ( in @ SV822 @ SV739 ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( ~ ! [SY3156: $i] :
                ~ ~ ! [SY3157: $i] :
                      ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3156 @ ( sK3_SY2100 @ SV109 ) )
                                      | ~ ( in @ SY3157 @ SV739 ) )
                                | ~ ~ ~ ! [SY3158: $i] :
                                          ~ ~ ( ~ ( in @ SY3158 @ SY3156 )
                                              | ~ ( in @ SY3158 @ SV739 ) ) )
                          | ~ ! [SY2947: $i] :
                                ( ~ ( in @ SY2947 @ ( sK3_SY2100 @ SV109 ) )
                                | ! [SX6: $i] :
                                    ( ~ ( in @ SX6 @ SY2947 )
                                    | ( in @ SX6 @ SY3156 ) )
                                | ( in @ SY3157 @ SY2947 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3713]) ).

thf(3781,plain,
    ! [SV109: $i,SV739: $i,SV818: $i] :
      ( ( ( in @ SV818 @ SV739 )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( ~ ! [SY3156: $i] :
                ~ ~ ! [SY3157: $i] :
                      ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3156 @ ( sK3_SY2100 @ SV109 ) )
                                      | ~ ( in @ SY3157 @ SV739 ) )
                                | ~ ~ ~ ! [SY3158: $i] :
                                          ~ ~ ( ~ ( in @ SY3158 @ SY3156 )
                                              | ~ ( in @ SY3158 @ SV739 ) ) )
                          | ~ ! [SY2947: $i] :
                                ( ~ ( in @ SY2947 @ ( sK3_SY2100 @ SV109 ) )
                                | ! [SX6: $i] :
                                    ( ~ ( in @ SX6 @ SY2947 )
                                    | ( in @ SX6 @ SY3156 ) )
                                | ( in @ SY3157 @ SY2947 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3714]) ).

thf(3782,plain,
    ! [SV110: $i,SV635: $i,SV805: $i] :
      ( ( ( in @ SV805 @ ( sK40_SY2119 @ SV635 @ SV110 ) )
        = $false )
      | ( ( ~ ( in @ SV805 @ SV110 ) )
        = $true )
      | ( ( in @ SV635 @ SV110 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3715]) ).

thf(3783,plain,
    ! [SV125: $i,SV796: $i,SV353: $i > $o] :
      ( ( ( SV353 @ SV796 )
        = $false )
      | ( ( in @ SV796 @ SV125 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( SV353 @ ( sK12_SY2657 @ SV353 @ SV125 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3717]) ).

thf(3784,plain,
    ! [SV353: $i > $o,SV125: $i,SV806: $i] :
      ( ( ( in @ SV806 @ SV125 )
        = $false )
      | ( ( ~ ( SV353 @ SV806 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( SV353 @ ( sK36_SY3079 @ SV353 @ SV125 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3718]) ).

thf(3785,plain,
    ! [SV125: $i,SV797: $i,SV353: $i > $o] :
      ( ( ( SV353 @ SV797 )
        = $false )
      | ( ( in @ SV797 @ SV125 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( ( sK12_SY2657 @ SV353 @ SV125 )
          = ( sK36_SY3079 @ SV353 @ SV125 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3719]) ).

thf(3786,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV767: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK101_SY3179 @ SV767 @ SV147 @ SV377 ) @ SV377 )
              | ~ ( SV147 @ ( sK101_SY3179 @ SV767 @ SV147 @ SV377 ) @ SV767 ) ) )
        = $true )
      | ( ( in @ SV767 @ ( sK47_SY2690 @ SV147 @ SV377 ) )
        = $false )
      | ( ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3720]) ).

thf(3787,plain,
    ! [SV767: $i,SV147: $i > $i > $o,SV377: $i,SV819: $i] :
      ( ( ( ~ ( ~ ( in @ SV819 @ SV377 )
              | ~ ( SV147 @ SV819 @ SV767 ) ) )
        = $false )
      | ( ( in @ SV767 @ ( sK47_SY2690 @ SV147 @ SV377 ) )
        = $true )
      | ( ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3721]) ).

thf(3788,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV743: $i] :
      ( ( ( ! [SY3218: $i] :
              ~ ( ~ ( ~ ( in @ SY3218 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) )
                    | ~ ! [SY2692: $i] :
                          ~ ~ ( ~ ( in @ SY2692 @ SV377 )
                              | ~ ( SV147 @ SY2692 @ SY3218 ) ) )
                | ~ ( ~ ~ ! [SY2693: $i] :
                            ~ ~ ( ~ ( in @ SY2693 @ SV377 )
                                | ~ ( SV147 @ SY2693 @ SY3218 ) )
                    | ( in @ SY3218 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) ) ) ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3722]) ).

thf(3789,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV743: $i,SV823: $i] :
      ( ( ( ~ ( ~ ( ~ ( in @ SV823 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) )
                  | ~ ! [SY3224: $i] :
                        ~ ~ ( ~ ( in @ SY3224 @ SV377 )
                            | ~ ( SV147 @ SY3224 @ SV823 ) ) )
              | ~ ( ~ ~ ! [SY3225: $i] :
                          ~ ~ ( ~ ( in @ SY3225 @ SV377 )
                              | ~ ( SV147 @ SY3225 @ SV823 ) )
                  | ( in @ SV823 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) ) ) ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV743
          = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3723]) ).

thf(3790,plain,
    ! [SV651: $i,SV824: $i,SV165: $i > $o] :
      ( ( ( ~ ( SV165 @ SV824 )
          | ( ( sK83_SY2244 @ SV651 @ SV165 )
            = SV824 ) )
        = $true )
      | ( ( SV165 @ ( sK48_SY2242 @ SV651 @ SV165 ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3725]) ).

thf(3791,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( SV165 @ ( sK91_SY2244 @ SV651 @ SV165 ) )
        = $true )
      | ( ( SV165 @ ( sK55_SY3172 @ SV651 @ SV165 ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3726]) ).

thf(3792,plain,
    ! [SV651: $i,SV165: $i > $o] :
      ( ( ( ! [SY3203: $i] :
              ( ~ ( SV165 @ SY3203 )
              | ( ( sK91_SY2244 @ SV651 @ SV165 )
                = SY3203 ) ) )
        = $true )
      | ( ( SV165 @ ( sK55_SY3172 @ SV651 @ SV165 ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3727]) ).

thf(3793,plain,
    ! [SV651: $i,SV825: $i,SV165: $i > $o] :
      ( ( ( ~ ( SV165 @ SV825 )
          | ( ( sK84_SY2244 @ SV651 @ SV165 )
            = SV825 ) )
        = $true )
      | ( ( ( sK48_SY2242 @ SV651 @ SV165 )
          = ( sK55_SY3172 @ SV651 @ SV165 ) )
        = $false )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3729]) ).

thf(3794,plain,
    ! [SV434: $i,SV659: $i > $o,SV209: $i,SV713: $i > $o] :
      ( ( ( ~ ( SV713 @ ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) )
          | ( SV659 @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) ) )
        = $false )
      | ( ( SV659 @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) )
        = $true )
      | ( ( ( dsetconstr @ SV209
            @ ^ [SY3097: $i] : ( SV659 @ SY3097 ) )
          = ( dsetconstr @ SV434
            @ ^ [SY3136: $i] : ( SV713 @ SY3136 ) ) )
        = $true )
      | ( ( SV209 = SV434 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3730]) ).

thf(3795,plain,
    ! [SV434: $i,SV659: $i > $o,SV209: $i,SV713: $i > $o] :
      ( ( ( ~ ( SV713 @ ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) ) )
        = $false )
      | ( ( SV713 @ ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) )
        = $false )
      | ( ( ( dsetconstr @ SV209
            @ ^ [SY3097: $i] : ( SV659 @ SY3097 ) )
          = ( dsetconstr @ SV434
            @ ^ [SY3136: $i] : ( SV713 @ SY3136 ) ) )
        = $true )
      | ( ( SV209 = SV434 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3731]) ).

thf(3796,plain,
    ! [SV209: $i,SV434: $i,SV713: $i > $o,SV659: $i > $o] :
      ( ( ( SV659 @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) )
        = $false )
      | ( ( SV713 @ ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) )
        = $false )
      | ( ( ( dsetconstr @ SV209
            @ ^ [SY3097: $i] : ( SV659 @ SY3097 ) )
          = ( dsetconstr @ SV434
            @ ^ [SY3136: $i] : ( SV713 @ SY3136 ) ) )
        = $true )
      | ( ( SV209 = SV434 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3731]) ).

thf(3797,plain,
    ! [SV660: $i,SV211: $i > $o] :
      ( ( ( SV211 @ ( sK92_SY2378 @ SV660 @ SV211 ) )
        = $true )
      | ( ( SV211 @ SV660 )
        = $false )
      | ( ( SV211 @ ( sK72_SY3099 @ SV660 @ SV211 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3732]) ).

thf(3798,plain,
    ! [SV660: $i,SV211: $i > $o] :
      ( ( ( ! [SY3204: $i] :
              ( ~ ( SV211 @ SY3204 )
              | ( ( sK92_SY2378 @ SV660 @ SV211 )
                = SY3204 ) ) )
        = $true )
      | ( ( SV211 @ SV660 )
        = $false )
      | ( ( SV211 @ ( sK72_SY3099 @ SV660 @ SV211 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3733]) ).

thf(3799,plain,
    ! [SV660: $i,SV826: $i,SV211: $i > $o] :
      ( ( ( ~ ( SV211 @ SV826 )
          | ( ( sK85_SY2378 @ SV660 @ SV211 )
            = SV826 ) )
        = $true )
      | ( ( SV211 @ SV660 )
        = $false )
      | ( ( SV660
          = ( sK72_SY3099 @ SV660 @ SV211 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3735]) ).

thf(3800,plain,
    ! [SV438: $i > $o,SV808: $i,SV214: $i > $o] :
      ( ( ( SV214 @ SV808 )
        = $false )
      | ( ( ~ ! [SY3205: $i] :
                ( ~ ( SV214 @ SY3205 )
                | ( SV808 = SY3205 ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3736]) ).

thf(3801,plain,
    ! [SV214: $i > $o,SV809: $i,SV438: $i > $o] :
      ( ( ( SV438 @ SV809 )
        = $false )
      | ( ( ~ ! [SY3206: $i] :
                ( ~ ( SV438 @ SY3206 )
                | ( SV809 = SY3206 ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3737]) ).

thf(3802,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ~ ! [SY2388: $i] :
                  ~ ~ ( ~ ( SV214 @ SY2388 )
                      | ~ ! [SY2389: $i] :
                            ( ~ ( SV214 @ SY2389 )
                            | ( SY2388 = SY2389 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3738]) ).

thf(3803,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ~ ! [SY2803: $i] :
                  ~ ~ ( ~ ( SV438 @ SY2803 )
                      | ~ ! [SY2804: $i] :
                            ( ~ ( SV438 @ SY2804 )
                            | ( SY2803 = SY2804 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3739]) ).

thf(3804,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ! [SY2388: $i] :
                ~ ~ ( ~ ( SV214 @ SY2388 )
                    | ~ ! [SY2389: $i] :
                          ( ~ ( SV214 @ SY2389 )
                          | ( SY2388 = SY2389 ) ) ) )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3740]) ).

thf(3805,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ! [SY2803: $i] :
                ~ ~ ( ~ ( SV438 @ SY2803 )
                    | ~ ! [SY2804: $i] :
                          ( ~ ( SV438 @ SY2804 )
                          | ( SY2803 = SY2804 ) ) ) )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3741]) ).

thf(3806,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ! [SY2388: $i] :
                ~ ~ ( ~ ( SV214 @ SY2388 )
                    | ~ ! [SY2389: $i] :
                          ( ~ ( SV214 @ SY2389 )
                          | ( SY2388 = SY2389 ) ) ) )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3742]) ).

thf(3807,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ! [SY2803: $i] :
                ~ ~ ( ~ ( SV438 @ SY2803 )
                    | ~ ! [SY2804: $i] :
                          ( ~ ( SV438 @ SY2804 )
                          | ( SY2803 = SY2804 ) ) ) )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3743]) ).

thf(3808,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ! [SY2388: $i] :
              ~ ~ ( ~ ( SV214 @ SY2388 )
                  | ~ ! [SY2389: $i] :
                        ( ~ ( SV214 @ SY2389 )
                        | ( SY2388 = SY2389 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3744]) ).

thf(3809,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ! [SY2803: $i] :
              ~ ~ ( ~ ( SV438 @ SY2803 )
                  | ~ ! [SY2804: $i] :
                        ( ~ ( SV438 @ SY2804 )
                        | ( SY2803 = SY2804 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3745]) ).

thf(3810,plain,
    ! [SV445: $i,SV579: $i,SV721: $i,SV221: $i] :
      ( ( ( ~ ( in @ ( sK103_SY3208 @ SV221 @ SV721 @ SV579 @ SV445 ) @ SV445 ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ SV221 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3747]) ).

thf(3811,plain,
    ! [SV221: $i,SV445: $i,SV721: $i,SV579: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK95_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ ( sK103_SY3208 @ SV221 @ SV721 @ SV579 @ SV445 ) ) @ SV721 )
          | ( in @ ( kpair @ ( sK95_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ ( sK103_SY3208 @ SV221 @ SV721 @ SV579 @ SV445 ) ) @ SV579 ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ SV221 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3747]) ).

thf(3812,plain,
    ! [SV221: $i,SV445: $i,SV721: $i,SV579: $i] :
      ( ( ( ~ ( in @ ( sK104_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ SV221 ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) @ SV445 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3748]) ).

thf(3813,plain,
    ! [SV221: $i,SV721: $i,SV579: $i,SV445: $i] :
      ( ( ( ! [SY3221: $i] :
              ( ~ ( in @ SY3221 @ SV445 )
              | ~ ( in @ ( kpair @ ( sK104_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ SY3221 ) @ SV721 )
              | ( in @ ( kpair @ ( sK104_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ SY3221 ) @ SV579 ) ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) @ SV445 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3748]) ).

thf(3814,plain,
    ! [SV221: $i,SV445: $i,SV721: $i,SV579: $i] :
      ( ( ( ~ ( in @ ( sK106_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ SV221 )
          | ! [SY3226: $i] :
              ( ~ ( in @ SY3226 @ SV445 )
              | ~ ( in @ ( kpair @ ( sK106_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ SY3226 ) @ SV721 )
              | ( in @ ( kpair @ ( sK106_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ SY3226 ) @ SV579 ) ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV579 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3749]) ).

thf(3815,plain,
    ! [SV221: $i,SV445: $i,SV721: $i,SV579: $i] :
      ( ( ( ~ ( in @ ( sK105_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ SV221 ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV721 )
        = $false )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3750]) ).

thf(3816,plain,
    ! [SV221: $i,SV721: $i,SV579: $i,SV445: $i] :
      ( ( ( ! [SY3222: $i] :
              ( ~ ( in @ SY3222 @ SV445 )
              | ~ ( in @ ( kpair @ ( sK105_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ SY3222 ) @ SV721 )
              | ( in @ ( kpair @ ( sK105_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ SY3222 ) @ SV579 ) ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV721 )
        = $false )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3750]) ).

thf(3817,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ~ ( SV253 @ ( sK99_SY2491 @ SV667 @ SV253 ) )
          | ~ ! [SY3215: $i] :
                ( ~ ( SV253 @ SY3215 )
                | ( ( sK99_SY2491 @ SV667 @ SV253 )
                  = SY3215 ) ) )
        = $false )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $true )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3751]) ).

thf(3818,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ~ ( SV253 @ ( sK96_SY2491 @ SV667 @ SV253 ) ) )
        = $false )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $true )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3752]) ).

thf(3819,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ~ ! [SY3209: $i] :
                ( ~ ( SV253 @ SY3209 )
                | ( ( sK96_SY2491 @ SV667 @ SV253 )
                  = SY3209 ) ) )
        = $false )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $true )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3752]) ).

thf(3820,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ~ ( SV253 @ ( sK97_SY2491 @ SV667 @ SV253 ) ) )
        = $false )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $false )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3753]) ).

thf(3821,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ~ ! [SY3210: $i] :
                ( ~ ( SV253 @ SY3210 )
                | ( ( sK97_SY2491 @ SV667 @ SV253 )
                  = SY3210 ) ) )
        = $false )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $false )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3753]) ).

thf(3822,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( SV253 @ ( sK93_SY2491 @ SV667 @ SV253 ) )
        = $true )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $false )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3754]) ).

thf(3823,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ! [SY3207: $i] :
              ( ~ ( SV253 @ SY3207 )
              | ( ( sK93_SY2491 @ SV667 @ SV253 )
                = SY3207 ) ) )
        = $true )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $false )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3755]) ).

thf(3824,plain,
    ! [SV620: $i,SV812: $i,SV37: $i > $o] :
      ( ( ( ~ ( SV37 @ SV812 )
          | ( SV812
            = ( sK86_SY1897 @ SV620 @ SV37 ) ) )
        = $true )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( SV37 @ ( sK59_SY3056 @ SV620 @ SV37 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3756]) ).

thf(3825,plain,
    ! [SV37: $i > $o,SV620: $i,SV812: $i] :
      ( ( ( ( SV812
           != ( sK86_SY1897 @ SV620 @ SV37 ) )
          | ( SV37 @ SV812 ) )
        = $true )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( SV37 @ ( sK59_SY3056 @ SV620 @ SV37 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3757]) ).

thf(3826,plain,
    ! [SV620: $i,SV810: $i,SV37: $i > $o] :
      ( ( ( ~ ( SV37 @ SV810 ) )
        = $true )
      | ( ( SV810
          = ( sK77_SY1897 @ SV620 @ SV37 ) )
        = $true )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( SV620
          = ( sK59_SY3056 @ SV620 @ SV37 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3758]) ).

thf(3827,plain,
    ! [SV37: $i > $o,SV620: $i,SV810: $i] :
      ( ( ( SV810
         != ( sK77_SY1897 @ SV620 @ SV37 ) )
        = $true )
      | ( ( SV37 @ SV810 )
        = $true )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( SV620
          = ( sK59_SY3056 @ SV620 @ SV37 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3759]) ).

thf(3828,plain,
    ! [SV624: $i,SV827: $i,SV48: $i > $o] :
      ( ( ( ~ ( SV48 @ SV827 )
          | ( ( sK87_SY1928 @ SV624 @ SV48 )
            = SV827 ) )
        = $true )
      | ( ( SV48 @ SV624 )
        = $false )
      | ( ( SV48 @ ( sK62_SY3060 @ SV624 @ SV48 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3763]) ).

thf(3829,plain,
    ! [SV624: $i,SV820: $i,SV48: $i > $o] :
      ( ( ( ~ ( SV48 @ SV820 ) )
        = $true )
      | ( ( ( sK79_SY1928 @ SV624 @ SV48 )
          = SV820 )
        = $true )
      | ( ( SV48 @ SV624 )
        = $false )
      | ( ( SV624
          = ( sK62_SY3060 @ SV624 @ SV48 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3764]) ).

thf(3830,plain,
    ! [SV775: $i,SV315: $i > $o,SV77: $i > $o] :
      ( ( ( SV77 @ ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) )
        = $true )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3765]) ).

thf(3831,plain,
    ! [SV775: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( SV775
          = ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) )
        = $false )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3766]) ).

thf(3832,plain,
    ! [SV315: $i > $o,SV821: $i,SV77: $i > $o] :
      ( ( ( ~ ( ~ ( SV77 @ SV821 )
              | ~ ! [SY3223: $i] :
                    ( ~ ( SV77 @ SY3223 )
                    | ( SV821 = SY3223 ) ) ) )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3767]) ).

thf(3833,plain,
    ! [SV315: $i > $o,SV816: $i,SV77: $i > $o] :
      ( ( ( ~ ( SV77 @ SV816 )
          | ~ ! [SY3216: $i] :
                ( ~ ( SV77 @ SY3216 )
                | ( SV816 = SY3216 ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3768]) ).

thf(3834,plain,
    ! [SV315: $i > $o,SV817: $i,SV77: $i > $o] :
      ( ( ( ~ ( SV77 @ SV817 )
          | ~ ! [SY3217: $i] :
                ( ~ ( SV77 @ SY3217 )
                | ( SV817 = SY3217 ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3769]) ).

thf(3835,plain,
    ! [SV315: $i > $o,SV813: $i,SV77: $i > $o] :
      ( ( ( ~ ( SV77 @ SV813 ) )
        = $true )
      | ( ( ~ ! [SY3211: $i] :
                ( ~ ( SV77 @ SY3211 )
                | ( SV813 = SY3211 ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3770]) ).

thf(3836,plain,
    ! [SV96: $i,SV332: $i,SV512: $i,SV685: $i,SV814: $i,SV791: $i] :
      ( ( ( ~ ( in @ ( kpair @ SV791 @ SV814 ) @ SV685 ) )
        = $true )
      | ( ( in @ ( kpair @ SV791 @ SV814 ) @ SV512 )
        = $true )
      | ( ( in @ SV814 @ SV332 )
        = $false )
      | ( ( in @ SV791 @ SV96 )
        = $false )
      | ( ( in @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) @ SV96 )
        = $true )
      | ( ( func @ SV96 @ SV332 @ SV685 )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV512 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3772]) ).

thf(3837,plain,
    ! [SV96: $i,SV332: $i,SV512: $i,SV685: $i,SV811: $i,SV780: $i] :
      ( ( ( in @ ( kpair @ SV780 @ SV811 ) @ SV685 )
        = $false )
      | ( ( in @ ( kpair @ SV780 @ SV811 ) @ SV512 )
        = $true )
      | ( ( in @ SV811 @ SV332 )
        = $false )
      | ( ( in @ SV780 @ SV96 )
        = $false )
      | ( ( ( ap @ SV96 @ SV332 @ SV512 @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) )
          = ( ap @ SV96 @ SV332 @ SV685 @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) ) )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV685 )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV512 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3773]) ).

thf(3838,plain,
    ! [SV102: $i,SV803: $i,SV336: $i > $o] :
      ( ( ( SV336 @ SV803 )
        = $false )
      | ( ( in @ SV803 @ SV102 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV102
            @ ^ [SY2630: $i] : ( SV336 @ SY2630 ) ) )
        = $true )
      | ( ( SV336 @ ( sK34_SY3074 @ SV336 @ SV102 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3775]) ).

thf(3839,plain,
    ! [SV804: $i,SV109: $i,SV795: $i] :
      ( ( ( in @ SV795 @ SV109 )
        = $false )
      | ( ( ~ ( in @ SV804 @ SV109 ) )
        = $true )
      | ( ( ~ ! [SY3202: $i] :
                ( ~ ( in @ SY3202 @ ( sK3_SY2100 @ SV109 ) )
                | ~ ( ~ ( ~ ( in @ SV795 @ SY3202 )
                        | ( in @ SV804 @ SY3202 ) )
                    | ~ ( ~ ( in @ SV804 @ SY3202 )
                        | ( in @ SV795 @ SY3202 ) ) ) )
          | ( SV795 = SV804 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3778]) ).

thf(3840,plain,
    ! [SV109: $i,SV776: $i,SV765: $i,SV828: $i] :
      ( ( ( ~ ( in @ SV828 @ SV765 )
          | ( in @ SV828 @ SV776 ) )
        = $true )
      | ( ( ! [SY3185: $i] :
              ( ~ ( in @ SY3185 @ SV776 )
              | ( in @ SY3185 @ SV765 ) ) )
        = $true )
      | ( ( in @ SV765 @ ( sK3_SY2100 @ SV109 ) )
        = $false )
      | ( ( in @ SV776 @ ( sK3_SY2100 @ SV109 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3779]) ).

thf(3841,plain,
    ! [SV109: $i,SV739: $i,SV822: $i] :
      ( ( ( in @ SV822 @ SV739 )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( ~ ! [SY3156: $i] :
                ~ ~ ! [SY3157: $i] :
                      ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3156 @ ( sK3_SY2100 @ SV109 ) )
                                      | ~ ( in @ SY3157 @ SV739 ) )
                                | ~ ~ ~ ! [SY3158: $i] :
                                          ~ ~ ( ~ ( in @ SY3158 @ SY3156 )
                                              | ~ ( in @ SY3158 @ SV739 ) ) )
                          | ~ ! [SY2947: $i] :
                                ( ~ ( in @ SY2947 @ ( sK3_SY2100 @ SV109 ) )
                                | ! [SX6: $i] :
                                    ( ~ ( in @ SX6 @ SY2947 )
                                    | ( in @ SX6 @ SY3156 ) )
                                | ( in @ SY3157 @ SY2947 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3780]) ).

thf(3842,plain,
    ! [SV818: $i,SV739: $i,SV109: $i] :
      ( ( ( ! [SY3156: $i] :
              ~ ~ ! [SY3157: $i] :
                    ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3156 @ ( sK3_SY2100 @ SV109 ) )
                                    | ~ ( in @ SY3157 @ SV739 ) )
                              | ~ ~ ~ ! [SY3158: $i] :
                                        ~ ~ ( ~ ( in @ SY3158 @ SY3156 )
                                            | ~ ( in @ SY3158 @ SV739 ) ) )
                        | ~ ! [SY2947: $i] :
                              ( ~ ( in @ SY2947 @ ( sK3_SY2100 @ SV109 ) )
                              | ! [SX6: $i] :
                                  ( ~ ( in @ SX6 @ SY2947 )
                                  | ( in @ SX6 @ SY3156 ) )
                              | ( in @ SY3157 @ SY2947 ) ) ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3781]) ).

thf(3843,plain,
    ! [SV635: $i,SV110: $i,SV805: $i] :
      ( ( ( in @ SV805 @ SV110 )
        = $false )
      | ( ( in @ SV805 @ ( sK40_SY2119 @ SV635 @ SV110 ) )
        = $false )
      | ( ( in @ SV635 @ SV110 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3782]) ).

thf(3844,plain,
    ! [SV125: $i,SV806: $i,SV353: $i > $o] :
      ( ( ( SV353 @ SV806 )
        = $false )
      | ( ( in @ SV806 @ SV125 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV125
            @ ^ [SY2660: $i] : ( SV353 @ SY2660 ) ) )
        = $true )
      | ( ( SV353 @ ( sK36_SY3079 @ SV353 @ SV125 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3784]) ).

thf(3845,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV767: $i] :
      ( ( ( ~ ( in @ ( sK101_SY3179 @ SV767 @ SV147 @ SV377 ) @ SV377 )
          | ~ ( SV147 @ ( sK101_SY3179 @ SV767 @ SV147 @ SV377 ) @ SV767 ) )
        = $false )
      | ( ( in @ SV767 @ ( sK47_SY2690 @ SV147 @ SV377 ) )
        = $false )
      | ( ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3786]) ).

thf(3846,plain,
    ! [SV767: $i,SV147: $i > $i > $o,SV377: $i,SV819: $i] :
      ( ( ( ~ ( in @ SV819 @ SV377 )
          | ~ ( SV147 @ SV819 @ SV767 ) )
        = $true )
      | ( ( in @ SV767 @ ( sK47_SY2690 @ SV147 @ SV377 ) )
        = $true )
      | ( ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3787]) ).

thf(3847,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV743: $i,SV829: $i] :
      ( ( ( ~ ( ~ ( ~ ( in @ SV829 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) )
                  | ~ ! [SY3227: $i] :
                        ~ ~ ( ~ ( in @ SY3227 @ SV377 )
                            | ~ ( SV147 @ SY3227 @ SV829 ) ) )
              | ~ ( ~ ~ ! [SY3228: $i] :
                          ~ ~ ( ~ ( in @ SY3228 @ SV377 )
                              | ~ ( SV147 @ SY3228 @ SV829 ) )
                  | ( in @ SV829 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) ) ) ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3788]) ).

thf(3848,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV743: $i,SV823: $i] :
      ( ( ( ~ ( ~ ( in @ SV823 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) )
              | ~ ! [SY3224: $i] :
                    ~ ~ ( ~ ( in @ SY3224 @ SV377 )
                        | ~ ( SV147 @ SY3224 @ SV823 ) ) )
          | ~ ( ~ ~ ! [SY3225: $i] :
                      ~ ~ ( ~ ( in @ SY3225 @ SV377 )
                          | ~ ( SV147 @ SY3225 @ SV823 ) )
              | ( in @ SV823 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) ) ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV743
          = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3789]) ).

thf(3849,plain,
    ! [SV651: $i,SV824: $i,SV165: $i > $o] :
      ( ( ( ~ ( SV165 @ SV824 ) )
        = $true )
      | ( ( ( sK83_SY2244 @ SV651 @ SV165 )
          = SV824 )
        = $true )
      | ( ( SV165 @ ( sK48_SY2242 @ SV651 @ SV165 ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3790]) ).

thf(3850,plain,
    ! [SV651: $i,SV830: $i,SV165: $i > $o] :
      ( ( ( ~ ( SV165 @ SV830 )
          | ( ( sK91_SY2244 @ SV651 @ SV165 )
            = SV830 ) )
        = $true )
      | ( ( SV165 @ ( sK55_SY3172 @ SV651 @ SV165 ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3792]) ).

thf(3851,plain,
    ! [SV651: $i,SV825: $i,SV165: $i > $o] :
      ( ( ( ~ ( SV165 @ SV825 ) )
        = $true )
      | ( ( ( sK84_SY2244 @ SV651 @ SV165 )
          = SV825 )
        = $true )
      | ( ( ( sK48_SY2242 @ SV651 @ SV165 )
          = ( sK55_SY3172 @ SV651 @ SV165 ) )
        = $false )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3793]) ).

thf(3852,plain,
    ! [SV434: $i,SV659: $i > $o,SV209: $i,SV713: $i > $o] :
      ( ( ( ~ ( SV713 @ ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) ) )
        = $false )
      | ( ( SV659 @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) )
        = $true )
      | ( ( ( dsetconstr @ SV209
            @ ^ [SY3097: $i] : ( SV659 @ SY3097 ) )
          = ( dsetconstr @ SV434
            @ ^ [SY3136: $i] : ( SV713 @ SY3136 ) ) )
        = $true )
      | ( ( SV209 = SV434 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3794]) ).

thf(3853,plain,
    ! [SV209: $i,SV434: $i,SV713: $i > $o,SV659: $i > $o] :
      ( ( ( SV659 @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) )
        = $false )
      | ( ( SV659 @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) )
        = $true )
      | ( ( ( dsetconstr @ SV209
            @ ^ [SY3097: $i] : ( SV659 @ SY3097 ) )
          = ( dsetconstr @ SV434
            @ ^ [SY3136: $i] : ( SV713 @ SY3136 ) ) )
        = $true )
      | ( ( SV209 = SV434 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3794]) ).

thf(3854,plain,
    ! [SV434: $i,SV659: $i > $o,SV209: $i,SV713: $i > $o] :
      ( ( ( SV713 @ ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) )
        = $true )
      | ( ( SV713 @ ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) )
        = $false )
      | ( ( ( dsetconstr @ SV209
            @ ^ [SY3097: $i] : ( SV659 @ SY3097 ) )
          = ( dsetconstr @ SV434
            @ ^ [SY3136: $i] : ( SV713 @ SY3136 ) ) )
        = $true )
      | ( ( SV209 = SV434 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3795]) ).

thf(3855,plain,
    ! [SV660: $i,SV831: $i,SV211: $i > $o] :
      ( ( ( ~ ( SV211 @ SV831 )
          | ( ( sK92_SY2378 @ SV660 @ SV211 )
            = SV831 ) )
        = $true )
      | ( ( SV211 @ SV660 )
        = $false )
      | ( ( SV211 @ ( sK72_SY3099 @ SV660 @ SV211 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3798]) ).

thf(3856,plain,
    ! [SV660: $i,SV826: $i,SV211: $i > $o] :
      ( ( ( ~ ( SV211 @ SV826 ) )
        = $true )
      | ( ( ( sK85_SY2378 @ SV660 @ SV211 )
          = SV826 )
        = $true )
      | ( ( SV211 @ SV660 )
        = $false )
      | ( ( SV660
          = ( sK72_SY3099 @ SV660 @ SV211 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3799]) ).

thf(3857,plain,
    ! [SV438: $i > $o,SV808: $i,SV214: $i > $o] :
      ( ( ( ! [SY3205: $i] :
              ( ~ ( SV214 @ SY3205 )
              | ( SV808 = SY3205 ) ) )
        = $false )
      | ( ( SV214 @ SV808 )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3800]) ).

thf(3858,plain,
    ! [SV214: $i > $o,SV809: $i,SV438: $i > $o] :
      ( ( ( ! [SY3206: $i] :
              ( ~ ( SV438 @ SY3206 )
              | ( SV809 = SY3206 ) ) )
        = $false )
      | ( ( SV438 @ SV809 )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3801]) ).

thf(3859,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ! [SY2388: $i] :
                ~ ~ ( ~ ( SV214 @ SY2388 )
                    | ~ ! [SY2389: $i] :
                          ( ~ ( SV214 @ SY2389 )
                          | ( SY2388 = SY2389 ) ) ) )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3802]) ).

thf(3860,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ! [SY2803: $i] :
                ~ ~ ( ~ ( SV438 @ SY2803 )
                    | ~ ! [SY2804: $i] :
                          ( ~ ( SV438 @ SY2804 )
                          | ( SY2803 = SY2804 ) ) ) )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3803]) ).

thf(3861,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ! [SY2388: $i] :
              ~ ~ ( ~ ( SV214 @ SY2388 )
                  | ~ ! [SY2389: $i] :
                        ( ~ ( SV214 @ SY2389 )
                        | ( SY2388 = SY2389 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3804]) ).

thf(3862,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ! [SY2803: $i] :
              ~ ~ ( ~ ( SV438 @ SY2803 )
                  | ~ ! [SY2804: $i] :
                        ( ~ ( SV438 @ SY2804 )
                        | ( SY2803 = SY2804 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3805]) ).

thf(3863,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ! [SY2388: $i] :
              ~ ~ ( ~ ( SV214 @ SY2388 )
                  | ~ ! [SY2389: $i] :
                        ( ~ ( SV214 @ SY2389 )
                        | ( SY2388 = SY2389 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3806]) ).

thf(3864,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ! [SY2803: $i] :
              ~ ~ ( ~ ( SV438 @ SY2803 )
                  | ~ ! [SY2804: $i] :
                        ( ~ ( SV438 @ SY2804 )
                        | ( SY2803 = SY2804 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3807]) ).

thf(3865,plain,
    ! [SV438: $i > $o,SV832: $i,SV214: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV214 @ SV832 )
                | ~ ! [SY3229: $i] :
                      ( ~ ( SV214 @ SY3229 )
                      | ( SV832 = SY3229 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3808]) ).

thf(3866,plain,
    ! [SV214: $i > $o,SV833: $i,SV438: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV438 @ SV833 )
                | ~ ! [SY3230: $i] :
                      ( ~ ( SV438 @ SY3230 )
                      | ( SV833 = SY3230 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3809]) ).

thf(3867,plain,
    ! [SV445: $i,SV579: $i,SV721: $i,SV221: $i] :
      ( ( ( in @ ( sK103_SY3208 @ SV221 @ SV721 @ SV579 @ SV445 ) @ SV445 )
        = $true )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ SV221 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3810]) ).

thf(3868,plain,
    ! [SV221: $i,SV445: $i,SV721: $i,SV579: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK95_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ ( sK103_SY3208 @ SV221 @ SV721 @ SV579 @ SV445 ) ) @ SV721 ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ SV221 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3811]) ).

thf(3869,plain,
    ! [SV221: $i,SV445: $i,SV721: $i,SV579: $i] :
      ( ( ( in @ ( kpair @ ( sK95_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ ( sK103_SY3208 @ SV221 @ SV721 @ SV579 @ SV445 ) ) @ SV579 )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ SV221 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3811]) ).

thf(3870,plain,
    ! [SV221: $i,SV445: $i,SV721: $i,SV579: $i] :
      ( ( ( in @ ( sK104_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ SV221 )
        = $true )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) @ SV445 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3812]) ).

thf(3871,plain,
    ! [SV445: $i,SV579: $i,SV721: $i,SV221: $i] :
      ( ( ( ~ ( in @ ( sK107_SY3221 @ SV221 @ SV721 @ SV579 @ SV445 ) @ SV445 )
          | ~ ( in @ ( kpair @ ( sK104_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ ( sK107_SY3221 @ SV221 @ SV721 @ SV579 @ SV445 ) ) @ SV721 )
          | ( in @ ( kpair @ ( sK104_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ ( sK107_SY3221 @ SV221 @ SV721 @ SV579 @ SV445 ) ) @ SV579 ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) @ SV445 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3813]) ).

thf(3872,plain,
    ! [SV221: $i,SV445: $i,SV721: $i,SV579: $i] :
      ( ( ( ~ ( in @ ( sK106_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ SV221 ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV579 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3814]) ).

thf(3873,plain,
    ! [SV221: $i,SV721: $i,SV579: $i,SV445: $i] :
      ( ( ( ! [SY3226: $i] :
              ( ~ ( in @ SY3226 @ SV445 )
              | ~ ( in @ ( kpair @ ( sK106_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ SY3226 ) @ SV721 )
              | ( in @ ( kpair @ ( sK106_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ SY3226 ) @ SV579 ) ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV579 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3814]) ).

thf(3874,plain,
    ! [SV221: $i,SV445: $i,SV721: $i,SV579: $i] :
      ( ( ( in @ ( sK105_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ SV221 )
        = $true )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV721 )
        = $false )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3815]) ).

thf(3875,plain,
    ! [SV445: $i,SV579: $i,SV721: $i,SV221: $i] :
      ( ( ( ~ ( in @ ( sK108_SY3222 @ SV221 @ SV721 @ SV579 @ SV445 ) @ SV445 )
          | ~ ( in @ ( kpair @ ( sK105_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ ( sK108_SY3222 @ SV221 @ SV721 @ SV579 @ SV445 ) ) @ SV721 )
          | ( in @ ( kpair @ ( sK105_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ ( sK108_SY3222 @ SV221 @ SV721 @ SV579 @ SV445 ) ) @ SV579 ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV721 )
        = $false )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3816]) ).

thf(3876,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ~ ( SV253 @ ( sK99_SY2491 @ SV667 @ SV253 ) ) )
        = $false )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $true )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3817]) ).

thf(3877,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ~ ! [SY3215: $i] :
                ( ~ ( SV253 @ SY3215 )
                | ( ( sK99_SY2491 @ SV667 @ SV253 )
                  = SY3215 ) ) )
        = $false )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $true )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3817]) ).

thf(3878,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( SV253 @ ( sK96_SY2491 @ SV667 @ SV253 ) )
        = $true )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $true )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3818]) ).

thf(3879,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ! [SY3209: $i] :
              ( ~ ( SV253 @ SY3209 )
              | ( ( sK96_SY2491 @ SV667 @ SV253 )
                = SY3209 ) ) )
        = $true )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $true )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3819]) ).

thf(3880,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( SV253 @ ( sK97_SY2491 @ SV667 @ SV253 ) )
        = $true )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $false )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3820]) ).

thf(3881,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ! [SY3210: $i] :
              ( ~ ( SV253 @ SY3210 )
              | ( ( sK97_SY2491 @ SV667 @ SV253 )
                = SY3210 ) ) )
        = $true )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $false )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3821]) ).

thf(3882,plain,
    ! [SV667: $i,SV834: $i,SV253: $i > $o] :
      ( ( ( ~ ( SV253 @ SV834 )
          | ( ( sK93_SY2491 @ SV667 @ SV253 )
            = SV834 ) )
        = $true )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $false )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3823]) ).

thf(3883,plain,
    ! [SV620: $i,SV812: $i,SV37: $i > $o] :
      ( ( ( ~ ( SV37 @ SV812 ) )
        = $true )
      | ( ( SV812
          = ( sK86_SY1897 @ SV620 @ SV37 ) )
        = $true )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( SV37 @ ( sK59_SY3056 @ SV620 @ SV37 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3824]) ).

thf(3884,plain,
    ! [SV37: $i > $o,SV620: $i,SV812: $i] :
      ( ( ( SV812
         != ( sK86_SY1897 @ SV620 @ SV37 ) )
        = $true )
      | ( ( SV37 @ SV812 )
        = $true )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( SV37 @ ( sK59_SY3056 @ SV620 @ SV37 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3825]) ).

thf(3885,plain,
    ! [SV620: $i,SV810: $i,SV37: $i > $o] :
      ( ( ( SV37 @ SV810 )
        = $false )
      | ( ( SV810
          = ( sK77_SY1897 @ SV620 @ SV37 ) )
        = $true )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( SV620
          = ( sK59_SY3056 @ SV620 @ SV37 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3826]) ).

thf(3886,plain,
    ! [SV37: $i > $o,SV620: $i,SV810: $i] :
      ( ( ( SV810
          = ( sK77_SY1897 @ SV620 @ SV37 ) )
        = $false )
      | ( ( SV37 @ SV810 )
        = $true )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( SV620
          = ( sK59_SY3056 @ SV620 @ SV37 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3827]) ).

thf(3887,plain,
    ! [SV624: $i,SV827: $i,SV48: $i > $o] :
      ( ( ( ~ ( SV48 @ SV827 ) )
        = $true )
      | ( ( ( sK87_SY1928 @ SV624 @ SV48 )
          = SV827 )
        = $true )
      | ( ( SV48 @ SV624 )
        = $false )
      | ( ( SV48 @ ( sK62_SY3060 @ SV624 @ SV48 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3828]) ).

thf(3888,plain,
    ! [SV624: $i,SV820: $i,SV48: $i > $o] :
      ( ( ( SV48 @ SV820 )
        = $false )
      | ( ( ( sK79_SY1928 @ SV624 @ SV48 )
          = SV820 )
        = $true )
      | ( ( SV48 @ SV624 )
        = $false )
      | ( ( SV624
          = ( sK62_SY3060 @ SV624 @ SV48 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3829]) ).

thf(3889,plain,
    ! [SV775: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( SV77 @ ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) )
        = $true )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3830]) ).

thf(3890,plain,
    ! [SV775: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ~ ! [SY2576: $i] :
                ~ ~ ( ~ ( SV315 @ SY2576 )
                    | ~ ! [SY2577: $i] :
                          ( ~ ( SV315 @ SY2577 )
                          | ( SY2576 = SY2577 ) ) ) )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( SV775
          = ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) )
        = $false )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3831]) ).

thf(3891,plain,
    ! [SV315: $i > $o,SV821: $i,SV77: $i > $o] :
      ( ( ( ~ ( SV77 @ SV821 )
          | ~ ! [SY3223: $i] :
                ( ~ ( SV77 @ SY3223 )
                | ( SV821 = SY3223 ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3832]) ).

thf(3892,plain,
    ! [SV315: $i > $o,SV816: $i,SV77: $i > $o] :
      ( ( ( ~ ( SV77 @ SV816 ) )
        = $true )
      | ( ( ~ ! [SY3216: $i] :
                ( ~ ( SV77 @ SY3216 )
                | ( SV816 = SY3216 ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3833]) ).

thf(3893,plain,
    ! [SV315: $i > $o,SV817: $i,SV77: $i > $o] :
      ( ( ( ~ ( SV77 @ SV817 ) )
        = $true )
      | ( ( ~ ! [SY3217: $i] :
                ( ~ ( SV77 @ SY3217 )
                | ( SV817 = SY3217 ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3834]) ).

thf(3894,plain,
    ! [SV315: $i > $o,SV813: $i,SV77: $i > $o] :
      ( ( ( SV77 @ SV813 )
        = $false )
      | ( ( ~ ! [SY3211: $i] :
                ( ~ ( SV77 @ SY3211 )
                | ( SV813 = SY3211 ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3835]) ).

thf(3895,plain,
    ! [SV96: $i,SV332: $i,SV512: $i,SV685: $i,SV814: $i,SV791: $i] :
      ( ( ( in @ ( kpair @ SV791 @ SV814 ) @ SV685 )
        = $false )
      | ( ( in @ ( kpair @ SV791 @ SV814 ) @ SV512 )
        = $true )
      | ( ( in @ SV814 @ SV332 )
        = $false )
      | ( ( in @ SV791 @ SV96 )
        = $false )
      | ( ( in @ ( sK65_SY3119 @ SV685 @ SV512 @ SV332 @ SV96 ) @ SV96 )
        = $true )
      | ( ( func @ SV96 @ SV332 @ SV685 )
        = $false )
      | ( ( func @ SV96 @ SV332 @ SV512 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3836]) ).

thf(3896,plain,
    ! [SV795: $i,SV109: $i,SV804: $i] :
      ( ( ( in @ SV804 @ SV109 )
        = $false )
      | ( ( in @ SV795 @ SV109 )
        = $false )
      | ( ( ~ ! [SY3202: $i] :
                ( ~ ( in @ SY3202 @ ( sK3_SY2100 @ SV109 ) )
                | ~ ( ~ ( ~ ( in @ SV795 @ SY3202 )
                        | ( in @ SV804 @ SY3202 ) )
                    | ~ ( ~ ( in @ SV804 @ SY3202 )
                        | ( in @ SV795 @ SY3202 ) ) ) )
          | ( SV795 = SV804 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3839]) ).

thf(3897,plain,
    ! [SV109: $i,SV776: $i,SV765: $i,SV828: $i] :
      ( ( ( ~ ( in @ SV828 @ SV765 ) )
        = $true )
      | ( ( in @ SV828 @ SV776 )
        = $true )
      | ( ( ! [SY3185: $i] :
              ( ~ ( in @ SY3185 @ SV776 )
              | ( in @ SY3185 @ SV765 ) ) )
        = $true )
      | ( ( in @ SV765 @ ( sK3_SY2100 @ SV109 ) )
        = $false )
      | ( ( in @ SV776 @ ( sK3_SY2100 @ SV109 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3840]) ).

thf(3898,plain,
    ! [SV822: $i,SV739: $i,SV109: $i] :
      ( ( ( ! [SY3156: $i] :
              ~ ~ ! [SY3157: $i] :
                    ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3156 @ ( sK3_SY2100 @ SV109 ) )
                                    | ~ ( in @ SY3157 @ SV739 ) )
                              | ~ ~ ~ ! [SY3158: $i] :
                                        ~ ~ ( ~ ( in @ SY3158 @ SY3156 )
                                            | ~ ( in @ SY3158 @ SV739 ) ) )
                        | ~ ! [SY2947: $i] :
                              ( ~ ( in @ SY2947 @ ( sK3_SY2100 @ SV109 ) )
                              | ! [SX6: $i] :
                                  ( ~ ( in @ SX6 @ SY2947 )
                                  | ( in @ SX6 @ SY3156 ) )
                              | ( in @ SY3157 @ SY2947 ) ) ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3841]) ).

thf(3899,plain,
    ! [SV109: $i,SV739: $i,SV818: $i] :
      ( ( ( ~ ~ ! [SY3231: $i] :
                  ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) )
                                  | ~ ( in @ SY3231 @ SV739 ) )
                            | ~ ~ ~ ! [SY3232: $i] :
                                      ~ ~ ( ~ ( in @ SY3232 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) )
                                          | ~ ( in @ SY3232 @ SV739 ) ) )
                      | ~ ! [SY3233: $i] :
                            ( ~ ( in @ SY3233 @ ( sK3_SY2100 @ SV109 ) )
                            | ! [SY3234: $i] :
                                ( ~ ( in @ SY3234 @ SY3233 )
                                | ( in @ SY3234 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) ) )
                            | ( in @ SY3231 @ SY3233 ) ) ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3842]) ).

thf(3900,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV767: $i] :
      ( ( ( ~ ( in @ ( sK101_SY3179 @ SV767 @ SV147 @ SV377 ) @ SV377 ) )
        = $false )
      | ( ( in @ SV767 @ ( sK47_SY2690 @ SV147 @ SV377 ) )
        = $false )
      | ( ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3845]) ).

thf(3901,plain,
    ! [SV377: $i,SV767: $i,SV147: $i > $i > $o] :
      ( ( ( ~ ( SV147 @ ( sK101_SY3179 @ SV767 @ SV147 @ SV377 ) @ SV767 ) )
        = $false )
      | ( ( in @ SV767 @ ( sK47_SY2690 @ SV147 @ SV377 ) )
        = $false )
      | ( ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3845]) ).

thf(3902,plain,
    ! [SV767: $i,SV147: $i > $i > $o,SV377: $i,SV819: $i] :
      ( ( ( ~ ( in @ SV819 @ SV377 ) )
        = $true )
      | ( ( ~ ( SV147 @ SV819 @ SV767 ) )
        = $true )
      | ( ( in @ SV767 @ ( sK47_SY2690 @ SV147 @ SV377 ) )
        = $true )
      | ( ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3846]) ).

thf(3903,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV743: $i,SV829: $i] :
      ( ( ( ~ ( ~ ( in @ SV829 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) )
              | ~ ! [SY3227: $i] :
                    ~ ~ ( ~ ( in @ SY3227 @ SV377 )
                        | ~ ( SV147 @ SY3227 @ SV829 ) ) )
          | ~ ( ~ ~ ! [SY3228: $i] :
                      ~ ~ ( ~ ( in @ SY3228 @ SV377 )
                          | ~ ( SV147 @ SY3228 @ SV829 ) )
              | ( in @ SV829 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) ) ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3847]) ).

thf(3904,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV743: $i,SV823: $i] :
      ( ( ( ~ ( ~ ( in @ SV823 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) )
              | ~ ! [SY3224: $i] :
                    ~ ~ ( ~ ( in @ SY3224 @ SV377 )
                        | ~ ( SV147 @ SY3224 @ SV823 ) ) ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV743
          = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3848]) ).

thf(3905,plain,
    ! [SV743: $i,SV823: $i,SV147: $i > $i > $o,SV377: $i] :
      ( ( ( ~ ( ~ ~ ! [SY3225: $i] :
                      ~ ~ ( ~ ( in @ SY3225 @ SV377 )
                          | ~ ( SV147 @ SY3225 @ SV823 ) )
              | ( in @ SV823 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) ) ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV743
          = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3848]) ).

thf(3906,plain,
    ! [SV651: $i,SV824: $i,SV165: $i > $o] :
      ( ( ( SV165 @ SV824 )
        = $false )
      | ( ( ( sK83_SY2244 @ SV651 @ SV165 )
          = SV824 )
        = $true )
      | ( ( SV165 @ ( sK48_SY2242 @ SV651 @ SV165 ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3849]) ).

thf(3907,plain,
    ! [SV651: $i,SV830: $i,SV165: $i > $o] :
      ( ( ( ~ ( SV165 @ SV830 ) )
        = $true )
      | ( ( ( sK91_SY2244 @ SV651 @ SV165 )
          = SV830 )
        = $true )
      | ( ( SV165 @ ( sK55_SY3172 @ SV651 @ SV165 ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3850]) ).

thf(3908,plain,
    ! [SV651: $i,SV825: $i,SV165: $i > $o] :
      ( ( ( SV165 @ SV825 )
        = $false )
      | ( ( ( sK84_SY2244 @ SV651 @ SV165 )
          = SV825 )
        = $true )
      | ( ( ( sK48_SY2242 @ SV651 @ SV165 )
          = ( sK55_SY3172 @ SV651 @ SV165 ) )
        = $false )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3851]) ).

thf(3909,plain,
    ! [SV434: $i,SV659: $i > $o,SV209: $i,SV713: $i > $o] :
      ( ( ( SV713 @ ( sK71_SY3174 @ SV209 @ SV659 @ SV713 @ SV434 ) )
        = $true )
      | ( ( SV659 @ ( sK50_SY3133 @ SV713 @ SV659 @ SV434 @ SV209 ) )
        = $true )
      | ( ( ( dsetconstr @ SV209
            @ ^ [SY3097: $i] : ( SV659 @ SY3097 ) )
          = ( dsetconstr @ SV434
            @ ^ [SY3136: $i] : ( SV713 @ SY3136 ) ) )
        = $true )
      | ( ( SV209 = SV434 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3852]) ).

thf(3910,plain,
    ! [SV660: $i,SV831: $i,SV211: $i > $o] :
      ( ( ( ~ ( SV211 @ SV831 ) )
        = $true )
      | ( ( ( sK92_SY2378 @ SV660 @ SV211 )
          = SV831 )
        = $true )
      | ( ( SV211 @ SV660 )
        = $false )
      | ( ( SV211 @ ( sK72_SY3099 @ SV660 @ SV211 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3855]) ).

thf(3911,plain,
    ! [SV660: $i,SV826: $i,SV211: $i > $o] :
      ( ( ( SV211 @ SV826 )
        = $false )
      | ( ( ( sK85_SY2378 @ SV660 @ SV211 )
          = SV826 )
        = $true )
      | ( ( SV211 @ SV660 )
        = $false )
      | ( ( SV660
          = ( sK72_SY3099 @ SV660 @ SV211 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3856]) ).

thf(3912,plain,
    ! [SV808: $i,SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK110_SY3205 @ SV438 @ SV808 @ SV214 ) )
          | ( SV808
            = ( sK110_SY3205 @ SV438 @ SV808 @ SV214 ) ) )
        = $false )
      | ( ( SV214 @ SV808 )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[3857]) ).

thf(3913,plain,
    ! [SV809: $i,SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK111_SY3206 @ SV214 @ SV809 @ SV438 ) )
          | ( SV809
            = ( sK111_SY3206 @ SV214 @ SV809 @ SV438 ) ) )
        = $false )
      | ( ( SV438 @ SV809 )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[3858]) ).

thf(3914,plain,
    ! [SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ! [SY2388: $i] :
              ~ ~ ( ~ ( SV214 @ SY2388 )
                  | ~ ! [SY2389: $i] :
                        ( ~ ( SV214 @ SY2389 )
                        | ( SY2388 = SY2389 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3859]) ).

thf(3915,plain,
    ! [SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ! [SY2803: $i] :
              ~ ~ ( ~ ( SV438 @ SY2803 )
                  | ~ ! [SY2804: $i] :
                        ( ~ ( SV438 @ SY2804 )
                        | ( SY2803 = SY2804 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3860]) ).

thf(3916,plain,
    ! [SV438: $i > $o,SV835: $i,SV214: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV214 @ SV835 )
                | ~ ! [SY3235: $i] :
                      ( ~ ( SV214 @ SY3235 )
                      | ( SV835 = SY3235 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3861]) ).

thf(3917,plain,
    ! [SV214: $i > $o,SV836: $i,SV438: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV438 @ SV836 )
                | ~ ! [SY3236: $i] :
                      ( ~ ( SV438 @ SY3236 )
                      | ( SV836 = SY3236 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3862]) ).

thf(3918,plain,
    ! [SV438: $i > $o,SV837: $i,SV214: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV214 @ SV837 )
                | ~ ! [SY3237: $i] :
                      ( ~ ( SV214 @ SY3237 )
                      | ( SV837 = SY3237 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3863]) ).

thf(3919,plain,
    ! [SV214: $i > $o,SV838: $i,SV438: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV438 @ SV838 )
                | ~ ! [SY3238: $i] :
                      ( ~ ( SV438 @ SY3238 )
                      | ( SV838 = SY3238 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3864]) ).

thf(3920,plain,
    ! [SV438: $i > $o,SV832: $i,SV214: $i > $o] :
      ( ( ( ~ ( ~ ( SV214 @ SV832 )
              | ~ ! [SY3229: $i] :
                    ( ~ ( SV214 @ SY3229 )
                    | ( SV832 = SY3229 ) ) ) )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3865]) ).

thf(3921,plain,
    ! [SV214: $i > $o,SV833: $i,SV438: $i > $o] :
      ( ( ( ~ ( ~ ( SV438 @ SV833 )
              | ~ ! [SY3230: $i] :
                    ( ~ ( SV438 @ SY3230 )
                    | ( SV833 = SY3230 ) ) ) )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3866]) ).

thf(3922,plain,
    ! [SV221: $i,SV445: $i,SV721: $i,SV579: $i] :
      ( ( ( in @ ( kpair @ ( sK95_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ ( sK103_SY3208 @ SV221 @ SV721 @ SV579 @ SV445 ) ) @ SV721 )
        = $true )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ SV221 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3868]) ).

thf(3923,plain,
    ! [SV445: $i,SV579: $i,SV721: $i,SV221: $i] :
      ( ( ( ~ ( in @ ( sK107_SY3221 @ SV221 @ SV721 @ SV579 @ SV445 ) @ SV445 ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) @ SV445 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3871]) ).

thf(3924,plain,
    ! [SV221: $i,SV445: $i,SV721: $i,SV579: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK104_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ ( sK107_SY3221 @ SV221 @ SV721 @ SV579 @ SV445 ) ) @ SV721 )
          | ( in @ ( kpair @ ( sK104_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ ( sK107_SY3221 @ SV221 @ SV721 @ SV579 @ SV445 ) ) @ SV579 ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) @ SV445 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3871]) ).

thf(3925,plain,
    ! [SV221: $i,SV445: $i,SV721: $i,SV579: $i] :
      ( ( ( in @ ( sK106_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ SV221 )
        = $true )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV579 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3872]) ).

thf(3926,plain,
    ! [SV445: $i,SV579: $i,SV721: $i,SV221: $i] :
      ( ( ( ~ ( in @ ( sK112_SY3226 @ SV221 @ SV721 @ SV579 @ SV445 ) @ SV445 )
          | ~ ( in @ ( kpair @ ( sK106_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ ( sK112_SY3226 @ SV221 @ SV721 @ SV579 @ SV445 ) ) @ SV721 )
          | ( in @ ( kpair @ ( sK106_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ ( sK112_SY3226 @ SV221 @ SV721 @ SV579 @ SV445 ) ) @ SV579 ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV579 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3873]) ).

thf(3927,plain,
    ! [SV445: $i,SV579: $i,SV721: $i,SV221: $i] :
      ( ( ( ~ ( in @ ( sK108_SY3222 @ SV221 @ SV721 @ SV579 @ SV445 ) @ SV445 ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV721 )
        = $false )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3875]) ).

thf(3928,plain,
    ! [SV221: $i,SV445: $i,SV721: $i,SV579: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK105_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ ( sK108_SY3222 @ SV221 @ SV721 @ SV579 @ SV445 ) ) @ SV721 )
          | ( in @ ( kpair @ ( sK105_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ ( sK108_SY3222 @ SV221 @ SV721 @ SV579 @ SV445 ) ) @ SV579 ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV721 )
        = $false )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3875]) ).

thf(3929,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( SV253 @ ( sK99_SY2491 @ SV667 @ SV253 ) )
        = $true )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $true )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3876]) ).

thf(3930,plain,
    ! [SV667: $i,SV253: $i > $o] :
      ( ( ( ! [SY3215: $i] :
              ( ~ ( SV253 @ SY3215 )
              | ( ( sK99_SY2491 @ SV667 @ SV253 )
                = SY3215 ) ) )
        = $true )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $true )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3877]) ).

thf(3931,plain,
    ! [SV667: $i,SV839: $i,SV253: $i > $o] :
      ( ( ( ~ ( SV253 @ SV839 )
          | ( ( sK96_SY2491 @ SV667 @ SV253 )
            = SV839 ) )
        = $true )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $true )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3879]) ).

thf(3932,plain,
    ! [SV667: $i,SV840: $i,SV253: $i > $o] :
      ( ( ( ~ ( SV253 @ SV840 )
          | ( ( sK97_SY2491 @ SV667 @ SV253 )
            = SV840 ) )
        = $true )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $false )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3881]) ).

thf(3933,plain,
    ! [SV667: $i,SV834: $i,SV253: $i > $o] :
      ( ( ( ~ ( SV253 @ SV834 ) )
        = $true )
      | ( ( ( sK93_SY2491 @ SV667 @ SV253 )
          = SV834 )
        = $true )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $false )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3882]) ).

thf(3934,plain,
    ! [SV620: $i,SV812: $i,SV37: $i > $o] :
      ( ( ( SV37 @ SV812 )
        = $false )
      | ( ( SV812
          = ( sK86_SY1897 @ SV620 @ SV37 ) )
        = $true )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( SV37 @ ( sK59_SY3056 @ SV620 @ SV37 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3883]) ).

thf(3935,plain,
    ! [SV37: $i > $o,SV620: $i,SV812: $i] :
      ( ( ( SV812
          = ( sK86_SY1897 @ SV620 @ SV37 ) )
        = $false )
      | ( ( SV37 @ SV812 )
        = $true )
      | ( ( SV37 @ SV620 )
        = $false )
      | ( ( SV37 @ ( sK59_SY3056 @ SV620 @ SV37 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3884]) ).

thf(3936,plain,
    ! [SV624: $i,SV827: $i,SV48: $i > $o] :
      ( ( ( SV48 @ SV827 )
        = $false )
      | ( ( ( sK87_SY1928 @ SV624 @ SV48 )
          = SV827 )
        = $true )
      | ( ( SV48 @ SV624 )
        = $false )
      | ( ( SV48 @ ( sK62_SY3060 @ SV624 @ SV48 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3887]) ).

thf(3937,plain,
    ! [SV775: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ~ ! [SY2576: $i] :
                ~ ~ ( ~ ( SV315 @ SY2576 )
                    | ~ ! [SY2577: $i] :
                          ( ~ ( SV315 @ SY2577 )
                          | ( SY2576 = SY2577 ) ) ) )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( SV77 @ ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) )
        = $true )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3889]) ).

thf(3938,plain,
    ! [SV775: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ! [SY2576: $i] :
              ~ ~ ( ~ ( SV315 @ SY2576 )
                  | ~ ! [SY2577: $i] :
                        ( ~ ( SV315 @ SY2577 )
                        | ( SY2576 = SY2577 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( SV775
          = ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) )
        = $false )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3890]) ).

thf(3939,plain,
    ! [SV315: $i > $o,SV821: $i,SV77: $i > $o] :
      ( ( ( ~ ( SV77 @ SV821 ) )
        = $true )
      | ( ( ~ ! [SY3223: $i] :
                ( ~ ( SV77 @ SY3223 )
                | ( SV821 = SY3223 ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3891]) ).

thf(3940,plain,
    ! [SV315: $i > $o,SV816: $i,SV77: $i > $o] :
      ( ( ( SV77 @ SV816 )
        = $false )
      | ( ( ~ ! [SY3216: $i] :
                ( ~ ( SV77 @ SY3216 )
                | ( SV816 = SY3216 ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3892]) ).

thf(3941,plain,
    ! [SV315: $i > $o,SV817: $i,SV77: $i > $o] :
      ( ( ( SV77 @ SV817 )
        = $false )
      | ( ( ~ ! [SY3217: $i] :
                ( ~ ( SV77 @ SY3217 )
                | ( SV817 = SY3217 ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3893]) ).

thf(3942,plain,
    ! [SV315: $i > $o,SV813: $i,SV77: $i > $o] :
      ( ( ( ! [SY3211: $i] :
              ( ~ ( SV77 @ SY3211 )
              | ( SV813 = SY3211 ) ) )
        = $false )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3894]) ).

thf(3943,plain,
    ! [SV804: $i,SV795: $i,SV109: $i] :
      ( ( ( ~ ! [SY3202: $i] :
                ( ~ ( in @ SY3202 @ ( sK3_SY2100 @ SV109 ) )
                | ~ ( ~ ( ~ ( in @ SV795 @ SY3202 )
                        | ( in @ SV804 @ SY3202 ) )
                    | ~ ( ~ ( in @ SV804 @ SY3202 )
                        | ( in @ SV795 @ SY3202 ) ) ) ) )
        = $true )
      | ( ( SV795 = SV804 )
        = $true )
      | ( ( in @ SV795 @ SV109 )
        = $false )
      | ( ( in @ SV804 @ SV109 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3896]) ).

thf(3944,plain,
    ! [SV109: $i,SV776: $i,SV765: $i,SV828: $i] :
      ( ( ( in @ SV828 @ SV765 )
        = $false )
      | ( ( in @ SV828 @ SV776 )
        = $true )
      | ( ( ! [SY3185: $i] :
              ( ~ ( in @ SY3185 @ SV776 )
              | ( in @ SY3185 @ SV765 ) ) )
        = $true )
      | ( ( in @ SV765 @ ( sK3_SY2100 @ SV109 ) )
        = $false )
      | ( ( in @ SV776 @ ( sK3_SY2100 @ SV109 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3897]) ).

thf(3945,plain,
    ! [SV109: $i,SV739: $i,SV822: $i] :
      ( ( ( ~ ~ ! [SY3239: $i] :
                  ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) )
                                  | ~ ( in @ SY3239 @ SV739 ) )
                            | ~ ~ ~ ! [SY3240: $i] :
                                      ~ ~ ( ~ ( in @ SY3240 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) )
                                          | ~ ( in @ SY3240 @ SV739 ) ) )
                      | ~ ! [SY3241: $i] :
                            ( ~ ( in @ SY3241 @ ( sK3_SY2100 @ SV109 ) )
                            | ! [SY3242: $i] :
                                ( ~ ( in @ SY3242 @ SY3241 )
                                | ( in @ SY3242 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) ) )
                            | ( in @ SY3239 @ SY3241 ) ) ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3898]) ).

thf(3946,plain,
    ! [SV109: $i,SV739: $i,SV818: $i] :
      ( ( ( ~ ! [SY3231: $i] :
                ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) )
                                | ~ ( in @ SY3231 @ SV739 ) )
                          | ~ ~ ~ ! [SY3232: $i] :
                                    ~ ~ ( ~ ( in @ SY3232 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) )
                                        | ~ ( in @ SY3232 @ SV739 ) ) )
                    | ~ ! [SY3233: $i] :
                          ( ~ ( in @ SY3233 @ ( sK3_SY2100 @ SV109 ) )
                          | ! [SY3234: $i] :
                              ( ~ ( in @ SY3234 @ SY3233 )
                              | ( in @ SY3234 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) ) )
                          | ( in @ SY3231 @ SY3233 ) ) ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3899]) ).

thf(3947,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV767: $i] :
      ( ( ( in @ ( sK101_SY3179 @ SV767 @ SV147 @ SV377 ) @ SV377 )
        = $true )
      | ( ( in @ SV767 @ ( sK47_SY2690 @ SV147 @ SV377 ) )
        = $false )
      | ( ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3900]) ).

thf(3948,plain,
    ! [SV377: $i,SV767: $i,SV147: $i > $i > $o] :
      ( ( ( SV147 @ ( sK101_SY3179 @ SV767 @ SV147 @ SV377 ) @ SV767 )
        = $true )
      | ( ( in @ SV767 @ ( sK47_SY2690 @ SV147 @ SV377 ) )
        = $false )
      | ( ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3901]) ).

thf(3949,plain,
    ! [SV767: $i,SV147: $i > $i > $o,SV377: $i,SV819: $i] :
      ( ( ( in @ SV819 @ SV377 )
        = $false )
      | ( ( ~ ( SV147 @ SV819 @ SV767 ) )
        = $true )
      | ( ( in @ SV767 @ ( sK47_SY2690 @ SV147 @ SV377 ) )
        = $true )
      | ( ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3902]) ).

thf(3950,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV743: $i,SV829: $i] :
      ( ( ( ~ ( ~ ( in @ SV829 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) )
              | ~ ! [SY3227: $i] :
                    ~ ~ ( ~ ( in @ SY3227 @ SV377 )
                        | ~ ( SV147 @ SY3227 @ SV829 ) ) ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3903]) ).

thf(3951,plain,
    ! [SV743: $i,SV829: $i,SV147: $i > $i > $o,SV377: $i] :
      ( ( ( ~ ( ~ ~ ! [SY3228: $i] :
                      ~ ~ ( ~ ( in @ SY3228 @ SV377 )
                          | ~ ( SV147 @ SY3228 @ SV829 ) )
              | ( in @ SV829 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) ) ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3903]) ).

thf(3952,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV743: $i,SV823: $i] :
      ( ( ( ~ ( in @ SV823 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) )
          | ~ ! [SY3224: $i] :
                ~ ~ ( ~ ( in @ SY3224 @ SV377 )
                    | ~ ( SV147 @ SY3224 @ SV823 ) ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV743
          = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3904]) ).

thf(3953,plain,
    ! [SV743: $i,SV823: $i,SV147: $i > $i > $o,SV377: $i] :
      ( ( ( ~ ~ ! [SY3225: $i] :
                  ~ ~ ( ~ ( in @ SY3225 @ SV377 )
                      | ~ ( SV147 @ SY3225 @ SV823 ) )
          | ( in @ SV823 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV743
          = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3905]) ).

thf(3954,plain,
    ! [SV651: $i,SV830: $i,SV165: $i > $o] :
      ( ( ( SV165 @ SV830 )
        = $false )
      | ( ( ( sK91_SY2244 @ SV651 @ SV165 )
          = SV830 )
        = $true )
      | ( ( SV165 @ ( sK55_SY3172 @ SV651 @ SV165 ) )
        = $true )
      | ( ( SV165 @ SV651 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3907]) ).

thf(3955,plain,
    ! [SV660: $i,SV831: $i,SV211: $i > $o] :
      ( ( ( SV211 @ SV831 )
        = $false )
      | ( ( ( sK92_SY2378 @ SV660 @ SV211 )
          = SV831 )
        = $true )
      | ( ( SV211 @ SV660 )
        = $false )
      | ( ( SV211 @ ( sK72_SY3099 @ SV660 @ SV211 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3910]) ).

thf(3956,plain,
    ! [SV808: $i,SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK110_SY3205 @ SV438 @ SV808 @ SV214 ) ) )
        = $false )
      | ( ( SV214 @ SV808 )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3912]) ).

thf(3957,plain,
    ! [SV214: $i > $o,SV438: $i > $o,SV808: $i] :
      ( ( ( SV808
          = ( sK110_SY3205 @ SV438 @ SV808 @ SV214 ) )
        = $false )
      | ( ( SV214 @ SV808 )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3912]) ).

thf(3958,plain,
    ! [SV809: $i,SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK111_SY3206 @ SV214 @ SV809 @ SV438 ) ) )
        = $false )
      | ( ( SV438 @ SV809 )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3913]) ).

thf(3959,plain,
    ! [SV438: $i > $o,SV214: $i > $o,SV809: $i] :
      ( ( ( SV809
          = ( sK111_SY3206 @ SV214 @ SV809 @ SV438 ) )
        = $false )
      | ( ( SV438 @ SV809 )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3913]) ).

thf(3960,plain,
    ! [SV438: $i > $o,SV841: $i,SV214: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV214 @ SV841 )
                | ~ ! [SY3243: $i] :
                      ( ~ ( SV214 @ SY3243 )
                      | ( SV841 = SY3243 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3914]) ).

thf(3961,plain,
    ! [SV214: $i > $o,SV842: $i,SV438: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV438 @ SV842 )
                | ~ ! [SY3244: $i] :
                      ( ~ ( SV438 @ SY3244 )
                      | ( SV842 = SY3244 ) ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3915]) ).

thf(3962,plain,
    ! [SV438: $i > $o,SV835: $i,SV214: $i > $o] :
      ( ( ( ~ ( ~ ( SV214 @ SV835 )
              | ~ ! [SY3235: $i] :
                    ( ~ ( SV214 @ SY3235 )
                    | ( SV835 = SY3235 ) ) ) )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3916]) ).

thf(3963,plain,
    ! [SV214: $i > $o,SV836: $i,SV438: $i > $o] :
      ( ( ( ~ ( ~ ( SV438 @ SV836 )
              | ~ ! [SY3236: $i] :
                    ( ~ ( SV438 @ SY3236 )
                    | ( SV836 = SY3236 ) ) ) )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3917]) ).

thf(3964,plain,
    ! [SV438: $i > $o,SV837: $i,SV214: $i > $o] :
      ( ( ( ~ ( ~ ( SV214 @ SV837 )
              | ~ ! [SY3237: $i] :
                    ( ~ ( SV214 @ SY3237 )
                    | ( SV837 = SY3237 ) ) ) )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3918]) ).

thf(3965,plain,
    ! [SV214: $i > $o,SV838: $i,SV438: $i > $o] :
      ( ( ( ~ ( ~ ( SV438 @ SV838 )
              | ~ ! [SY3238: $i] :
                    ( ~ ( SV438 @ SY3238 )
                    | ( SV838 = SY3238 ) ) ) )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3919]) ).

thf(3966,plain,
    ! [SV438: $i > $o,SV832: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV832 )
          | ~ ! [SY3229: $i] :
                ( ~ ( SV214 @ SY3229 )
                | ( SV832 = SY3229 ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3920]) ).

thf(3967,plain,
    ! [SV214: $i > $o,SV833: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV833 )
          | ~ ! [SY3230: $i] :
                ( ~ ( SV438 @ SY3230 )
                | ( SV833 = SY3230 ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3921]) ).

thf(3968,plain,
    ! [SV445: $i,SV579: $i,SV721: $i,SV221: $i] :
      ( ( ( in @ ( sK107_SY3221 @ SV221 @ SV721 @ SV579 @ SV445 ) @ SV445 )
        = $true )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) @ SV445 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3923]) ).

thf(3969,plain,
    ! [SV221: $i,SV445: $i,SV721: $i,SV579: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK104_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ ( sK107_SY3221 @ SV221 @ SV721 @ SV579 @ SV445 ) ) @ SV721 ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) @ SV445 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3924]) ).

thf(3970,plain,
    ! [SV221: $i,SV445: $i,SV721: $i,SV579: $i] :
      ( ( ( in @ ( kpair @ ( sK104_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ ( sK107_SY3221 @ SV221 @ SV721 @ SV579 @ SV445 ) ) @ SV579 )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) @ SV445 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3924]) ).

thf(3971,plain,
    ! [SV445: $i,SV579: $i,SV721: $i,SV221: $i] :
      ( ( ( ~ ( in @ ( sK112_SY3226 @ SV221 @ SV721 @ SV579 @ SV445 ) @ SV445 ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV579 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3926]) ).

thf(3972,plain,
    ! [SV221: $i,SV445: $i,SV721: $i,SV579: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK106_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ ( sK112_SY3226 @ SV221 @ SV721 @ SV579 @ SV445 ) ) @ SV721 )
          | ( in @ ( kpair @ ( sK106_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ ( sK112_SY3226 @ SV221 @ SV721 @ SV579 @ SV445 ) ) @ SV579 ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV579 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3926]) ).

thf(3973,plain,
    ! [SV445: $i,SV579: $i,SV721: $i,SV221: $i] :
      ( ( ( in @ ( sK108_SY3222 @ SV221 @ SV721 @ SV579 @ SV445 ) @ SV445 )
        = $true )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV721 )
        = $false )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3927]) ).

thf(3974,plain,
    ! [SV221: $i,SV445: $i,SV721: $i,SV579: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK105_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ ( sK108_SY3222 @ SV221 @ SV721 @ SV579 @ SV445 ) ) @ SV721 ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV721 )
        = $false )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3928]) ).

thf(3975,plain,
    ! [SV221: $i,SV445: $i,SV721: $i,SV579: $i] :
      ( ( ( in @ ( kpair @ ( sK105_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ ( sK108_SY3222 @ SV221 @ SV721 @ SV579 @ SV445 ) ) @ SV579 )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV721 )
        = $false )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3928]) ).

thf(3976,plain,
    ! [SV667: $i,SV843: $i,SV253: $i > $o] :
      ( ( ( ~ ( SV253 @ SV843 )
          | ( ( sK99_SY2491 @ SV667 @ SV253 )
            = SV843 ) )
        = $true )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $true )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3930]) ).

thf(3977,plain,
    ! [SV667: $i,SV839: $i,SV253: $i > $o] :
      ( ( ( ~ ( SV253 @ SV839 ) )
        = $true )
      | ( ( ( sK96_SY2491 @ SV667 @ SV253 )
          = SV839 )
        = $true )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $true )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3931]) ).

thf(3978,plain,
    ! [SV667: $i,SV840: $i,SV253: $i > $o] :
      ( ( ( ~ ( SV253 @ SV840 ) )
        = $true )
      | ( ( ( sK97_SY2491 @ SV667 @ SV253 )
          = SV840 )
        = $true )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $false )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3932]) ).

thf(3979,plain,
    ! [SV667: $i,SV834: $i,SV253: $i > $o] :
      ( ( ( SV253 @ SV834 )
        = $false )
      | ( ( ( sK93_SY2491 @ SV667 @ SV253 )
          = SV834 )
        = $true )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $false )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3933]) ).

thf(3980,plain,
    ! [SV775: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ! [SY2576: $i] :
              ~ ~ ( ~ ( SV315 @ SY2576 )
                  | ~ ! [SY2577: $i] :
                        ( ~ ( SV315 @ SY2577 )
                        | ( SY2576 = SY2577 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( SV77 @ ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) )
        = $true )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3937]) ).

thf(3981,plain,
    ! [SV775: $i,SV77: $i > $o,SV844: $i,SV315: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV315 @ SV844 )
                | ~ ! [SY3245: $i] :
                      ( ~ ( SV315 @ SY3245 )
                      | ( SV844 = SY3245 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( SV775
          = ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) )
        = $false )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3938]) ).

thf(3982,plain,
    ! [SV315: $i > $o,SV821: $i,SV77: $i > $o] :
      ( ( ( SV77 @ SV821 )
        = $false )
      | ( ( ~ ! [SY3223: $i] :
                ( ~ ( SV77 @ SY3223 )
                | ( SV821 = SY3223 ) ) )
        = $true )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3939]) ).

thf(3983,plain,
    ! [SV315: $i > $o,SV816: $i,SV77: $i > $o] :
      ( ( ( ! [SY3216: $i] :
              ( ~ ( SV77 @ SY3216 )
              | ( SV816 = SY3216 ) ) )
        = $false )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3940]) ).

thf(3984,plain,
    ! [SV315: $i > $o,SV817: $i,SV77: $i > $o] :
      ( ( ( ! [SY3217: $i] :
              ( ~ ( SV77 @ SY3217 )
              | ( SV817 = SY3217 ) ) )
        = $false )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3941]) ).

thf(3985,plain,
    ! [SV813: $i,SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ~ ( SV77 @ ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) )
          | ( SV813
            = ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) ) )
        = $false )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3942]) ).

thf(3986,plain,
    ! [SV804: $i,SV795: $i,SV109: $i] :
      ( ( ( ! [SY3202: $i] :
              ( ~ ( in @ SY3202 @ ( sK3_SY2100 @ SV109 ) )
              | ~ ( ~ ( ~ ( in @ SV795 @ SY3202 )
                      | ( in @ SV804 @ SY3202 ) )
                  | ~ ( ~ ( in @ SV804 @ SY3202 )
                      | ( in @ SV795 @ SY3202 ) ) ) ) )
        = $false )
      | ( ( SV795 = SV804 )
        = $true )
      | ( ( in @ SV795 @ SV109 )
        = $false )
      | ( ( in @ SV804 @ SV109 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3943]) ).

thf(3987,plain,
    ! [SV109: $i,SV828: $i,SV765: $i,SV776: $i,SV845: $i] :
      ( ( ( ~ ( in @ SV845 @ SV776 )
          | ( in @ SV845 @ SV765 ) )
        = $true )
      | ( ( in @ SV828 @ SV776 )
        = $true )
      | ( ( in @ SV828 @ SV765 )
        = $false )
      | ( ( in @ SV765 @ ( sK3_SY2100 @ SV109 ) )
        = $false )
      | ( ( in @ SV776 @ ( sK3_SY2100 @ SV109 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3944]) ).

thf(3988,plain,
    ! [SV109: $i,SV739: $i,SV822: $i] :
      ( ( ( ~ ! [SY3239: $i] :
                ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) )
                                | ~ ( in @ SY3239 @ SV739 ) )
                          | ~ ~ ~ ! [SY3240: $i] :
                                    ~ ~ ( ~ ( in @ SY3240 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) )
                                        | ~ ( in @ SY3240 @ SV739 ) ) )
                    | ~ ! [SY3241: $i] :
                          ( ~ ( in @ SY3241 @ ( sK3_SY2100 @ SV109 ) )
                          | ! [SY3242: $i] :
                              ( ~ ( in @ SY3242 @ SY3241 )
                              | ( in @ SY3242 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) ) )
                          | ( in @ SY3239 @ SY3241 ) ) ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3945]) ).

thf(3989,plain,
    ! [SV109: $i,SV739: $i,SV818: $i] :
      ( ( ( ! [SY3231: $i] :
              ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) )
                              | ~ ( in @ SY3231 @ SV739 ) )
                        | ~ ~ ~ ! [SY3232: $i] :
                                  ~ ~ ( ~ ( in @ SY3232 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) )
                                      | ~ ( in @ SY3232 @ SV739 ) ) )
                  | ~ ! [SY3233: $i] :
                        ( ~ ( in @ SY3233 @ ( sK3_SY2100 @ SV109 ) )
                        | ! [SY3234: $i] :
                            ( ~ ( in @ SY3234 @ SY3233 )
                            | ( in @ SY3234 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) ) )
                        | ( in @ SY3231 @ SY3233 ) ) ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3946]) ).

thf(3990,plain,
    ! [SV377: $i,SV767: $i,SV819: $i,SV147: $i > $i > $o] :
      ( ( ( SV147 @ SV819 @ SV767 )
        = $false )
      | ( ( in @ SV819 @ SV377 )
        = $false )
      | ( ( in @ SV767 @ ( sK47_SY2690 @ SV147 @ SV377 ) )
        = $true )
      | ( ( in @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV377 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3949]) ).

thf(3991,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV743: $i,SV829: $i] :
      ( ( ( ~ ( in @ SV829 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) )
          | ~ ! [SY3227: $i] :
                ~ ~ ( ~ ( in @ SY3227 @ SV377 )
                    | ~ ( SV147 @ SY3227 @ SV829 ) ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3950]) ).

thf(3992,plain,
    ! [SV743: $i,SV829: $i,SV147: $i > $i > $o,SV377: $i] :
      ( ( ( ~ ~ ! [SY3228: $i] :
                  ~ ~ ( ~ ( in @ SY3228 @ SV377 )
                      | ~ ( SV147 @ SY3228 @ SV829 ) )
          | ( in @ SV829 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3951]) ).

thf(3993,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV743: $i,SV823: $i] :
      ( ( ( ~ ( in @ SV823 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) ) )
        = $true )
      | ( ( ~ ! [SY3224: $i] :
                ~ ~ ( ~ ( in @ SY3224 @ SV377 )
                    | ~ ( SV147 @ SY3224 @ SV823 ) ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV743
          = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3952]) ).

thf(3994,plain,
    ! [SV743: $i,SV823: $i,SV147: $i > $i > $o,SV377: $i] :
      ( ( ( ~ ~ ! [SY3225: $i] :
                  ~ ~ ( ~ ( in @ SY3225 @ SV377 )
                      | ~ ( SV147 @ SY3225 @ SV823 ) ) )
        = $true )
      | ( ( in @ SV823 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV743
          = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3953]) ).

thf(3995,plain,
    ! [SV808: $i,SV438: $i > $o,SV214: $i > $o] :
      ( ( ( SV214 @ ( sK110_SY3205 @ SV438 @ SV808 @ SV214 ) )
        = $true )
      | ( ( SV214 @ SV808 )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3956]) ).

thf(3996,plain,
    ! [SV808: $i,SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ! [SY2801: $i] :
              ~ ~ ( ~ ( SV438 @ SY2801 )
                  | ~ ! [SY2802: $i] :
                        ( ~ ( SV438 @ SY2802 )
                        | ( SY2801 = SY2802 ) ) ) )
        = $false )
      | ( ( SV214 @ SV808 )
        = $false )
      | ( ( SV808
          = ( sK110_SY3205 @ SV438 @ SV808 @ SV214 ) )
        = $false )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3957]) ).

thf(3997,plain,
    ! [SV809: $i,SV214: $i > $o,SV438: $i > $o] :
      ( ( ( SV438 @ ( sK111_SY3206 @ SV214 @ SV809 @ SV438 ) )
        = $true )
      | ( ( SV438 @ SV809 )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3958]) ).

thf(3998,plain,
    ! [SV809: $i,SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ! [SY2394: $i] :
              ~ ~ ( ~ ( SV214 @ SY2394 )
                  | ~ ! [SY2395: $i] :
                        ( ~ ( SV214 @ SY2395 )
                        | ( SY2394 = SY2395 ) ) ) )
        = $false )
      | ( ( SV438 @ SV809 )
        = $false )
      | ( ( SV809
          = ( sK111_SY3206 @ SV214 @ SV809 @ SV438 ) )
        = $false )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3959]) ).

thf(3999,plain,
    ! [SV438: $i > $o,SV841: $i,SV214: $i > $o] :
      ( ( ( ~ ( ~ ( SV214 @ SV841 )
              | ~ ! [SY3243: $i] :
                    ( ~ ( SV214 @ SY3243 )
                    | ( SV841 = SY3243 ) ) ) )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3960]) ).

thf(4000,plain,
    ! [SV214: $i > $o,SV842: $i,SV438: $i > $o] :
      ( ( ( ~ ( ~ ( SV438 @ SV842 )
              | ~ ! [SY3244: $i] :
                    ( ~ ( SV438 @ SY3244 )
                    | ( SV842 = SY3244 ) ) ) )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3961]) ).

thf(4001,plain,
    ! [SV438: $i > $o,SV835: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV835 )
          | ~ ! [SY3235: $i] :
                ( ~ ( SV214 @ SY3235 )
                | ( SV835 = SY3235 ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3962]) ).

thf(4002,plain,
    ! [SV214: $i > $o,SV836: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV836 )
          | ~ ! [SY3236: $i] :
                ( ~ ( SV438 @ SY3236 )
                | ( SV836 = SY3236 ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3963]) ).

thf(4003,plain,
    ! [SV438: $i > $o,SV837: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV837 )
          | ~ ! [SY3237: $i] :
                ( ~ ( SV214 @ SY3237 )
                | ( SV837 = SY3237 ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3964]) ).

thf(4004,plain,
    ! [SV214: $i > $o,SV838: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV838 )
          | ~ ! [SY3238: $i] :
                ( ~ ( SV438 @ SY3238 )
                | ( SV838 = SY3238 ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3965]) ).

thf(4005,plain,
    ! [SV438: $i > $o,SV832: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV832 ) )
        = $true )
      | ( ( ~ ! [SY3229: $i] :
                ( ~ ( SV214 @ SY3229 )
                | ( SV832 = SY3229 ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3966]) ).

thf(4006,plain,
    ! [SV214: $i > $o,SV833: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV833 ) )
        = $true )
      | ( ( ~ ! [SY3230: $i] :
                ( ~ ( SV438 @ SY3230 )
                | ( SV833 = SY3230 ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3967]) ).

thf(4007,plain,
    ! [SV221: $i,SV445: $i,SV721: $i,SV579: $i] :
      ( ( ( in @ ( kpair @ ( sK104_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ ( sK107_SY3221 @ SV221 @ SV721 @ SV579 @ SV445 ) ) @ SV721 )
        = $true )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) @ SV445 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3969]) ).

thf(4008,plain,
    ! [SV445: $i,SV579: $i,SV721: $i,SV221: $i] :
      ( ( ( in @ ( sK112_SY3226 @ SV221 @ SV721 @ SV579 @ SV445 ) @ SV445 )
        = $true )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV579 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3971]) ).

thf(4009,plain,
    ! [SV221: $i,SV445: $i,SV721: $i,SV579: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK106_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ ( sK112_SY3226 @ SV221 @ SV721 @ SV579 @ SV445 ) ) @ SV721 ) )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV579 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3972]) ).

thf(4010,plain,
    ! [SV221: $i,SV445: $i,SV721: $i,SV579: $i] :
      ( ( ( in @ ( kpair @ ( sK106_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ ( sK112_SY3226 @ SV221 @ SV721 @ SV579 @ SV445 ) ) @ SV579 )
        = $false )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV579 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3972]) ).

thf(4011,plain,
    ! [SV221: $i,SV445: $i,SV721: $i,SV579: $i] :
      ( ( ( in @ ( kpair @ ( sK105_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ ( sK108_SY3222 @ SV221 @ SV721 @ SV579 @ SV445 ) ) @ SV721 )
        = $true )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV721 )
        = $false )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3974]) ).

thf(4012,plain,
    ! [SV667: $i,SV843: $i,SV253: $i > $o] :
      ( ( ( ~ ( SV253 @ SV843 ) )
        = $true )
      | ( ( ( sK99_SY2491 @ SV667 @ SV253 )
          = SV843 )
        = $true )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $true )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3976]) ).

thf(4013,plain,
    ! [SV667: $i,SV839: $i,SV253: $i > $o] :
      ( ( ( SV253 @ SV839 )
        = $false )
      | ( ( ( sK96_SY2491 @ SV667 @ SV253 )
          = SV839 )
        = $true )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $true )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3977]) ).

thf(4014,plain,
    ! [SV667: $i,SV840: $i,SV253: $i > $o] :
      ( ( ( SV253 @ SV840 )
        = $false )
      | ( ( ( sK97_SY2491 @ SV667 @ SV253 )
          = SV840 )
        = $true )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $false )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3978]) ).

thf(4015,plain,
    ! [SV775: $i,SV77: $i > $o,SV846: $i,SV315: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV315 @ SV846 )
                | ~ ! [SY3246: $i] :
                      ( ~ ( SV315 @ SY3246 )
                      | ( SV846 = SY3246 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( SV77 @ ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) )
        = $true )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3980]) ).

thf(4016,plain,
    ! [SV775: $i,SV77: $i > $o,SV844: $i,SV315: $i > $o] :
      ( ( ( ~ ( ~ ( SV315 @ SV844 )
              | ~ ! [SY3245: $i] :
                    ( ~ ( SV315 @ SY3245 )
                    | ( SV844 = SY3245 ) ) ) )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( SV775
          = ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) )
        = $false )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3981]) ).

thf(4017,plain,
    ! [SV315: $i > $o,SV821: $i,SV77: $i > $o] :
      ( ( ( ! [SY3223: $i] :
              ( ~ ( SV77 @ SY3223 )
              | ( SV821 = SY3223 ) ) )
        = $false )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3982]) ).

thf(4018,plain,
    ! [SV816: $i,SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ~ ( SV77 @ ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) )
          | ( SV816
            = ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) ) )
        = $false )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3983]) ).

thf(4019,plain,
    ! [SV817: $i,SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ~ ( SV77 @ ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) )
          | ( SV817
            = ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) ) )
        = $false )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[3984]) ).

thf(4020,plain,
    ! [SV813: $i,SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ~ ( SV77 @ ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) ) )
        = $false )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3985]) ).

thf(4021,plain,
    ! [SV77: $i > $o,SV315: $i > $o,SV813: $i] :
      ( ( ( SV813
          = ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) )
        = $false )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3985]) ).

thf(4022,plain,
    ! [SV109: $i,SV795: $i,SV804: $i] :
      ( ( ( ~ ( in @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) )
          | ~ ( ~ ( ~ ( in @ SV795 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) )
                  | ( in @ SV804 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) ) )
              | ~ ( ~ ( in @ SV804 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) )
                  | ( in @ SV795 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) ) ) ) )
        = $false )
      | ( ( SV795 = SV804 )
        = $true )
      | ( ( in @ SV795 @ SV109 )
        = $false )
      | ( ( in @ SV804 @ SV109 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3986]) ).

thf(4023,plain,
    ! [SV109: $i,SV828: $i,SV765: $i,SV776: $i,SV845: $i] :
      ( ( ( ~ ( in @ SV845 @ SV776 ) )
        = $true )
      | ( ( in @ SV845 @ SV765 )
        = $true )
      | ( ( in @ SV828 @ SV776 )
        = $true )
      | ( ( in @ SV828 @ SV765 )
        = $false )
      | ( ( in @ SV765 @ ( sK3_SY2100 @ SV109 ) )
        = $false )
      | ( ( in @ SV776 @ ( sK3_SY2100 @ SV109 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3987]) ).

thf(4024,plain,
    ! [SV109: $i,SV739: $i,SV822: $i] :
      ( ( ( ! [SY3239: $i] :
              ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) )
                              | ~ ( in @ SY3239 @ SV739 ) )
                        | ~ ~ ~ ! [SY3240: $i] :
                                  ~ ~ ( ~ ( in @ SY3240 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) )
                                      | ~ ( in @ SY3240 @ SV739 ) ) )
                  | ~ ! [SY3241: $i] :
                        ( ~ ( in @ SY3241 @ ( sK3_SY2100 @ SV109 ) )
                        | ! [SY3242: $i] :
                            ( ~ ( in @ SY3242 @ SY3241 )
                            | ( in @ SY3242 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) ) )
                        | ( in @ SY3239 @ SY3241 ) ) ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3988]) ).

thf(4025,plain,
    ! [SV109: $i,SV739: $i,SV818: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) )
                            | ~ ( in @ ( sK118_SY3231 @ SV109 @ SV739 @ SV818 ) @ SV739 ) )
                      | ~ ~ ~ ! [SY3232: $i] :
                                ~ ~ ( ~ ( in @ SY3232 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) )
                                    | ~ ( in @ SY3232 @ SV739 ) ) )
                | ~ ! [SY3248: $i] :
                      ( ~ ( in @ SY3248 @ ( sK3_SY2100 @ SV109 ) )
                      | ! [SY3234: $i] :
                          ( ~ ( in @ SY3234 @ SY3248 )
                          | ( in @ SY3234 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) ) )
                      | ( in @ ( sK118_SY3231 @ SV109 @ SV739 @ SV818 ) @ SY3248 ) ) ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[3989]) ).

thf(4026,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV743: $i,SV829: $i] :
      ( ( ( ~ ( in @ SV829 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) ) )
        = $true )
      | ( ( ~ ! [SY3227: $i] :
                ~ ~ ( ~ ( in @ SY3227 @ SV377 )
                    | ~ ( SV147 @ SY3227 @ SV829 ) ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3991]) ).

thf(4027,plain,
    ! [SV743: $i,SV829: $i,SV147: $i > $i > $o,SV377: $i] :
      ( ( ( ~ ~ ! [SY3228: $i] :
                  ~ ~ ( ~ ( in @ SY3228 @ SV377 )
                      | ~ ( SV147 @ SY3228 @ SV829 ) ) )
        = $true )
      | ( ( in @ SV829 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3992]) ).

thf(4028,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV743: $i,SV823: $i] :
      ( ( ( in @ SV823 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $false )
      | ( ( ~ ! [SY3224: $i] :
                ~ ~ ( ~ ( in @ SY3224 @ SV377 )
                    | ~ ( SV147 @ SY3224 @ SV823 ) ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV743
          = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3993]) ).

thf(4029,plain,
    ! [SV743: $i,SV823: $i,SV147: $i > $i > $o,SV377: $i] :
      ( ( ( ~ ! [SY3225: $i] :
                ~ ~ ( ~ ( in @ SY3225 @ SV377 )
                    | ~ ( SV147 @ SY3225 @ SV823 ) ) )
        = $false )
      | ( ( in @ SV823 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV743
          = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3994]) ).

thf(4030,plain,
    ! [SV808: $i,SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ! [SY2801: $i] :
              ~ ~ ( ~ ( SV438 @ SY2801 )
                  | ~ ! [SY2802: $i] :
                        ( ~ ( SV438 @ SY2802 )
                        | ( SY2801 = SY2802 ) ) ) )
        = $false )
      | ( ( SV214 @ SV808 )
        = $false )
      | ( ( SV214 @ ( sK110_SY3205 @ SV438 @ SV808 @ SV214 ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3995]) ).

thf(4031,plain,
    ! [SV214: $i > $o,SV808: $i,SV438: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV438 @ ( sK119_SY2801 @ SV808 @ SV214 @ SV438 ) )
                | ~ ! [SY3250: $i] :
                      ( ~ ( SV438 @ SY3250 )
                      | ( ( sK119_SY2801 @ SV808 @ SV214 @ SV438 )
                        = SY3250 ) ) ) )
        = $false )
      | ( ( SV214 @ SV808 )
        = $false )
      | ( ( SV808
          = ( sK110_SY3205 @ SV438 @ SV808 @ SV214 ) )
        = $false )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[3996]) ).

thf(4032,plain,
    ! [SV809: $i,SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ! [SY2394: $i] :
              ~ ~ ( ~ ( SV214 @ SY2394 )
                  | ~ ! [SY2395: $i] :
                        ( ~ ( SV214 @ SY2395 )
                        | ( SY2394 = SY2395 ) ) ) )
        = $false )
      | ( ( SV438 @ SV809 )
        = $false )
      | ( ( SV438 @ ( sK111_SY3206 @ SV214 @ SV809 @ SV438 ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3997]) ).

thf(4033,plain,
    ! [SV438: $i > $o,SV809: $i,SV214: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV214 @ ( sK120_SY2394 @ SV809 @ SV438 @ SV214 ) )
                | ~ ! [SY3251: $i] :
                      ( ~ ( SV214 @ SY3251 )
                      | ( ( sK120_SY2394 @ SV809 @ SV438 @ SV214 )
                        = SY3251 ) ) ) )
        = $false )
      | ( ( SV438 @ SV809 )
        = $false )
      | ( ( SV809
          = ( sK111_SY3206 @ SV214 @ SV809 @ SV438 ) )
        = $false )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[3998]) ).

thf(4034,plain,
    ! [SV438: $i > $o,SV841: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV841 )
          | ~ ! [SY3243: $i] :
                ( ~ ( SV214 @ SY3243 )
                | ( SV841 = SY3243 ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3999]) ).

thf(4035,plain,
    ! [SV214: $i > $o,SV842: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV842 )
          | ~ ! [SY3244: $i] :
                ( ~ ( SV438 @ SY3244 )
                | ( SV842 = SY3244 ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4000]) ).

thf(4036,plain,
    ! [SV438: $i > $o,SV835: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV835 ) )
        = $true )
      | ( ( ~ ! [SY3235: $i] :
                ( ~ ( SV214 @ SY3235 )
                | ( SV835 = SY3235 ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4001]) ).

thf(4037,plain,
    ! [SV214: $i > $o,SV836: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV836 ) )
        = $true )
      | ( ( ~ ! [SY3236: $i] :
                ( ~ ( SV438 @ SY3236 )
                | ( SV836 = SY3236 ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4002]) ).

thf(4038,plain,
    ! [SV438: $i > $o,SV837: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV837 ) )
        = $true )
      | ( ( ~ ! [SY3237: $i] :
                ( ~ ( SV214 @ SY3237 )
                | ( SV837 = SY3237 ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4003]) ).

thf(4039,plain,
    ! [SV214: $i > $o,SV838: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV838 ) )
        = $true )
      | ( ( ~ ! [SY3238: $i] :
                ( ~ ( SV438 @ SY3238 )
                | ( SV838 = SY3238 ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4004]) ).

thf(4040,plain,
    ! [SV438: $i > $o,SV832: $i,SV214: $i > $o] :
      ( ( ( SV214 @ SV832 )
        = $false )
      | ( ( ~ ! [SY3229: $i] :
                ( ~ ( SV214 @ SY3229 )
                | ( SV832 = SY3229 ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4005]) ).

thf(4041,plain,
    ! [SV214: $i > $o,SV833: $i,SV438: $i > $o] :
      ( ( ( SV438 @ SV833 )
        = $false )
      | ( ( ~ ! [SY3230: $i] :
                ( ~ ( SV438 @ SY3230 )
                | ( SV833 = SY3230 ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4006]) ).

thf(4042,plain,
    ! [SV221: $i,SV445: $i,SV721: $i,SV579: $i] :
      ( ( ( in @ ( kpair @ ( sK106_SY3142 @ SV579 @ SV721 @ SV445 @ SV221 ) @ ( sK112_SY3226 @ SV221 @ SV721 @ SV579 @ SV445 ) ) @ SV721 )
        = $true )
      | ( ( SV579 = SV721 )
        = $true )
      | ( ( in @ ( kpair @ ( sK73_SY3140 @ SV721 @ SV579 @ SV445 @ SV221 ) @ ( sK76_SY3182 @ SV221 @ SV579 @ SV721 @ SV445 ) ) @ SV579 )
        = $true )
      | ( ( subset @ SV721 @ ( cartprod @ SV221 @ SV445 ) )
        = $false )
      | ( ( subset @ SV579 @ ( cartprod @ SV221 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4009]) ).

thf(4043,plain,
    ! [SV667: $i,SV843: $i,SV253: $i > $o] :
      ( ( ( SV253 @ SV843 )
        = $false )
      | ( ( ( sK99_SY2491 @ SV667 @ SV253 )
          = SV843 )
        = $true )
      | ( ( SV253 @ ( sK37_SY3106 @ SV667 @ SV253 ) )
        = $true )
      | ( ( ( sK37_SY3106 @ SV667 @ SV253 )
          = SV667 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4012]) ).

thf(4044,plain,
    ! [SV775: $i,SV77: $i > $o,SV846: $i,SV315: $i > $o] :
      ( ( ( ~ ( ~ ( SV315 @ SV846 )
              | ~ ! [SY3246: $i] :
                    ( ~ ( SV315 @ SY3246 )
                    | ( SV846 = SY3246 ) ) ) )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( SV77 @ ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) )
        = $true )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4015]) ).

thf(4045,plain,
    ! [SV775: $i,SV77: $i > $o,SV844: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ SV844 )
          | ~ ! [SY3245: $i] :
                ( ~ ( SV315 @ SY3245 )
                | ( SV844 = SY3245 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( SV775
          = ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) )
        = $false )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4016]) ).

thf(4046,plain,
    ! [SV821: $i,SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ~ ( SV77 @ ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) )
          | ( SV821
            = ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) ) )
        = $false )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[4017]) ).

thf(4047,plain,
    ! [SV816: $i,SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ~ ( SV77 @ ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) ) )
        = $false )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4018]) ).

thf(4048,plain,
    ! [SV77: $i > $o,SV315: $i > $o,SV816: $i] :
      ( ( ( SV816
          = ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) )
        = $false )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4018]) ).

thf(4049,plain,
    ! [SV817: $i,SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ~ ( SV77 @ ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) ) )
        = $false )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4019]) ).

thf(4050,plain,
    ! [SV77: $i > $o,SV315: $i > $o,SV817: $i] :
      ( ( ( SV817
          = ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) )
        = $false )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4019]) ).

thf(4051,plain,
    ! [SV813: $i,SV315: $i > $o,SV77: $i > $o] :
      ( ( ( SV77 @ ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) )
        = $true )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4020]) ).

thf(4052,plain,
    ! [SV813: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( SV813
          = ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4021]) ).

thf(4053,plain,
    ! [SV109: $i,SV795: $i,SV804: $i] :
      ( ( ( ~ ( in @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) ) )
        = $false )
      | ( ( SV795 = SV804 )
        = $true )
      | ( ( in @ SV795 @ SV109 )
        = $false )
      | ( ( in @ SV804 @ SV109 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4022]) ).

thf(4054,plain,
    ! [SV109: $i,SV804: $i,SV795: $i] :
      ( ( ( ~ ( ~ ( ~ ( in @ SV795 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) )
                  | ( in @ SV804 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) ) )
              | ~ ( ~ ( in @ SV804 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) )
                  | ( in @ SV795 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) ) ) ) )
        = $false )
      | ( ( SV795 = SV804 )
        = $true )
      | ( ( in @ SV795 @ SV109 )
        = $false )
      | ( ( in @ SV804 @ SV109 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4022]) ).

thf(4055,plain,
    ! [SV109: $i,SV828: $i,SV765: $i,SV776: $i,SV845: $i] :
      ( ( ( in @ SV845 @ SV776 )
        = $false )
      | ( ( in @ SV845 @ SV765 )
        = $true )
      | ( ( in @ SV828 @ SV776 )
        = $true )
      | ( ( in @ SV828 @ SV765 )
        = $false )
      | ( ( in @ SV765 @ ( sK3_SY2100 @ SV109 ) )
        = $false )
      | ( ( in @ SV776 @ ( sK3_SY2100 @ SV109 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4023]) ).

thf(4056,plain,
    ! [SV109: $i,SV739: $i,SV822: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) )
                            | ~ ( in @ ( sK122_SY3239 @ SV109 @ SV739 @ SV822 ) @ SV739 ) )
                      | ~ ~ ~ ! [SY3240: $i] :
                                ~ ~ ( ~ ( in @ SY3240 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) )
                                    | ~ ( in @ SY3240 @ SV739 ) ) )
                | ~ ! [SY3253: $i] :
                      ( ~ ( in @ SY3253 @ ( sK3_SY2100 @ SV109 ) )
                      | ! [SY3242: $i] :
                          ( ~ ( in @ SY3242 @ SY3253 )
                          | ( in @ SY3242 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) ) )
                      | ( in @ ( sK122_SY3239 @ SV109 @ SV739 @ SV822 ) @ SY3253 ) ) ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[4024]) ).

thf(4057,plain,
    ! [SV109: $i,SV739: $i,SV818: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) )
                          | ~ ( in @ ( sK118_SY3231 @ SV109 @ SV739 @ SV818 ) @ SV739 ) )
                    | ~ ~ ~ ! [SY3232: $i] :
                              ~ ~ ( ~ ( in @ SY3232 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) )
                                  | ~ ( in @ SY3232 @ SV739 ) ) )
              | ~ ! [SY3248: $i] :
                    ( ~ ( in @ SY3248 @ ( sK3_SY2100 @ SV109 ) )
                    | ! [SY3234: $i] :
                        ( ~ ( in @ SY3234 @ SY3248 )
                        | ( in @ SY3234 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) ) )
                    | ( in @ ( sK118_SY3231 @ SV109 @ SV739 @ SV818 ) @ SY3248 ) ) ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4025]) ).

thf(4058,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV743: $i,SV829: $i] :
      ( ( ( in @ SV829 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $false )
      | ( ( ~ ! [SY3227: $i] :
                ~ ~ ( ~ ( in @ SY3227 @ SV377 )
                    | ~ ( SV147 @ SY3227 @ SV829 ) ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4026]) ).

thf(4059,plain,
    ! [SV743: $i,SV829: $i,SV147: $i > $i > $o,SV377: $i] :
      ( ( ( ~ ! [SY3228: $i] :
                ~ ~ ( ~ ( in @ SY3228 @ SV377 )
                    | ~ ( SV147 @ SY3228 @ SV829 ) ) )
        = $false )
      | ( ( in @ SV829 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4027]) ).

thf(4060,plain,
    ! [SV743: $i,SV823: $i,SV147: $i > $i > $o,SV377: $i] :
      ( ( ( ! [SY3224: $i] :
              ~ ~ ( ~ ( in @ SY3224 @ SV377 )
                  | ~ ( SV147 @ SY3224 @ SV823 ) ) )
        = $false )
      | ( ( in @ SV823 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV743
          = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4028]) ).

thf(4061,plain,
    ! [SV743: $i,SV823: $i,SV147: $i > $i > $o,SV377: $i] :
      ( ( ( ! [SY3225: $i] :
              ~ ~ ( ~ ( in @ SY3225 @ SV377 )
                  | ~ ( SV147 @ SY3225 @ SV823 ) ) )
        = $true )
      | ( ( in @ SV823 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV743
          = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4029]) ).

thf(4062,plain,
    ! [SV214: $i > $o,SV808: $i,SV438: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV438 @ ( sK123_SY2801 @ SV808 @ SV214 @ SV438 ) )
                | ~ ! [SY3255: $i] :
                      ( ~ ( SV438 @ SY3255 )
                      | ( ( sK123_SY2801 @ SV808 @ SV214 @ SV438 )
                        = SY3255 ) ) ) )
        = $false )
      | ( ( SV214 @ SV808 )
        = $false )
      | ( ( SV214 @ ( sK110_SY3205 @ SV438 @ SV808 @ SV214 ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[4030]) ).

thf(4063,plain,
    ! [SV214: $i > $o,SV808: $i,SV438: $i > $o] :
      ( ( ( ~ ( ~ ( SV438 @ ( sK119_SY2801 @ SV808 @ SV214 @ SV438 ) )
              | ~ ! [SY3250: $i] :
                    ( ~ ( SV438 @ SY3250 )
                    | ( ( sK119_SY2801 @ SV808 @ SV214 @ SV438 )
                      = SY3250 ) ) ) )
        = $true )
      | ( ( SV214 @ SV808 )
        = $false )
      | ( ( SV808
          = ( sK110_SY3205 @ SV438 @ SV808 @ SV214 ) )
        = $false )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4031]) ).

thf(4064,plain,
    ! [SV438: $i > $o,SV809: $i,SV214: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV214 @ ( sK124_SY2394 @ SV809 @ SV438 @ SV214 ) )
                | ~ ! [SY3256: $i] :
                      ( ~ ( SV214 @ SY3256 )
                      | ( ( sK124_SY2394 @ SV809 @ SV438 @ SV214 )
                        = SY3256 ) ) ) )
        = $false )
      | ( ( SV438 @ SV809 )
        = $false )
      | ( ( SV438 @ ( sK111_SY3206 @ SV214 @ SV809 @ SV438 ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[4032]) ).

thf(4065,plain,
    ! [SV438: $i > $o,SV809: $i,SV214: $i > $o] :
      ( ( ( ~ ( ~ ( SV214 @ ( sK120_SY2394 @ SV809 @ SV438 @ SV214 ) )
              | ~ ! [SY3251: $i] :
                    ( ~ ( SV214 @ SY3251 )
                    | ( ( sK120_SY2394 @ SV809 @ SV438 @ SV214 )
                      = SY3251 ) ) ) )
        = $true )
      | ( ( SV438 @ SV809 )
        = $false )
      | ( ( SV809
          = ( sK111_SY3206 @ SV214 @ SV809 @ SV438 ) )
        = $false )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4033]) ).

thf(4066,plain,
    ! [SV438: $i > $o,SV841: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV841 ) )
        = $true )
      | ( ( ~ ! [SY3243: $i] :
                ( ~ ( SV214 @ SY3243 )
                | ( SV841 = SY3243 ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4034]) ).

thf(4067,plain,
    ! [SV214: $i > $o,SV842: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV842 ) )
        = $true )
      | ( ( ~ ! [SY3244: $i] :
                ( ~ ( SV438 @ SY3244 )
                | ( SV842 = SY3244 ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4035]) ).

thf(4068,plain,
    ! [SV438: $i > $o,SV835: $i,SV214: $i > $o] :
      ( ( ( SV214 @ SV835 )
        = $false )
      | ( ( ~ ! [SY3235: $i] :
                ( ~ ( SV214 @ SY3235 )
                | ( SV835 = SY3235 ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4036]) ).

thf(4069,plain,
    ! [SV214: $i > $o,SV836: $i,SV438: $i > $o] :
      ( ( ( SV438 @ SV836 )
        = $false )
      | ( ( ~ ! [SY3236: $i] :
                ( ~ ( SV438 @ SY3236 )
                | ( SV836 = SY3236 ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4037]) ).

thf(4070,plain,
    ! [SV438: $i > $o,SV837: $i,SV214: $i > $o] :
      ( ( ( SV214 @ SV837 )
        = $false )
      | ( ( ~ ! [SY3237: $i] :
                ( ~ ( SV214 @ SY3237 )
                | ( SV837 = SY3237 ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4038]) ).

thf(4071,plain,
    ! [SV214: $i > $o,SV838: $i,SV438: $i > $o] :
      ( ( ( SV438 @ SV838 )
        = $false )
      | ( ( ~ ! [SY3238: $i] :
                ( ~ ( SV438 @ SY3238 )
                | ( SV838 = SY3238 ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4039]) ).

thf(4072,plain,
    ! [SV438: $i > $o,SV832: $i,SV214: $i > $o] :
      ( ( ( ! [SY3229: $i] :
              ( ~ ( SV214 @ SY3229 )
              | ( SV832 = SY3229 ) ) )
        = $false )
      | ( ( SV214 @ SV832 )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4040]) ).

thf(4073,plain,
    ! [SV214: $i > $o,SV833: $i,SV438: $i > $o] :
      ( ( ( ! [SY3230: $i] :
              ( ~ ( SV438 @ SY3230 )
              | ( SV833 = SY3230 ) ) )
        = $false )
      | ( ( SV438 @ SV833 )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4041]) ).

thf(4074,plain,
    ! [SV775: $i,SV77: $i > $o,SV846: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ SV846 )
          | ~ ! [SY3246: $i] :
                ( ~ ( SV315 @ SY3246 )
                | ( SV846 = SY3246 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( SV77 @ ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) )
        = $true )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4044]) ).

thf(4075,plain,
    ! [SV775: $i,SV77: $i > $o,SV844: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ SV844 ) )
        = $true )
      | ( ( ~ ! [SY3245: $i] :
                ( ~ ( SV315 @ SY3245 )
                | ( SV844 = SY3245 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( SV775
          = ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) )
        = $false )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4045]) ).

thf(4076,plain,
    ! [SV821: $i,SV315: $i > $o,SV77: $i > $o] :
      ( ( ( ~ ( SV77 @ ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) ) )
        = $false )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4046]) ).

thf(4077,plain,
    ! [SV77: $i > $o,SV315: $i > $o,SV821: $i] :
      ( ( ( SV821
          = ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) )
        = $false )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4046]) ).

thf(4078,plain,
    ! [SV816: $i,SV315: $i > $o,SV77: $i > $o] :
      ( ( ( SV77 @ ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) )
        = $true )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4047]) ).

thf(4079,plain,
    ! [SV816: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( SV816
          = ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4048]) ).

thf(4080,plain,
    ! [SV817: $i,SV315: $i > $o,SV77: $i > $o] :
      ( ( ( SV77 @ ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) )
        = $true )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4049]) ).

thf(4081,plain,
    ! [SV817: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( SV817
          = ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4050]) ).

thf(4082,plain,
    ! [SV813: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( SV77 @ ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4051]) ).

thf(4083,plain,
    ! [SV813: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ~ ! [SY2576: $i] :
                ~ ~ ( ~ ( SV315 @ SY2576 )
                    | ~ ! [SY2577: $i] :
                          ( ~ ( SV315 @ SY2577 )
                          | ( SY2576 = SY2577 ) ) ) )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( SV813
          = ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4052]) ).

thf(4084,plain,
    ! [SV109: $i,SV795: $i,SV804: $i] :
      ( ( ( in @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) )
        = $true )
      | ( ( SV795 = SV804 )
        = $true )
      | ( ( in @ SV795 @ SV109 )
        = $false )
      | ( ( in @ SV804 @ SV109 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4053]) ).

thf(4085,plain,
    ! [SV109: $i,SV804: $i,SV795: $i] :
      ( ( ( ~ ( ~ ( in @ SV795 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) )
              | ( in @ SV804 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) ) )
          | ~ ( ~ ( in @ SV804 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) )
              | ( in @ SV795 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) ) ) )
        = $true )
      | ( ( SV795 = SV804 )
        = $true )
      | ( ( in @ SV795 @ SV109 )
        = $false )
      | ( ( in @ SV804 @ SV109 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4054]) ).

thf(4086,plain,
    ! [SV109: $i,SV739: $i,SV822: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) )
                          | ~ ( in @ ( sK122_SY3239 @ SV109 @ SV739 @ SV822 ) @ SV739 ) )
                    | ~ ~ ~ ! [SY3240: $i] :
                              ~ ~ ( ~ ( in @ SY3240 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) )
                                  | ~ ( in @ SY3240 @ SV739 ) ) )
              | ~ ! [SY3253: $i] :
                    ( ~ ( in @ SY3253 @ ( sK3_SY2100 @ SV109 ) )
                    | ! [SY3242: $i] :
                        ( ~ ( in @ SY3242 @ SY3253 )
                        | ( in @ SY3242 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) ) )
                    | ( in @ ( sK122_SY3239 @ SV109 @ SV739 @ SV822 ) @ SY3253 ) ) ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4056]) ).

thf(4087,plain,
    ! [SV109: $i,SV739: $i,SV818: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) )
                      | ~ ( in @ ( sK118_SY3231 @ SV109 @ SV739 @ SV818 ) @ SV739 ) )
                | ~ ~ ~ ! [SY3232: $i] :
                          ~ ~ ( ~ ( in @ SY3232 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) )
                              | ~ ( in @ SY3232 @ SV739 ) ) )
          | ~ ! [SY3248: $i] :
                ( ~ ( in @ SY3248 @ ( sK3_SY2100 @ SV109 ) )
                | ! [SY3234: $i] :
                    ( ~ ( in @ SY3234 @ SY3248 )
                    | ( in @ SY3234 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) ) )
                | ( in @ ( sK118_SY3231 @ SV109 @ SV739 @ SV818 ) @ SY3248 ) ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4057]) ).

thf(4088,plain,
    ! [SV743: $i,SV829: $i,SV147: $i > $i > $o,SV377: $i] :
      ( ( ( ! [SY3227: $i] :
              ~ ~ ( ~ ( in @ SY3227 @ SV377 )
                  | ~ ( SV147 @ SY3227 @ SV829 ) ) )
        = $false )
      | ( ( in @ SV829 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4058]) ).

thf(4089,plain,
    ! [SV743: $i,SV829: $i,SV147: $i > $i > $o,SV377: $i] :
      ( ( ( ! [SY3228: $i] :
              ~ ~ ( ~ ( in @ SY3228 @ SV377 )
                  | ~ ( SV147 @ SY3228 @ SV829 ) ) )
        = $true )
      | ( ( in @ SV829 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4059]) ).

thf(4090,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV823: $i,SV743: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK125_SY3224 @ SV743 @ SV823 @ SV147 @ SV377 ) @ SV377 )
                | ~ ( SV147 @ ( sK125_SY3224 @ SV743 @ SV823 @ SV147 @ SV377 ) @ SV823 ) ) )
        = $false )
      | ( ( in @ SV823 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV743
          = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[4060]) ).

thf(4091,plain,
    ! [SV743: $i,SV823: $i,SV147: $i > $i > $o,SV377: $i,SV847: $i] :
      ( ( ( ~ ~ ( ~ ( in @ SV847 @ SV377 )
                | ~ ( SV147 @ SV847 @ SV823 ) ) )
        = $true )
      | ( ( in @ SV823 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV743
          = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4061]) ).

thf(4092,plain,
    ! [SV214: $i > $o,SV808: $i,SV438: $i > $o] :
      ( ( ( ~ ( ~ ( SV438 @ ( sK123_SY2801 @ SV808 @ SV214 @ SV438 ) )
              | ~ ! [SY3255: $i] :
                    ( ~ ( SV438 @ SY3255 )
                    | ( ( sK123_SY2801 @ SV808 @ SV214 @ SV438 )
                      = SY3255 ) ) ) )
        = $true )
      | ( ( SV214 @ SV808 )
        = $false )
      | ( ( SV214 @ ( sK110_SY3205 @ SV438 @ SV808 @ SV214 ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4062]) ).

thf(4093,plain,
    ! [SV214: $i > $o,SV808: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK119_SY2801 @ SV808 @ SV214 @ SV438 ) )
          | ~ ! [SY3250: $i] :
                ( ~ ( SV438 @ SY3250 )
                | ( ( sK119_SY2801 @ SV808 @ SV214 @ SV438 )
                  = SY3250 ) ) )
        = $false )
      | ( ( SV214 @ SV808 )
        = $false )
      | ( ( SV808
          = ( sK110_SY3205 @ SV438 @ SV808 @ SV214 ) )
        = $false )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4063]) ).

thf(4094,plain,
    ! [SV438: $i > $o,SV809: $i,SV214: $i > $o] :
      ( ( ( ~ ( ~ ( SV214 @ ( sK124_SY2394 @ SV809 @ SV438 @ SV214 ) )
              | ~ ! [SY3256: $i] :
                    ( ~ ( SV214 @ SY3256 )
                    | ( ( sK124_SY2394 @ SV809 @ SV438 @ SV214 )
                      = SY3256 ) ) ) )
        = $true )
      | ( ( SV438 @ SV809 )
        = $false )
      | ( ( SV438 @ ( sK111_SY3206 @ SV214 @ SV809 @ SV438 ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4064]) ).

thf(4095,plain,
    ! [SV438: $i > $o,SV809: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK120_SY2394 @ SV809 @ SV438 @ SV214 ) )
          | ~ ! [SY3251: $i] :
                ( ~ ( SV214 @ SY3251 )
                | ( ( sK120_SY2394 @ SV809 @ SV438 @ SV214 )
                  = SY3251 ) ) )
        = $false )
      | ( ( SV438 @ SV809 )
        = $false )
      | ( ( SV809
          = ( sK111_SY3206 @ SV214 @ SV809 @ SV438 ) )
        = $false )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4065]) ).

thf(4096,plain,
    ! [SV438: $i > $o,SV841: $i,SV214: $i > $o] :
      ( ( ( SV214 @ SV841 )
        = $false )
      | ( ( ~ ! [SY3243: $i] :
                ( ~ ( SV214 @ SY3243 )
                | ( SV841 = SY3243 ) ) )
        = $true )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4066]) ).

thf(4097,plain,
    ! [SV214: $i > $o,SV842: $i,SV438: $i > $o] :
      ( ( ( SV438 @ SV842 )
        = $false )
      | ( ( ~ ! [SY3244: $i] :
                ( ~ ( SV438 @ SY3244 )
                | ( SV842 = SY3244 ) ) )
        = $true )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4067]) ).

thf(4098,plain,
    ! [SV438: $i > $o,SV835: $i,SV214: $i > $o] :
      ( ( ( ! [SY3235: $i] :
              ( ~ ( SV214 @ SY3235 )
              | ( SV835 = SY3235 ) ) )
        = $false )
      | ( ( SV214 @ SV835 )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4068]) ).

thf(4099,plain,
    ! [SV214: $i > $o,SV836: $i,SV438: $i > $o] :
      ( ( ( ! [SY3236: $i] :
              ( ~ ( SV438 @ SY3236 )
              | ( SV836 = SY3236 ) ) )
        = $false )
      | ( ( SV438 @ SV836 )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4069]) ).

thf(4100,plain,
    ! [SV438: $i > $o,SV837: $i,SV214: $i > $o] :
      ( ( ( ! [SY3237: $i] :
              ( ~ ( SV214 @ SY3237 )
              | ( SV837 = SY3237 ) ) )
        = $false )
      | ( ( SV214 @ SV837 )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4070]) ).

thf(4101,plain,
    ! [SV214: $i > $o,SV838: $i,SV438: $i > $o] :
      ( ( ( ! [SY3238: $i] :
              ( ~ ( SV438 @ SY3238 )
              | ( SV838 = SY3238 ) ) )
        = $false )
      | ( ( SV438 @ SV838 )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4071]) ).

thf(4102,plain,
    ! [SV832: $i,SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK126_SY3229 @ SV438 @ SV832 @ SV214 ) )
          | ( SV832
            = ( sK126_SY3229 @ SV438 @ SV832 @ SV214 ) ) )
        = $false )
      | ( ( SV214 @ SV832 )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[4072]) ).

thf(4103,plain,
    ! [SV833: $i,SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK127_SY3230 @ SV214 @ SV833 @ SV438 ) )
          | ( SV833
            = ( sK127_SY3230 @ SV214 @ SV833 @ SV438 ) ) )
        = $false )
      | ( ( SV438 @ SV833 )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[4073]) ).

thf(4104,plain,
    ! [SV775: $i,SV77: $i > $o,SV846: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ SV846 ) )
        = $true )
      | ( ( ~ ! [SY3246: $i] :
                ( ~ ( SV315 @ SY3246 )
                | ( SV846 = SY3246 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( SV77 @ ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) )
        = $true )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4074]) ).

thf(4105,plain,
    ! [SV775: $i,SV77: $i > $o,SV844: $i,SV315: $i > $o] :
      ( ( ( SV315 @ SV844 )
        = $false )
      | ( ( ~ ! [SY3245: $i] :
                ( ~ ( SV315 @ SY3245 )
                | ( SV844 = SY3245 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( SV775
          = ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) )
        = $false )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4075]) ).

thf(4106,plain,
    ! [SV821: $i,SV315: $i > $o,SV77: $i > $o] :
      ( ( ( SV77 @ ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) )
        = $true )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) )
          | ( ( descr
              @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
            = ( descr
              @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4076]) ).

thf(4107,plain,
    ! [SV821: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( SV821
          = ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4077]) ).

thf(4108,plain,
    ! [SV816: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( SV77 @ ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4078]) ).

thf(4109,plain,
    ! [SV816: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ~ ! [SY2576: $i] :
                ~ ~ ( ~ ( SV315 @ SY2576 )
                    | ~ ! [SY2577: $i] :
                          ( ~ ( SV315 @ SY2577 )
                          | ( SY2576 = SY2577 ) ) ) )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( SV816
          = ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4079]) ).

thf(4110,plain,
    ! [SV817: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( SV77 @ ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4080]) ).

thf(4111,plain,
    ! [SV817: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ~ ! [SY2576: $i] :
                ~ ~ ( ~ ( SV315 @ SY2576 )
                    | ~ ! [SY2577: $i] :
                          ( ~ ( SV315 @ SY2577 )
                          | ( SY2576 = SY2577 ) ) ) )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( SV817
          = ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4081]) ).

thf(4112,plain,
    ! [SV813: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ~ ! [SY2576: $i] :
                ~ ~ ( ~ ( SV315 @ SY2576 )
                    | ~ ! [SY2577: $i] :
                          ( ~ ( SV315 @ SY2577 )
                          | ( SY2576 = SY2577 ) ) ) )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( SV77 @ ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4082]) ).

thf(4113,plain,
    ! [SV813: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ! [SY2576: $i] :
              ~ ~ ( ~ ( SV315 @ SY2576 )
                  | ~ ! [SY2577: $i] :
                        ( ~ ( SV315 @ SY2577 )
                        | ( SY2576 = SY2577 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( SV813
          = ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4083]) ).

thf(4114,plain,
    ! [SV109: $i,SV804: $i,SV795: $i] :
      ( ( ( ~ ( ~ ( in @ SV795 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) )
              | ( in @ SV804 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( in @ SV804 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) )
              | ( in @ SV795 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) ) ) )
        = $true )
      | ( ( SV795 = SV804 )
        = $true )
      | ( ( in @ SV795 @ SV109 )
        = $false )
      | ( ( in @ SV804 @ SV109 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4085]) ).

thf(4115,plain,
    ! [SV109: $i,SV739: $i,SV822: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) )
                      | ~ ( in @ ( sK122_SY3239 @ SV109 @ SV739 @ SV822 ) @ SV739 ) )
                | ~ ~ ~ ! [SY3240: $i] :
                          ~ ~ ( ~ ( in @ SY3240 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) )
                              | ~ ( in @ SY3240 @ SV739 ) ) )
          | ~ ! [SY3253: $i] :
                ( ~ ( in @ SY3253 @ ( sK3_SY2100 @ SV109 ) )
                | ! [SY3242: $i] :
                    ( ~ ( in @ SY3242 @ SY3253 )
                    | ( in @ SY3242 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) ) )
                | ( in @ ( sK122_SY3239 @ SV109 @ SV739 @ SV822 ) @ SY3253 ) ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4086]) ).

thf(4116,plain,
    ! [SV109: $i,SV739: $i,SV818: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) )
                      | ~ ( in @ ( sK118_SY3231 @ SV109 @ SV739 @ SV818 ) @ SV739 ) )
                | ~ ~ ~ ! [SY3232: $i] :
                          ~ ~ ( ~ ( in @ SY3232 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) )
                              | ~ ( in @ SY3232 @ SV739 ) ) ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4087]) ).

thf(4117,plain,
    ! [SV739: $i,SV818: $i,SV109: $i] :
      ( ( ( ~ ! [SY3248: $i] :
                ( ~ ( in @ SY3248 @ ( sK3_SY2100 @ SV109 ) )
                | ! [SY3234: $i] :
                    ( ~ ( in @ SY3234 @ SY3248 )
                    | ( in @ SY3234 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) ) )
                | ( in @ ( sK118_SY3231 @ SV109 @ SV739 @ SV818 ) @ SY3248 ) ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4087]) ).

thf(4118,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV829: $i,SV743: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK128_SY3227 @ SV743 @ SV829 @ SV147 @ SV377 ) @ SV377 )
                | ~ ( SV147 @ ( sK128_SY3227 @ SV743 @ SV829 @ SV147 @ SV377 ) @ SV829 ) ) )
        = $false )
      | ( ( in @ SV829 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[4088]) ).

thf(4119,plain,
    ! [SV743: $i,SV829: $i,SV147: $i > $i > $o,SV377: $i,SV848: $i] :
      ( ( ( ~ ~ ( ~ ( in @ SV848 @ SV377 )
                | ~ ( SV147 @ SV848 @ SV829 ) ) )
        = $true )
      | ( ( in @ SV829 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[4089]) ).

thf(4120,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV823: $i,SV743: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK125_SY3224 @ SV743 @ SV823 @ SV147 @ SV377 ) @ SV377 )
              | ~ ( SV147 @ ( sK125_SY3224 @ SV743 @ SV823 @ SV147 @ SV377 ) @ SV823 ) ) )
        = $true )
      | ( ( in @ SV823 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV743
          = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4090]) ).

thf(4121,plain,
    ! [SV743: $i,SV823: $i,SV147: $i > $i > $o,SV377: $i,SV847: $i] :
      ( ( ( ~ ( ~ ( in @ SV847 @ SV377 )
              | ~ ( SV147 @ SV847 @ SV823 ) ) )
        = $false )
      | ( ( in @ SV823 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV743
          = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4091]) ).

thf(4122,plain,
    ! [SV214: $i > $o,SV808: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK123_SY2801 @ SV808 @ SV214 @ SV438 ) )
          | ~ ! [SY3255: $i] :
                ( ~ ( SV438 @ SY3255 )
                | ( ( sK123_SY2801 @ SV808 @ SV214 @ SV438 )
                  = SY3255 ) ) )
        = $false )
      | ( ( SV214 @ SV808 )
        = $false )
      | ( ( SV214 @ ( sK110_SY3205 @ SV438 @ SV808 @ SV214 ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4092]) ).

thf(4123,plain,
    ! [SV214: $i > $o,SV808: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK119_SY2801 @ SV808 @ SV214 @ SV438 ) ) )
        = $false )
      | ( ( SV214 @ SV808 )
        = $false )
      | ( ( SV808
          = ( sK110_SY3205 @ SV438 @ SV808 @ SV214 ) )
        = $false )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4093]) ).

thf(4124,plain,
    ! [SV214: $i > $o,SV808: $i,SV438: $i > $o] :
      ( ( ( ~ ! [SY3250: $i] :
                ( ~ ( SV438 @ SY3250 )
                | ( ( sK119_SY2801 @ SV808 @ SV214 @ SV438 )
                  = SY3250 ) ) )
        = $false )
      | ( ( SV214 @ SV808 )
        = $false )
      | ( ( SV808
          = ( sK110_SY3205 @ SV438 @ SV808 @ SV214 ) )
        = $false )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4093]) ).

thf(4125,plain,
    ! [SV438: $i > $o,SV809: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK124_SY2394 @ SV809 @ SV438 @ SV214 ) )
          | ~ ! [SY3256: $i] :
                ( ~ ( SV214 @ SY3256 )
                | ( ( sK124_SY2394 @ SV809 @ SV438 @ SV214 )
                  = SY3256 ) ) )
        = $false )
      | ( ( SV438 @ SV809 )
        = $false )
      | ( ( SV438 @ ( sK111_SY3206 @ SV214 @ SV809 @ SV438 ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4094]) ).

thf(4126,plain,
    ! [SV438: $i > $o,SV809: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK120_SY2394 @ SV809 @ SV438 @ SV214 ) ) )
        = $false )
      | ( ( SV438 @ SV809 )
        = $false )
      | ( ( SV809
          = ( sK111_SY3206 @ SV214 @ SV809 @ SV438 ) )
        = $false )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4095]) ).

thf(4127,plain,
    ! [SV438: $i > $o,SV809: $i,SV214: $i > $o] :
      ( ( ( ~ ! [SY3251: $i] :
                ( ~ ( SV214 @ SY3251 )
                | ( ( sK120_SY2394 @ SV809 @ SV438 @ SV214 )
                  = SY3251 ) ) )
        = $false )
      | ( ( SV438 @ SV809 )
        = $false )
      | ( ( SV809
          = ( sK111_SY3206 @ SV214 @ SV809 @ SV438 ) )
        = $false )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4095]) ).

thf(4128,plain,
    ! [SV438: $i > $o,SV841: $i,SV214: $i > $o] :
      ( ( ( ! [SY3243: $i] :
              ( ~ ( SV214 @ SY3243 )
              | ( SV841 = SY3243 ) ) )
        = $false )
      | ( ( SV214 @ SV841 )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4096]) ).

thf(4129,plain,
    ! [SV214: $i > $o,SV842: $i,SV438: $i > $o] :
      ( ( ( ! [SY3244: $i] :
              ( ~ ( SV438 @ SY3244 )
              | ( SV842 = SY3244 ) ) )
        = $false )
      | ( ( SV438 @ SV842 )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4097]) ).

thf(4130,plain,
    ! [SV835: $i,SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK129_SY3235 @ SV438 @ SV835 @ SV214 ) )
          | ( SV835
            = ( sK129_SY3235 @ SV438 @ SV835 @ SV214 ) ) )
        = $false )
      | ( ( SV214 @ SV835 )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[4098]) ).

thf(4131,plain,
    ! [SV836: $i,SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK130_SY3236 @ SV214 @ SV836 @ SV438 ) )
          | ( SV836
            = ( sK130_SY3236 @ SV214 @ SV836 @ SV438 ) ) )
        = $false )
      | ( ( SV438 @ SV836 )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[4099]) ).

thf(4132,plain,
    ! [SV837: $i,SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK131_SY3237 @ SV438 @ SV837 @ SV214 ) )
          | ( SV837
            = ( sK131_SY3237 @ SV438 @ SV837 @ SV214 ) ) )
        = $false )
      | ( ( SV214 @ SV837 )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[4100]) ).

thf(4133,plain,
    ! [SV838: $i,SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK132_SY3238 @ SV214 @ SV838 @ SV438 ) )
          | ( SV838
            = ( sK132_SY3238 @ SV214 @ SV838 @ SV438 ) ) )
        = $false )
      | ( ( SV438 @ SV838 )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[4101]) ).

thf(4134,plain,
    ! [SV832: $i,SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK126_SY3229 @ SV438 @ SV832 @ SV214 ) ) )
        = $false )
      | ( ( SV214 @ SV832 )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4102]) ).

thf(4135,plain,
    ! [SV214: $i > $o,SV438: $i > $o,SV832: $i] :
      ( ( ( SV832
          = ( sK126_SY3229 @ SV438 @ SV832 @ SV214 ) )
        = $false )
      | ( ( SV214 @ SV832 )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4102]) ).

thf(4136,plain,
    ! [SV833: $i,SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK127_SY3230 @ SV214 @ SV833 @ SV438 ) ) )
        = $false )
      | ( ( SV438 @ SV833 )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4103]) ).

thf(4137,plain,
    ! [SV438: $i > $o,SV214: $i > $o,SV833: $i] :
      ( ( ( SV833
          = ( sK127_SY3230 @ SV214 @ SV833 @ SV438 ) )
        = $false )
      | ( ( SV438 @ SV833 )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4103]) ).

thf(4138,plain,
    ! [SV775: $i,SV77: $i > $o,SV846: $i,SV315: $i > $o] :
      ( ( ( SV315 @ SV846 )
        = $false )
      | ( ( ~ ! [SY3246: $i] :
                ( ~ ( SV315 @ SY3246 )
                | ( SV846 = SY3246 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( SV77 @ ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) )
        = $true )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4104]) ).

thf(4139,plain,
    ! [SV775: $i,SV77: $i > $o,SV844: $i,SV315: $i > $o] :
      ( ( ( ! [SY3245: $i] :
              ( ~ ( SV315 @ SY3245 )
              | ( SV844 = SY3245 ) ) )
        = $false )
      | ( ( SV315 @ SV844 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( SV775
          = ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) )
        = $false )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4105]) ).

thf(4140,plain,
    ! [SV821: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ~ ~ ! [SY2576: $i] :
                  ~ ~ ( ~ ( SV315 @ SY2576 )
                      | ~ ! [SY2577: $i] :
                            ( ~ ( SV315 @ SY2577 )
                            | ( SY2576 = SY2577 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( SV77 @ ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4106]) ).

thf(4141,plain,
    ! [SV821: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ~ ! [SY2576: $i] :
                ~ ~ ( ~ ( SV315 @ SY2576 )
                    | ~ ! [SY2577: $i] :
                          ( ~ ( SV315 @ SY2577 )
                          | ( SY2576 = SY2577 ) ) ) )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( SV821
          = ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4107]) ).

thf(4142,plain,
    ! [SV816: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ~ ! [SY2576: $i] :
                ~ ~ ( ~ ( SV315 @ SY2576 )
                    | ~ ! [SY2577: $i] :
                          ( ~ ( SV315 @ SY2577 )
                          | ( SY2576 = SY2577 ) ) ) )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( SV77 @ ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4108]) ).

thf(4143,plain,
    ! [SV816: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ! [SY2576: $i] :
              ~ ~ ( ~ ( SV315 @ SY2576 )
                  | ~ ! [SY2577: $i] :
                        ( ~ ( SV315 @ SY2577 )
                        | ( SY2576 = SY2577 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( SV816
          = ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4109]) ).

thf(4144,plain,
    ! [SV817: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ~ ! [SY2576: $i] :
                ~ ~ ( ~ ( SV315 @ SY2576 )
                    | ~ ! [SY2577: $i] :
                          ( ~ ( SV315 @ SY2577 )
                          | ( SY2576 = SY2577 ) ) ) )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( SV77 @ ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4110]) ).

thf(4145,plain,
    ! [SV817: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ! [SY2576: $i] :
              ~ ~ ( ~ ( SV315 @ SY2576 )
                  | ~ ! [SY2577: $i] :
                        ( ~ ( SV315 @ SY2577 )
                        | ( SY2576 = SY2577 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( SV817
          = ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4111]) ).

thf(4146,plain,
    ! [SV813: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ! [SY2576: $i] :
              ~ ~ ( ~ ( SV315 @ SY2576 )
                  | ~ ! [SY2577: $i] :
                        ( ~ ( SV315 @ SY2577 )
                        | ( SY2576 = SY2577 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( SV77 @ ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4112]) ).

thf(4147,plain,
    ! [SV813: $i,SV77: $i > $o,SV849: $i,SV315: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV315 @ SV849 )
                | ~ ! [SY3257: $i] :
                      ( ~ ( SV315 @ SY3257 )
                      | ( SV849 = SY3257 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( SV813
          = ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4113]) ).

thf(4148,plain,
    ! [SV109: $i,SV804: $i,SV795: $i] :
      ( ( ( ~ ( in @ SV795 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) )
          | ( in @ SV804 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) ) )
        = $false )
      | ( ( ~ ( ~ ( in @ SV804 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) )
              | ( in @ SV795 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) ) ) )
        = $true )
      | ( ( SV795 = SV804 )
        = $true )
      | ( ( in @ SV795 @ SV109 )
        = $false )
      | ( ( in @ SV804 @ SV109 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4114]) ).

thf(4149,plain,
    ! [SV109: $i,SV739: $i,SV822: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) )
                      | ~ ( in @ ( sK122_SY3239 @ SV109 @ SV739 @ SV822 ) @ SV739 ) )
                | ~ ~ ~ ! [SY3240: $i] :
                          ~ ~ ( ~ ( in @ SY3240 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) )
                              | ~ ( in @ SY3240 @ SV739 ) ) ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4115]) ).

thf(4150,plain,
    ! [SV739: $i,SV822: $i,SV109: $i] :
      ( ( ( ~ ! [SY3253: $i] :
                ( ~ ( in @ SY3253 @ ( sK3_SY2100 @ SV109 ) )
                | ! [SY3242: $i] :
                    ( ~ ( in @ SY3242 @ SY3253 )
                    | ( in @ SY3242 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) ) )
                | ( in @ ( sK122_SY3239 @ SV109 @ SV739 @ SV822 ) @ SY3253 ) ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4115]) ).

thf(4151,plain,
    ! [SV109: $i,SV739: $i,SV818: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) )
                    | ~ ( in @ ( sK118_SY3231 @ SV109 @ SV739 @ SV818 ) @ SV739 ) )
              | ~ ~ ~ ! [SY3232: $i] :
                        ~ ~ ( ~ ( in @ SY3232 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) )
                            | ~ ( in @ SY3232 @ SV739 ) ) ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4116]) ).

thf(4152,plain,
    ! [SV739: $i,SV818: $i,SV109: $i] :
      ( ( ( ! [SY3248: $i] :
              ( ~ ( in @ SY3248 @ ( sK3_SY2100 @ SV109 ) )
              | ! [SY3234: $i] :
                  ( ~ ( in @ SY3234 @ SY3248 )
                  | ( in @ SY3234 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) ) )
              | ( in @ ( sK118_SY3231 @ SV109 @ SV739 @ SV818 ) @ SY3248 ) ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4117]) ).

thf(4153,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV829: $i,SV743: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK128_SY3227 @ SV743 @ SV829 @ SV147 @ SV377 ) @ SV377 )
              | ~ ( SV147 @ ( sK128_SY3227 @ SV743 @ SV829 @ SV147 @ SV377 ) @ SV829 ) ) )
        = $true )
      | ( ( in @ SV829 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4118]) ).

thf(4154,plain,
    ! [SV743: $i,SV829: $i,SV147: $i > $i > $o,SV377: $i,SV848: $i] :
      ( ( ( ~ ( ~ ( in @ SV848 @ SV377 )
              | ~ ( SV147 @ SV848 @ SV829 ) ) )
        = $false )
      | ( ( in @ SV829 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4119]) ).

thf(4155,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV823: $i,SV743: $i] :
      ( ( ( ~ ( in @ ( sK125_SY3224 @ SV743 @ SV823 @ SV147 @ SV377 ) @ SV377 )
          | ~ ( SV147 @ ( sK125_SY3224 @ SV743 @ SV823 @ SV147 @ SV377 ) @ SV823 ) )
        = $false )
      | ( ( in @ SV823 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV743
          = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4120]) ).

thf(4156,plain,
    ! [SV743: $i,SV823: $i,SV147: $i > $i > $o,SV377: $i,SV847: $i] :
      ( ( ( ~ ( in @ SV847 @ SV377 )
          | ~ ( SV147 @ SV847 @ SV823 ) )
        = $true )
      | ( ( in @ SV823 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV743
          = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4121]) ).

thf(4157,plain,
    ! [SV214: $i > $o,SV808: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK123_SY2801 @ SV808 @ SV214 @ SV438 ) ) )
        = $false )
      | ( ( SV214 @ SV808 )
        = $false )
      | ( ( SV214 @ ( sK110_SY3205 @ SV438 @ SV808 @ SV214 ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4122]) ).

thf(4158,plain,
    ! [SV214: $i > $o,SV808: $i,SV438: $i > $o] :
      ( ( ( ~ ! [SY3255: $i] :
                ( ~ ( SV438 @ SY3255 )
                | ( ( sK123_SY2801 @ SV808 @ SV214 @ SV438 )
                  = SY3255 ) ) )
        = $false )
      | ( ( SV214 @ SV808 )
        = $false )
      | ( ( SV214 @ ( sK110_SY3205 @ SV438 @ SV808 @ SV214 ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4122]) ).

thf(4159,plain,
    ! [SV214: $i > $o,SV808: $i,SV438: $i > $o] :
      ( ( ( SV438 @ ( sK119_SY2801 @ SV808 @ SV214 @ SV438 ) )
        = $true )
      | ( ( SV214 @ SV808 )
        = $false )
      | ( ( SV808
          = ( sK110_SY3205 @ SV438 @ SV808 @ SV214 ) )
        = $false )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4123]) ).

thf(4160,plain,
    ! [SV214: $i > $o,SV808: $i,SV438: $i > $o] :
      ( ( ( ! [SY3250: $i] :
              ( ~ ( SV438 @ SY3250 )
              | ( ( sK119_SY2801 @ SV808 @ SV214 @ SV438 )
                = SY3250 ) ) )
        = $true )
      | ( ( SV214 @ SV808 )
        = $false )
      | ( ( SV808
          = ( sK110_SY3205 @ SV438 @ SV808 @ SV214 ) )
        = $false )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4124]) ).

thf(4161,plain,
    ! [SV438: $i > $o,SV809: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK124_SY2394 @ SV809 @ SV438 @ SV214 ) ) )
        = $false )
      | ( ( SV438 @ SV809 )
        = $false )
      | ( ( SV438 @ ( sK111_SY3206 @ SV214 @ SV809 @ SV438 ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4125]) ).

thf(4162,plain,
    ! [SV438: $i > $o,SV809: $i,SV214: $i > $o] :
      ( ( ( ~ ! [SY3256: $i] :
                ( ~ ( SV214 @ SY3256 )
                | ( ( sK124_SY2394 @ SV809 @ SV438 @ SV214 )
                  = SY3256 ) ) )
        = $false )
      | ( ( SV438 @ SV809 )
        = $false )
      | ( ( SV438 @ ( sK111_SY3206 @ SV214 @ SV809 @ SV438 ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4125]) ).

thf(4163,plain,
    ! [SV438: $i > $o,SV809: $i,SV214: $i > $o] :
      ( ( ( SV214 @ ( sK120_SY2394 @ SV809 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ SV809 )
        = $false )
      | ( ( SV809
          = ( sK111_SY3206 @ SV214 @ SV809 @ SV438 ) )
        = $false )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4126]) ).

thf(4164,plain,
    ! [SV438: $i > $o,SV809: $i,SV214: $i > $o] :
      ( ( ( ! [SY3251: $i] :
              ( ~ ( SV214 @ SY3251 )
              | ( ( sK120_SY2394 @ SV809 @ SV438 @ SV214 )
                = SY3251 ) ) )
        = $true )
      | ( ( SV438 @ SV809 )
        = $false )
      | ( ( SV809
          = ( sK111_SY3206 @ SV214 @ SV809 @ SV438 ) )
        = $false )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4127]) ).

thf(4165,plain,
    ! [SV841: $i,SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK133_SY3243 @ SV438 @ SV841 @ SV214 ) )
          | ( SV841
            = ( sK133_SY3243 @ SV438 @ SV841 @ SV214 ) ) )
        = $false )
      | ( ( SV214 @ SV841 )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[4128]) ).

thf(4166,plain,
    ! [SV842: $i,SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK134_SY3244 @ SV214 @ SV842 @ SV438 ) )
          | ( SV842
            = ( sK134_SY3244 @ SV214 @ SV842 @ SV438 ) ) )
        = $false )
      | ( ( SV438 @ SV842 )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[4129]) ).

thf(4167,plain,
    ! [SV835: $i,SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK129_SY3235 @ SV438 @ SV835 @ SV214 ) ) )
        = $false )
      | ( ( SV214 @ SV835 )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4130]) ).

thf(4168,plain,
    ! [SV214: $i > $o,SV438: $i > $o,SV835: $i] :
      ( ( ( SV835
          = ( sK129_SY3235 @ SV438 @ SV835 @ SV214 ) )
        = $false )
      | ( ( SV214 @ SV835 )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4130]) ).

thf(4169,plain,
    ! [SV836: $i,SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK130_SY3236 @ SV214 @ SV836 @ SV438 ) ) )
        = $false )
      | ( ( SV438 @ SV836 )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4131]) ).

thf(4170,plain,
    ! [SV438: $i > $o,SV214: $i > $o,SV836: $i] :
      ( ( ( SV836
          = ( sK130_SY3236 @ SV214 @ SV836 @ SV438 ) )
        = $false )
      | ( ( SV438 @ SV836 )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4131]) ).

thf(4171,plain,
    ! [SV837: $i,SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK131_SY3237 @ SV438 @ SV837 @ SV214 ) ) )
        = $false )
      | ( ( SV214 @ SV837 )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4132]) ).

thf(4172,plain,
    ! [SV214: $i > $o,SV438: $i > $o,SV837: $i] :
      ( ( ( SV837
          = ( sK131_SY3237 @ SV438 @ SV837 @ SV214 ) )
        = $false )
      | ( ( SV214 @ SV837 )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4132]) ).

thf(4173,plain,
    ! [SV838: $i,SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK132_SY3238 @ SV214 @ SV838 @ SV438 ) ) )
        = $false )
      | ( ( SV438 @ SV838 )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4133]) ).

thf(4174,plain,
    ! [SV438: $i > $o,SV214: $i > $o,SV838: $i] :
      ( ( ( SV838
          = ( sK132_SY3238 @ SV214 @ SV838 @ SV438 ) )
        = $false )
      | ( ( SV438 @ SV838 )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4133]) ).

thf(4175,plain,
    ! [SV832: $i,SV438: $i > $o,SV214: $i > $o] :
      ( ( ( SV214 @ ( sK126_SY3229 @ SV438 @ SV832 @ SV214 ) )
        = $true )
      | ( ( SV214 @ SV832 )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4134]) ).

thf(4176,plain,
    ! [SV832: $i,SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ! [SY2801: $i] :
              ~ ~ ( ~ ( SV438 @ SY2801 )
                  | ~ ! [SY2802: $i] :
                        ( ~ ( SV438 @ SY2802 )
                        | ( SY2801 = SY2802 ) ) ) )
        = $false )
      | ( ( SV214 @ SV832 )
        = $false )
      | ( ( SV832
          = ( sK126_SY3229 @ SV438 @ SV832 @ SV214 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4135]) ).

thf(4177,plain,
    ! [SV833: $i,SV214: $i > $o,SV438: $i > $o] :
      ( ( ( SV438 @ ( sK127_SY3230 @ SV214 @ SV833 @ SV438 ) )
        = $true )
      | ( ( SV438 @ SV833 )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4136]) ).

thf(4178,plain,
    ! [SV833: $i,SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ! [SY2394: $i] :
              ~ ~ ( ~ ( SV214 @ SY2394 )
                  | ~ ! [SY2395: $i] :
                        ( ~ ( SV214 @ SY2395 )
                        | ( SY2394 = SY2395 ) ) ) )
        = $false )
      | ( ( SV438 @ SV833 )
        = $false )
      | ( ( SV833
          = ( sK127_SY3230 @ SV214 @ SV833 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4137]) ).

thf(4179,plain,
    ! [SV775: $i,SV77: $i > $o,SV846: $i,SV315: $i > $o] :
      ( ( ( ! [SY3246: $i] :
              ( ~ ( SV315 @ SY3246 )
              | ( SV846 = SY3246 ) ) )
        = $false )
      | ( ( SV315 @ SV846 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( SV77 @ ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) )
        = $true )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4138]) ).

thf(4180,plain,
    ! [SV844: $i,SV77: $i > $o,SV775: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ ( sK135_SY3245 @ SV775 @ SV77 @ SV844 @ SV315 ) )
          | ( SV844
            = ( sK135_SY3245 @ SV775 @ SV77 @ SV844 @ SV315 ) ) )
        = $false )
      | ( ( SV315 @ SV844 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( SV775
          = ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) )
        = $false )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[4139]) ).

thf(4181,plain,
    ! [SV821: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ~ ! [SY2576: $i] :
                ~ ~ ( ~ ( SV315 @ SY2576 )
                    | ~ ! [SY2577: $i] :
                          ( ~ ( SV315 @ SY2577 )
                          | ( SY2576 = SY2577 ) ) ) )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( SV77 @ ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4140]) ).

thf(4182,plain,
    ! [SV821: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ! [SY2576: $i] :
              ~ ~ ( ~ ( SV315 @ SY2576 )
                  | ~ ! [SY2577: $i] :
                        ( ~ ( SV315 @ SY2577 )
                        | ( SY2576 = SY2577 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( SV821
          = ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4141]) ).

thf(4183,plain,
    ! [SV816: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ! [SY2576: $i] :
              ~ ~ ( ~ ( SV315 @ SY2576 )
                  | ~ ! [SY2577: $i] :
                        ( ~ ( SV315 @ SY2577 )
                        | ( SY2576 = SY2577 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( SV77 @ ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4142]) ).

thf(4184,plain,
    ! [SV816: $i,SV77: $i > $o,SV850: $i,SV315: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV315 @ SV850 )
                | ~ ! [SY3258: $i] :
                      ( ~ ( SV315 @ SY3258 )
                      | ( SV850 = SY3258 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( SV816
          = ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4143]) ).

thf(4185,plain,
    ! [SV817: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ! [SY2576: $i] :
              ~ ~ ( ~ ( SV315 @ SY2576 )
                  | ~ ! [SY2577: $i] :
                        ( ~ ( SV315 @ SY2577 )
                        | ( SY2576 = SY2577 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( SV77 @ ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4144]) ).

thf(4186,plain,
    ! [SV817: $i,SV77: $i > $o,SV851: $i,SV315: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV315 @ SV851 )
                | ~ ! [SY3259: $i] :
                      ( ~ ( SV315 @ SY3259 )
                      | ( SV851 = SY3259 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( SV817
          = ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[4145]) ).

thf(4187,plain,
    ! [SV813: $i,SV77: $i > $o,SV852: $i,SV315: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV315 @ SV852 )
                | ~ ! [SY3260: $i] :
                      ( ~ ( SV315 @ SY3260 )
                      | ( SV852 = SY3260 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( SV77 @ ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4146]) ).

thf(4188,plain,
    ! [SV813: $i,SV77: $i > $o,SV849: $i,SV315: $i > $o] :
      ( ( ( ~ ( ~ ( SV315 @ SV849 )
              | ~ ! [SY3257: $i] :
                    ( ~ ( SV315 @ SY3257 )
                    | ( SV849 = SY3257 ) ) ) )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( SV813
          = ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4147]) ).

thf(4189,plain,
    ! [SV109: $i,SV804: $i,SV795: $i] :
      ( ( ( ~ ( in @ SV795 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) ) )
        = $false )
      | ( ( ~ ( ~ ( in @ SV804 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) )
              | ( in @ SV795 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) ) ) )
        = $true )
      | ( ( SV795 = SV804 )
        = $true )
      | ( ( in @ SV795 @ SV109 )
        = $false )
      | ( ( in @ SV804 @ SV109 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4148]) ).

thf(4190,plain,
    ! [SV109: $i,SV795: $i,SV804: $i] :
      ( ( ( in @ SV804 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) )
        = $false )
      | ( ( ~ ( ~ ( in @ SV804 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) )
              | ( in @ SV795 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) ) ) )
        = $true )
      | ( ( SV795 = SV804 )
        = $true )
      | ( ( in @ SV795 @ SV109 )
        = $false )
      | ( ( in @ SV804 @ SV109 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4148]) ).

thf(4191,plain,
    ! [SV109: $i,SV739: $i,SV822: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) )
                    | ~ ( in @ ( sK122_SY3239 @ SV109 @ SV739 @ SV822 ) @ SV739 ) )
              | ~ ~ ~ ! [SY3240: $i] :
                        ~ ~ ( ~ ( in @ SY3240 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) )
                            | ~ ( in @ SY3240 @ SV739 ) ) ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4149]) ).

thf(4192,plain,
    ! [SV739: $i,SV822: $i,SV109: $i] :
      ( ( ( ! [SY3253: $i] :
              ( ~ ( in @ SY3253 @ ( sK3_SY2100 @ SV109 ) )
              | ! [SY3242: $i] :
                  ( ~ ( in @ SY3242 @ SY3253 )
                  | ( in @ SY3242 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) ) )
              | ( in @ ( sK122_SY3239 @ SV109 @ SV739 @ SV822 ) @ SY3253 ) ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4150]) ).

thf(4193,plain,
    ! [SV109: $i,SV739: $i,SV818: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) )
                | ~ ( in @ ( sK118_SY3231 @ SV109 @ SV739 @ SV818 ) @ SV739 ) )
          | ~ ~ ~ ! [SY3232: $i] :
                    ~ ~ ( ~ ( in @ SY3232 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) )
                        | ~ ( in @ SY3232 @ SV739 ) ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4151]) ).

thf(4194,plain,
    ! [SV739: $i,SV818: $i,SV109: $i,SV853: $i] :
      ( ( ( ~ ( in @ SV853 @ ( sK3_SY2100 @ SV109 ) )
          | ! [SY3261: $i] :
              ( ~ ( in @ SY3261 @ SV853 )
              | ( in @ SY3261 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) ) )
          | ( in @ ( sK118_SY3231 @ SV109 @ SV739 @ SV818 ) @ SV853 ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4152]) ).

thf(4195,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV829: $i,SV743: $i] :
      ( ( ( ~ ( in @ ( sK128_SY3227 @ SV743 @ SV829 @ SV147 @ SV377 ) @ SV377 )
          | ~ ( SV147 @ ( sK128_SY3227 @ SV743 @ SV829 @ SV147 @ SV377 ) @ SV829 ) )
        = $false )
      | ( ( in @ SV829 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4153]) ).

thf(4196,plain,
    ! [SV743: $i,SV829: $i,SV147: $i > $i > $o,SV377: $i,SV848: $i] :
      ( ( ( ~ ( in @ SV848 @ SV377 )
          | ~ ( SV147 @ SV848 @ SV829 ) )
        = $true )
      | ( ( in @ SV829 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4154]) ).

thf(4197,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV823: $i,SV743: $i] :
      ( ( ( ~ ( in @ ( sK125_SY3224 @ SV743 @ SV823 @ SV147 @ SV377 ) @ SV377 ) )
        = $false )
      | ( ( in @ SV823 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV743
          = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4155]) ).

thf(4198,plain,
    ! [SV377: $i,SV823: $i,SV743: $i,SV147: $i > $i > $o] :
      ( ( ( ~ ( SV147 @ ( sK125_SY3224 @ SV743 @ SV823 @ SV147 @ SV377 ) @ SV823 ) )
        = $false )
      | ( ( in @ SV823 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV743
          = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4155]) ).

thf(4199,plain,
    ! [SV743: $i,SV823: $i,SV147: $i > $i > $o,SV377: $i,SV847: $i] :
      ( ( ( ~ ( in @ SV847 @ SV377 ) )
        = $true )
      | ( ( ~ ( SV147 @ SV847 @ SV823 ) )
        = $true )
      | ( ( in @ SV823 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV743
          = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4156]) ).

thf(4200,plain,
    ! [SV214: $i > $o,SV808: $i,SV438: $i > $o] :
      ( ( ( SV438 @ ( sK123_SY2801 @ SV808 @ SV214 @ SV438 ) )
        = $true )
      | ( ( SV214 @ SV808 )
        = $false )
      | ( ( SV214 @ ( sK110_SY3205 @ SV438 @ SV808 @ SV214 ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4157]) ).

thf(4201,plain,
    ! [SV214: $i > $o,SV808: $i,SV438: $i > $o] :
      ( ( ( ! [SY3255: $i] :
              ( ~ ( SV438 @ SY3255 )
              | ( ( sK123_SY2801 @ SV808 @ SV214 @ SV438 )
                = SY3255 ) ) )
        = $true )
      | ( ( SV214 @ SV808 )
        = $false )
      | ( ( SV214 @ ( sK110_SY3205 @ SV438 @ SV808 @ SV214 ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4158]) ).

thf(4202,plain,
    ! [SV214: $i > $o,SV808: $i,SV854: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV854 )
          | ( ( sK119_SY2801 @ SV808 @ SV214 @ SV438 )
            = SV854 ) )
        = $true )
      | ( ( SV214 @ SV808 )
        = $false )
      | ( ( SV808
          = ( sK110_SY3205 @ SV438 @ SV808 @ SV214 ) )
        = $false )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[4160]) ).

thf(4203,plain,
    ! [SV438: $i > $o,SV809: $i,SV214: $i > $o] :
      ( ( ( SV214 @ ( sK124_SY2394 @ SV809 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ SV809 )
        = $false )
      | ( ( SV438 @ ( sK111_SY3206 @ SV214 @ SV809 @ SV438 ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4161]) ).

thf(4204,plain,
    ! [SV438: $i > $o,SV809: $i,SV214: $i > $o] :
      ( ( ( ! [SY3256: $i] :
              ( ~ ( SV214 @ SY3256 )
              | ( ( sK124_SY2394 @ SV809 @ SV438 @ SV214 )
                = SY3256 ) ) )
        = $true )
      | ( ( SV438 @ SV809 )
        = $false )
      | ( ( SV438 @ ( sK111_SY3206 @ SV214 @ SV809 @ SV438 ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4162]) ).

thf(4205,plain,
    ! [SV438: $i > $o,SV809: $i,SV855: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV855 )
          | ( ( sK120_SY2394 @ SV809 @ SV438 @ SV214 )
            = SV855 ) )
        = $true )
      | ( ( SV438 @ SV809 )
        = $false )
      | ( ( SV809
          = ( sK111_SY3206 @ SV214 @ SV809 @ SV438 ) )
        = $false )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[4164]) ).

thf(4206,plain,
    ! [SV841: $i,SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK133_SY3243 @ SV438 @ SV841 @ SV214 ) ) )
        = $false )
      | ( ( SV214 @ SV841 )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4165]) ).

thf(4207,plain,
    ! [SV214: $i > $o,SV438: $i > $o,SV841: $i] :
      ( ( ( SV841
          = ( sK133_SY3243 @ SV438 @ SV841 @ SV214 ) )
        = $false )
      | ( ( SV214 @ SV841 )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4165]) ).

thf(4208,plain,
    ! [SV842: $i,SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK134_SY3244 @ SV214 @ SV842 @ SV438 ) ) )
        = $false )
      | ( ( SV438 @ SV842 )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4166]) ).

thf(4209,plain,
    ! [SV438: $i > $o,SV214: $i > $o,SV842: $i] :
      ( ( ( SV842
          = ( sK134_SY3244 @ SV214 @ SV842 @ SV438 ) )
        = $false )
      | ( ( SV438 @ SV842 )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4166]) ).

thf(4210,plain,
    ! [SV835: $i,SV438: $i > $o,SV214: $i > $o] :
      ( ( ( SV214 @ ( sK129_SY3235 @ SV438 @ SV835 @ SV214 ) )
        = $true )
      | ( ( SV214 @ SV835 )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4167]) ).

thf(4211,plain,
    ! [SV835: $i,SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ! [SY2801: $i] :
              ~ ~ ( ~ ( SV438 @ SY2801 )
                  | ~ ! [SY2802: $i] :
                        ( ~ ( SV438 @ SY2802 )
                        | ( SY2801 = SY2802 ) ) ) )
        = $false )
      | ( ( SV214 @ SV835 )
        = $false )
      | ( ( SV835
          = ( sK129_SY3235 @ SV438 @ SV835 @ SV214 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4168]) ).

thf(4212,plain,
    ! [SV836: $i,SV214: $i > $o,SV438: $i > $o] :
      ( ( ( SV438 @ ( sK130_SY3236 @ SV214 @ SV836 @ SV438 ) )
        = $true )
      | ( ( SV438 @ SV836 )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4169]) ).

thf(4213,plain,
    ! [SV836: $i,SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ! [SY2394: $i] :
              ~ ~ ( ~ ( SV214 @ SY2394 )
                  | ~ ! [SY2395: $i] :
                        ( ~ ( SV214 @ SY2395 )
                        | ( SY2394 = SY2395 ) ) ) )
        = $false )
      | ( ( SV438 @ SV836 )
        = $false )
      | ( ( SV836
          = ( sK130_SY3236 @ SV214 @ SV836 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4170]) ).

thf(4214,plain,
    ! [SV837: $i,SV438: $i > $o,SV214: $i > $o] :
      ( ( ( SV214 @ ( sK131_SY3237 @ SV438 @ SV837 @ SV214 ) )
        = $true )
      | ( ( SV214 @ SV837 )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4171]) ).

thf(4215,plain,
    ! [SV837: $i,SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ! [SY2801: $i] :
              ~ ~ ( ~ ( SV438 @ SY2801 )
                  | ~ ! [SY2802: $i] :
                        ( ~ ( SV438 @ SY2802 )
                        | ( SY2801 = SY2802 ) ) ) )
        = $false )
      | ( ( SV214 @ SV837 )
        = $false )
      | ( ( SV837
          = ( sK131_SY3237 @ SV438 @ SV837 @ SV214 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4172]) ).

thf(4216,plain,
    ! [SV838: $i,SV214: $i > $o,SV438: $i > $o] :
      ( ( ( SV438 @ ( sK132_SY3238 @ SV214 @ SV838 @ SV438 ) )
        = $true )
      | ( ( SV438 @ SV838 )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4173]) ).

thf(4217,plain,
    ! [SV838: $i,SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ! [SY2394: $i] :
              ~ ~ ( ~ ( SV214 @ SY2394 )
                  | ~ ! [SY2395: $i] :
                        ( ~ ( SV214 @ SY2395 )
                        | ( SY2394 = SY2395 ) ) ) )
        = $false )
      | ( ( SV438 @ SV838 )
        = $false )
      | ( ( SV838
          = ( sK132_SY3238 @ SV214 @ SV838 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4174]) ).

thf(4218,plain,
    ! [SV832: $i,SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ! [SY2801: $i] :
              ~ ~ ( ~ ( SV438 @ SY2801 )
                  | ~ ! [SY2802: $i] :
                        ( ~ ( SV438 @ SY2802 )
                        | ( SY2801 = SY2802 ) ) ) )
        = $false )
      | ( ( SV214 @ SV832 )
        = $false )
      | ( ( SV214 @ ( sK126_SY3229 @ SV438 @ SV832 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4175]) ).

thf(4219,plain,
    ! [SV214: $i > $o,SV832: $i,SV438: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV438 @ ( sK136_SY2801 @ SV832 @ SV214 @ SV438 ) )
                | ~ ! [SY3262: $i] :
                      ( ~ ( SV438 @ SY3262 )
                      | ( ( sK136_SY2801 @ SV832 @ SV214 @ SV438 )
                        = SY3262 ) ) ) )
        = $false )
      | ( ( SV214 @ SV832 )
        = $false )
      | ( ( SV832
          = ( sK126_SY3229 @ SV438 @ SV832 @ SV214 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[4176]) ).

thf(4220,plain,
    ! [SV833: $i,SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ! [SY2394: $i] :
              ~ ~ ( ~ ( SV214 @ SY2394 )
                  | ~ ! [SY2395: $i] :
                        ( ~ ( SV214 @ SY2395 )
                        | ( SY2394 = SY2395 ) ) ) )
        = $false )
      | ( ( SV438 @ SV833 )
        = $false )
      | ( ( SV438 @ ( sK127_SY3230 @ SV214 @ SV833 @ SV438 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4177]) ).

thf(4221,plain,
    ! [SV438: $i > $o,SV833: $i,SV214: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV214 @ ( sK137_SY2394 @ SV833 @ SV438 @ SV214 ) )
                | ~ ! [SY3263: $i] :
                      ( ~ ( SV214 @ SY3263 )
                      | ( ( sK137_SY2394 @ SV833 @ SV438 @ SV214 )
                        = SY3263 ) ) ) )
        = $false )
      | ( ( SV438 @ SV833 )
        = $false )
      | ( ( SV833
          = ( sK127_SY3230 @ SV214 @ SV833 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[4178]) ).

thf(4222,plain,
    ! [SV846: $i,SV77: $i > $o,SV775: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ ( sK138_SY3246 @ SV775 @ SV77 @ SV846 @ SV315 ) )
          | ( SV846
            = ( sK138_SY3246 @ SV775 @ SV77 @ SV846 @ SV315 ) ) )
        = $false )
      | ( ( SV315 @ SV846 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( SV77 @ ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) )
        = $true )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[4179]) ).

thf(4223,plain,
    ! [SV844: $i,SV77: $i > $o,SV775: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ ( sK135_SY3245 @ SV775 @ SV77 @ SV844 @ SV315 ) ) )
        = $false )
      | ( ( SV315 @ SV844 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( SV775
          = ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) )
        = $false )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4180]) ).

thf(4224,plain,
    ! [SV315: $i > $o,SV77: $i > $o,SV775: $i,SV844: $i] :
      ( ( ( SV844
          = ( sK135_SY3245 @ SV775 @ SV77 @ SV844 @ SV315 ) )
        = $false )
      | ( ( SV315 @ SV844 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( SV775
          = ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) )
        = $false )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4180]) ).

thf(4225,plain,
    ! [SV821: $i,SV77: $i > $o,SV315: $i > $o] :
      ( ( ( ! [SY2576: $i] :
              ~ ~ ( ~ ( SV315 @ SY2576 )
                  | ~ ! [SY2577: $i] :
                        ( ~ ( SV315 @ SY2577 )
                        | ( SY2576 = SY2577 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( SV77 @ ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4181]) ).

thf(4226,plain,
    ! [SV821: $i,SV77: $i > $o,SV856: $i,SV315: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV315 @ SV856 )
                | ~ ! [SY3264: $i] :
                      ( ~ ( SV315 @ SY3264 )
                      | ( SV856 = SY3264 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( SV821
          = ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[4182]) ).

thf(4227,plain,
    ! [SV816: $i,SV77: $i > $o,SV857: $i,SV315: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV315 @ SV857 )
                | ~ ! [SY3265: $i] :
                      ( ~ ( SV315 @ SY3265 )
                      | ( SV857 = SY3265 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( SV77 @ ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4183]) ).

thf(4228,plain,
    ! [SV816: $i,SV77: $i > $o,SV850: $i,SV315: $i > $o] :
      ( ( ( ~ ( ~ ( SV315 @ SV850 )
              | ~ ! [SY3258: $i] :
                    ( ~ ( SV315 @ SY3258 )
                    | ( SV850 = SY3258 ) ) ) )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( SV816
          = ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4184]) ).

thf(4229,plain,
    ! [SV817: $i,SV77: $i > $o,SV858: $i,SV315: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV315 @ SV858 )
                | ~ ! [SY3266: $i] :
                      ( ~ ( SV315 @ SY3266 )
                      | ( SV858 = SY3266 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( SV77 @ ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[4185]) ).

thf(4230,plain,
    ! [SV817: $i,SV77: $i > $o,SV851: $i,SV315: $i > $o] :
      ( ( ( ~ ( ~ ( SV315 @ SV851 )
              | ~ ! [SY3259: $i] :
                    ( ~ ( SV315 @ SY3259 )
                    | ( SV851 = SY3259 ) ) ) )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( SV817
          = ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4186]) ).

thf(4231,plain,
    ! [SV813: $i,SV77: $i > $o,SV852: $i,SV315: $i > $o] :
      ( ( ( ~ ( ~ ( SV315 @ SV852 )
              | ~ ! [SY3260: $i] :
                    ( ~ ( SV315 @ SY3260 )
                    | ( SV852 = SY3260 ) ) ) )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( SV77 @ ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4187]) ).

thf(4232,plain,
    ! [SV813: $i,SV77: $i > $o,SV849: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ SV849 )
          | ~ ! [SY3257: $i] :
                ( ~ ( SV315 @ SY3257 )
                | ( SV849 = SY3257 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( SV813
          = ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4188]) ).

thf(4233,plain,
    ! [SV109: $i,SV804: $i,SV795: $i] :
      ( ( ( in @ SV795 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) )
        = $true )
      | ( ( ~ ( ~ ( in @ SV804 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) )
              | ( in @ SV795 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) ) ) )
        = $true )
      | ( ( SV795 = SV804 )
        = $true )
      | ( ( in @ SV795 @ SV109 )
        = $false )
      | ( ( in @ SV804 @ SV109 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4189]) ).

thf(4234,plain,
    ! [SV109: $i,SV795: $i,SV804: $i] :
      ( ( ( ~ ( in @ SV804 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) )
          | ( in @ SV795 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) ) )
        = $false )
      | ( ( in @ SV804 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) )
        = $false )
      | ( ( SV795 = SV804 )
        = $true )
      | ( ( in @ SV795 @ SV109 )
        = $false )
      | ( ( in @ SV804 @ SV109 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4190]) ).

thf(4235,plain,
    ! [SV109: $i,SV739: $i,SV822: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) )
                | ~ ( in @ ( sK122_SY3239 @ SV109 @ SV739 @ SV822 ) @ SV739 ) )
          | ~ ~ ~ ! [SY3240: $i] :
                    ~ ~ ( ~ ( in @ SY3240 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) )
                        | ~ ( in @ SY3240 @ SV739 ) ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4191]) ).

thf(4236,plain,
    ! [SV739: $i,SV822: $i,SV109: $i,SV859: $i] :
      ( ( ( ~ ( in @ SV859 @ ( sK3_SY2100 @ SV109 ) )
          | ! [SY3267: $i] :
              ( ~ ( in @ SY3267 @ SV859 )
              | ( in @ SY3267 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) ) )
          | ( in @ ( sK122_SY3239 @ SV109 @ SV739 @ SV822 ) @ SV859 ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4192]) ).

thf(4237,plain,
    ! [SV109: $i,SV739: $i,SV818: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) )
                | ~ ( in @ ( sK118_SY3231 @ SV109 @ SV739 @ SV818 ) @ SV739 ) ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4193]) ).

thf(4238,plain,
    ! [SV109: $i,SV739: $i,SV818: $i] :
      ( ( ( ~ ~ ~ ! [SY3232: $i] :
                    ~ ~ ( ~ ( in @ SY3232 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) )
                        | ~ ( in @ SY3232 @ SV739 ) ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4193]) ).

thf(4239,plain,
    ! [SV739: $i,SV818: $i,SV109: $i,SV853: $i] :
      ( ( ( ~ ( in @ SV853 @ ( sK3_SY2100 @ SV109 ) ) )
        = $true )
      | ( ( ! [SY3261: $i] :
              ( ~ ( in @ SY3261 @ SV853 )
              | ( in @ SY3261 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) ) )
          | ( in @ ( sK118_SY3231 @ SV109 @ SV739 @ SV818 ) @ SV853 ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4194]) ).

thf(4240,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV829: $i,SV743: $i] :
      ( ( ( ~ ( in @ ( sK128_SY3227 @ SV743 @ SV829 @ SV147 @ SV377 ) @ SV377 ) )
        = $false )
      | ( ( in @ SV829 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4195]) ).

thf(4241,plain,
    ! [SV377: $i,SV829: $i,SV743: $i,SV147: $i > $i > $o] :
      ( ( ( ~ ( SV147 @ ( sK128_SY3227 @ SV743 @ SV829 @ SV147 @ SV377 ) @ SV829 ) )
        = $false )
      | ( ( in @ SV829 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4195]) ).

thf(4242,plain,
    ! [SV743: $i,SV829: $i,SV147: $i > $i > $o,SV377: $i,SV848: $i] :
      ( ( ( ~ ( in @ SV848 @ SV377 ) )
        = $true )
      | ( ( ~ ( SV147 @ SV848 @ SV829 ) )
        = $true )
      | ( ( in @ SV829 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4196]) ).

thf(4243,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV823: $i,SV743: $i] :
      ( ( ( in @ ( sK125_SY3224 @ SV743 @ SV823 @ SV147 @ SV377 ) @ SV377 )
        = $true )
      | ( ( in @ SV823 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV743
          = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4197]) ).

thf(4244,plain,
    ! [SV377: $i,SV823: $i,SV743: $i,SV147: $i > $i > $o] :
      ( ( ( SV147 @ ( sK125_SY3224 @ SV743 @ SV823 @ SV147 @ SV377 ) @ SV823 )
        = $true )
      | ( ( in @ SV823 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV743
          = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4198]) ).

thf(4245,plain,
    ! [SV743: $i,SV823: $i,SV147: $i > $i > $o,SV377: $i,SV847: $i] :
      ( ( ( in @ SV847 @ SV377 )
        = $false )
      | ( ( ~ ( SV147 @ SV847 @ SV823 ) )
        = $true )
      | ( ( in @ SV823 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV743
          = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4199]) ).

thf(4246,plain,
    ! [SV214: $i > $o,SV808: $i,SV860: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV860 )
          | ( ( sK123_SY2801 @ SV808 @ SV214 @ SV438 )
            = SV860 ) )
        = $true )
      | ( ( SV214 @ SV808 )
        = $false )
      | ( ( SV214 @ ( sK110_SY3205 @ SV438 @ SV808 @ SV214 ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[4201]) ).

thf(4247,plain,
    ! [SV214: $i > $o,SV808: $i,SV854: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV854 ) )
        = $true )
      | ( ( ( sK119_SY2801 @ SV808 @ SV214 @ SV438 )
          = SV854 )
        = $true )
      | ( ( SV214 @ SV808 )
        = $false )
      | ( ( SV808
          = ( sK110_SY3205 @ SV438 @ SV808 @ SV214 ) )
        = $false )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4202]) ).

thf(4248,plain,
    ! [SV438: $i > $o,SV809: $i,SV861: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV861 )
          | ( ( sK124_SY2394 @ SV809 @ SV438 @ SV214 )
            = SV861 ) )
        = $true )
      | ( ( SV438 @ SV809 )
        = $false )
      | ( ( SV438 @ ( sK111_SY3206 @ SV214 @ SV809 @ SV438 ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[4204]) ).

thf(4249,plain,
    ! [SV438: $i > $o,SV809: $i,SV855: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV855 ) )
        = $true )
      | ( ( ( sK120_SY2394 @ SV809 @ SV438 @ SV214 )
          = SV855 )
        = $true )
      | ( ( SV438 @ SV809 )
        = $false )
      | ( ( SV809
          = ( sK111_SY3206 @ SV214 @ SV809 @ SV438 ) )
        = $false )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4205]) ).

thf(4250,plain,
    ! [SV841: $i,SV438: $i > $o,SV214: $i > $o] :
      ( ( ( SV214 @ ( sK133_SY3243 @ SV438 @ SV841 @ SV214 ) )
        = $true )
      | ( ( SV214 @ SV841 )
        = $false )
      | ( ( ~ ! [SY2801: $i] :
                ~ ~ ( ~ ( SV438 @ SY2801 )
                    | ~ ! [SY2802: $i] :
                          ( ~ ( SV438 @ SY2802 )
                          | ( SY2801 = SY2802 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4206]) ).

thf(4251,plain,
    ! [SV841: $i,SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ! [SY2801: $i] :
              ~ ~ ( ~ ( SV438 @ SY2801 )
                  | ~ ! [SY2802: $i] :
                        ( ~ ( SV438 @ SY2802 )
                        | ( SY2801 = SY2802 ) ) ) )
        = $false )
      | ( ( SV214 @ SV841 )
        = $false )
      | ( ( SV841
          = ( sK133_SY3243 @ SV438 @ SV841 @ SV214 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4207]) ).

thf(4252,plain,
    ! [SV842: $i,SV214: $i > $o,SV438: $i > $o] :
      ( ( ( SV438 @ ( sK134_SY3244 @ SV214 @ SV842 @ SV438 ) )
        = $true )
      | ( ( SV438 @ SV842 )
        = $false )
      | ( ( ~ ! [SY2394: $i] :
                ~ ~ ( ~ ( SV214 @ SY2394 )
                    | ~ ! [SY2395: $i] :
                          ( ~ ( SV214 @ SY2395 )
                          | ( SY2394 = SY2395 ) ) ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4208]) ).

thf(4253,plain,
    ! [SV842: $i,SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ! [SY2394: $i] :
              ~ ~ ( ~ ( SV214 @ SY2394 )
                  | ~ ! [SY2395: $i] :
                        ( ~ ( SV214 @ SY2395 )
                        | ( SY2394 = SY2395 ) ) ) )
        = $false )
      | ( ( SV438 @ SV842 )
        = $false )
      | ( ( SV842
          = ( sK134_SY3244 @ SV214 @ SV842 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4209]) ).

thf(4254,plain,
    ! [SV835: $i,SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ! [SY2801: $i] :
              ~ ~ ( ~ ( SV438 @ SY2801 )
                  | ~ ! [SY2802: $i] :
                        ( ~ ( SV438 @ SY2802 )
                        | ( SY2801 = SY2802 ) ) ) )
        = $false )
      | ( ( SV214 @ SV835 )
        = $false )
      | ( ( SV214 @ ( sK129_SY3235 @ SV438 @ SV835 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4210]) ).

thf(4255,plain,
    ! [SV214: $i > $o,SV835: $i,SV438: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV438 @ ( sK139_SY2801 @ SV835 @ SV214 @ SV438 ) )
                | ~ ! [SY3268: $i] :
                      ( ~ ( SV438 @ SY3268 )
                      | ( ( sK139_SY2801 @ SV835 @ SV214 @ SV438 )
                        = SY3268 ) ) ) )
        = $false )
      | ( ( SV214 @ SV835 )
        = $false )
      | ( ( SV835
          = ( sK129_SY3235 @ SV438 @ SV835 @ SV214 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[4211]) ).

thf(4256,plain,
    ! [SV836: $i,SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ! [SY2394: $i] :
              ~ ~ ( ~ ( SV214 @ SY2394 )
                  | ~ ! [SY2395: $i] :
                        ( ~ ( SV214 @ SY2395 )
                        | ( SY2394 = SY2395 ) ) ) )
        = $false )
      | ( ( SV438 @ SV836 )
        = $false )
      | ( ( SV438 @ ( sK130_SY3236 @ SV214 @ SV836 @ SV438 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4212]) ).

thf(4257,plain,
    ! [SV438: $i > $o,SV836: $i,SV214: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV214 @ ( sK140_SY2394 @ SV836 @ SV438 @ SV214 ) )
                | ~ ! [SY3269: $i] :
                      ( ~ ( SV214 @ SY3269 )
                      | ( ( sK140_SY2394 @ SV836 @ SV438 @ SV214 )
                        = SY3269 ) ) ) )
        = $false )
      | ( ( SV438 @ SV836 )
        = $false )
      | ( ( SV836
          = ( sK130_SY3236 @ SV214 @ SV836 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[4213]) ).

thf(4258,plain,
    ! [SV837: $i,SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ! [SY2801: $i] :
              ~ ~ ( ~ ( SV438 @ SY2801 )
                  | ~ ! [SY2802: $i] :
                        ( ~ ( SV438 @ SY2802 )
                        | ( SY2801 = SY2802 ) ) ) )
        = $false )
      | ( ( SV214 @ SV837 )
        = $false )
      | ( ( SV214 @ ( sK131_SY3237 @ SV438 @ SV837 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4214]) ).

thf(4259,plain,
    ! [SV214: $i > $o,SV837: $i,SV438: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV438 @ ( sK141_SY2801 @ SV837 @ SV214 @ SV438 ) )
                | ~ ! [SY3270: $i] :
                      ( ~ ( SV438 @ SY3270 )
                      | ( ( sK141_SY2801 @ SV837 @ SV214 @ SV438 )
                        = SY3270 ) ) ) )
        = $false )
      | ( ( SV214 @ SV837 )
        = $false )
      | ( ( SV837
          = ( sK131_SY3237 @ SV438 @ SV837 @ SV214 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[4215]) ).

thf(4260,plain,
    ! [SV838: $i,SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ! [SY2394: $i] :
              ~ ~ ( ~ ( SV214 @ SY2394 )
                  | ~ ! [SY2395: $i] :
                        ( ~ ( SV214 @ SY2395 )
                        | ( SY2394 = SY2395 ) ) ) )
        = $false )
      | ( ( SV438 @ SV838 )
        = $false )
      | ( ( SV438 @ ( sK132_SY3238 @ SV214 @ SV838 @ SV438 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4216]) ).

thf(4261,plain,
    ! [SV438: $i > $o,SV838: $i,SV214: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV214 @ ( sK142_SY2394 @ SV838 @ SV438 @ SV214 ) )
                | ~ ! [SY3271: $i] :
                      ( ~ ( SV214 @ SY3271 )
                      | ( ( sK142_SY2394 @ SV838 @ SV438 @ SV214 )
                        = SY3271 ) ) ) )
        = $false )
      | ( ( SV438 @ SV838 )
        = $false )
      | ( ( SV838
          = ( sK132_SY3238 @ SV214 @ SV838 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[4217]) ).

thf(4262,plain,
    ! [SV214: $i > $o,SV832: $i,SV438: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV438 @ ( sK143_SY2801 @ SV832 @ SV214 @ SV438 ) )
                | ~ ! [SY3272: $i] :
                      ( ~ ( SV438 @ SY3272 )
                      | ( ( sK143_SY2801 @ SV832 @ SV214 @ SV438 )
                        = SY3272 ) ) ) )
        = $false )
      | ( ( SV214 @ SV832 )
        = $false )
      | ( ( SV214 @ ( sK126_SY3229 @ SV438 @ SV832 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[4218]) ).

thf(4263,plain,
    ! [SV214: $i > $o,SV832: $i,SV438: $i > $o] :
      ( ( ( ~ ( ~ ( SV438 @ ( sK136_SY2801 @ SV832 @ SV214 @ SV438 ) )
              | ~ ! [SY3262: $i] :
                    ( ~ ( SV438 @ SY3262 )
                    | ( ( sK136_SY2801 @ SV832 @ SV214 @ SV438 )
                      = SY3262 ) ) ) )
        = $true )
      | ( ( SV214 @ SV832 )
        = $false )
      | ( ( SV832
          = ( sK126_SY3229 @ SV438 @ SV832 @ SV214 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4219]) ).

thf(4264,plain,
    ! [SV438: $i > $o,SV833: $i,SV214: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV214 @ ( sK144_SY2394 @ SV833 @ SV438 @ SV214 ) )
                | ~ ! [SY3273: $i] :
                      ( ~ ( SV214 @ SY3273 )
                      | ( ( sK144_SY2394 @ SV833 @ SV438 @ SV214 )
                        = SY3273 ) ) ) )
        = $false )
      | ( ( SV438 @ SV833 )
        = $false )
      | ( ( SV438 @ ( sK127_SY3230 @ SV214 @ SV833 @ SV438 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[4220]) ).

thf(4265,plain,
    ! [SV438: $i > $o,SV833: $i,SV214: $i > $o] :
      ( ( ( ~ ( ~ ( SV214 @ ( sK137_SY2394 @ SV833 @ SV438 @ SV214 ) )
              | ~ ! [SY3263: $i] :
                    ( ~ ( SV214 @ SY3263 )
                    | ( ( sK137_SY2394 @ SV833 @ SV438 @ SV214 )
                      = SY3263 ) ) ) )
        = $true )
      | ( ( SV438 @ SV833 )
        = $false )
      | ( ( SV833
          = ( sK127_SY3230 @ SV214 @ SV833 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4221]) ).

thf(4266,plain,
    ! [SV846: $i,SV77: $i > $o,SV775: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ ( sK138_SY3246 @ SV775 @ SV77 @ SV846 @ SV315 ) ) )
        = $false )
      | ( ( SV315 @ SV846 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( SV77 @ ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) )
        = $true )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4222]) ).

thf(4267,plain,
    ! [SV315: $i > $o,SV77: $i > $o,SV775: $i,SV846: $i] :
      ( ( ( SV846
          = ( sK138_SY3246 @ SV775 @ SV77 @ SV846 @ SV315 ) )
        = $false )
      | ( ( SV315 @ SV846 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( SV77 @ ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) )
        = $true )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4222]) ).

thf(4268,plain,
    ! [SV844: $i,SV77: $i > $o,SV775: $i,SV315: $i > $o] :
      ( ( ( SV315 @ ( sK135_SY3245 @ SV775 @ SV77 @ SV844 @ SV315 ) )
        = $true )
      | ( ( SV315 @ SV844 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( SV775
          = ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) )
        = $false )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4223]) ).

thf(4269,plain,
    ! [SV821: $i,SV77: $i > $o,SV862: $i,SV315: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV315 @ SV862 )
                | ~ ! [SY3274: $i] :
                      ( ~ ( SV315 @ SY3274 )
                      | ( SV862 = SY3274 ) ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( SV77 @ ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[4225]) ).

thf(4270,plain,
    ! [SV821: $i,SV77: $i > $o,SV856: $i,SV315: $i > $o] :
      ( ( ( ~ ( ~ ( SV315 @ SV856 )
              | ~ ! [SY3264: $i] :
                    ( ~ ( SV315 @ SY3264 )
                    | ( SV856 = SY3264 ) ) ) )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( SV821
          = ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4226]) ).

thf(4271,plain,
    ! [SV816: $i,SV77: $i > $o,SV857: $i,SV315: $i > $o] :
      ( ( ( ~ ( ~ ( SV315 @ SV857 )
              | ~ ! [SY3265: $i] :
                    ( ~ ( SV315 @ SY3265 )
                    | ( SV857 = SY3265 ) ) ) )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( SV77 @ ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4227]) ).

thf(4272,plain,
    ! [SV816: $i,SV77: $i > $o,SV850: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ SV850 )
          | ~ ! [SY3258: $i] :
                ( ~ ( SV315 @ SY3258 )
                | ( SV850 = SY3258 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( SV816
          = ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4228]) ).

thf(4273,plain,
    ! [SV817: $i,SV77: $i > $o,SV858: $i,SV315: $i > $o] :
      ( ( ( ~ ( ~ ( SV315 @ SV858 )
              | ~ ! [SY3266: $i] :
                    ( ~ ( SV315 @ SY3266 )
                    | ( SV858 = SY3266 ) ) ) )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( SV77 @ ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4229]) ).

thf(4274,plain,
    ! [SV817: $i,SV77: $i > $o,SV851: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ SV851 )
          | ~ ! [SY3259: $i] :
                ( ~ ( SV315 @ SY3259 )
                | ( SV851 = SY3259 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( SV817
          = ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4230]) ).

thf(4275,plain,
    ! [SV813: $i,SV77: $i > $o,SV852: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ SV852 )
          | ~ ! [SY3260: $i] :
                ( ~ ( SV315 @ SY3260 )
                | ( SV852 = SY3260 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( SV77 @ ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4231]) ).

thf(4276,plain,
    ! [SV813: $i,SV77: $i > $o,SV849: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ SV849 ) )
        = $true )
      | ( ( ~ ! [SY3257: $i] :
                ( ~ ( SV315 @ SY3257 )
                | ( SV849 = SY3257 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( SV813
          = ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4232]) ).

thf(4277,plain,
    ! [SV109: $i,SV795: $i,SV804: $i] :
      ( ( ( ~ ( in @ SV804 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) )
          | ( in @ SV795 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) ) )
        = $false )
      | ( ( in @ SV795 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) )
        = $true )
      | ( ( SV795 = SV804 )
        = $true )
      | ( ( in @ SV795 @ SV109 )
        = $false )
      | ( ( in @ SV804 @ SV109 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4233]) ).

thf(4278,plain,
    ! [SV109: $i,SV795: $i,SV804: $i] :
      ( ( ( ~ ( in @ SV804 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) ) )
        = $false )
      | ( ( in @ SV804 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) )
        = $false )
      | ( ( SV795 = SV804 )
        = $true )
      | ( ( in @ SV795 @ SV109 )
        = $false )
      | ( ( in @ SV804 @ SV109 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4234]) ).

thf(4279,plain,
    ! [SV109: $i,SV804: $i,SV795: $i] :
      ( ( ( in @ SV795 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) )
        = $false )
      | ( ( in @ SV804 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) )
        = $false )
      | ( ( SV795 = SV804 )
        = $true )
      | ( ( in @ SV795 @ SV109 )
        = $false )
      | ( ( in @ SV804 @ SV109 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4234]) ).

thf(4280,plain,
    ! [SV109: $i,SV739: $i,SV822: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) )
                | ~ ( in @ ( sK122_SY3239 @ SV109 @ SV739 @ SV822 ) @ SV739 ) ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4235]) ).

thf(4281,plain,
    ! [SV109: $i,SV739: $i,SV822: $i] :
      ( ( ( ~ ~ ~ ! [SY3240: $i] :
                    ~ ~ ( ~ ( in @ SY3240 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) )
                        | ~ ( in @ SY3240 @ SV739 ) ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4235]) ).

thf(4282,plain,
    ! [SV739: $i,SV822: $i,SV109: $i,SV859: $i] :
      ( ( ( ~ ( in @ SV859 @ ( sK3_SY2100 @ SV109 ) ) )
        = $true )
      | ( ( ! [SY3267: $i] :
              ( ~ ( in @ SY3267 @ SV859 )
              | ( in @ SY3267 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) ) )
          | ( in @ ( sK122_SY3239 @ SV109 @ SV739 @ SV822 ) @ SV859 ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4236]) ).

thf(4283,plain,
    ! [SV109: $i,SV739: $i,SV818: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) )
              | ~ ( in @ ( sK118_SY3231 @ SV109 @ SV739 @ SV818 ) @ SV739 ) ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4237]) ).

thf(4284,plain,
    ! [SV109: $i,SV739: $i,SV818: $i] :
      ( ( ( ~ ~ ! [SY3232: $i] :
                  ~ ~ ( ~ ( in @ SY3232 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) )
                      | ~ ( in @ SY3232 @ SV739 ) ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4238]) ).

thf(4285,plain,
    ! [SV739: $i,SV818: $i,SV109: $i,SV853: $i] :
      ( ( ( in @ SV853 @ ( sK3_SY2100 @ SV109 ) )
        = $false )
      | ( ( ! [SY3261: $i] :
              ( ~ ( in @ SY3261 @ SV853 )
              | ( in @ SY3261 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) ) )
          | ( in @ ( sK118_SY3231 @ SV109 @ SV739 @ SV818 ) @ SV853 ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4239]) ).

thf(4286,plain,
    ! [SV377: $i,SV147: $i > $i > $o,SV829: $i,SV743: $i] :
      ( ( ( in @ ( sK128_SY3227 @ SV743 @ SV829 @ SV147 @ SV377 ) @ SV377 )
        = $true )
      | ( ( in @ SV829 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4240]) ).

thf(4287,plain,
    ! [SV377: $i,SV829: $i,SV743: $i,SV147: $i > $i > $o] :
      ( ( ( SV147 @ ( sK128_SY3227 @ SV743 @ SV829 @ SV147 @ SV377 ) @ SV829 )
        = $true )
      | ( ( in @ SV829 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4241]) ).

thf(4288,plain,
    ! [SV743: $i,SV829: $i,SV147: $i > $i > $o,SV377: $i,SV848: $i] :
      ( ( ( in @ SV848 @ SV377 )
        = $false )
      | ( ( ~ ( SV147 @ SV848 @ SV829 ) )
        = $true )
      | ( ( in @ SV829 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4242]) ).

thf(4289,plain,
    ! [SV743: $i,SV377: $i,SV823: $i,SV847: $i,SV147: $i > $i > $o] :
      ( ( ( SV147 @ SV847 @ SV823 )
        = $false )
      | ( ( in @ SV847 @ SV377 )
        = $false )
      | ( ( in @ SV823 @ ( sK98_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV743
          = ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4245]) ).

thf(4290,plain,
    ! [SV214: $i > $o,SV808: $i,SV860: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV860 ) )
        = $true )
      | ( ( ( sK123_SY2801 @ SV808 @ SV214 @ SV438 )
          = SV860 )
        = $true )
      | ( ( SV214 @ SV808 )
        = $false )
      | ( ( SV214 @ ( sK110_SY3205 @ SV438 @ SV808 @ SV214 ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4246]) ).

thf(4291,plain,
    ! [SV214: $i > $o,SV808: $i,SV854: $i,SV438: $i > $o] :
      ( ( ( SV438 @ SV854 )
        = $false )
      | ( ( ( sK119_SY2801 @ SV808 @ SV214 @ SV438 )
          = SV854 )
        = $true )
      | ( ( SV214 @ SV808 )
        = $false )
      | ( ( SV808
          = ( sK110_SY3205 @ SV438 @ SV808 @ SV214 ) )
        = $false )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4247]) ).

thf(4292,plain,
    ! [SV438: $i > $o,SV809: $i,SV861: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV861 ) )
        = $true )
      | ( ( ( sK124_SY2394 @ SV809 @ SV438 @ SV214 )
          = SV861 )
        = $true )
      | ( ( SV438 @ SV809 )
        = $false )
      | ( ( SV438 @ ( sK111_SY3206 @ SV214 @ SV809 @ SV438 ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4248]) ).

thf(4293,plain,
    ! [SV438: $i > $o,SV809: $i,SV855: $i,SV214: $i > $o] :
      ( ( ( SV214 @ SV855 )
        = $false )
      | ( ( ( sK120_SY2394 @ SV809 @ SV438 @ SV214 )
          = SV855 )
        = $true )
      | ( ( SV438 @ SV809 )
        = $false )
      | ( ( SV809
          = ( sK111_SY3206 @ SV214 @ SV809 @ SV438 ) )
        = $false )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4249]) ).

thf(4294,plain,
    ! [SV841: $i,SV214: $i > $o,SV438: $i > $o] :
      ( ( ( ! [SY2801: $i] :
              ~ ~ ( ~ ( SV438 @ SY2801 )
                  | ~ ! [SY2802: $i] :
                        ( ~ ( SV438 @ SY2802 )
                        | ( SY2801 = SY2802 ) ) ) )
        = $false )
      | ( ( SV214 @ SV841 )
        = $false )
      | ( ( SV214 @ ( sK133_SY3243 @ SV438 @ SV841 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4250]) ).

thf(4295,plain,
    ! [SV214: $i > $o,SV841: $i,SV438: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV438 @ ( sK145_SY2801 @ SV841 @ SV214 @ SV438 ) )
                | ~ ! [SY3275: $i] :
                      ( ~ ( SV438 @ SY3275 )
                      | ( ( sK145_SY2801 @ SV841 @ SV214 @ SV438 )
                        = SY3275 ) ) ) )
        = $false )
      | ( ( SV214 @ SV841 )
        = $false )
      | ( ( SV841
          = ( sK133_SY3243 @ SV438 @ SV841 @ SV214 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[4251]) ).

thf(4296,plain,
    ! [SV842: $i,SV438: $i > $o,SV214: $i > $o] :
      ( ( ( ! [SY2394: $i] :
              ~ ~ ( ~ ( SV214 @ SY2394 )
                  | ~ ! [SY2395: $i] :
                        ( ~ ( SV214 @ SY2395 )
                        | ( SY2394 = SY2395 ) ) ) )
        = $false )
      | ( ( SV438 @ SV842 )
        = $false )
      | ( ( SV438 @ ( sK134_SY3244 @ SV214 @ SV842 @ SV438 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4252]) ).

thf(4297,plain,
    ! [SV438: $i > $o,SV842: $i,SV214: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV214 @ ( sK146_SY2394 @ SV842 @ SV438 @ SV214 ) )
                | ~ ! [SY3276: $i] :
                      ( ~ ( SV214 @ SY3276 )
                      | ( ( sK146_SY2394 @ SV842 @ SV438 @ SV214 )
                        = SY3276 ) ) ) )
        = $false )
      | ( ( SV438 @ SV842 )
        = $false )
      | ( ( SV842
          = ( sK134_SY3244 @ SV214 @ SV842 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[4253]) ).

thf(4298,plain,
    ! [SV214: $i > $o,SV835: $i,SV438: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV438 @ ( sK147_SY2801 @ SV835 @ SV214 @ SV438 ) )
                | ~ ! [SY3277: $i] :
                      ( ~ ( SV438 @ SY3277 )
                      | ( ( sK147_SY2801 @ SV835 @ SV214 @ SV438 )
                        = SY3277 ) ) ) )
        = $false )
      | ( ( SV214 @ SV835 )
        = $false )
      | ( ( SV214 @ ( sK129_SY3235 @ SV438 @ SV835 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[4254]) ).

thf(4299,plain,
    ! [SV214: $i > $o,SV835: $i,SV438: $i > $o] :
      ( ( ( ~ ( ~ ( SV438 @ ( sK139_SY2801 @ SV835 @ SV214 @ SV438 ) )
              | ~ ! [SY3268: $i] :
                    ( ~ ( SV438 @ SY3268 )
                    | ( ( sK139_SY2801 @ SV835 @ SV214 @ SV438 )
                      = SY3268 ) ) ) )
        = $true )
      | ( ( SV214 @ SV835 )
        = $false )
      | ( ( SV835
          = ( sK129_SY3235 @ SV438 @ SV835 @ SV214 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4255]) ).

thf(4300,plain,
    ! [SV438: $i > $o,SV836: $i,SV214: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV214 @ ( sK148_SY2394 @ SV836 @ SV438 @ SV214 ) )
                | ~ ! [SY3278: $i] :
                      ( ~ ( SV214 @ SY3278 )
                      | ( ( sK148_SY2394 @ SV836 @ SV438 @ SV214 )
                        = SY3278 ) ) ) )
        = $false )
      | ( ( SV438 @ SV836 )
        = $false )
      | ( ( SV438 @ ( sK130_SY3236 @ SV214 @ SV836 @ SV438 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[4256]) ).

thf(4301,plain,
    ! [SV438: $i > $o,SV836: $i,SV214: $i > $o] :
      ( ( ( ~ ( ~ ( SV214 @ ( sK140_SY2394 @ SV836 @ SV438 @ SV214 ) )
              | ~ ! [SY3269: $i] :
                    ( ~ ( SV214 @ SY3269 )
                    | ( ( sK140_SY2394 @ SV836 @ SV438 @ SV214 )
                      = SY3269 ) ) ) )
        = $true )
      | ( ( SV438 @ SV836 )
        = $false )
      | ( ( SV836
          = ( sK130_SY3236 @ SV214 @ SV836 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4257]) ).

thf(4302,plain,
    ! [SV214: $i > $o,SV837: $i,SV438: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV438 @ ( sK149_SY2801 @ SV837 @ SV214 @ SV438 ) )
                | ~ ! [SY3279: $i] :
                      ( ~ ( SV438 @ SY3279 )
                      | ( ( sK149_SY2801 @ SV837 @ SV214 @ SV438 )
                        = SY3279 ) ) ) )
        = $false )
      | ( ( SV214 @ SV837 )
        = $false )
      | ( ( SV214 @ ( sK131_SY3237 @ SV438 @ SV837 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[4258]) ).

thf(4303,plain,
    ! [SV214: $i > $o,SV837: $i,SV438: $i > $o] :
      ( ( ( ~ ( ~ ( SV438 @ ( sK141_SY2801 @ SV837 @ SV214 @ SV438 ) )
              | ~ ! [SY3270: $i] :
                    ( ~ ( SV438 @ SY3270 )
                    | ( ( sK141_SY2801 @ SV837 @ SV214 @ SV438 )
                      = SY3270 ) ) ) )
        = $true )
      | ( ( SV214 @ SV837 )
        = $false )
      | ( ( SV837
          = ( sK131_SY3237 @ SV438 @ SV837 @ SV214 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4259]) ).

thf(4304,plain,
    ! [SV438: $i > $o,SV838: $i,SV214: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV214 @ ( sK150_SY2394 @ SV838 @ SV438 @ SV214 ) )
                | ~ ! [SY3280: $i] :
                      ( ~ ( SV214 @ SY3280 )
                      | ( ( sK150_SY2394 @ SV838 @ SV438 @ SV214 )
                        = SY3280 ) ) ) )
        = $false )
      | ( ( SV438 @ SV838 )
        = $false )
      | ( ( SV438 @ ( sK132_SY3238 @ SV214 @ SV838 @ SV438 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[4260]) ).

thf(4305,plain,
    ! [SV438: $i > $o,SV838: $i,SV214: $i > $o] :
      ( ( ( ~ ( ~ ( SV214 @ ( sK142_SY2394 @ SV838 @ SV438 @ SV214 ) )
              | ~ ! [SY3271: $i] :
                    ( ~ ( SV214 @ SY3271 )
                    | ( ( sK142_SY2394 @ SV838 @ SV438 @ SV214 )
                      = SY3271 ) ) ) )
        = $true )
      | ( ( SV438 @ SV838 )
        = $false )
      | ( ( SV838
          = ( sK132_SY3238 @ SV214 @ SV838 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4261]) ).

thf(4306,plain,
    ! [SV214: $i > $o,SV832: $i,SV438: $i > $o] :
      ( ( ( ~ ( ~ ( SV438 @ ( sK143_SY2801 @ SV832 @ SV214 @ SV438 ) )
              | ~ ! [SY3272: $i] :
                    ( ~ ( SV438 @ SY3272 )
                    | ( ( sK143_SY2801 @ SV832 @ SV214 @ SV438 )
                      = SY3272 ) ) ) )
        = $true )
      | ( ( SV214 @ SV832 )
        = $false )
      | ( ( SV214 @ ( sK126_SY3229 @ SV438 @ SV832 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4262]) ).

thf(4307,plain,
    ! [SV214: $i > $o,SV832: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK136_SY2801 @ SV832 @ SV214 @ SV438 ) )
          | ~ ! [SY3262: $i] :
                ( ~ ( SV438 @ SY3262 )
                | ( ( sK136_SY2801 @ SV832 @ SV214 @ SV438 )
                  = SY3262 ) ) )
        = $false )
      | ( ( SV214 @ SV832 )
        = $false )
      | ( ( SV832
          = ( sK126_SY3229 @ SV438 @ SV832 @ SV214 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4263]) ).

thf(4308,plain,
    ! [SV438: $i > $o,SV833: $i,SV214: $i > $o] :
      ( ( ( ~ ( ~ ( SV214 @ ( sK144_SY2394 @ SV833 @ SV438 @ SV214 ) )
              | ~ ! [SY3273: $i] :
                    ( ~ ( SV214 @ SY3273 )
                    | ( ( sK144_SY2394 @ SV833 @ SV438 @ SV214 )
                      = SY3273 ) ) ) )
        = $true )
      | ( ( SV438 @ SV833 )
        = $false )
      | ( ( SV438 @ ( sK127_SY3230 @ SV214 @ SV833 @ SV438 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4264]) ).

thf(4309,plain,
    ! [SV438: $i > $o,SV833: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK137_SY2394 @ SV833 @ SV438 @ SV214 ) )
          | ~ ! [SY3263: $i] :
                ( ~ ( SV214 @ SY3263 )
                | ( ( sK137_SY2394 @ SV833 @ SV438 @ SV214 )
                  = SY3263 ) ) )
        = $false )
      | ( ( SV438 @ SV833 )
        = $false )
      | ( ( SV833
          = ( sK127_SY3230 @ SV214 @ SV833 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4265]) ).

thf(4310,plain,
    ! [SV846: $i,SV77: $i > $o,SV775: $i,SV315: $i > $o] :
      ( ( ( SV315 @ ( sK138_SY3246 @ SV775 @ SV77 @ SV846 @ SV315 ) )
        = $true )
      | ( ( SV315 @ SV846 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV775 )
        = $false )
      | ( ( SV77 @ ( sK100_SY3183 @ SV315 @ SV775 @ SV77 ) )
        = $true )
      | ( ( ( sK7_SY2572 @ SV315 @ SV77 )
          = ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4266]) ).

thf(4311,plain,
    ! [SV821: $i,SV77: $i > $o,SV862: $i,SV315: $i > $o] :
      ( ( ( ~ ( ~ ( SV315 @ SV862 )
              | ~ ! [SY3274: $i] :
                    ( ~ ( SV315 @ SY3274 )
                    | ( SV862 = SY3274 ) ) ) )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( SV77 @ ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4269]) ).

thf(4312,plain,
    ! [SV821: $i,SV77: $i > $o,SV856: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ SV856 )
          | ~ ! [SY3264: $i] :
                ( ~ ( SV315 @ SY3264 )
                | ( SV856 = SY3264 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( SV821
          = ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4270]) ).

thf(4313,plain,
    ! [SV816: $i,SV77: $i > $o,SV857: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ SV857 )
          | ~ ! [SY3265: $i] :
                ( ~ ( SV315 @ SY3265 )
                | ( SV857 = SY3265 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( SV77 @ ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4271]) ).

thf(4314,plain,
    ! [SV816: $i,SV77: $i > $o,SV850: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ SV850 ) )
        = $true )
      | ( ( ~ ! [SY3258: $i] :
                ( ~ ( SV315 @ SY3258 )
                | ( SV850 = SY3258 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( SV816
          = ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4272]) ).

thf(4315,plain,
    ! [SV817: $i,SV77: $i > $o,SV858: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ SV858 )
          | ~ ! [SY3266: $i] :
                ( ~ ( SV315 @ SY3266 )
                | ( SV858 = SY3266 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( SV77 @ ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4273]) ).

thf(4316,plain,
    ! [SV817: $i,SV77: $i > $o,SV851: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ SV851 ) )
        = $true )
      | ( ( ~ ! [SY3259: $i] :
                ( ~ ( SV315 @ SY3259 )
                | ( SV851 = SY3259 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( SV817
          = ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4274]) ).

thf(4317,plain,
    ! [SV813: $i,SV77: $i > $o,SV852: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ SV852 ) )
        = $true )
      | ( ( ~ ! [SY3260: $i] :
                ( ~ ( SV315 @ SY3260 )
                | ( SV852 = SY3260 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( SV77 @ ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4275]) ).

thf(4318,plain,
    ! [SV813: $i,SV77: $i > $o,SV849: $i,SV315: $i > $o] :
      ( ( ( SV315 @ SV849 )
        = $false )
      | ( ( ~ ! [SY3257: $i] :
                ( ~ ( SV315 @ SY3257 )
                | ( SV849 = SY3257 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( SV813
          = ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4276]) ).

thf(4319,plain,
    ! [SV109: $i,SV795: $i,SV804: $i] :
      ( ( ( ~ ( in @ SV804 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) ) )
        = $false )
      | ( ( in @ SV795 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) )
        = $true )
      | ( ( SV795 = SV804 )
        = $true )
      | ( ( in @ SV795 @ SV109 )
        = $false )
      | ( ( in @ SV804 @ SV109 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4277]) ).

thf(4320,plain,
    ! [SV109: $i,SV804: $i,SV795: $i] :
      ( ( ( in @ SV795 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) )
        = $false )
      | ( ( in @ SV795 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) )
        = $true )
      | ( ( SV795 = SV804 )
        = $true )
      | ( ( in @ SV795 @ SV109 )
        = $false )
      | ( ( in @ SV804 @ SV109 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4277]) ).

thf(4321,plain,
    ! [SV109: $i,SV795: $i,SV804: $i] :
      ( ( ( in @ SV804 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) )
        = $true )
      | ( ( in @ SV804 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) )
        = $false )
      | ( ( SV795 = SV804 )
        = $true )
      | ( ( in @ SV795 @ SV109 )
        = $false )
      | ( ( in @ SV804 @ SV109 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4278]) ).

thf(4322,plain,
    ! [SV109: $i,SV739: $i,SV822: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) )
              | ~ ( in @ ( sK122_SY3239 @ SV109 @ SV739 @ SV822 ) @ SV739 ) ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4280]) ).

thf(4323,plain,
    ! [SV109: $i,SV739: $i,SV822: $i] :
      ( ( ( ~ ~ ! [SY3240: $i] :
                  ~ ~ ( ~ ( in @ SY3240 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) )
                      | ~ ( in @ SY3240 @ SV739 ) ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4281]) ).

thf(4324,plain,
    ! [SV739: $i,SV822: $i,SV109: $i,SV859: $i] :
      ( ( ( in @ SV859 @ ( sK3_SY2100 @ SV109 ) )
        = $false )
      | ( ( ! [SY3267: $i] :
              ( ~ ( in @ SY3267 @ SV859 )
              | ( in @ SY3267 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) ) )
          | ( in @ ( sK122_SY3239 @ SV109 @ SV739 @ SV822 ) @ SV859 ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4282]) ).

thf(4325,plain,
    ! [SV109: $i,SV739: $i,SV818: $i] :
      ( ( ( ~ ( in @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) )
          | ~ ( in @ ( sK118_SY3231 @ SV109 @ SV739 @ SV818 ) @ SV739 ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4283]) ).

thf(4326,plain,
    ! [SV109: $i,SV739: $i,SV818: $i] :
      ( ( ( ~ ! [SY3232: $i] :
                ~ ~ ( ~ ( in @ SY3232 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) )
                    | ~ ( in @ SY3232 @ SV739 ) ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4284]) ).

thf(4327,plain,
    ! [SV109: $i,SV739: $i,SV818: $i,SV853: $i] :
      ( ( ( ! [SY3261: $i] :
              ( ~ ( in @ SY3261 @ SV853 )
              | ( in @ SY3261 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) ) ) )
        = $true )
      | ( ( in @ ( sK118_SY3231 @ SV109 @ SV739 @ SV818 ) @ SV853 )
        = $true )
      | ( ( in @ SV853 @ ( sK3_SY2100 @ SV109 ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4285]) ).

thf(4328,plain,
    ! [SV743: $i,SV377: $i,SV829: $i,SV848: $i,SV147: $i > $i > $o] :
      ( ( ( SV147 @ SV848 @ SV829 )
        = $false )
      | ( ( in @ SV848 @ SV377 )
        = $false )
      | ( ( in @ SV829 @ ( sK102_SY2690 @ SV743 @ SV147 @ SV377 ) )
        = $true )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ SV743 )
        = $false )
      | ( ( SV147 @ ( sK13_SY2687 @ SV147 @ SV377 ) @ ( sK82_SY3162 @ SV743 @ SV377 @ SV147 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4288]) ).

thf(4329,plain,
    ! [SV214: $i > $o,SV808: $i,SV860: $i,SV438: $i > $o] :
      ( ( ( SV438 @ SV860 )
        = $false )
      | ( ( ( sK123_SY2801 @ SV808 @ SV214 @ SV438 )
          = SV860 )
        = $true )
      | ( ( SV214 @ SV808 )
        = $false )
      | ( ( SV214 @ ( sK110_SY3205 @ SV438 @ SV808 @ SV214 ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4290]) ).

thf(4330,plain,
    ! [SV438: $i > $o,SV809: $i,SV861: $i,SV214: $i > $o] :
      ( ( ( SV214 @ SV861 )
        = $false )
      | ( ( ( sK124_SY2394 @ SV809 @ SV438 @ SV214 )
          = SV861 )
        = $true )
      | ( ( SV438 @ SV809 )
        = $false )
      | ( ( SV438 @ ( sK111_SY3206 @ SV214 @ SV809 @ SV438 ) )
        = $true )
      | ( ( ( sK17_SY2797 @ SV438 @ SV214 )
          = ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4292]) ).

thf(4331,plain,
    ! [SV214: $i > $o,SV841: $i,SV438: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV438 @ ( sK151_SY2801 @ SV841 @ SV214 @ SV438 ) )
                | ~ ! [SY3281: $i] :
                      ( ~ ( SV438 @ SY3281 )
                      | ( ( sK151_SY2801 @ SV841 @ SV214 @ SV438 )
                        = SY3281 ) ) ) )
        = $false )
      | ( ( SV214 @ SV841 )
        = $false )
      | ( ( SV214 @ ( sK133_SY3243 @ SV438 @ SV841 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[4294]) ).

thf(4332,plain,
    ! [SV214: $i > $o,SV841: $i,SV438: $i > $o] :
      ( ( ( ~ ( ~ ( SV438 @ ( sK145_SY2801 @ SV841 @ SV214 @ SV438 ) )
              | ~ ! [SY3275: $i] :
                    ( ~ ( SV438 @ SY3275 )
                    | ( ( sK145_SY2801 @ SV841 @ SV214 @ SV438 )
                      = SY3275 ) ) ) )
        = $true )
      | ( ( SV214 @ SV841 )
        = $false )
      | ( ( SV841
          = ( sK133_SY3243 @ SV438 @ SV841 @ SV214 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4295]) ).

thf(4333,plain,
    ! [SV438: $i > $o,SV842: $i,SV214: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV214 @ ( sK152_SY2394 @ SV842 @ SV438 @ SV214 ) )
                | ~ ! [SY3282: $i] :
                      ( ~ ( SV214 @ SY3282 )
                      | ( ( sK152_SY2394 @ SV842 @ SV438 @ SV214 )
                        = SY3282 ) ) ) )
        = $false )
      | ( ( SV438 @ SV842 )
        = $false )
      | ( ( SV438 @ ( sK134_SY3244 @ SV214 @ SV842 @ SV438 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[4296]) ).

thf(4334,plain,
    ! [SV438: $i > $o,SV842: $i,SV214: $i > $o] :
      ( ( ( ~ ( ~ ( SV214 @ ( sK146_SY2394 @ SV842 @ SV438 @ SV214 ) )
              | ~ ! [SY3276: $i] :
                    ( ~ ( SV214 @ SY3276 )
                    | ( ( sK146_SY2394 @ SV842 @ SV438 @ SV214 )
                      = SY3276 ) ) ) )
        = $true )
      | ( ( SV438 @ SV842 )
        = $false )
      | ( ( SV842
          = ( sK134_SY3244 @ SV214 @ SV842 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4297]) ).

thf(4335,plain,
    ! [SV214: $i > $o,SV835: $i,SV438: $i > $o] :
      ( ( ( ~ ( ~ ( SV438 @ ( sK147_SY2801 @ SV835 @ SV214 @ SV438 ) )
              | ~ ! [SY3277: $i] :
                    ( ~ ( SV438 @ SY3277 )
                    | ( ( sK147_SY2801 @ SV835 @ SV214 @ SV438 )
                      = SY3277 ) ) ) )
        = $true )
      | ( ( SV214 @ SV835 )
        = $false )
      | ( ( SV214 @ ( sK129_SY3235 @ SV438 @ SV835 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4298]) ).

thf(4336,plain,
    ! [SV214: $i > $o,SV835: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK139_SY2801 @ SV835 @ SV214 @ SV438 ) )
          | ~ ! [SY3268: $i] :
                ( ~ ( SV438 @ SY3268 )
                | ( ( sK139_SY2801 @ SV835 @ SV214 @ SV438 )
                  = SY3268 ) ) )
        = $false )
      | ( ( SV214 @ SV835 )
        = $false )
      | ( ( SV835
          = ( sK129_SY3235 @ SV438 @ SV835 @ SV214 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4299]) ).

thf(4337,plain,
    ! [SV438: $i > $o,SV836: $i,SV214: $i > $o] :
      ( ( ( ~ ( ~ ( SV214 @ ( sK148_SY2394 @ SV836 @ SV438 @ SV214 ) )
              | ~ ! [SY3278: $i] :
                    ( ~ ( SV214 @ SY3278 )
                    | ( ( sK148_SY2394 @ SV836 @ SV438 @ SV214 )
                      = SY3278 ) ) ) )
        = $true )
      | ( ( SV438 @ SV836 )
        = $false )
      | ( ( SV438 @ ( sK130_SY3236 @ SV214 @ SV836 @ SV438 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4300]) ).

thf(4338,plain,
    ! [SV438: $i > $o,SV836: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK140_SY2394 @ SV836 @ SV438 @ SV214 ) )
          | ~ ! [SY3269: $i] :
                ( ~ ( SV214 @ SY3269 )
                | ( ( sK140_SY2394 @ SV836 @ SV438 @ SV214 )
                  = SY3269 ) ) )
        = $false )
      | ( ( SV438 @ SV836 )
        = $false )
      | ( ( SV836
          = ( sK130_SY3236 @ SV214 @ SV836 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4301]) ).

thf(4339,plain,
    ! [SV214: $i > $o,SV837: $i,SV438: $i > $o] :
      ( ( ( ~ ( ~ ( SV438 @ ( sK149_SY2801 @ SV837 @ SV214 @ SV438 ) )
              | ~ ! [SY3279: $i] :
                    ( ~ ( SV438 @ SY3279 )
                    | ( ( sK149_SY2801 @ SV837 @ SV214 @ SV438 )
                      = SY3279 ) ) ) )
        = $true )
      | ( ( SV214 @ SV837 )
        = $false )
      | ( ( SV214 @ ( sK131_SY3237 @ SV438 @ SV837 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4302]) ).

thf(4340,plain,
    ! [SV214: $i > $o,SV837: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK141_SY2801 @ SV837 @ SV214 @ SV438 ) )
          | ~ ! [SY3270: $i] :
                ( ~ ( SV438 @ SY3270 )
                | ( ( sK141_SY2801 @ SV837 @ SV214 @ SV438 )
                  = SY3270 ) ) )
        = $false )
      | ( ( SV214 @ SV837 )
        = $false )
      | ( ( SV837
          = ( sK131_SY3237 @ SV438 @ SV837 @ SV214 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4303]) ).

thf(4341,plain,
    ! [SV438: $i > $o,SV838: $i,SV214: $i > $o] :
      ( ( ( ~ ( ~ ( SV214 @ ( sK150_SY2394 @ SV838 @ SV438 @ SV214 ) )
              | ~ ! [SY3280: $i] :
                    ( ~ ( SV214 @ SY3280 )
                    | ( ( sK150_SY2394 @ SV838 @ SV438 @ SV214 )
                      = SY3280 ) ) ) )
        = $true )
      | ( ( SV438 @ SV838 )
        = $false )
      | ( ( SV438 @ ( sK132_SY3238 @ SV214 @ SV838 @ SV438 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4304]) ).

thf(4342,plain,
    ! [SV438: $i > $o,SV838: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK142_SY2394 @ SV838 @ SV438 @ SV214 ) )
          | ~ ! [SY3271: $i] :
                ( ~ ( SV214 @ SY3271 )
                | ( ( sK142_SY2394 @ SV838 @ SV438 @ SV214 )
                  = SY3271 ) ) )
        = $false )
      | ( ( SV438 @ SV838 )
        = $false )
      | ( ( SV838
          = ( sK132_SY3238 @ SV214 @ SV838 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4305]) ).

thf(4343,plain,
    ! [SV214: $i > $o,SV832: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK143_SY2801 @ SV832 @ SV214 @ SV438 ) )
          | ~ ! [SY3272: $i] :
                ( ~ ( SV438 @ SY3272 )
                | ( ( sK143_SY2801 @ SV832 @ SV214 @ SV438 )
                  = SY3272 ) ) )
        = $false )
      | ( ( SV214 @ SV832 )
        = $false )
      | ( ( SV214 @ ( sK126_SY3229 @ SV438 @ SV832 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4306]) ).

thf(4344,plain,
    ! [SV214: $i > $o,SV832: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK136_SY2801 @ SV832 @ SV214 @ SV438 ) ) )
        = $false )
      | ( ( SV214 @ SV832 )
        = $false )
      | ( ( SV832
          = ( sK126_SY3229 @ SV438 @ SV832 @ SV214 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4307]) ).

thf(4345,plain,
    ! [SV214: $i > $o,SV832: $i,SV438: $i > $o] :
      ( ( ( ~ ! [SY3262: $i] :
                ( ~ ( SV438 @ SY3262 )
                | ( ( sK136_SY2801 @ SV832 @ SV214 @ SV438 )
                  = SY3262 ) ) )
        = $false )
      | ( ( SV214 @ SV832 )
        = $false )
      | ( ( SV832
          = ( sK126_SY3229 @ SV438 @ SV832 @ SV214 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4307]) ).

thf(4346,plain,
    ! [SV438: $i > $o,SV833: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK144_SY2394 @ SV833 @ SV438 @ SV214 ) )
          | ~ ! [SY3273: $i] :
                ( ~ ( SV214 @ SY3273 )
                | ( ( sK144_SY2394 @ SV833 @ SV438 @ SV214 )
                  = SY3273 ) ) )
        = $false )
      | ( ( SV438 @ SV833 )
        = $false )
      | ( ( SV438 @ ( sK127_SY3230 @ SV214 @ SV833 @ SV438 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4308]) ).

thf(4347,plain,
    ! [SV438: $i > $o,SV833: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK137_SY2394 @ SV833 @ SV438 @ SV214 ) ) )
        = $false )
      | ( ( SV438 @ SV833 )
        = $false )
      | ( ( SV833
          = ( sK127_SY3230 @ SV214 @ SV833 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4309]) ).

thf(4348,plain,
    ! [SV438: $i > $o,SV833: $i,SV214: $i > $o] :
      ( ( ( ~ ! [SY3263: $i] :
                ( ~ ( SV214 @ SY3263 )
                | ( ( sK137_SY2394 @ SV833 @ SV438 @ SV214 )
                  = SY3263 ) ) )
        = $false )
      | ( ( SV438 @ SV833 )
        = $false )
      | ( ( SV833
          = ( sK127_SY3230 @ SV214 @ SV833 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4309]) ).

thf(4349,plain,
    ! [SV821: $i,SV77: $i > $o,SV862: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ SV862 )
          | ~ ! [SY3274: $i] :
                ( ~ ( SV315 @ SY3274 )
                | ( SV862 = SY3274 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( SV77 @ ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4311]) ).

thf(4350,plain,
    ! [SV821: $i,SV77: $i > $o,SV856: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ SV856 ) )
        = $true )
      | ( ( ~ ! [SY3264: $i] :
                ( ~ ( SV315 @ SY3264 )
                | ( SV856 = SY3264 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( SV821
          = ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4312]) ).

thf(4351,plain,
    ! [SV816: $i,SV77: $i > $o,SV857: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ SV857 ) )
        = $true )
      | ( ( ~ ! [SY3265: $i] :
                ( ~ ( SV315 @ SY3265 )
                | ( SV857 = SY3265 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( SV77 @ ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4313]) ).

thf(4352,plain,
    ! [SV816: $i,SV77: $i > $o,SV850: $i,SV315: $i > $o] :
      ( ( ( SV315 @ SV850 )
        = $false )
      | ( ( ~ ! [SY3258: $i] :
                ( ~ ( SV315 @ SY3258 )
                | ( SV850 = SY3258 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( SV816
          = ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4314]) ).

thf(4353,plain,
    ! [SV817: $i,SV77: $i > $o,SV858: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ SV858 ) )
        = $true )
      | ( ( ~ ! [SY3266: $i] :
                ( ~ ( SV315 @ SY3266 )
                | ( SV858 = SY3266 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( SV77 @ ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4315]) ).

thf(4354,plain,
    ! [SV817: $i,SV77: $i > $o,SV851: $i,SV315: $i > $o] :
      ( ( ( SV315 @ SV851 )
        = $false )
      | ( ( ~ ! [SY3259: $i] :
                ( ~ ( SV315 @ SY3259 )
                | ( SV851 = SY3259 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( SV817
          = ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4316]) ).

thf(4355,plain,
    ! [SV813: $i,SV77: $i > $o,SV852: $i,SV315: $i > $o] :
      ( ( ( SV315 @ SV852 )
        = $false )
      | ( ( ~ ! [SY3260: $i] :
                ( ~ ( SV315 @ SY3260 )
                | ( SV852 = SY3260 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( SV77 @ ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4317]) ).

thf(4356,plain,
    ! [SV813: $i,SV77: $i > $o,SV849: $i,SV315: $i > $o] :
      ( ( ( ! [SY3257: $i] :
              ( ~ ( SV315 @ SY3257 )
              | ( SV849 = SY3257 ) ) )
        = $false )
      | ( ( SV315 @ SV849 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( SV813
          = ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4318]) ).

thf(4357,plain,
    ! [SV109: $i,SV795: $i,SV804: $i] :
      ( ( ( in @ SV804 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) )
        = $true )
      | ( ( in @ SV795 @ ( sK117_SY3202 @ SV804 @ SV795 @ SV109 ) )
        = $true )
      | ( ( SV795 = SV804 )
        = $true )
      | ( ( in @ SV795 @ SV109 )
        = $false )
      | ( ( in @ SV804 @ SV109 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4319]) ).

thf(4358,plain,
    ! [SV109: $i,SV739: $i,SV822: $i] :
      ( ( ( ~ ( in @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) )
          | ~ ( in @ ( sK122_SY3239 @ SV109 @ SV739 @ SV822 ) @ SV739 ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4322]) ).

thf(4359,plain,
    ! [SV109: $i,SV739: $i,SV822: $i] :
      ( ( ( ~ ! [SY3240: $i] :
                ~ ~ ( ~ ( in @ SY3240 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) )
                    | ~ ( in @ SY3240 @ SV739 ) ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4323]) ).

thf(4360,plain,
    ! [SV109: $i,SV739: $i,SV822: $i,SV859: $i] :
      ( ( ( ! [SY3267: $i] :
              ( ~ ( in @ SY3267 @ SV859 )
              | ( in @ SY3267 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) ) ) )
        = $true )
      | ( ( in @ ( sK122_SY3239 @ SV109 @ SV739 @ SV822 ) @ SV859 )
        = $true )
      | ( ( in @ SV859 @ ( sK3_SY2100 @ SV109 ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4324]) ).

thf(4361,plain,
    ! [SV109: $i,SV739: $i,SV818: $i] :
      ( ( ( ~ ( in @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4325]) ).

thf(4362,plain,
    ! [SV818: $i,SV739: $i,SV109: $i] :
      ( ( ( ~ ( in @ ( sK118_SY3231 @ SV109 @ SV739 @ SV818 ) @ SV739 ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4325]) ).

thf(4363,plain,
    ! [SV109: $i,SV739: $i,SV818: $i] :
      ( ( ( ! [SY3232: $i] :
              ~ ~ ( ~ ( in @ SY3232 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) )
                  | ~ ( in @ SY3232 @ SV739 ) ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4326]) ).

thf(4364,plain,
    ! [SV109: $i,SV739: $i,SV818: $i,SV853: $i,SV863: $i] :
      ( ( ( ~ ( in @ SV863 @ SV853 )
          | ( in @ SV863 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) ) )
        = $true )
      | ( ( in @ ( sK118_SY3231 @ SV109 @ SV739 @ SV818 ) @ SV853 )
        = $true )
      | ( ( in @ SV853 @ ( sK3_SY2100 @ SV109 ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4327]) ).

thf(4365,plain,
    ! [SV214: $i > $o,SV841: $i,SV438: $i > $o] :
      ( ( ( ~ ( ~ ( SV438 @ ( sK151_SY2801 @ SV841 @ SV214 @ SV438 ) )
              | ~ ! [SY3281: $i] :
                    ( ~ ( SV438 @ SY3281 )
                    | ( ( sK151_SY2801 @ SV841 @ SV214 @ SV438 )
                      = SY3281 ) ) ) )
        = $true )
      | ( ( SV214 @ SV841 )
        = $false )
      | ( ( SV214 @ ( sK133_SY3243 @ SV438 @ SV841 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4331]) ).

thf(4366,plain,
    ! [SV214: $i > $o,SV841: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK145_SY2801 @ SV841 @ SV214 @ SV438 ) )
          | ~ ! [SY3275: $i] :
                ( ~ ( SV438 @ SY3275 )
                | ( ( sK145_SY2801 @ SV841 @ SV214 @ SV438 )
                  = SY3275 ) ) )
        = $false )
      | ( ( SV214 @ SV841 )
        = $false )
      | ( ( SV841
          = ( sK133_SY3243 @ SV438 @ SV841 @ SV214 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4332]) ).

thf(4367,plain,
    ! [SV438: $i > $o,SV842: $i,SV214: $i > $o] :
      ( ( ( ~ ( ~ ( SV214 @ ( sK152_SY2394 @ SV842 @ SV438 @ SV214 ) )
              | ~ ! [SY3282: $i] :
                    ( ~ ( SV214 @ SY3282 )
                    | ( ( sK152_SY2394 @ SV842 @ SV438 @ SV214 )
                      = SY3282 ) ) ) )
        = $true )
      | ( ( SV438 @ SV842 )
        = $false )
      | ( ( SV438 @ ( sK134_SY3244 @ SV214 @ SV842 @ SV438 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4333]) ).

thf(4368,plain,
    ! [SV438: $i > $o,SV842: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK146_SY2394 @ SV842 @ SV438 @ SV214 ) )
          | ~ ! [SY3276: $i] :
                ( ~ ( SV214 @ SY3276 )
                | ( ( sK146_SY2394 @ SV842 @ SV438 @ SV214 )
                  = SY3276 ) ) )
        = $false )
      | ( ( SV438 @ SV842 )
        = $false )
      | ( ( SV842
          = ( sK134_SY3244 @ SV214 @ SV842 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4334]) ).

thf(4369,plain,
    ! [SV214: $i > $o,SV835: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK147_SY2801 @ SV835 @ SV214 @ SV438 ) )
          | ~ ! [SY3277: $i] :
                ( ~ ( SV438 @ SY3277 )
                | ( ( sK147_SY2801 @ SV835 @ SV214 @ SV438 )
                  = SY3277 ) ) )
        = $false )
      | ( ( SV214 @ SV835 )
        = $false )
      | ( ( SV214 @ ( sK129_SY3235 @ SV438 @ SV835 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4335]) ).

thf(4370,plain,
    ! [SV214: $i > $o,SV835: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK139_SY2801 @ SV835 @ SV214 @ SV438 ) ) )
        = $false )
      | ( ( SV214 @ SV835 )
        = $false )
      | ( ( SV835
          = ( sK129_SY3235 @ SV438 @ SV835 @ SV214 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4336]) ).

thf(4371,plain,
    ! [SV214: $i > $o,SV835: $i,SV438: $i > $o] :
      ( ( ( ~ ! [SY3268: $i] :
                ( ~ ( SV438 @ SY3268 )
                | ( ( sK139_SY2801 @ SV835 @ SV214 @ SV438 )
                  = SY3268 ) ) )
        = $false )
      | ( ( SV214 @ SV835 )
        = $false )
      | ( ( SV835
          = ( sK129_SY3235 @ SV438 @ SV835 @ SV214 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4336]) ).

thf(4372,plain,
    ! [SV438: $i > $o,SV836: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK148_SY2394 @ SV836 @ SV438 @ SV214 ) )
          | ~ ! [SY3278: $i] :
                ( ~ ( SV214 @ SY3278 )
                | ( ( sK148_SY2394 @ SV836 @ SV438 @ SV214 )
                  = SY3278 ) ) )
        = $false )
      | ( ( SV438 @ SV836 )
        = $false )
      | ( ( SV438 @ ( sK130_SY3236 @ SV214 @ SV836 @ SV438 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4337]) ).

thf(4373,plain,
    ! [SV438: $i > $o,SV836: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK140_SY2394 @ SV836 @ SV438 @ SV214 ) ) )
        = $false )
      | ( ( SV438 @ SV836 )
        = $false )
      | ( ( SV836
          = ( sK130_SY3236 @ SV214 @ SV836 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4338]) ).

thf(4374,plain,
    ! [SV438: $i > $o,SV836: $i,SV214: $i > $o] :
      ( ( ( ~ ! [SY3269: $i] :
                ( ~ ( SV214 @ SY3269 )
                | ( ( sK140_SY2394 @ SV836 @ SV438 @ SV214 )
                  = SY3269 ) ) )
        = $false )
      | ( ( SV438 @ SV836 )
        = $false )
      | ( ( SV836
          = ( sK130_SY3236 @ SV214 @ SV836 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4338]) ).

thf(4375,plain,
    ! [SV214: $i > $o,SV837: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK149_SY2801 @ SV837 @ SV214 @ SV438 ) )
          | ~ ! [SY3279: $i] :
                ( ~ ( SV438 @ SY3279 )
                | ( ( sK149_SY2801 @ SV837 @ SV214 @ SV438 )
                  = SY3279 ) ) )
        = $false )
      | ( ( SV214 @ SV837 )
        = $false )
      | ( ( SV214 @ ( sK131_SY3237 @ SV438 @ SV837 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4339]) ).

thf(4376,plain,
    ! [SV214: $i > $o,SV837: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK141_SY2801 @ SV837 @ SV214 @ SV438 ) ) )
        = $false )
      | ( ( SV214 @ SV837 )
        = $false )
      | ( ( SV837
          = ( sK131_SY3237 @ SV438 @ SV837 @ SV214 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4340]) ).

thf(4377,plain,
    ! [SV214: $i > $o,SV837: $i,SV438: $i > $o] :
      ( ( ( ~ ! [SY3270: $i] :
                ( ~ ( SV438 @ SY3270 )
                | ( ( sK141_SY2801 @ SV837 @ SV214 @ SV438 )
                  = SY3270 ) ) )
        = $false )
      | ( ( SV214 @ SV837 )
        = $false )
      | ( ( SV837
          = ( sK131_SY3237 @ SV438 @ SV837 @ SV214 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4340]) ).

thf(4378,plain,
    ! [SV438: $i > $o,SV838: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK150_SY2394 @ SV838 @ SV438 @ SV214 ) )
          | ~ ! [SY3280: $i] :
                ( ~ ( SV214 @ SY3280 )
                | ( ( sK150_SY2394 @ SV838 @ SV438 @ SV214 )
                  = SY3280 ) ) )
        = $false )
      | ( ( SV438 @ SV838 )
        = $false )
      | ( ( SV438 @ ( sK132_SY3238 @ SV214 @ SV838 @ SV438 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4341]) ).

thf(4379,plain,
    ! [SV438: $i > $o,SV838: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK142_SY2394 @ SV838 @ SV438 @ SV214 ) ) )
        = $false )
      | ( ( SV438 @ SV838 )
        = $false )
      | ( ( SV838
          = ( sK132_SY3238 @ SV214 @ SV838 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4342]) ).

thf(4380,plain,
    ! [SV438: $i > $o,SV838: $i,SV214: $i > $o] :
      ( ( ( ~ ! [SY3271: $i] :
                ( ~ ( SV214 @ SY3271 )
                | ( ( sK142_SY2394 @ SV838 @ SV438 @ SV214 )
                  = SY3271 ) ) )
        = $false )
      | ( ( SV438 @ SV838 )
        = $false )
      | ( ( SV838
          = ( sK132_SY3238 @ SV214 @ SV838 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4342]) ).

thf(4381,plain,
    ! [SV214: $i > $o,SV832: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK143_SY2801 @ SV832 @ SV214 @ SV438 ) ) )
        = $false )
      | ( ( SV214 @ SV832 )
        = $false )
      | ( ( SV214 @ ( sK126_SY3229 @ SV438 @ SV832 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4343]) ).

thf(4382,plain,
    ! [SV214: $i > $o,SV832: $i,SV438: $i > $o] :
      ( ( ( ~ ! [SY3272: $i] :
                ( ~ ( SV438 @ SY3272 )
                | ( ( sK143_SY2801 @ SV832 @ SV214 @ SV438 )
                  = SY3272 ) ) )
        = $false )
      | ( ( SV214 @ SV832 )
        = $false )
      | ( ( SV214 @ ( sK126_SY3229 @ SV438 @ SV832 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4343]) ).

thf(4383,plain,
    ! [SV214: $i > $o,SV832: $i,SV438: $i > $o] :
      ( ( ( SV438 @ ( sK136_SY2801 @ SV832 @ SV214 @ SV438 ) )
        = $true )
      | ( ( SV214 @ SV832 )
        = $false )
      | ( ( SV832
          = ( sK126_SY3229 @ SV438 @ SV832 @ SV214 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4344]) ).

thf(4384,plain,
    ! [SV214: $i > $o,SV832: $i,SV438: $i > $o] :
      ( ( ( ! [SY3262: $i] :
              ( ~ ( SV438 @ SY3262 )
              | ( ( sK136_SY2801 @ SV832 @ SV214 @ SV438 )
                = SY3262 ) ) )
        = $true )
      | ( ( SV214 @ SV832 )
        = $false )
      | ( ( SV832
          = ( sK126_SY3229 @ SV438 @ SV832 @ SV214 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4345]) ).

thf(4385,plain,
    ! [SV438: $i > $o,SV833: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK144_SY2394 @ SV833 @ SV438 @ SV214 ) ) )
        = $false )
      | ( ( SV438 @ SV833 )
        = $false )
      | ( ( SV438 @ ( sK127_SY3230 @ SV214 @ SV833 @ SV438 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4346]) ).

thf(4386,plain,
    ! [SV438: $i > $o,SV833: $i,SV214: $i > $o] :
      ( ( ( ~ ! [SY3273: $i] :
                ( ~ ( SV214 @ SY3273 )
                | ( ( sK144_SY2394 @ SV833 @ SV438 @ SV214 )
                  = SY3273 ) ) )
        = $false )
      | ( ( SV438 @ SV833 )
        = $false )
      | ( ( SV438 @ ( sK127_SY3230 @ SV214 @ SV833 @ SV438 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4346]) ).

thf(4387,plain,
    ! [SV438: $i > $o,SV833: $i,SV214: $i > $o] :
      ( ( ( SV214 @ ( sK137_SY2394 @ SV833 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ SV833 )
        = $false )
      | ( ( SV833
          = ( sK127_SY3230 @ SV214 @ SV833 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4347]) ).

thf(4388,plain,
    ! [SV438: $i > $o,SV833: $i,SV214: $i > $o] :
      ( ( ( ! [SY3263: $i] :
              ( ~ ( SV214 @ SY3263 )
              | ( ( sK137_SY2394 @ SV833 @ SV438 @ SV214 )
                = SY3263 ) ) )
        = $true )
      | ( ( SV438 @ SV833 )
        = $false )
      | ( ( SV833
          = ( sK127_SY3230 @ SV214 @ SV833 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4348]) ).

thf(4389,plain,
    ! [SV821: $i,SV77: $i > $o,SV862: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ SV862 ) )
        = $true )
      | ( ( ~ ! [SY3274: $i] :
                ( ~ ( SV315 @ SY3274 )
                | ( SV862 = SY3274 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( SV77 @ ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4349]) ).

thf(4390,plain,
    ! [SV821: $i,SV77: $i > $o,SV856: $i,SV315: $i > $o] :
      ( ( ( SV315 @ SV856 )
        = $false )
      | ( ( ~ ! [SY3264: $i] :
                ( ~ ( SV315 @ SY3264 )
                | ( SV856 = SY3264 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( SV821
          = ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4350]) ).

thf(4391,plain,
    ! [SV816: $i,SV77: $i > $o,SV857: $i,SV315: $i > $o] :
      ( ( ( SV315 @ SV857 )
        = $false )
      | ( ( ~ ! [SY3265: $i] :
                ( ~ ( SV315 @ SY3265 )
                | ( SV857 = SY3265 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( SV77 @ ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4351]) ).

thf(4392,plain,
    ! [SV816: $i,SV77: $i > $o,SV850: $i,SV315: $i > $o] :
      ( ( ( ! [SY3258: $i] :
              ( ~ ( SV315 @ SY3258 )
              | ( SV850 = SY3258 ) ) )
        = $false )
      | ( ( SV315 @ SV850 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( SV816
          = ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4352]) ).

thf(4393,plain,
    ! [SV817: $i,SV77: $i > $o,SV858: $i,SV315: $i > $o] :
      ( ( ( SV315 @ SV858 )
        = $false )
      | ( ( ~ ! [SY3266: $i] :
                ( ~ ( SV315 @ SY3266 )
                | ( SV858 = SY3266 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( SV77 @ ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4353]) ).

thf(4394,plain,
    ! [SV817: $i,SV77: $i > $o,SV851: $i,SV315: $i > $o] :
      ( ( ( ! [SY3259: $i] :
              ( ~ ( SV315 @ SY3259 )
              | ( SV851 = SY3259 ) ) )
        = $false )
      | ( ( SV315 @ SV851 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( SV817
          = ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4354]) ).

thf(4395,plain,
    ! [SV813: $i,SV77: $i > $o,SV852: $i,SV315: $i > $o] :
      ( ( ( ! [SY3260: $i] :
              ( ~ ( SV315 @ SY3260 )
              | ( SV852 = SY3260 ) ) )
        = $false )
      | ( ( SV315 @ SV852 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( SV77 @ ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4355]) ).

thf(4396,plain,
    ! [SV849: $i,SV77: $i > $o,SV813: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ ( sK153_SY3257 @ SV813 @ SV77 @ SV849 @ SV315 ) )
          | ( SV849
            = ( sK153_SY3257 @ SV813 @ SV77 @ SV849 @ SV315 ) ) )
        = $false )
      | ( ( SV315 @ SV849 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( SV813
          = ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[4356]) ).

thf(4397,plain,
    ! [SV109: $i,SV739: $i,SV822: $i] :
      ( ( ( ~ ( in @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4358]) ).

thf(4398,plain,
    ! [SV822: $i,SV739: $i,SV109: $i] :
      ( ( ( ~ ( in @ ( sK122_SY3239 @ SV109 @ SV739 @ SV822 ) @ SV739 ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4358]) ).

thf(4399,plain,
    ! [SV109: $i,SV739: $i,SV822: $i] :
      ( ( ( ! [SY3240: $i] :
              ~ ~ ( ~ ( in @ SY3240 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) )
                  | ~ ( in @ SY3240 @ SV739 ) ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4359]) ).

thf(4400,plain,
    ! [SV109: $i,SV739: $i,SV822: $i,SV859: $i,SV864: $i] :
      ( ( ( ~ ( in @ SV864 @ SV859 )
          | ( in @ SV864 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) ) )
        = $true )
      | ( ( in @ ( sK122_SY3239 @ SV109 @ SV739 @ SV822 ) @ SV859 )
        = $true )
      | ( ( in @ SV859 @ ( sK3_SY2100 @ SV109 ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4360]) ).

thf(4401,plain,
    ! [SV109: $i,SV739: $i,SV818: $i] :
      ( ( ( in @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4361]) ).

thf(4402,plain,
    ! [SV818: $i,SV739: $i,SV109: $i] :
      ( ( ( in @ ( sK118_SY3231 @ SV109 @ SV739 @ SV818 ) @ SV739 )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4362]) ).

thf(4403,plain,
    ! [SV109: $i,SV739: $i,SV818: $i,SV865: $i] :
      ( ( ( ~ ~ ( ~ ( in @ SV865 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) )
                | ~ ( in @ SV865 @ SV739 ) ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4363]) ).

thf(4404,plain,
    ! [SV109: $i,SV739: $i,SV818: $i,SV853: $i,SV863: $i] :
      ( ( ( ~ ( in @ SV863 @ SV853 ) )
        = $true )
      | ( ( in @ SV863 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) )
        = $true )
      | ( ( in @ ( sK118_SY3231 @ SV109 @ SV739 @ SV818 ) @ SV853 )
        = $true )
      | ( ( in @ SV853 @ ( sK3_SY2100 @ SV109 ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4364]) ).

thf(4405,plain,
    ! [SV214: $i > $o,SV841: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK151_SY2801 @ SV841 @ SV214 @ SV438 ) )
          | ~ ! [SY3281: $i] :
                ( ~ ( SV438 @ SY3281 )
                | ( ( sK151_SY2801 @ SV841 @ SV214 @ SV438 )
                  = SY3281 ) ) )
        = $false )
      | ( ( SV214 @ SV841 )
        = $false )
      | ( ( SV214 @ ( sK133_SY3243 @ SV438 @ SV841 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4365]) ).

thf(4406,plain,
    ! [SV214: $i > $o,SV841: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK145_SY2801 @ SV841 @ SV214 @ SV438 ) ) )
        = $false )
      | ( ( SV214 @ SV841 )
        = $false )
      | ( ( SV841
          = ( sK133_SY3243 @ SV438 @ SV841 @ SV214 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4366]) ).

thf(4407,plain,
    ! [SV214: $i > $o,SV841: $i,SV438: $i > $o] :
      ( ( ( ~ ! [SY3275: $i] :
                ( ~ ( SV438 @ SY3275 )
                | ( ( sK145_SY2801 @ SV841 @ SV214 @ SV438 )
                  = SY3275 ) ) )
        = $false )
      | ( ( SV214 @ SV841 )
        = $false )
      | ( ( SV841
          = ( sK133_SY3243 @ SV438 @ SV841 @ SV214 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4366]) ).

thf(4408,plain,
    ! [SV438: $i > $o,SV842: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK152_SY2394 @ SV842 @ SV438 @ SV214 ) )
          | ~ ! [SY3282: $i] :
                ( ~ ( SV214 @ SY3282 )
                | ( ( sK152_SY2394 @ SV842 @ SV438 @ SV214 )
                  = SY3282 ) ) )
        = $false )
      | ( ( SV438 @ SV842 )
        = $false )
      | ( ( SV438 @ ( sK134_SY3244 @ SV214 @ SV842 @ SV438 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4367]) ).

thf(4409,plain,
    ! [SV438: $i > $o,SV842: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK146_SY2394 @ SV842 @ SV438 @ SV214 ) ) )
        = $false )
      | ( ( SV438 @ SV842 )
        = $false )
      | ( ( SV842
          = ( sK134_SY3244 @ SV214 @ SV842 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4368]) ).

thf(4410,plain,
    ! [SV438: $i > $o,SV842: $i,SV214: $i > $o] :
      ( ( ( ~ ! [SY3276: $i] :
                ( ~ ( SV214 @ SY3276 )
                | ( ( sK146_SY2394 @ SV842 @ SV438 @ SV214 )
                  = SY3276 ) ) )
        = $false )
      | ( ( SV438 @ SV842 )
        = $false )
      | ( ( SV842
          = ( sK134_SY3244 @ SV214 @ SV842 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4368]) ).

thf(4411,plain,
    ! [SV214: $i > $o,SV835: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK147_SY2801 @ SV835 @ SV214 @ SV438 ) ) )
        = $false )
      | ( ( SV214 @ SV835 )
        = $false )
      | ( ( SV214 @ ( sK129_SY3235 @ SV438 @ SV835 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4369]) ).

thf(4412,plain,
    ! [SV214: $i > $o,SV835: $i,SV438: $i > $o] :
      ( ( ( ~ ! [SY3277: $i] :
                ( ~ ( SV438 @ SY3277 )
                | ( ( sK147_SY2801 @ SV835 @ SV214 @ SV438 )
                  = SY3277 ) ) )
        = $false )
      | ( ( SV214 @ SV835 )
        = $false )
      | ( ( SV214 @ ( sK129_SY3235 @ SV438 @ SV835 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4369]) ).

thf(4413,plain,
    ! [SV214: $i > $o,SV835: $i,SV438: $i > $o] :
      ( ( ( SV438 @ ( sK139_SY2801 @ SV835 @ SV214 @ SV438 ) )
        = $true )
      | ( ( SV214 @ SV835 )
        = $false )
      | ( ( SV835
          = ( sK129_SY3235 @ SV438 @ SV835 @ SV214 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4370]) ).

thf(4414,plain,
    ! [SV214: $i > $o,SV835: $i,SV438: $i > $o] :
      ( ( ( ! [SY3268: $i] :
              ( ~ ( SV438 @ SY3268 )
              | ( ( sK139_SY2801 @ SV835 @ SV214 @ SV438 )
                = SY3268 ) ) )
        = $true )
      | ( ( SV214 @ SV835 )
        = $false )
      | ( ( SV835
          = ( sK129_SY3235 @ SV438 @ SV835 @ SV214 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4371]) ).

thf(4415,plain,
    ! [SV438: $i > $o,SV836: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK148_SY2394 @ SV836 @ SV438 @ SV214 ) ) )
        = $false )
      | ( ( SV438 @ SV836 )
        = $false )
      | ( ( SV438 @ ( sK130_SY3236 @ SV214 @ SV836 @ SV438 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4372]) ).

thf(4416,plain,
    ! [SV438: $i > $o,SV836: $i,SV214: $i > $o] :
      ( ( ( ~ ! [SY3278: $i] :
                ( ~ ( SV214 @ SY3278 )
                | ( ( sK148_SY2394 @ SV836 @ SV438 @ SV214 )
                  = SY3278 ) ) )
        = $false )
      | ( ( SV438 @ SV836 )
        = $false )
      | ( ( SV438 @ ( sK130_SY3236 @ SV214 @ SV836 @ SV438 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4372]) ).

thf(4417,plain,
    ! [SV438: $i > $o,SV836: $i,SV214: $i > $o] :
      ( ( ( SV214 @ ( sK140_SY2394 @ SV836 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ SV836 )
        = $false )
      | ( ( SV836
          = ( sK130_SY3236 @ SV214 @ SV836 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4373]) ).

thf(4418,plain,
    ! [SV438: $i > $o,SV836: $i,SV214: $i > $o] :
      ( ( ( ! [SY3269: $i] :
              ( ~ ( SV214 @ SY3269 )
              | ( ( sK140_SY2394 @ SV836 @ SV438 @ SV214 )
                = SY3269 ) ) )
        = $true )
      | ( ( SV438 @ SV836 )
        = $false )
      | ( ( SV836
          = ( sK130_SY3236 @ SV214 @ SV836 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4374]) ).

thf(4419,plain,
    ! [SV214: $i > $o,SV837: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK149_SY2801 @ SV837 @ SV214 @ SV438 ) ) )
        = $false )
      | ( ( SV214 @ SV837 )
        = $false )
      | ( ( SV214 @ ( sK131_SY3237 @ SV438 @ SV837 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4375]) ).

thf(4420,plain,
    ! [SV214: $i > $o,SV837: $i,SV438: $i > $o] :
      ( ( ( ~ ! [SY3279: $i] :
                ( ~ ( SV438 @ SY3279 )
                | ( ( sK149_SY2801 @ SV837 @ SV214 @ SV438 )
                  = SY3279 ) ) )
        = $false )
      | ( ( SV214 @ SV837 )
        = $false )
      | ( ( SV214 @ ( sK131_SY3237 @ SV438 @ SV837 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4375]) ).

thf(4421,plain,
    ! [SV214: $i > $o,SV837: $i,SV438: $i > $o] :
      ( ( ( SV438 @ ( sK141_SY2801 @ SV837 @ SV214 @ SV438 ) )
        = $true )
      | ( ( SV214 @ SV837 )
        = $false )
      | ( ( SV837
          = ( sK131_SY3237 @ SV438 @ SV837 @ SV214 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4376]) ).

thf(4422,plain,
    ! [SV214: $i > $o,SV837: $i,SV438: $i > $o] :
      ( ( ( ! [SY3270: $i] :
              ( ~ ( SV438 @ SY3270 )
              | ( ( sK141_SY2801 @ SV837 @ SV214 @ SV438 )
                = SY3270 ) ) )
        = $true )
      | ( ( SV214 @ SV837 )
        = $false )
      | ( ( SV837
          = ( sK131_SY3237 @ SV438 @ SV837 @ SV214 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4377]) ).

thf(4423,plain,
    ! [SV438: $i > $o,SV838: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK150_SY2394 @ SV838 @ SV438 @ SV214 ) ) )
        = $false )
      | ( ( SV438 @ SV838 )
        = $false )
      | ( ( SV438 @ ( sK132_SY3238 @ SV214 @ SV838 @ SV438 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4378]) ).

thf(4424,plain,
    ! [SV438: $i > $o,SV838: $i,SV214: $i > $o] :
      ( ( ( ~ ! [SY3280: $i] :
                ( ~ ( SV214 @ SY3280 )
                | ( ( sK150_SY2394 @ SV838 @ SV438 @ SV214 )
                  = SY3280 ) ) )
        = $false )
      | ( ( SV438 @ SV838 )
        = $false )
      | ( ( SV438 @ ( sK132_SY3238 @ SV214 @ SV838 @ SV438 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4378]) ).

thf(4425,plain,
    ! [SV438: $i > $o,SV838: $i,SV214: $i > $o] :
      ( ( ( SV214 @ ( sK142_SY2394 @ SV838 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ SV838 )
        = $false )
      | ( ( SV838
          = ( sK132_SY3238 @ SV214 @ SV838 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4379]) ).

thf(4426,plain,
    ! [SV438: $i > $o,SV838: $i,SV214: $i > $o] :
      ( ( ( ! [SY3271: $i] :
              ( ~ ( SV214 @ SY3271 )
              | ( ( sK142_SY2394 @ SV838 @ SV438 @ SV214 )
                = SY3271 ) ) )
        = $true )
      | ( ( SV438 @ SV838 )
        = $false )
      | ( ( SV838
          = ( sK132_SY3238 @ SV214 @ SV838 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4380]) ).

thf(4427,plain,
    ! [SV214: $i > $o,SV832: $i,SV438: $i > $o] :
      ( ( ( SV438 @ ( sK143_SY2801 @ SV832 @ SV214 @ SV438 ) )
        = $true )
      | ( ( SV214 @ SV832 )
        = $false )
      | ( ( SV214 @ ( sK126_SY3229 @ SV438 @ SV832 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4381]) ).

thf(4428,plain,
    ! [SV214: $i > $o,SV832: $i,SV438: $i > $o] :
      ( ( ( ! [SY3272: $i] :
              ( ~ ( SV438 @ SY3272 )
              | ( ( sK143_SY2801 @ SV832 @ SV214 @ SV438 )
                = SY3272 ) ) )
        = $true )
      | ( ( SV214 @ SV832 )
        = $false )
      | ( ( SV214 @ ( sK126_SY3229 @ SV438 @ SV832 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4382]) ).

thf(4429,plain,
    ! [SV214: $i > $o,SV832: $i,SV866: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV866 )
          | ( ( sK136_SY2801 @ SV832 @ SV214 @ SV438 )
            = SV866 ) )
        = $true )
      | ( ( SV214 @ SV832 )
        = $false )
      | ( ( SV832
          = ( sK126_SY3229 @ SV438 @ SV832 @ SV214 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4384]) ).

thf(4430,plain,
    ! [SV438: $i > $o,SV833: $i,SV214: $i > $o] :
      ( ( ( SV214 @ ( sK144_SY2394 @ SV833 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ SV833 )
        = $false )
      | ( ( SV438 @ ( sK127_SY3230 @ SV214 @ SV833 @ SV438 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4385]) ).

thf(4431,plain,
    ! [SV438: $i > $o,SV833: $i,SV214: $i > $o] :
      ( ( ( ! [SY3273: $i] :
              ( ~ ( SV214 @ SY3273 )
              | ( ( sK144_SY2394 @ SV833 @ SV438 @ SV214 )
                = SY3273 ) ) )
        = $true )
      | ( ( SV438 @ SV833 )
        = $false )
      | ( ( SV438 @ ( sK127_SY3230 @ SV214 @ SV833 @ SV438 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4386]) ).

thf(4432,plain,
    ! [SV438: $i > $o,SV833: $i,SV867: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV867 )
          | ( ( sK137_SY2394 @ SV833 @ SV438 @ SV214 )
            = SV867 ) )
        = $true )
      | ( ( SV438 @ SV833 )
        = $false )
      | ( ( SV833
          = ( sK127_SY3230 @ SV214 @ SV833 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4388]) ).

thf(4433,plain,
    ! [SV821: $i,SV77: $i > $o,SV862: $i,SV315: $i > $o] :
      ( ( ( SV315 @ SV862 )
        = $false )
      | ( ( ~ ! [SY3274: $i] :
                ( ~ ( SV315 @ SY3274 )
                | ( SV862 = SY3274 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( SV77 @ ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4389]) ).

thf(4434,plain,
    ! [SV821: $i,SV77: $i > $o,SV856: $i,SV315: $i > $o] :
      ( ( ( ! [SY3264: $i] :
              ( ~ ( SV315 @ SY3264 )
              | ( SV856 = SY3264 ) ) )
        = $false )
      | ( ( SV315 @ SV856 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( SV821
          = ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4390]) ).

thf(4435,plain,
    ! [SV816: $i,SV77: $i > $o,SV857: $i,SV315: $i > $o] :
      ( ( ( ! [SY3265: $i] :
              ( ~ ( SV315 @ SY3265 )
              | ( SV857 = SY3265 ) ) )
        = $false )
      | ( ( SV315 @ SV857 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( SV77 @ ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4391]) ).

thf(4436,plain,
    ! [SV850: $i,SV77: $i > $o,SV816: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ ( sK154_SY3258 @ SV816 @ SV77 @ SV850 @ SV315 ) )
          | ( SV850
            = ( sK154_SY3258 @ SV816 @ SV77 @ SV850 @ SV315 ) ) )
        = $false )
      | ( ( SV315 @ SV850 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( SV816
          = ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[4392]) ).

thf(4437,plain,
    ! [SV817: $i,SV77: $i > $o,SV858: $i,SV315: $i > $o] :
      ( ( ( ! [SY3266: $i] :
              ( ~ ( SV315 @ SY3266 )
              | ( SV858 = SY3266 ) ) )
        = $false )
      | ( ( SV315 @ SV858 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( SV77 @ ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4393]) ).

thf(4438,plain,
    ! [SV851: $i,SV77: $i > $o,SV817: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ ( sK155_SY3259 @ SV817 @ SV77 @ SV851 @ SV315 ) )
          | ( SV851
            = ( sK155_SY3259 @ SV817 @ SV77 @ SV851 @ SV315 ) ) )
        = $false )
      | ( ( SV315 @ SV851 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( SV817
          = ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[4394]) ).

thf(4439,plain,
    ! [SV852: $i,SV77: $i > $o,SV813: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ ( sK156_SY3260 @ SV813 @ SV77 @ SV852 @ SV315 ) )
          | ( SV852
            = ( sK156_SY3260 @ SV813 @ SV77 @ SV852 @ SV315 ) ) )
        = $false )
      | ( ( SV315 @ SV852 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( SV77 @ ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[4395]) ).

thf(4440,plain,
    ! [SV849: $i,SV77: $i > $o,SV813: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ ( sK153_SY3257 @ SV813 @ SV77 @ SV849 @ SV315 ) ) )
        = $false )
      | ( ( SV315 @ SV849 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( SV813
          = ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4396]) ).

thf(4441,plain,
    ! [SV315: $i > $o,SV77: $i > $o,SV813: $i,SV849: $i] :
      ( ( ( SV849
          = ( sK153_SY3257 @ SV813 @ SV77 @ SV849 @ SV315 ) )
        = $false )
      | ( ( SV315 @ SV849 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( SV813
          = ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4396]) ).

thf(4442,plain,
    ! [SV109: $i,SV739: $i,SV822: $i] :
      ( ( ( in @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) @ ( sK3_SY2100 @ SV109 ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4397]) ).

thf(4443,plain,
    ! [SV822: $i,SV739: $i,SV109: $i] :
      ( ( ( in @ ( sK122_SY3239 @ SV109 @ SV739 @ SV822 ) @ SV739 )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4398]) ).

thf(4444,plain,
    ! [SV109: $i,SV739: $i,SV822: $i,SV868: $i] :
      ( ( ( ~ ~ ( ~ ( in @ SV868 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) )
                | ~ ( in @ SV868 @ SV739 ) ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4399]) ).

thf(4445,plain,
    ! [SV109: $i,SV739: $i,SV822: $i,SV859: $i,SV864: $i] :
      ( ( ( ~ ( in @ SV864 @ SV859 ) )
        = $true )
      | ( ( in @ SV864 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) )
        = $true )
      | ( ( in @ ( sK122_SY3239 @ SV109 @ SV739 @ SV822 ) @ SV859 )
        = $true )
      | ( ( in @ SV859 @ ( sK3_SY2100 @ SV109 ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4400]) ).

thf(4446,plain,
    ! [SV109: $i,SV739: $i,SV818: $i,SV865: $i] :
      ( ( ( ~ ( ~ ( in @ SV865 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) )
              | ~ ( in @ SV865 @ SV739 ) ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4403]) ).

thf(4447,plain,
    ! [SV109: $i,SV739: $i,SV818: $i,SV853: $i,SV863: $i] :
      ( ( ( in @ SV863 @ SV853 )
        = $false )
      | ( ( in @ SV863 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) )
        = $true )
      | ( ( in @ ( sK118_SY3231 @ SV109 @ SV739 @ SV818 ) @ SV853 )
        = $true )
      | ( ( in @ SV853 @ ( sK3_SY2100 @ SV109 ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4404]) ).

thf(4448,plain,
    ! [SV214: $i > $o,SV841: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ ( sK151_SY2801 @ SV841 @ SV214 @ SV438 ) ) )
        = $false )
      | ( ( SV214 @ SV841 )
        = $false )
      | ( ( SV214 @ ( sK133_SY3243 @ SV438 @ SV841 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4405]) ).

thf(4449,plain,
    ! [SV214: $i > $o,SV841: $i,SV438: $i > $o] :
      ( ( ( ~ ! [SY3281: $i] :
                ( ~ ( SV438 @ SY3281 )
                | ( ( sK151_SY2801 @ SV841 @ SV214 @ SV438 )
                  = SY3281 ) ) )
        = $false )
      | ( ( SV214 @ SV841 )
        = $false )
      | ( ( SV214 @ ( sK133_SY3243 @ SV438 @ SV841 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4405]) ).

thf(4450,plain,
    ! [SV214: $i > $o,SV841: $i,SV438: $i > $o] :
      ( ( ( SV438 @ ( sK145_SY2801 @ SV841 @ SV214 @ SV438 ) )
        = $true )
      | ( ( SV214 @ SV841 )
        = $false )
      | ( ( SV841
          = ( sK133_SY3243 @ SV438 @ SV841 @ SV214 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4406]) ).

thf(4451,plain,
    ! [SV214: $i > $o,SV841: $i,SV438: $i > $o] :
      ( ( ( ! [SY3275: $i] :
              ( ~ ( SV438 @ SY3275 )
              | ( ( sK145_SY2801 @ SV841 @ SV214 @ SV438 )
                = SY3275 ) ) )
        = $true )
      | ( ( SV214 @ SV841 )
        = $false )
      | ( ( SV841
          = ( sK133_SY3243 @ SV438 @ SV841 @ SV214 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4407]) ).

thf(4452,plain,
    ! [SV438: $i > $o,SV842: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ ( sK152_SY2394 @ SV842 @ SV438 @ SV214 ) ) )
        = $false )
      | ( ( SV438 @ SV842 )
        = $false )
      | ( ( SV438 @ ( sK134_SY3244 @ SV214 @ SV842 @ SV438 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4408]) ).

thf(4453,plain,
    ! [SV438: $i > $o,SV842: $i,SV214: $i > $o] :
      ( ( ( ~ ! [SY3282: $i] :
                ( ~ ( SV214 @ SY3282 )
                | ( ( sK152_SY2394 @ SV842 @ SV438 @ SV214 )
                  = SY3282 ) ) )
        = $false )
      | ( ( SV438 @ SV842 )
        = $false )
      | ( ( SV438 @ ( sK134_SY3244 @ SV214 @ SV842 @ SV438 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4408]) ).

thf(4454,plain,
    ! [SV438: $i > $o,SV842: $i,SV214: $i > $o] :
      ( ( ( SV214 @ ( sK146_SY2394 @ SV842 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ SV842 )
        = $false )
      | ( ( SV842
          = ( sK134_SY3244 @ SV214 @ SV842 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4409]) ).

thf(4455,plain,
    ! [SV438: $i > $o,SV842: $i,SV214: $i > $o] :
      ( ( ( ! [SY3276: $i] :
              ( ~ ( SV214 @ SY3276 )
              | ( ( sK146_SY2394 @ SV842 @ SV438 @ SV214 )
                = SY3276 ) ) )
        = $true )
      | ( ( SV438 @ SV842 )
        = $false )
      | ( ( SV842
          = ( sK134_SY3244 @ SV214 @ SV842 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4410]) ).

thf(4456,plain,
    ! [SV214: $i > $o,SV835: $i,SV438: $i > $o] :
      ( ( ( SV438 @ ( sK147_SY2801 @ SV835 @ SV214 @ SV438 ) )
        = $true )
      | ( ( SV214 @ SV835 )
        = $false )
      | ( ( SV214 @ ( sK129_SY3235 @ SV438 @ SV835 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4411]) ).

thf(4457,plain,
    ! [SV214: $i > $o,SV835: $i,SV438: $i > $o] :
      ( ( ( ! [SY3277: $i] :
              ( ~ ( SV438 @ SY3277 )
              | ( ( sK147_SY2801 @ SV835 @ SV214 @ SV438 )
                = SY3277 ) ) )
        = $true )
      | ( ( SV214 @ SV835 )
        = $false )
      | ( ( SV214 @ ( sK129_SY3235 @ SV438 @ SV835 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4412]) ).

thf(4458,plain,
    ! [SV214: $i > $o,SV835: $i,SV869: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV869 )
          | ( ( sK139_SY2801 @ SV835 @ SV214 @ SV438 )
            = SV869 ) )
        = $true )
      | ( ( SV214 @ SV835 )
        = $false )
      | ( ( SV835
          = ( sK129_SY3235 @ SV438 @ SV835 @ SV214 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4414]) ).

thf(4459,plain,
    ! [SV438: $i > $o,SV836: $i,SV214: $i > $o] :
      ( ( ( SV214 @ ( sK148_SY2394 @ SV836 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ SV836 )
        = $false )
      | ( ( SV438 @ ( sK130_SY3236 @ SV214 @ SV836 @ SV438 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4415]) ).

thf(4460,plain,
    ! [SV438: $i > $o,SV836: $i,SV214: $i > $o] :
      ( ( ( ! [SY3278: $i] :
              ( ~ ( SV214 @ SY3278 )
              | ( ( sK148_SY2394 @ SV836 @ SV438 @ SV214 )
                = SY3278 ) ) )
        = $true )
      | ( ( SV438 @ SV836 )
        = $false )
      | ( ( SV438 @ ( sK130_SY3236 @ SV214 @ SV836 @ SV438 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4416]) ).

thf(4461,plain,
    ! [SV438: $i > $o,SV836: $i,SV870: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV870 )
          | ( ( sK140_SY2394 @ SV836 @ SV438 @ SV214 )
            = SV870 ) )
        = $true )
      | ( ( SV438 @ SV836 )
        = $false )
      | ( ( SV836
          = ( sK130_SY3236 @ SV214 @ SV836 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4418]) ).

thf(4462,plain,
    ! [SV214: $i > $o,SV837: $i,SV438: $i > $o] :
      ( ( ( SV438 @ ( sK149_SY2801 @ SV837 @ SV214 @ SV438 ) )
        = $true )
      | ( ( SV214 @ SV837 )
        = $false )
      | ( ( SV214 @ ( sK131_SY3237 @ SV438 @ SV837 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4419]) ).

thf(4463,plain,
    ! [SV214: $i > $o,SV837: $i,SV438: $i > $o] :
      ( ( ( ! [SY3279: $i] :
              ( ~ ( SV438 @ SY3279 )
              | ( ( sK149_SY2801 @ SV837 @ SV214 @ SV438 )
                = SY3279 ) ) )
        = $true )
      | ( ( SV214 @ SV837 )
        = $false )
      | ( ( SV214 @ ( sK131_SY3237 @ SV438 @ SV837 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4420]) ).

thf(4464,plain,
    ! [SV214: $i > $o,SV837: $i,SV871: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV871 )
          | ( ( sK141_SY2801 @ SV837 @ SV214 @ SV438 )
            = SV871 ) )
        = $true )
      | ( ( SV214 @ SV837 )
        = $false )
      | ( ( SV837
          = ( sK131_SY3237 @ SV438 @ SV837 @ SV214 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[4422]) ).

thf(4465,plain,
    ! [SV438: $i > $o,SV838: $i,SV214: $i > $o] :
      ( ( ( SV214 @ ( sK150_SY2394 @ SV838 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ SV838 )
        = $false )
      | ( ( SV438 @ ( sK132_SY3238 @ SV214 @ SV838 @ SV438 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4423]) ).

thf(4466,plain,
    ! [SV438: $i > $o,SV838: $i,SV214: $i > $o] :
      ( ( ( ! [SY3280: $i] :
              ( ~ ( SV214 @ SY3280 )
              | ( ( sK150_SY2394 @ SV838 @ SV438 @ SV214 )
                = SY3280 ) ) )
        = $true )
      | ( ( SV438 @ SV838 )
        = $false )
      | ( ( SV438 @ ( sK132_SY3238 @ SV214 @ SV838 @ SV438 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4424]) ).

thf(4467,plain,
    ! [SV438: $i > $o,SV838: $i,SV872: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV872 )
          | ( ( sK142_SY2394 @ SV838 @ SV438 @ SV214 )
            = SV872 ) )
        = $true )
      | ( ( SV438 @ SV838 )
        = $false )
      | ( ( SV838
          = ( sK132_SY3238 @ SV214 @ SV838 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[4426]) ).

thf(4468,plain,
    ! [SV214: $i > $o,SV832: $i,SV873: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV873 )
          | ( ( sK143_SY2801 @ SV832 @ SV214 @ SV438 )
            = SV873 ) )
        = $true )
      | ( ( SV214 @ SV832 )
        = $false )
      | ( ( SV214 @ ( sK126_SY3229 @ SV438 @ SV832 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4428]) ).

thf(4469,plain,
    ! [SV214: $i > $o,SV832: $i,SV866: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV866 ) )
        = $true )
      | ( ( ( sK136_SY2801 @ SV832 @ SV214 @ SV438 )
          = SV866 )
        = $true )
      | ( ( SV214 @ SV832 )
        = $false )
      | ( ( SV832
          = ( sK126_SY3229 @ SV438 @ SV832 @ SV214 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4429]) ).

thf(4470,plain,
    ! [SV438: $i > $o,SV833: $i,SV874: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV874 )
          | ( ( sK144_SY2394 @ SV833 @ SV438 @ SV214 )
            = SV874 ) )
        = $true )
      | ( ( SV438 @ SV833 )
        = $false )
      | ( ( SV438 @ ( sK127_SY3230 @ SV214 @ SV833 @ SV438 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4431]) ).

thf(4471,plain,
    ! [SV438: $i > $o,SV833: $i,SV867: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV867 ) )
        = $true )
      | ( ( ( sK137_SY2394 @ SV833 @ SV438 @ SV214 )
          = SV867 )
        = $true )
      | ( ( SV438 @ SV833 )
        = $false )
      | ( ( SV833
          = ( sK127_SY3230 @ SV214 @ SV833 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4432]) ).

thf(4472,plain,
    ! [SV821: $i,SV77: $i > $o,SV862: $i,SV315: $i > $o] :
      ( ( ( ! [SY3274: $i] :
              ( ~ ( SV315 @ SY3274 )
              | ( SV862 = SY3274 ) ) )
        = $false )
      | ( ( SV315 @ SV862 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( SV77 @ ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4433]) ).

thf(4473,plain,
    ! [SV856: $i,SV77: $i > $o,SV821: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ ( sK157_SY3264 @ SV821 @ SV77 @ SV856 @ SV315 ) )
          | ( SV856
            = ( sK157_SY3264 @ SV821 @ SV77 @ SV856 @ SV315 ) ) )
        = $false )
      | ( ( SV315 @ SV856 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( SV821
          = ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[4434]) ).

thf(4474,plain,
    ! [SV857: $i,SV77: $i > $o,SV816: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ ( sK158_SY3265 @ SV816 @ SV77 @ SV857 @ SV315 ) )
          | ( SV857
            = ( sK158_SY3265 @ SV816 @ SV77 @ SV857 @ SV315 ) ) )
        = $false )
      | ( ( SV315 @ SV857 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( SV77 @ ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[4435]) ).

thf(4475,plain,
    ! [SV850: $i,SV77: $i > $o,SV816: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ ( sK154_SY3258 @ SV816 @ SV77 @ SV850 @ SV315 ) ) )
        = $false )
      | ( ( SV315 @ SV850 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( SV816
          = ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4436]) ).

thf(4476,plain,
    ! [SV315: $i > $o,SV77: $i > $o,SV816: $i,SV850: $i] :
      ( ( ( SV850
          = ( sK154_SY3258 @ SV816 @ SV77 @ SV850 @ SV315 ) )
        = $false )
      | ( ( SV315 @ SV850 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( SV816
          = ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4436]) ).

thf(4477,plain,
    ! [SV858: $i,SV77: $i > $o,SV817: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ ( sK159_SY3266 @ SV817 @ SV77 @ SV858 @ SV315 ) )
          | ( SV858
            = ( sK159_SY3266 @ SV817 @ SV77 @ SV858 @ SV315 ) ) )
        = $false )
      | ( ( SV315 @ SV858 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( SV77 @ ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[4437]) ).

thf(4478,plain,
    ! [SV851: $i,SV77: $i > $o,SV817: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ ( sK155_SY3259 @ SV817 @ SV77 @ SV851 @ SV315 ) ) )
        = $false )
      | ( ( SV315 @ SV851 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( SV817
          = ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4438]) ).

thf(4479,plain,
    ! [SV315: $i > $o,SV77: $i > $o,SV817: $i,SV851: $i] :
      ( ( ( SV851
          = ( sK155_SY3259 @ SV817 @ SV77 @ SV851 @ SV315 ) )
        = $false )
      | ( ( SV315 @ SV851 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( SV817
          = ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4438]) ).

thf(4480,plain,
    ! [SV852: $i,SV77: $i > $o,SV813: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ ( sK156_SY3260 @ SV813 @ SV77 @ SV852 @ SV315 ) ) )
        = $false )
      | ( ( SV315 @ SV852 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( SV77 @ ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4439]) ).

thf(4481,plain,
    ! [SV315: $i > $o,SV77: $i > $o,SV813: $i,SV852: $i] :
      ( ( ( SV852
          = ( sK156_SY3260 @ SV813 @ SV77 @ SV852 @ SV315 ) )
        = $false )
      | ( ( SV315 @ SV852 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( SV77 @ ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4439]) ).

thf(4482,plain,
    ! [SV849: $i,SV77: $i > $o,SV813: $i,SV315: $i > $o] :
      ( ( ( SV315 @ ( sK153_SY3257 @ SV813 @ SV77 @ SV849 @ SV315 ) )
        = $true )
      | ( ( SV315 @ SV849 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( SV813
          = ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4440]) ).

thf(4483,plain,
    ! [SV109: $i,SV739: $i,SV822: $i,SV868: $i] :
      ( ( ( ~ ( ~ ( in @ SV868 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) )
              | ~ ( in @ SV868 @ SV739 ) ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4444]) ).

thf(4484,plain,
    ! [SV109: $i,SV739: $i,SV822: $i,SV859: $i,SV864: $i] :
      ( ( ( in @ SV864 @ SV859 )
        = $false )
      | ( ( in @ SV864 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) )
        = $true )
      | ( ( in @ ( sK122_SY3239 @ SV109 @ SV739 @ SV822 ) @ SV859 )
        = $true )
      | ( ( in @ SV859 @ ( sK3_SY2100 @ SV109 ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4445]) ).

thf(4485,plain,
    ! [SV109: $i,SV739: $i,SV818: $i,SV865: $i] :
      ( ( ( ~ ( in @ SV865 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) )
          | ~ ( in @ SV865 @ SV739 ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4446]) ).

thf(4486,plain,
    ! [SV214: $i > $o,SV841: $i,SV438: $i > $o] :
      ( ( ( SV438 @ ( sK151_SY2801 @ SV841 @ SV214 @ SV438 ) )
        = $true )
      | ( ( SV214 @ SV841 )
        = $false )
      | ( ( SV214 @ ( sK133_SY3243 @ SV438 @ SV841 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4448]) ).

thf(4487,plain,
    ! [SV214: $i > $o,SV841: $i,SV438: $i > $o] :
      ( ( ( ! [SY3281: $i] :
              ( ~ ( SV438 @ SY3281 )
              | ( ( sK151_SY2801 @ SV841 @ SV214 @ SV438 )
                = SY3281 ) ) )
        = $true )
      | ( ( SV214 @ SV841 )
        = $false )
      | ( ( SV214 @ ( sK133_SY3243 @ SV438 @ SV841 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4449]) ).

thf(4488,plain,
    ! [SV214: $i > $o,SV841: $i,SV875: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV875 )
          | ( ( sK145_SY2801 @ SV841 @ SV214 @ SV438 )
            = SV875 ) )
        = $true )
      | ( ( SV214 @ SV841 )
        = $false )
      | ( ( SV841
          = ( sK133_SY3243 @ SV438 @ SV841 @ SV214 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[4451]) ).

thf(4489,plain,
    ! [SV438: $i > $o,SV842: $i,SV214: $i > $o] :
      ( ( ( SV214 @ ( sK152_SY2394 @ SV842 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ SV842 )
        = $false )
      | ( ( SV438 @ ( sK134_SY3244 @ SV214 @ SV842 @ SV438 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4452]) ).

thf(4490,plain,
    ! [SV438: $i > $o,SV842: $i,SV214: $i > $o] :
      ( ( ( ! [SY3282: $i] :
              ( ~ ( SV214 @ SY3282 )
              | ( ( sK152_SY2394 @ SV842 @ SV438 @ SV214 )
                = SY3282 ) ) )
        = $true )
      | ( ( SV438 @ SV842 )
        = $false )
      | ( ( SV438 @ ( sK134_SY3244 @ SV214 @ SV842 @ SV438 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4453]) ).

thf(4491,plain,
    ! [SV438: $i > $o,SV842: $i,SV876: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV876 )
          | ( ( sK146_SY2394 @ SV842 @ SV438 @ SV214 )
            = SV876 ) )
        = $true )
      | ( ( SV438 @ SV842 )
        = $false )
      | ( ( SV842
          = ( sK134_SY3244 @ SV214 @ SV842 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[4455]) ).

thf(4492,plain,
    ! [SV214: $i > $o,SV835: $i,SV877: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV877 )
          | ( ( sK147_SY2801 @ SV835 @ SV214 @ SV438 )
            = SV877 ) )
        = $true )
      | ( ( SV214 @ SV835 )
        = $false )
      | ( ( SV214 @ ( sK129_SY3235 @ SV438 @ SV835 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4457]) ).

thf(4493,plain,
    ! [SV214: $i > $o,SV835: $i,SV869: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV869 ) )
        = $true )
      | ( ( ( sK139_SY2801 @ SV835 @ SV214 @ SV438 )
          = SV869 )
        = $true )
      | ( ( SV214 @ SV835 )
        = $false )
      | ( ( SV835
          = ( sK129_SY3235 @ SV438 @ SV835 @ SV214 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4458]) ).

thf(4494,plain,
    ! [SV438: $i > $o,SV836: $i,SV878: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV878 )
          | ( ( sK148_SY2394 @ SV836 @ SV438 @ SV214 )
            = SV878 ) )
        = $true )
      | ( ( SV438 @ SV836 )
        = $false )
      | ( ( SV438 @ ( sK130_SY3236 @ SV214 @ SV836 @ SV438 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4460]) ).

thf(4495,plain,
    ! [SV438: $i > $o,SV836: $i,SV870: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV870 ) )
        = $true )
      | ( ( ( sK140_SY2394 @ SV836 @ SV438 @ SV214 )
          = SV870 )
        = $true )
      | ( ( SV438 @ SV836 )
        = $false )
      | ( ( SV836
          = ( sK130_SY3236 @ SV214 @ SV836 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4461]) ).

thf(4496,plain,
    ! [SV214: $i > $o,SV837: $i,SV879: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV879 )
          | ( ( sK149_SY2801 @ SV837 @ SV214 @ SV438 )
            = SV879 ) )
        = $true )
      | ( ( SV214 @ SV837 )
        = $false )
      | ( ( SV214 @ ( sK131_SY3237 @ SV438 @ SV837 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[4463]) ).

thf(4497,plain,
    ! [SV214: $i > $o,SV837: $i,SV871: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV871 ) )
        = $true )
      | ( ( ( sK141_SY2801 @ SV837 @ SV214 @ SV438 )
          = SV871 )
        = $true )
      | ( ( SV214 @ SV837 )
        = $false )
      | ( ( SV837
          = ( sK131_SY3237 @ SV438 @ SV837 @ SV214 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4464]) ).

thf(4498,plain,
    ! [SV438: $i > $o,SV838: $i,SV880: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV880 )
          | ( ( sK150_SY2394 @ SV838 @ SV438 @ SV214 )
            = SV880 ) )
        = $true )
      | ( ( SV438 @ SV838 )
        = $false )
      | ( ( SV438 @ ( sK132_SY3238 @ SV214 @ SV838 @ SV438 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[4466]) ).

thf(4499,plain,
    ! [SV438: $i > $o,SV838: $i,SV872: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV872 ) )
        = $true )
      | ( ( ( sK142_SY2394 @ SV838 @ SV438 @ SV214 )
          = SV872 )
        = $true )
      | ( ( SV438 @ SV838 )
        = $false )
      | ( ( SV838
          = ( sK132_SY3238 @ SV214 @ SV838 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4467]) ).

thf(4500,plain,
    ! [SV214: $i > $o,SV832: $i,SV873: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV873 ) )
        = $true )
      | ( ( ( sK143_SY2801 @ SV832 @ SV214 @ SV438 )
          = SV873 )
        = $true )
      | ( ( SV214 @ SV832 )
        = $false )
      | ( ( SV214 @ ( sK126_SY3229 @ SV438 @ SV832 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4468]) ).

thf(4501,plain,
    ! [SV214: $i > $o,SV832: $i,SV866: $i,SV438: $i > $o] :
      ( ( ( SV438 @ SV866 )
        = $false )
      | ( ( ( sK136_SY2801 @ SV832 @ SV214 @ SV438 )
          = SV866 )
        = $true )
      | ( ( SV214 @ SV832 )
        = $false )
      | ( ( SV832
          = ( sK126_SY3229 @ SV438 @ SV832 @ SV214 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4469]) ).

thf(4502,plain,
    ! [SV438: $i > $o,SV833: $i,SV874: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV874 ) )
        = $true )
      | ( ( ( sK144_SY2394 @ SV833 @ SV438 @ SV214 )
          = SV874 )
        = $true )
      | ( ( SV438 @ SV833 )
        = $false )
      | ( ( SV438 @ ( sK127_SY3230 @ SV214 @ SV833 @ SV438 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4470]) ).

thf(4503,plain,
    ! [SV438: $i > $o,SV833: $i,SV867: $i,SV214: $i > $o] :
      ( ( ( SV214 @ SV867 )
        = $false )
      | ( ( ( sK137_SY2394 @ SV833 @ SV438 @ SV214 )
          = SV867 )
        = $true )
      | ( ( SV438 @ SV833 )
        = $false )
      | ( ( SV833
          = ( sK127_SY3230 @ SV214 @ SV833 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4471]) ).

thf(4504,plain,
    ! [SV862: $i,SV77: $i > $o,SV821: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ ( sK160_SY3274 @ SV821 @ SV77 @ SV862 @ SV315 ) )
          | ( SV862
            = ( sK160_SY3274 @ SV821 @ SV77 @ SV862 @ SV315 ) ) )
        = $false )
      | ( ( SV315 @ SV862 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( SV77 @ ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[4472]) ).

thf(4505,plain,
    ! [SV856: $i,SV77: $i > $o,SV821: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ ( sK157_SY3264 @ SV821 @ SV77 @ SV856 @ SV315 ) ) )
        = $false )
      | ( ( SV315 @ SV856 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( SV821
          = ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4473]) ).

thf(4506,plain,
    ! [SV315: $i > $o,SV77: $i > $o,SV821: $i,SV856: $i] :
      ( ( ( SV856
          = ( sK157_SY3264 @ SV821 @ SV77 @ SV856 @ SV315 ) )
        = $false )
      | ( ( SV315 @ SV856 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( SV821
          = ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4473]) ).

thf(4507,plain,
    ! [SV857: $i,SV77: $i > $o,SV816: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ ( sK158_SY3265 @ SV816 @ SV77 @ SV857 @ SV315 ) ) )
        = $false )
      | ( ( SV315 @ SV857 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( SV77 @ ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4474]) ).

thf(4508,plain,
    ! [SV315: $i > $o,SV77: $i > $o,SV816: $i,SV857: $i] :
      ( ( ( SV857
          = ( sK158_SY3265 @ SV816 @ SV77 @ SV857 @ SV315 ) )
        = $false )
      | ( ( SV315 @ SV857 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( SV77 @ ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4474]) ).

thf(4509,plain,
    ! [SV850: $i,SV77: $i > $o,SV816: $i,SV315: $i > $o] :
      ( ( ( SV315 @ ( sK154_SY3258 @ SV816 @ SV77 @ SV850 @ SV315 ) )
        = $true )
      | ( ( SV315 @ SV850 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( SV816
          = ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4475]) ).

thf(4510,plain,
    ! [SV858: $i,SV77: $i > $o,SV817: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ ( sK159_SY3266 @ SV817 @ SV77 @ SV858 @ SV315 ) ) )
        = $false )
      | ( ( SV315 @ SV858 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( SV77 @ ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4477]) ).

thf(4511,plain,
    ! [SV315: $i > $o,SV77: $i > $o,SV817: $i,SV858: $i] :
      ( ( ( SV858
          = ( sK159_SY3266 @ SV817 @ SV77 @ SV858 @ SV315 ) )
        = $false )
      | ( ( SV315 @ SV858 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( SV77 @ ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4477]) ).

thf(4512,plain,
    ! [SV851: $i,SV77: $i > $o,SV817: $i,SV315: $i > $o] :
      ( ( ( SV315 @ ( sK155_SY3259 @ SV817 @ SV77 @ SV851 @ SV315 ) )
        = $true )
      | ( ( SV315 @ SV851 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( SV817
          = ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4478]) ).

thf(4513,plain,
    ! [SV852: $i,SV77: $i > $o,SV813: $i,SV315: $i > $o] :
      ( ( ( SV315 @ ( sK156_SY3260 @ SV813 @ SV77 @ SV852 @ SV315 ) )
        = $true )
      | ( ( SV315 @ SV852 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV813 )
        = $false )
      | ( ( SV77 @ ( sK114_SY3211 @ SV315 @ SV813 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4480]) ).

thf(4514,plain,
    ! [SV109: $i,SV739: $i,SV822: $i,SV868: $i] :
      ( ( ( ~ ( in @ SV868 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) )
          | ~ ( in @ SV868 @ SV739 ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4483]) ).

thf(4515,plain,
    ! [SV109: $i,SV739: $i,SV818: $i,SV865: $i] :
      ( ( ( ~ ( in @ SV865 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) ) )
        = $true )
      | ( ( ~ ( in @ SV865 @ SV739 ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4485]) ).

thf(4516,plain,
    ! [SV214: $i > $o,SV841: $i,SV881: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV881 )
          | ( ( sK151_SY2801 @ SV841 @ SV214 @ SV438 )
            = SV881 ) )
        = $true )
      | ( ( SV214 @ SV841 )
        = $false )
      | ( ( SV214 @ ( sK133_SY3243 @ SV438 @ SV841 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[4487]) ).

thf(4517,plain,
    ! [SV214: $i > $o,SV841: $i,SV875: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV875 ) )
        = $true )
      | ( ( ( sK145_SY2801 @ SV841 @ SV214 @ SV438 )
          = SV875 )
        = $true )
      | ( ( SV214 @ SV841 )
        = $false )
      | ( ( SV841
          = ( sK133_SY3243 @ SV438 @ SV841 @ SV214 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4488]) ).

thf(4518,plain,
    ! [SV438: $i > $o,SV842: $i,SV882: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV882 )
          | ( ( sK152_SY2394 @ SV842 @ SV438 @ SV214 )
            = SV882 ) )
        = $true )
      | ( ( SV438 @ SV842 )
        = $false )
      | ( ( SV438 @ ( sK134_SY3244 @ SV214 @ SV842 @ SV438 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[4490]) ).

thf(4519,plain,
    ! [SV438: $i > $o,SV842: $i,SV876: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV876 ) )
        = $true )
      | ( ( ( sK146_SY2394 @ SV842 @ SV438 @ SV214 )
          = SV876 )
        = $true )
      | ( ( SV438 @ SV842 )
        = $false )
      | ( ( SV842
          = ( sK134_SY3244 @ SV214 @ SV842 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4491]) ).

thf(4520,plain,
    ! [SV214: $i > $o,SV835: $i,SV877: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV877 ) )
        = $true )
      | ( ( ( sK147_SY2801 @ SV835 @ SV214 @ SV438 )
          = SV877 )
        = $true )
      | ( ( SV214 @ SV835 )
        = $false )
      | ( ( SV214 @ ( sK129_SY3235 @ SV438 @ SV835 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4492]) ).

thf(4521,plain,
    ! [SV214: $i > $o,SV835: $i,SV869: $i,SV438: $i > $o] :
      ( ( ( SV438 @ SV869 )
        = $false )
      | ( ( ( sK139_SY2801 @ SV835 @ SV214 @ SV438 )
          = SV869 )
        = $true )
      | ( ( SV214 @ SV835 )
        = $false )
      | ( ( SV835
          = ( sK129_SY3235 @ SV438 @ SV835 @ SV214 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4493]) ).

thf(4522,plain,
    ! [SV438: $i > $o,SV836: $i,SV878: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV878 ) )
        = $true )
      | ( ( ( sK148_SY2394 @ SV836 @ SV438 @ SV214 )
          = SV878 )
        = $true )
      | ( ( SV438 @ SV836 )
        = $false )
      | ( ( SV438 @ ( sK130_SY3236 @ SV214 @ SV836 @ SV438 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4494]) ).

thf(4523,plain,
    ! [SV438: $i > $o,SV836: $i,SV870: $i,SV214: $i > $o] :
      ( ( ( SV214 @ SV870 )
        = $false )
      | ( ( ( sK140_SY2394 @ SV836 @ SV438 @ SV214 )
          = SV870 )
        = $true )
      | ( ( SV438 @ SV836 )
        = $false )
      | ( ( SV836
          = ( sK130_SY3236 @ SV214 @ SV836 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4495]) ).

thf(4524,plain,
    ! [SV214: $i > $o,SV837: $i,SV879: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV879 ) )
        = $true )
      | ( ( ( sK149_SY2801 @ SV837 @ SV214 @ SV438 )
          = SV879 )
        = $true )
      | ( ( SV214 @ SV837 )
        = $false )
      | ( ( SV214 @ ( sK131_SY3237 @ SV438 @ SV837 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4496]) ).

thf(4525,plain,
    ! [SV214: $i > $o,SV837: $i,SV871: $i,SV438: $i > $o] :
      ( ( ( SV438 @ SV871 )
        = $false )
      | ( ( ( sK141_SY2801 @ SV837 @ SV214 @ SV438 )
          = SV871 )
        = $true )
      | ( ( SV214 @ SV837 )
        = $false )
      | ( ( SV837
          = ( sK131_SY3237 @ SV438 @ SV837 @ SV214 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4497]) ).

thf(4526,plain,
    ! [SV438: $i > $o,SV838: $i,SV880: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV880 ) )
        = $true )
      | ( ( ( sK150_SY2394 @ SV838 @ SV438 @ SV214 )
          = SV880 )
        = $true )
      | ( ( SV438 @ SV838 )
        = $false )
      | ( ( SV438 @ ( sK132_SY3238 @ SV214 @ SV838 @ SV438 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4498]) ).

thf(4527,plain,
    ! [SV438: $i > $o,SV838: $i,SV872: $i,SV214: $i > $o] :
      ( ( ( SV214 @ SV872 )
        = $false )
      | ( ( ( sK142_SY2394 @ SV838 @ SV438 @ SV214 )
          = SV872 )
        = $true )
      | ( ( SV438 @ SV838 )
        = $false )
      | ( ( SV838
          = ( sK132_SY3238 @ SV214 @ SV838 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4499]) ).

thf(4528,plain,
    ! [SV214: $i > $o,SV832: $i,SV873: $i,SV438: $i > $o] :
      ( ( ( SV438 @ SV873 )
        = $false )
      | ( ( ( sK143_SY2801 @ SV832 @ SV214 @ SV438 )
          = SV873 )
        = $true )
      | ( ( SV214 @ SV832 )
        = $false )
      | ( ( SV214 @ ( sK126_SY3229 @ SV438 @ SV832 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4500]) ).

thf(4529,plain,
    ! [SV438: $i > $o,SV833: $i,SV874: $i,SV214: $i > $o] :
      ( ( ( SV214 @ SV874 )
        = $false )
      | ( ( ( sK144_SY2394 @ SV833 @ SV438 @ SV214 )
          = SV874 )
        = $true )
      | ( ( SV438 @ SV833 )
        = $false )
      | ( ( SV438 @ ( sK127_SY3230 @ SV214 @ SV833 @ SV438 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4502]) ).

thf(4530,plain,
    ! [SV862: $i,SV77: $i > $o,SV821: $i,SV315: $i > $o] :
      ( ( ( ~ ( SV315 @ ( sK160_SY3274 @ SV821 @ SV77 @ SV862 @ SV315 ) ) )
        = $false )
      | ( ( SV315 @ SV862 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( SV77 @ ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4504]) ).

thf(4531,plain,
    ! [SV315: $i > $o,SV77: $i > $o,SV821: $i,SV862: $i] :
      ( ( ( SV862
          = ( sK160_SY3274 @ SV821 @ SV77 @ SV862 @ SV315 ) )
        = $false )
      | ( ( SV315 @ SV862 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( SV77 @ ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[4504]) ).

thf(4532,plain,
    ! [SV856: $i,SV77: $i > $o,SV821: $i,SV315: $i > $o] :
      ( ( ( SV315 @ ( sK157_SY3264 @ SV821 @ SV77 @ SV856 @ SV315 ) )
        = $true )
      | ( ( SV315 @ SV856 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( SV821
          = ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) )
        = $false )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4505]) ).

thf(4533,plain,
    ! [SV857: $i,SV77: $i > $o,SV816: $i,SV315: $i > $o] :
      ( ( ( SV315 @ ( sK158_SY3265 @ SV816 @ SV77 @ SV857 @ SV315 ) )
        = $true )
      | ( ( SV315 @ SV857 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV816 )
        = $false )
      | ( ( SV77 @ ( sK115_SY3216 @ SV315 @ SV816 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4507]) ).

thf(4534,plain,
    ! [SV858: $i,SV77: $i > $o,SV817: $i,SV315: $i > $o] :
      ( ( ( SV315 @ ( sK159_SY3266 @ SV817 @ SV77 @ SV858 @ SV315 ) )
        = $true )
      | ( ( SV315 @ SV858 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV817 )
        = $false )
      | ( ( SV77 @ ( sK116_SY3217 @ SV315 @ SV817 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $false )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4510]) ).

thf(4535,plain,
    ! [SV109: $i,SV739: $i,SV822: $i,SV868: $i] :
      ( ( ( ~ ( in @ SV868 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) ) )
        = $true )
      | ( ( ~ ( in @ SV868 @ SV739 ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4514]) ).

thf(4536,plain,
    ! [SV109: $i,SV739: $i,SV818: $i,SV865: $i] :
      ( ( ( in @ SV865 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) )
        = $false )
      | ( ( ~ ( in @ SV865 @ SV739 ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4515]) ).

thf(4537,plain,
    ! [SV214: $i > $o,SV841: $i,SV881: $i,SV438: $i > $o] :
      ( ( ( ~ ( SV438 @ SV881 ) )
        = $true )
      | ( ( ( sK151_SY2801 @ SV841 @ SV214 @ SV438 )
          = SV881 )
        = $true )
      | ( ( SV214 @ SV841 )
        = $false )
      | ( ( SV214 @ ( sK133_SY3243 @ SV438 @ SV841 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4516]) ).

thf(4538,plain,
    ! [SV214: $i > $o,SV841: $i,SV875: $i,SV438: $i > $o] :
      ( ( ( SV438 @ SV875 )
        = $false )
      | ( ( ( sK145_SY2801 @ SV841 @ SV214 @ SV438 )
          = SV875 )
        = $true )
      | ( ( SV214 @ SV841 )
        = $false )
      | ( ( SV841
          = ( sK133_SY3243 @ SV438 @ SV841 @ SV214 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4517]) ).

thf(4539,plain,
    ! [SV438: $i > $o,SV842: $i,SV882: $i,SV214: $i > $o] :
      ( ( ( ~ ( SV214 @ SV882 ) )
        = $true )
      | ( ( ( sK152_SY2394 @ SV842 @ SV438 @ SV214 )
          = SV882 )
        = $true )
      | ( ( SV438 @ SV842 )
        = $false )
      | ( ( SV438 @ ( sK134_SY3244 @ SV214 @ SV842 @ SV438 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4518]) ).

thf(4540,plain,
    ! [SV438: $i > $o,SV842: $i,SV876: $i,SV214: $i > $o] :
      ( ( ( SV214 @ SV876 )
        = $false )
      | ( ( ( sK146_SY2394 @ SV842 @ SV438 @ SV214 )
          = SV876 )
        = $true )
      | ( ( SV438 @ SV842 )
        = $false )
      | ( ( SV842
          = ( sK134_SY3244 @ SV214 @ SV842 @ SV438 ) )
        = $false )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4519]) ).

thf(4541,plain,
    ! [SV214: $i > $o,SV835: $i,SV877: $i,SV438: $i > $o] :
      ( ( ( SV438 @ SV877 )
        = $false )
      | ( ( ( sK147_SY2801 @ SV835 @ SV214 @ SV438 )
          = SV877 )
        = $true )
      | ( ( SV214 @ SV835 )
        = $false )
      | ( ( SV214 @ ( sK129_SY3235 @ SV438 @ SV835 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4520]) ).

thf(4542,plain,
    ! [SV438: $i > $o,SV836: $i,SV878: $i,SV214: $i > $o] :
      ( ( ( SV214 @ SV878 )
        = $false )
      | ( ( ( sK148_SY2394 @ SV836 @ SV438 @ SV214 )
          = SV878 )
        = $true )
      | ( ( SV438 @ SV836 )
        = $false )
      | ( ( SV438 @ ( sK130_SY3236 @ SV214 @ SV836 @ SV438 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4522]) ).

thf(4543,plain,
    ! [SV214: $i > $o,SV837: $i,SV879: $i,SV438: $i > $o] :
      ( ( ( SV438 @ SV879 )
        = $false )
      | ( ( ( sK149_SY2801 @ SV837 @ SV214 @ SV438 )
          = SV879 )
        = $true )
      | ( ( SV214 @ SV837 )
        = $false )
      | ( ( SV214 @ ( sK131_SY3237 @ SV438 @ SV837 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4524]) ).

thf(4544,plain,
    ! [SV438: $i > $o,SV838: $i,SV880: $i,SV214: $i > $o] :
      ( ( ( SV214 @ SV880 )
        = $false )
      | ( ( ( sK150_SY2394 @ SV838 @ SV438 @ SV214 )
          = SV880 )
        = $true )
      | ( ( SV438 @ SV838 )
        = $false )
      | ( ( SV438 @ ( sK132_SY3238 @ SV214 @ SV838 @ SV438 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $false )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4526]) ).

thf(4545,plain,
    ! [SV862: $i,SV77: $i > $o,SV821: $i,SV315: $i > $o] :
      ( ( ( SV315 @ ( sK160_SY3274 @ SV821 @ SV77 @ SV862 @ SV315 ) )
        = $true )
      | ( ( SV315 @ SV862 )
        = $false )
      | ( ( ( descr
            @ ^ [SY2005: $i] : ( SV77 @ SY2005 ) )
          = ( descr
            @ ^ [SY2579: $i] : ( SV315 @ SY2579 ) ) )
        = $true )
      | ( ( SV77 @ SV821 )
        = $false )
      | ( ( SV77 @ ( sK121_SY3223 @ SV315 @ SV821 @ SV77 ) )
        = $true )
      | ( ( SV77 @ ( sK7_SY2572 @ SV315 @ SV77 ) )
        = $true )
      | ( ( SV315 @ ( sK18_SY3065 @ SV77 @ SV315 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[4530]) ).

thf(4546,plain,
    ! [SV109: $i,SV739: $i,SV822: $i,SV868: $i] :
      ( ( ( in @ SV868 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) )
        = $false )
      | ( ( ~ ( in @ SV868 @ SV739 ) )
        = $true )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4535]) ).

thf(4547,plain,
    ! [SV109: $i,SV818: $i,SV739: $i,SV865: $i] :
      ( ( ( in @ SV865 @ SV739 )
        = $false )
      | ( ( in @ SV865 @ ( sK109_SY3156 @ SV818 @ SV739 @ SV109 ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV109 )
        = $false )
      | ( ( in @ SV818 @ SV739 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4536]) ).

thf(4548,plain,
    ! [SV214: $i > $o,SV841: $i,SV881: $i,SV438: $i > $o] :
      ( ( ( SV438 @ SV881 )
        = $false )
      | ( ( ( sK151_SY2801 @ SV841 @ SV214 @ SV438 )
          = SV881 )
        = $true )
      | ( ( SV214 @ SV841 )
        = $false )
      | ( ( SV214 @ ( sK133_SY3243 @ SV438 @ SV841 @ SV214 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4537]) ).

thf(4549,plain,
    ! [SV438: $i > $o,SV842: $i,SV882: $i,SV214: $i > $o] :
      ( ( ( SV214 @ SV882 )
        = $false )
      | ( ( ( sK152_SY2394 @ SV842 @ SV438 @ SV214 )
          = SV882 )
        = $true )
      | ( ( SV438 @ SV842 )
        = $false )
      | ( ( SV438 @ ( sK134_SY3244 @ SV214 @ SV842 @ SV438 ) )
        = $true )
      | ( ( SV214 @ ( sK17_SY2797 @ SV438 @ SV214 ) )
        = $true )
      | ( ( SV438 @ ( sK26_SY3100 @ SV214 @ SV438 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4539]) ).

thf(4550,plain,
    ! [SV109: $i,SV822: $i,SV739: $i,SV868: $i] :
      ( ( ( in @ SV868 @ SV739 )
        = $false )
      | ( ( in @ SV868 @ ( sK113_SY3156 @ SV822 @ SV739 @ SV109 ) )
        = $false )
      | ( ( in @ ( sK80_SY3154 @ SV109 @ SV739 ) @ SV739 )
        = $true )
      | ( ( in @ SV822 @ SV739 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4546]) ).

thf(4551,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[456,4550,4549,4548,4547,4545,4544,4543,4542,4541,4540,4538,4534,4533,4532,4531,4529,4528,4527,4525,4523,4521,4513,4512,4511,4509,4508,4506,4503,4501,4489,4486,4484,4482,4481,4479,4476,4465,4462,4459,4456,4454,4450,4447,4443,4442,4441,4430,4427,4425,4421,4417,4413,4402,4401,4387,4383,4357,4330,4329,4328,4321,4320,4310,4293,4291,4289,4287,4286,4279,4268,4267,4244,4243,4224,4203,4200,4163,4159,4084,4055,4043,4042,4014,4013,4011,4010,4008,4007,3990,3979,3975,3973,3970,3968,3955,3954,3948,3947,3936,3935,3934,3929,3925,3922,3911,3909,3908,3906,3895,3888,3886,3885,3880,3878,3874,3870,3869,3867,3854,3853,3844,3843,3838,3837,3822,3797,3796,3791,3785,3783,3777,3776,3774,3771,3762,3761,3760,3746,3734,3728,3724,3716,3706,3703,3702,3700,3699,3692,3689,3687,3658,3657,3656,3655,3654,3653,3643,3628,3627,3624,3622,3619,3617,3611,3581,3578,3575,3572,3564,3562,3557,3556,3545,3540,3539,3528,3526,3523,3516,3511,3496,3495,3492,3491,3490,3489,3486,3485,3484,3483,3480,3479,3478,3477,3476,3475,3474,3472,3468,3455,3437,3428,3424,3423,3420,3411,3410,3393,3392,3391,3389,3388,3384,3381,3377,3374,3370,3367,3356,3355,3354,3350,3349,3345,3339,3326,3322,3319,3318,3317,3315,3302,3284,3283,3282,3278,3270,3269,3267,3266,3264,3263,3259,3242,3241,3238,3237,3236,3234,3233,3230,3224,3190,3186,3185,3183,3182,3180,3179,3167,3160,3156,3143,3141,3140,3138,3134,3132,3125,3122,3119,3096,3087,3085,3065,3049,3046,3043,3040,3036,3028,3021,3020,3005,3004,3003,2999,2994,2993,2992,2975,2955,2953,2933,2932,2931,2929,2928,2914,2901,2900,2899,2886,2878,2877,2876,2871,2869,2868,2866,2865,2863,2860,2852,2851,2849,2848,2847,2845,2844,2831,2830,2811,2810,2806,2804,2803,2802,2800,2787,2781,2760,2757,2746,2739,2737,2736,2735,2732,2723,2722,2697,2685,2657,2656,2646,2634,2628,2606,2604,2587,2586,2585,2582,2569,2559,2558,2557,2556,2551,2549,2539,2537,2532,2531,2525,2513,2510,2508,2507,2506,2505,2504,2503,2502,2491,2490,2476,2472,2470,2467,2464,2460,2448,2447,2418,2414,2412,2411,2407,2406,2404,2394,2376,2375,2367,2341,2337,2322,2319,2318,2312,2302,2295,2288,2283,2279,2276,2265,2263,2261,2255,2254,2252,2251,2247,2245,2236,2219,2190,2188,2187,2181,2152,2126,2119,2105,2100,2099,2095,2088,2083,2064,2060,2055,2051,2020,2018,1989,1978,1977,1975,1973,1972,1929,1926,1924,1921,1920,1910,1909,1893,1890,1883,1860,1856,1850,1837,1830,1808,1786,1774,1765,1762,1760,1754,1748,1740,1726,1723,1715,1680,1679,1675,1671,1662,1660,1656,1655,1654,1653,1646,1645,1635,1630,1624,1592,1584,1583,1582,1577,1567,1566,1550,1549,1548,1530,1426,1391,1390,1389,1384,1382,1364,1328,1321,1309,1308,1307,1293,1292,1291,1041,1040,1039,1038,1037,1036,1035,1034,1033,1032,1031,1030,1029,1027,1026,1025,1024,1023,1022,1021,1020,783,782,781,778,777,775,760,759,758,522,498,460]) ).

thf(4552,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[4551]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SEU745^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04  % Command  : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.18  % Computer : n026.cluster.edu
% 0.07/0.18  % Model    : x86_64 x86_64
% 0.07/0.18  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18  % Memory   : 8046.5625MB
% 0.07/0.18  % OS       : Linux 6.8.0-71-generic
% 0.07/0.18  % CPULimit : 300
% 0.07/0.18  % WCLimit  : 300
% 0.07/0.18  % DateTime : Tue Oct  6 15:36:16 UTC 2026
% 0.07/0.18  % CPUTime  : 
% 0.07/0.18  Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 87.51/14.83  .
% 87.51/14.83  
% 87.51/14.83   No.of.Axioms: 0
% 87.51/14.83  
% 87.51/14.83   Length.of.Defs: 61289
% 87.51/14.83  
% 87.51/14.83   Contains.Choice.Funs: true
% 87.51/14.83  ..............................................................................................................................................................................................
% 87.51/14.83  
% 87.51/14.83  ********************************
% 87.51/14.83  *   All subproblems solved!    *
% 87.51/14.83  ********************************
% 87.51/14.83  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:261,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:4551,loop_count:0,foatp_calls:1,translation:fof_full)
% 87.51/14.83  
% 87.51/14.83  %**** Beginning of derivation protocol ****
% 87.51/14.83  % SZS output start CNFRefutation
% See solution above
% 87.51/14.86  
% 87.51/14.86  %**** End of derivation protocol ****
% 87.51/14.86  %**** no. of clauses in derivation: 4552 ****
% 87.51/14.86  %**** clause counter: 4551 ****
% 87.51/14.86  
% 87.51/14.86  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:261,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:4551,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------