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

%------------------------------------------------------------------------------
% File     : LEO-II---2.3.1
% Problem  : SEU741^1 : 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 : n008.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 10:47:17 AM UTC 2026

% Result   : Theorem 71.41s 12.29s
% Output   : CNFRefutation 12.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   38
%            Number of leaves      :  262
% Syntax   : Number of formulae    : 4326 (1792 unt;   0 typ; 261 def)
%            Number of atoms       : 35531 (13073 equ;   0 cnn)
%            Maximal formula atoms :  263 (   8 avg)
%            Number of connectives : 84992 (12747   ~;13002   |; 450   &;56486   @)
%                                         (  42 <=>;2265  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  271 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  : 1939 (1939   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  396 ( 393 usr; 266 con; 0-4 aty)
%            Number of variables   : 16565 (1129   ^;15305   !; 131   ?;16565   :)

% 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_inCongP,type,
    inCongP: $o ).

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

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

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

thf(tp_infuncsetfunc,type,
    infuncsetfunc: $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_sK10_B,type,
    sK10_B: $i > ( $i > $i > $o ) > $i ).

thf(tp_sK11_Xy,type,
    sK11_Xy: $i > $i > ( $i > $i > $o ) > $i ).

thf(tp_sK12_SY24,type,
    sK12_SY24: $i > ( $i > $i > $o ) > $i ).

thf(tp_sK13_SY1837,type,
    sK13_SY1837: $i > $i > ( $i > $i > $o ) > $i ).

thf(tp_sK14_B,type,
    sK14_B: $i > $i ).

thf(tp_sK15_B,type,
    sK15_B: $i > $i ).

thf(tp_sK16_SY1855,type,
    sK16_SY1855: $i > $i > $i > $i ).

thf(tp_sK17_SY1842,type,
    sK17_SY1842: $i > $i > $i ).

thf(tp_sK18_SY1856,type,
    sK18_SY1856: $i > $i > $i ).

thf(tp_sK19_Xx,type,
    sK19_Xx: $i > $i > $i ).

thf(tp_sK1_A,type,
    sK1_A: $i ).

thf(tp_sK20_SY57,type,
    sK20_SY57: $i > ( $i > $o ) > $i ).

thf(tp_sK21_Xx,type,
    sK21_Xx: ( $i > $o ) > $i ).

thf(tp_sK22_SY74,type,
    sK22_SY74: $i > ( $i > $o ) > $i ).

thf(tp_sK23_Xx,type,
    sK23_Xx: ( $i > $o ) > $i ).

thf(tp_sK24_SY86,type,
    sK24_SY86: $i > ( $i > $o ) > $i ).

thf(tp_sK25_Xx,type,
    sK25_Xx: $i > $i > $i ).

thf(tp_sK26_Xx,type,
    sK26_Xx: $i > $i > $i ).

thf(tp_sK27_Xx,type,
    sK27_Xx: $i > $i ).

thf(tp_sK28_Xx,type,
    sK28_Xx: $i > $i ).

thf(tp_sK29_Xx,type,
    sK29_Xx: $i > $i ).

thf(tp_sK2_SY1822,type,
    sK2_SY1822: $i ).

thf(tp_sK30_Xx,type,
    sK30_Xx: $i > $i > $i ).

thf(tp_sK31_B,type,
    sK31_B: $o > $i > $i > $i ).

thf(tp_sK32_Xx,type,
    sK32_Xx: ( $i > $o ) > $i ).

thf(tp_sK33_SY142,type,
    sK33_SY142: $i > ( $i > $o ) > $i ).

thf(tp_sK34_Xx,type,
    sK34_Xx: $i > $i ).

thf(tp_sK35_Xx,type,
    sK35_Xx: ( $i > $o ) > $i > $i ).

thf(tp_sK36_Xx,type,
    sK36_Xx: ( $i > $o ) > $i > $i ).

thf(tp_sK37_Xx,type,
    sK37_Xx: ( $i > $o ) > $i > $i ).

thf(tp_sK38_Xx,type,
    sK38_Xx: ( $i > $o ) > $i > $i ).

thf(tp_sK39_Xx,type,
    sK39_Xx: ( $i > $o ) > $i > $i ).

thf(tp_sK3_SY1826,type,
    sK3_SY1826: $i ).

thf(tp_sK40_Xx,type,
    sK40_Xx: ( $i > $o ) > $i > $i ).

thf(tp_sK41_SY198,type,
    sK41_SY198: ( $i > $o ) > $i ).

thf(tp_sK42_Xy,type,
    sK42_Xy: $i > ( $i > $o ) > $i ).

thf(tp_sK43_SY205,type,
    sK43_SY205: ( $i > $o ) > $i ).

thf(tp_sK44_Xx,type,
    sK44_Xx: ( $i > $o ) > $i ).

thf(tp_sK45_SY1868,type,
    sK45_SY1868: ( $i > $o ) > $i ).

thf(tp_sK46_SY211,type,
    sK46_SY211: ( $i > $o ) > $i ).

thf(tp_sK47_Xy,type,
    sK47_Xy: $i > ( $i > $o ) > $i ).

thf(tp_sK48_SY224,type,
    sK48_SY224: $i > ( $i > $o ) > $i ).

thf(tp_sK49_SY232,type,
    sK49_SY232: ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK4_SY1829,type,
    sK4_SY1829: $i ).

thf(tp_sK50_SY236,type,
    sK50_SY236: $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK51_Xx,type,
    sK51_Xx: ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK52_SY1871,type,
    sK52_SY1871: ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK53_SY235,type,
    sK53_SY235: ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK54_SY233,type,
    sK54_SY233: $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK55_Xx,type,
    sK55_Xx: ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK56_SY1873,type,
    sK56_SY1873: ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK57_SY248,type,
    sK57_SY248: $i > ( $i > $o ) > $i ).

thf(tp_sK58_SY260,type,
    sK58_SY260: $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK59_SY257,type,
    sK59_SY257: $i > ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK5_SY1831,type,
    sK5_SY1831: $i ).

thf(tp_sK60_Xx,type,
    sK60_Xx: ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK61_SY1874,type,
    sK61_SY1874: ( $i > $o ) > ( $i > $o ) > $i ).

thf(tp_sK62_Xx,type,
    sK62_Xx: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).

thf(tp_sK63_SY1875,type,
    sK63_SY1875: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).

thf(tp_sK64_Xx,type,
    sK64_Xx: $i > $i > $i ).

thf(tp_sK65_Xx,type,
    sK65_Xx: $i > $i > $i ).

thf(tp_sK66_Xx,type,
    sK66_Xx: $i > $i > $i ).

thf(tp_sK67_Xx,type,
    sK67_Xx: $i > $i > $i > $i ).

thf(tp_sK68_SY1876,type,
    sK68_SY1876: $i > $i > $i > $i ).

thf(tp_sK69_X,type,
    sK69_X: $i > $i > $i ).

thf(tp_sK6_Xx,type,
    sK6_Xx: $i > $i > $i ).

thf(tp_sK70_Xx,type,
    sK70_Xx: ( $i > $o ) > $i > $i ).

thf(tp_sK71_SY1877,type,
    sK71_SY1877: ( $i > $o ) > $i > $i ).

thf(tp_sK72_Xx,type,
    sK72_Xx: ( $i > $o ) > $i > $i ).

thf(tp_sK73_Xy,type,
    sK73_Xy: $i > ( $i > $o ) > $i > $i ).

thf(tp_sK74_Xx,type,
    sK74_Xx: ( $i > $o ) > $i > $i ).

thf(tp_sK75_SY1878,type,
    sK75_SY1878: ( $i > $o ) > $i > $i ).

thf(tp_sK76_Xx,type,
    sK76_Xx: ( $i > $i ) > $i > $i > $i ).

thf(tp_sK77_Xx,type,
    sK77_Xx: ( $i > $i ) > $i > $i > $i ).

thf(tp_sK78_Xx,type,
    sK78_Xx: ( $i > $i ) > $i > $i > $i ).

thf(tp_sK79_Xx,type,
    sK79_Xx: ( $i > $o ) > $i > $i > $i > $i ).

thf(tp_sK7_Xx,type,
    sK7_Xx: $i > $i > $i ).

thf(tp_sK80_SY1879,type,
    sK80_SY1879: ( $i > $o ) > $i > $i > $i > $i ).

thf(tp_sK81_Xx,type,
    sK81_Xx: ( $i > $o ) > $i > $i > $i > $i ).

thf(tp_sK82_SY1880,type,
    sK82_SY1880: ( $i > $o ) > $i > $i > $i > $i ).

thf(tp_sK83_Xx,type,
    sK83_Xx: $i > $i > $i > $i > $i ).

thf(tp_sK84_Xx,type,
    sK84_Xx: $i > $i > $i > $i > $i ).

thf(tp_sK85_SY1881,type,
    sK85_SY1881: $i > $i > $i > $i > $i ).

thf(tp_sK86_Xx,type,
    sK86_Xx: $i > $i > $i > $i > $i ).

thf(tp_sK87_SY1882,type,
    sK87_SY1882: $i > $i > $i > $i > $i ).

thf(tp_sK88_Xx,type,
    sK88_Xx: $i > $i > $i > $i > $i ).

thf(tp_sK89_SY1883,type,
    sK89_SY1883: $i > $i > $i > $i > $i ).

thf(tp_sK8_B,type,
    sK8_B: $i > $i > $i ).

thf(tp_sK90_Xx,type,
    sK90_Xx: $i > $i > $i > $i > $i ).

thf(tp_sK91_Xx,type,
    sK91_Xx: $i > $i > $i > $i > $i ).

thf(tp_sK92_Xx,type,
    sK92_Xx: ( $i > $i ) > $i > $i > $i ).

thf(tp_sK93_Xx,type,
    sK93_Xx: ( $i > $i ) > $i > $i > $i ).

thf(tp_sK94_Xx,type,
    sK94_Xx: ( $i > $i ) > $i > $i > $i ).

thf(tp_sK95_Xx,type,
    sK95_Xx: $i > $i > $i > $i ).

thf(tp_sK96_Xx,type,
    sK96_Xx: $i > $i > $i > $i ).

thf(tp_sK97_Xx,type,
    sK97_Xx: $i > $i > $i > $i ).

thf(tp_sK98_Xx,type,
    sK98_Xx: $i > $i > $i > $i ).

thf(tp_sK9_Xx,type,
    sK9_Xx: $i > $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(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(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(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(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
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [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(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
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
    = $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 ) ) )
                   => ( ! [SY22: $i > $i > $o,SY23: $i] :
                          ( ! [SY24: $i] :
                              ( ( in @ SY24 @ SY23 )
                             => ? [SY26: $i] :
                                  ( ( SY22 @ SY24 @ SY26 )
                                  & ! [SY27: $i] :
                                      ( ( SY22 @ SY24 @ SY27 )
                                     => ( SY26 = SY27 ) ) ) )
                         => ? [B: $i] :
                            ! [Xx: $i] :
                              ( ( in @ Xx @ B )
                            <=> ? [Xy: $i] :
                                  ( ( in @ Xy @ SY23 )
                                  & ( SY22 @ 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 ) ) ) ) ) )
                         => ( ! [SY54: $i > $o] :
                                ( ? [SY56: $i] :
                                    ( ( SY54 @ SY56 )
                                    & ! [SY57: $i] :
                                        ( ( SY54 @ SY57 )
                                       => ( SY56 = SY57 ) ) )
                               => ( SY54
                                  @ ( descr
                                    @ ^ [Xx: $i] : ( SY54 @ 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 ) )
                                 => ( ! [SY71: $i > $o] :
                                        ( ? [SY73: $i] :
                                            ( ( SY71 @ SY73 )
                                            & ! [SY74: $i] :
                                                ( ( SY71 @ SY74 )
                                               => ( SY73 = SY74 ) ) )
                                       => ? [Xx: $i] :
                                            ( ( SY71 @ Xx )
                                            & ! [Xy: $i] :
                                                ( ( SY71 @ 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 )
                                           => ( ! [SY83: $i > $o] :
                                                  ( ? [SY85: $i] :
                                                      ( ( SY83 @ SY85 )
                                                      & ! [SY86: $i] :
                                                          ( ( SY83 @ SY86 )
                                                         => ( SY85 = SY86 ) ) )
                                                 => ? [Xx: $i] : ( SY83 @ 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 ) ) )
                                                     => ( ! [SY100: $i] :
                                                            ( ( SY100 != emptyset )
                                                           => ? [Xx: $i] : ( in @ Xx @ SY100 ) )
                                                       => ( ! [SY102: $i,SY103: $i > $o,SY104: $i] :
                                                              ( ( in @ SY104 @ SY102 )
                                                             => ( ( SY103 @ SY104 )
                                                               => ( ( dsetconstr @ SY102
                                                                    @ ^ [Xy: $i] : ( SY103 @ Xy ) )
                                                                 != emptyset ) ) )
                                                         => ( ! [SY106: $i] :
                                                                ( ? [Xx: $i] : ( in @ Xx @ SY106 )
                                                               => ( SY106 != 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 ) ) ) )
                                                                                     => ( ! [SY139: $i > $o] :
                                                                                            ( ? [SY141: $i] :
                                                                                                ( ( SY139 @ SY141 )
                                                                                                & ! [SY142: $i] :
                                                                                                    ( ( SY139 @ SY142 )
                                                                                                   => ( SY141 = SY142 ) ) )
                                                                                           => ? [Xx: $i] :
                                                                                              ! [Xy: $i] :
                                                                                                ( ( SY139 @ Xy )
                                                                                              <=> ( Xy = Xx ) ) )
                                                                                       => ( ! [SY145: $i] :
                                                                                              ( ( SY145 != emptyset )
                                                                                             => ? [Xx: $i] :
                                                                                                  ( ( in @ Xx @ SY145 )
                                                                                                  & $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 ) ) )
                                                                                                                           => ( ! [SY194: $i > $o] :
                                                                                                                                  ( ? [Xx: $i] :
                                                                                                                                      ( ( SY194 @ Xx )
                                                                                                                                      & ! [Xy: $i] :
                                                                                                                                          ( ( SY194 @ Xy )
                                                                                                                                         => ( Xx = Xy ) ) )
                                                                                                                                 => ? [SY198: $i] :
                                                                                                                                      ( ( SY194 @ SY198 )
                                                                                                                                      & ! [SY199: $i] :
                                                                                                                                          ( ( SY194 @ SY199 )
                                                                                                                                         => ( SY198 = SY199 ) ) ) )
                                                                                                                             => ( ! [SY200: $i > $o] :
                                                                                                                                    ( ? [Xx: $i] : ( SY200 @ Xx )
                                                                                                                                   => ( ! [Xx: $i,Xy: $i] :
                                                                                                                                          ( ( SY200 @ Xx )
                                                                                                                                         => ( ( SY200 @ Xy )
                                                                                                                                           => ( Xx = Xy ) ) )
                                                                                                                                     => ? [SY205: $i] :
                                                                                                                                          ( ( SY200 @ SY205 )
                                                                                                                                          & ! [SY206: $i] :
                                                                                                                                              ( ( SY200 @ SY206 )
                                                                                                                                             => ( SY205 = SY206 ) ) ) ) )
                                                                                                                               => ( ! [SY207: $i > $o] :
                                                                                                                                      ( ? [Xx: $i] :
                                                                                                                                        ! [Xy: $i] :
                                                                                                                                          ( ( SY207 @ Xy )
                                                                                                                                        <=> ( Xy = Xx ) )
                                                                                                                                     => ? [SY211: $i] :
                                                                                                                                          ( ( SY207 @ SY211 )
                                                                                                                                          & ! [SY212: $i] :
                                                                                                                                              ( ( SY207 @ SY212 )
                                                                                                                                             => ( SY211 = SY212 ) ) ) )
                                                                                                                                 => ( ! [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 ) ) ) )
                                                                                                                                     => ( ! [SY221: $i > $o] :
                                                                                                                                            ( ? [SY223: $i] :
                                                                                                                                                ( ( SY221 @ SY223 )
                                                                                                                                                & ! [SY224: $i] :
                                                                                                                                                    ( ( SY221 @ SY224 )
                                                                                                                                                   => ( SY223 = SY224 ) ) )
                                                                                                                                           => ! [Xx: $i,Xy: $i] :
                                                                                                                                                ( ( SY221 @ Xx )
                                                                                                                                               => ( ( SY221 @ Xy )
                                                                                                                                                 => ( Xx = Xy ) ) ) )
                                                                                                                                       => ( ! [SY227: $i > $o,SY228: $i > $o] :
                                                                                                                                              ( ! [Xx: $i,Xy: $i] :
                                                                                                                                                  ( ( Xx = Xy )
                                                                                                                                                 => ( ( SY227 @ Xx )
                                                                                                                                                  <=> ( SY228 @ Xy ) ) )
                                                                                                                                             => ( ? [SY232: $i] :
                                                                                                                                                    ( ( SY227 @ SY232 )
                                                                                                                                                    & ! [SY233: $i] :
                                                                                                                                                        ( ( SY227 @ SY233 )
                                                                                                                                                       => ( SY232 = SY233 ) ) )
                                                                                                                                              <=> ? [SY235: $i] :
                                                                                                                                                    ( ( SY228 @ SY235 )
                                                                                                                                                    & ! [SY236: $i] :
                                                                                                                                                        ( ( SY228 @ SY236 )
                                                                                                                                                       => ( SY235 = SY236 ) ) ) ) )
                                                                                                                                         => ( ( 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 )
                                                                                                                                                   => ( ! [SY245: $i > $o] :
                                                                                                                                                          ( ? [SY247: $i] :
                                                                                                                                                              ( ( SY245 @ SY247 )
                                                                                                                                                              & ! [SY248: $i] :
                                                                                                                                                                  ( ( SY245 @ SY248 )
                                                                                                                                                                 => ( SY247 = SY248 ) ) )
                                                                                                                                                         => ! [Xx: $i,Xy: $i] :
                                                                                                                                                              ( ( SY245 @ Xx )
                                                                                                                                                             => ( ( SY245 @ Xy )
                                                                                                                                                               => ( Xx = Xy ) ) ) )
                                                                                                                                                     => ( ! [SY251: $i > $o,SY252: $i > $o] :
                                                                                                                                                            ( ! [Xx: $i,Xy: $i] :
                                                                                                                                                                ( ( Xx = Xy )
                                                                                                                                                               => ( ( SY251 @ Xx )
                                                                                                                                                                <=> ( SY252 @ Xy ) ) )
                                                                                                                                                           => ( ? [SY256: $i] :
                                                                                                                                                                  ( ( SY251 @ SY256 )
                                                                                                                                                                  & ! [SY257: $i] :
                                                                                                                                                                      ( ( SY251 @ SY257 )
                                                                                                                                                                     => ( SY256 = SY257 ) ) )
                                                                                                                                                             => ( ? [SY259: $i] :
                                                                                                                                                                    ( ( SY252 @ SY259 )
                                                                                                                                                                    & ! [SY260: $i] :
                                                                                                                                                                        ( ( SY252 @ SY260 )
                                                                                                                                                                       => ( SY259 = SY260 ) ) )
                                                                                                                                                               => ( ( descr
                                                                                                                                                                    @ ^ [Xx: $i] : ( SY251 @ Xx ) )
                                                                                                                                                                  = ( descr
                                                                                                                                                                    @ ^ [Xx: $i] : ( SY252 @ 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 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                       => ( ! [SY479: $i,SY480: $i > $o] :
                                                                                                                                                                                                                                                                                                                              ( ( singleton
                                                                                                                                                                                                                                                                                                                                @ ( dsetconstr @ SY479
                                                                                                                                                                                                                                                                                                                                  @ ^ [SY484: $i] : ( SY480 @ SY484 ) ) )
                                                                                                                                                                                                                                                                                                                             => ? [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( in @ Xx @ SY479 )
                                                                                                                                                                                                                                                                                                                                  & ( SY480 @ Xx ) ) )
                                                                                                                                                                                                                                                                                                                         => ( ! [SY486: $i,SY487: $i > $o,SY488: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( in @ SY488 @ SY486 )
                                                                                                                                                                                                                                                                                                                               => ( ( SY487 @ SY488 )
                                                                                                                                                                                                                                                                                                                                 => ( ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( in @ Xy @ SY486 )
                                                                                                                                                                                                                                                                                                                                       => ( ( SY487 @ Xy )
                                                                                                                                                                                                                                                                                                                                         => ( Xy = SY488 ) ) )
                                                                                                                                                                                                                                                                                                                                   => ( singleton
                                                                                                                                                                                                                                                                                                                                      @ ( dsetconstr @ SY486
                                                                                                                                                                                                                                                                                                                                        @ ^ [SY493: $i] : ( SY487 @ SY493 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                                           => ( ! [SY494: $i,SY495: $i > $o] :
                                                                                                                                                                                                                                                                                                                                  ( ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                      ( ( in @ Xx @ SY494 )
                                                                                                                                                                                                                                                                                                                                     => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                          ( ( in @ Xy @ SY494 )
                                                                                                                                                                                                                                                                                                                                         => ( ( SY495 @ Xx )
                                                                                                                                                                                                                                                                                                                                           => ( ( SY495 @ Xy )
                                                                                                                                                                                                                                                                                                                                             => ( Xx = Xy ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                 => ( ? [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( in @ Xx @ SY494 )
                                                                                                                                                                                                                                                                                                                                        & ( SY495 @ Xx ) )
                                                                                                                                                                                                                                                                                                                                   => ( singleton
                                                                                                                                                                                                                                                                                                                                      @ ( dsetconstr @ SY494
                                                                                                                                                                                                                                                                                                                                        @ ^ [SY502: $i] : ( SY495 @ SY502 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                             => ( ! [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 ) )
                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [SY586: $i,SY587: $i,SY588: $i > $i > $o] :
                                                                                                                                                                                                                                                                                                                                                                                        ( subset
                                                                                                                                                                                                                                                                                                                                                                                        @ ( dpsetconstr @ SY586 @ SY587
                                                                                                                                                                                                                                                                                                                                                                                          @ ^ [Xx: $i,Xy: $i] : ( SY588 @ Xx @ Xy ) )
                                                                                                                                                                                                                                                                                                                                                                                        @ ( cartprod @ SY586 @ SY587 ) )
                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [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 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [SY662: $i,SY663: $i,SY664: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( subset @ SY664 @ ( cartprod @ SY662 @ SY663 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [Xphi: $i > $o] :
                                                                                                                                                                                                                                                                                                                                                                                                                        ( ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ Xx @ SY662 )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ Xy @ SY663 )
                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( in @ ( kpair @ Xx @ Xy ) @ SY664 )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ Xx @ SY664 )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ( Xphi @ Xx ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [SY672: $i,SY673: $i,SY674: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( subset @ SY674 @ ( cartprod @ SY672 @ SY673 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [Xphi: $i > $o] :
                                                                                                                                                                                                                                                                                                                                                                                                                          ( ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ Xx @ SY672 )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ Xy @ SY673 )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( in @ ( kpair @ Xx @ Xy ) @ SY674 )
                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ Xx @ SY674 )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ( Xphi @ Xx ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [SY682: $i,SY683: $i > $o] :
                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( singleton
                                                                                                                                                                                                                                                                                                                                                                                                                          @ ( dsetconstr @ SY682
                                                                                                                                                                                                                                                                                                                                                                                                                            @ ^ [SY687: $i] : ( SY683 @ SY687 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ Xx @ SY682 )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ Xy @ SY682 )
                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ( SY683 @ Xx )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( SY683 @ 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 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [SY715: $i,SY716: $i,SY717: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( subset @ SY717 @ ( cartprod @ SY715 @ SY716 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [SY721: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( subset @ SY721 @ ( cartprod @ SY715 @ SY716 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ Xx @ SY715 )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ Xy @ SY716 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ( in @ ( kpair @ Xx @ Xy ) @ SY717 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( in @ ( kpair @ Xx @ Xy ) @ SY721 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( subset @ SY717 @ SY721 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [SY727: $i,SY728: $i,SY729: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( subset @ SY729 @ ( cartprod @ SY727 @ SY728 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [SY733: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( subset @ SY733 @ ( cartprod @ SY727 @ SY728 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                         => ( ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ Xx @ SY727 )
                                                                                                                                                                                                                                                                                                                                                                                                                                               => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                    ( ( in @ Xy @ SY728 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ( in @ ( kpair @ Xx @ Xy ) @ SY729 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( in @ ( kpair @ Xx @ Xy ) @ SY733 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                           => ( ! [Xx: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                  ( ( in @ Xx @ SY727 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                 => ! [Xy: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ Xy @ SY728 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                     => ( ( in @ ( kpair @ Xx @ Xy ) @ SY733 )
                                                                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ ( kpair @ Xx @ Xy ) @ SY729 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                             => ( SY729 = SY733 ) ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
    = $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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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,
    ( ( ! [SY22: $i > $i > $o,SY23: $i] :
          ( ! [SY24: $i] :
              ( ( in @ SY24 @ SY23 )
             => ? [SY26: $i] :
                  ( ( SY22 @ SY24 @ SY26 )
                  & ! [SY27: $i] :
                      ( ( SY22 @ SY24 @ SY27 )
                     => ( SY26 = SY27 ) ) ) )
         => ? [B: $i] :
            ! [Xx: $i] :
              ( ( in @ Xx @ B )
            <=> ? [Xy: $i] :
                  ( ( in @ Xy @ SY23 )
                  & ( SY22 @ 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,
    ( ( ! [SY54: $i > $o] :
          ( ? [SY56: $i] :
              ( ( SY54 @ SY56 )
              & ! [SY57: $i] :
                  ( ( SY54 @ SY57 )
                 => ( SY56 = SY57 ) ) )
         => ( SY54
            @ ( descr
              @ ^ [Xx: $i] : ( SY54 @ 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,
    ( ( ! [SY71: $i > $o] :
          ( ? [SY73: $i] :
              ( ( SY71 @ SY73 )
              & ! [SY74: $i] :
                  ( ( SY71 @ SY74 )
                 => ( SY73 = SY74 ) ) )
         => ? [Xx: $i] :
              ( ( SY71 @ Xx )
              & ! [Xy: $i] :
                  ( ( SY71 @ 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,
    ( ( ! [SY83: $i > $o] :
          ( ? [SY85: $i] :
              ( ( SY83 @ SY85 )
              & ! [SY86: $i] :
                  ( ( SY83 @ SY86 )
                 => ( SY85 = SY86 ) ) )
         => ? [Xx: $i] : ( SY83 @ 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,
    ( ( ! [SY100: $i] :
          ( ( SY100 != emptyset )
         => ? [Xx: $i] : ( in @ Xx @ SY100 ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(30,plain,
    ( ( ! [SY102: $i,SY103: $i > $o,SY104: $i] :
          ( ( in @ SY104 @ SY102 )
         => ( ( SY103 @ SY104 )
           => ( ( dsetconstr @ SY102
                @ ^ [Xy: $i] : ( SY103 @ Xy ) )
             != emptyset ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(31,plain,
    ( ( ! [SY106: $i] :
          ( ? [Xx: $i] : ( in @ Xx @ SY106 )
         => ( SY106 != 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,
    ( ( ! [SY139: $i > $o] :
          ( ? [SY141: $i] :
              ( ( SY139 @ SY141 )
              & ! [SY142: $i] :
                  ( ( SY139 @ SY142 )
                 => ( SY141 = SY142 ) ) )
         => ? [Xx: $i] :
            ! [Xy: $i] :
              ( ( SY139 @ Xy )
            <=> ( Xy = Xx ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(46,plain,
    ( ( ! [SY145: $i] :
          ( ( SY145 != emptyset )
         => ? [Xx: $i] :
              ( ( in @ Xx @ SY145 )
              & $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,
    ( ( ! [SY194: $i > $o] :
          ( ? [Xx: $i] :
              ( ( SY194 @ Xx )
              & ! [Xy: $i] :
                  ( ( SY194 @ Xy )
                 => ( Xx = Xy ) ) )
         => ? [SY198: $i] :
              ( ( SY194 @ SY198 )
              & ! [SY199: $i] :
                  ( ( SY194 @ SY199 )
                 => ( SY198 = SY199 ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(65,plain,
    ( ( ! [SY200: $i > $o] :
          ( ? [Xx: $i] : ( SY200 @ Xx )
         => ( ! [Xx: $i,Xy: $i] :
                ( ( SY200 @ Xx )
               => ( ( SY200 @ Xy )
                 => ( Xx = Xy ) ) )
           => ? [SY205: $i] :
                ( ( SY200 @ SY205 )
                & ! [SY206: $i] :
                    ( ( SY200 @ SY206 )
                   => ( SY205 = SY206 ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(66,plain,
    ( ( ! [SY207: $i > $o] :
          ( ? [Xx: $i] :
            ! [Xy: $i] :
              ( ( SY207 @ Xy )
            <=> ( Xy = Xx ) )
         => ? [SY211: $i] :
              ( ( SY207 @ SY211 )
              & ! [SY212: $i] :
                  ( ( SY207 @ SY212 )
                 => ( SY211 = SY212 ) ) ) ) )
    = $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,
    ( ( ! [SY221: $i > $o] :
          ( ? [SY223: $i] :
              ( ( SY221 @ SY223 )
              & ! [SY224: $i] :
                  ( ( SY221 @ SY224 )
                 => ( SY223 = SY224 ) ) )
         => ! [Xx: $i,Xy: $i] :
              ( ( SY221 @ Xx )
             => ( ( SY221 @ Xy )
               => ( Xx = Xy ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(70,plain,
    ( ( ! [SY227: $i > $o,SY228: $i > $o] :
          ( ! [Xx: $i,Xy: $i] :
              ( ( Xx = Xy )
             => ( ( SY227 @ Xx )
              <=> ( SY228 @ Xy ) ) )
         => ( ? [SY232: $i] :
                ( ( SY227 @ SY232 )
                & ! [SY233: $i] :
                    ( ( SY227 @ SY233 )
                   => ( SY232 = SY233 ) ) )
          <=> ? [SY235: $i] :
                ( ( SY228 @ SY235 )
                & ! [SY236: $i] :
                    ( ( SY228 @ SY236 )
                   => ( SY235 = SY236 ) ) ) ) ) )
    = $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,
    ( ( ! [SY245: $i > $o] :
          ( ? [SY247: $i] :
              ( ( SY245 @ SY247 )
              & ! [SY248: $i] :
                  ( ( SY245 @ SY248 )
                 => ( SY247 = SY248 ) ) )
         => ! [Xx: $i,Xy: $i] :
              ( ( SY245 @ Xx )
             => ( ( SY245 @ Xy )
               => ( Xx = Xy ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(77,plain,
    ( ( ! [SY251: $i > $o,SY252: $i > $o] :
          ( ! [Xx: $i,Xy: $i] :
              ( ( Xx = Xy )
             => ( ( SY251 @ Xx )
              <=> ( SY252 @ Xy ) ) )
         => ( ? [SY256: $i] :
                ( ( SY251 @ SY256 )
                & ! [SY257: $i] :
                    ( ( SY251 @ SY257 )
                   => ( SY256 = SY257 ) ) )
           => ( ? [SY259: $i] :
                  ( ( SY252 @ SY259 )
                  & ! [SY260: $i] :
                      ( ( SY252 @ SY260 )
                     => ( SY259 = SY260 ) ) )
             => ( ( descr
                  @ ^ [Xx: $i] : ( SY251 @ Xx ) )
                = ( descr
                  @ ^ [Xx: $i] : ( SY252 @ 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,
    ( ( ! [SY479: $i,SY480: $i > $o] :
          ( ( singleton
            @ ( dsetconstr @ SY479
              @ ^ [SY484: $i] : ( SY480 @ SY484 ) ) )
         => ? [Xx: $i] :
              ( ( in @ Xx @ SY479 )
              & ( SY480 @ Xx ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(159,plain,
    ( ( ! [SY486: $i,SY487: $i > $o,SY488: $i] :
          ( ( in @ SY488 @ SY486 )
         => ( ( SY487 @ SY488 )
           => ( ! [Xy: $i] :
                  ( ( in @ Xy @ SY486 )
                 => ( ( SY487 @ Xy )
                   => ( Xy = SY488 ) ) )
             => ( singleton
                @ ( dsetconstr @ SY486
                  @ ^ [SY493: $i] : ( SY487 @ SY493 ) ) ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(160,plain,
    ( ( ! [SY494: $i,SY495: $i > $o] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ SY494 )
             => ! [Xy: $i] :
                  ( ( in @ Xy @ SY494 )
                 => ( ( SY495 @ Xx )
                   => ( ( SY495 @ Xy )
                     => ( Xx = Xy ) ) ) ) )
         => ( ? [Xx: $i] :
                ( ( in @ Xx @ SY494 )
                & ( SY495 @ Xx ) )
           => ( singleton
              @ ( dsetconstr @ SY494
                @ ^ [SY502: $i] : ( SY495 @ SY502 ) ) ) ) ) )
    = $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,
    ( ( ! [SY586: $i,SY587: $i,SY588: $i > $i > $o] :
          ( subset
          @ ( dpsetconstr @ SY586 @ SY587
            @ ^ [Xx: $i,Xy: $i] : ( SY588 @ Xx @ Xy ) )
          @ ( cartprod @ SY586 @ SY587 ) ) )
    = $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,
    ( ( ! [SY662: $i,SY663: $i,SY664: $i] :
          ( ( subset @ SY664 @ ( cartprod @ SY662 @ SY663 ) )
         => ! [Xphi: $i > $o] :
              ( ! [Xx: $i] :
                  ( ( in @ Xx @ SY662 )
                 => ! [Xy: $i] :
                      ( ( in @ Xy @ SY663 )
                     => ( ( in @ ( kpair @ Xx @ Xy ) @ SY664 )
                       => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ SY664 )
                 => ( Xphi @ Xx ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(202,plain,
    ( ( ! [SY672: $i,SY673: $i,SY674: $i] :
          ( ( subset @ SY674 @ ( cartprod @ SY672 @ SY673 ) )
         => ! [Xphi: $i > $o] :
              ( ! [Xx: $i] :
                  ( ( in @ Xx @ SY672 )
                 => ! [Xy: $i] :
                      ( ( in @ Xy @ SY673 )
                     => ( ( in @ ( kpair @ Xx @ Xy ) @ SY674 )
                       => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
             => ! [Xx: $i] :
                  ( ( in @ Xx @ SY674 )
                 => ( Xphi @ Xx ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(203,plain,
    ( ( ! [SY682: $i,SY683: $i > $o] :
          ( ( singleton
            @ ( dsetconstr @ SY682
              @ ^ [SY687: $i] : ( SY683 @ SY687 ) ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ SY682 )
             => ! [Xy: $i] :
                  ( ( in @ Xy @ SY682 )
                 => ( ( SY683 @ Xx )
                   => ( ( SY683 @ 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,
    ( ( ! [SY715: $i,SY716: $i,SY717: $i] :
          ( ( subset @ SY717 @ ( cartprod @ SY715 @ SY716 ) )
         => ! [SY721: $i] :
              ( ( subset @ SY721 @ ( cartprod @ SY715 @ SY716 ) )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ SY715 )
                   => ! [Xy: $i] :
                        ( ( in @ Xy @ SY716 )
                       => ( ( in @ ( kpair @ Xx @ Xy ) @ SY717 )
                         => ( in @ ( kpair @ Xx @ Xy ) @ SY721 ) ) ) )
               => ( subset @ SY717 @ SY721 ) ) ) ) )
    = $true ),
    inference(standard_cnf,[status(thm)],[3]) ).

thf(210,plain,
    ( ( ! [SY727: $i,SY728: $i,SY729: $i] :
          ( ( subset @ SY729 @ ( cartprod @ SY727 @ SY728 ) )
         => ! [SY733: $i] :
              ( ( subset @ SY733 @ ( cartprod @ SY727 @ SY728 ) )
             => ( ! [Xx: $i] :
                    ( ( in @ Xx @ SY727 )
                   => ! [Xy: $i] :
                        ( ( in @ Xy @ SY728 )
                       => ( ( in @ ( kpair @ Xx @ Xy ) @ SY729 )
                         => ( in @ ( kpair @ Xx @ Xy ) @ SY733 ) ) ) )
               => ( ! [Xx: $i] :
                      ( ( in @ Xx @ SY727 )
                     => ! [Xy: $i] :
                          ( ( in @ Xy @ SY728 )
                         => ( ( in @ ( kpair @ Xx @ Xy ) @ SY733 )
                           => ( in @ ( kpair @ Xx @ Xy ) @ SY729 ) ) ) )
                 => ( SY729 = SY733 ) ) ) ) ) )
    = $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 ) ) ) ) ) ) ) )
    = $false ),
    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 @ ( binunion @ Y @ Z ) ) ) ) ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[261]) ).

thf(263,plain,
    ( ( ( in @ sK2_SY1822 @ ( powerset @ sK1_A ) )
      & ( in @ sK3_SY1826 @ ( powerset @ sK1_A ) )
      & ( in @ sK4_SY1829 @ ( powerset @ sK1_A ) )
      & ( in @ sK5_SY1831 @ sK1_A )
      & ( in @ sK5_SY1831 @ ( binintersect @ sK2_SY1822 @ sK3_SY1826 ) )
      & ~ ( in @ sK5_SY1831 @ ( binunion @ sK3_SY1826 @ sK4_SY1829 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[262]) ).

thf(264,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( ~ ( in @ ( sK6_Xx @ B @ A ) @ A )
              | ~ ( in @ ( sK6_Xx @ B @ A ) @ B ) )
            & ( ( in @ ( sK6_Xx @ B @ A ) @ A )
              | ( in @ ( sK6_Xx @ B @ A ) @ B ) ) )
          | ( A = B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[4]) ).

thf(265,plain,
    ( ( ! [Xx: $i] :
          ( ! [A: $i,Xy: $i] :
              ( ~ ( in @ Xy @ ( setadjoin @ Xx @ A ) )
              | ( Xy = Xx )
              | ( in @ Xy @ A ) )
          & ! [A: $i,Xy: $i] :
              ( ( Xy != Xx )
              | ( in @ Xy @ ( setadjoin @ Xx @ A ) ) )
          & ! [A: $i,Xy: $i] :
              ( ~ ( in @ Xy @ A )
              | ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[6]) ).

thf(266,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( in @ ( sK7_Xx @ B @ A ) @ B )
            & ~ ( in @ ( sK7_Xx @ B @ A ) @ A ) )
          | ( in @ B @ ( powerset @ A ) ) )
      & ! [A: $i,B: $i] :
          ( ~ ( in @ B @ ( powerset @ A ) )
          | ! [Xx: $i] :
              ( ~ ( in @ Xx @ B )
              | ( in @ Xx @ A ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[7]) ).

thf(267,plain,
    ( ( ! [A: $i,Xx: $i] :
          ( ! [B: $i] :
              ( ~ ( in @ Xx @ B )
              | ~ ( in @ B @ A ) )
          | ( in @ Xx @ ( setunion @ A ) ) )
      & ! [A: $i,Xx: $i] :
          ( ~ ( in @ Xx @ ( setunion @ A ) )
          | ( ( in @ Xx @ ( sK8_B @ Xx @ A ) )
            & ( in @ ( sK8_B @ Xx @ A ) @ A ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[8]) ).

thf(268,plain,
    ( ( ! [Xx: $i] :
          ( ~ ( in @ Xx @ omega )
          | ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[10]) ).

thf(269,plain,
    ( ( ! [A: $i] :
          ( ( ( in @ ( sK9_Xx @ A ) @ omega )
            & ( in @ ( sK9_Xx @ A ) @ A )
            & ~ ( in @ ( setadjoin @ ( sK9_Xx @ A ) @ ( sK9_Xx @ A ) ) @ A ) )
          | ~ ( in @ emptyset @ A )
          | ! [Xx: $i] :
              ( ~ ( in @ Xx @ omega )
              | ( in @ Xx @ A ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[11]) ).

thf(270,plain,
    ( ( ! [SY22: $i > $i > $o,SY23: $i] :
          ( ( ( in @ ( sK12_SY24 @ SY23 @ SY22 ) @ SY23 )
            & ! [SY1836: $i] :
                ( ( ( SY22 @ ( sK12_SY24 @ SY23 @ SY22 ) @ ( sK13_SY1837 @ SY1836 @ SY23 @ SY22 ) )
                  & ( SY1836
                   != ( sK13_SY1837 @ SY1836 @ SY23 @ SY22 ) ) )
                | ~ ( SY22 @ ( sK12_SY24 @ SY23 @ SY22 ) @ SY1836 ) ) )
          | ( ! [SY1832: $i] :
                ( ! [Xy: $i] :
                    ( ~ ( SY22 @ Xy @ SY1832 )
                    | ~ ( in @ Xy @ SY23 ) )
                | ( in @ SY1832 @ ( sK10_B @ SY23 @ SY22 ) ) )
            & ! [SY1834: $i] :
                ( ~ ( in @ SY1834 @ ( sK10_B @ SY23 @ SY22 ) )
                | ( ( SY22 @ ( sK11_Xy @ SY1834 @ SY23 @ SY22 ) @ SY1834 )
                  & ( in @ ( sK11_Xy @ SY1834 @ SY23 @ SY22 ) @ SY23 ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[12]) ).

thf(271,plain,
    ( ( ! [A: $i] :
          ( ! [Xx: $i] :
              ~ ( in @ Xx @ A )
          | ( ( in @ ( sK14_B @ A ) @ A )
            & ! [SY1838: $i] :
                ( ~ ( in @ SY1838 @ ( sK14_B @ A ) )
                | ~ ( in @ SY1838 @ A ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[13]) ).

thf(272,plain,
    ( ( ! [A: $i] :
          ( ! [SY1839: $i] :
              ( ( ( in @ ( sK19_Xx @ SY1839 @ A ) @ SY1839 )
                & ~ ( in @ ( sK19_Xx @ SY1839 @ A ) @ A ) )
              | ! [Xx: $i] :
                  ~ ( in @ Xx @ SY1839 )
              | ( ! [SY1860: $i] :
                    ( ~ ( in @ SY1860 @ ( sK15_B @ A ) )
                    | ! [SY1858: $i] :
                        ( ~ ( in @ SY1858 @ SY1860 )
                        | ( in @ SY1858 @ ( sK17_SY1842 @ SY1839 @ A ) ) )
                    | ( in @ ( sK18_SY1856 @ SY1839 @ A ) @ SY1860 ) )
                & ( in @ ( sK17_SY1842 @ SY1839 @ A ) @ ( sK15_B @ A ) )
                & ( in @ ( sK18_SY1856 @ SY1839 @ A ) @ SY1839 )
                & ! [SY1859: $i] :
                    ( ~ ( in @ SY1859 @ ( sK17_SY1842 @ SY1839 @ A ) )
                    | ~ ( in @ SY1859 @ SY1839 ) ) ) )
          & ! [SY1847: $i,SY1848: $i] :
              ( ~ ( in @ SY1847 @ ( sK15_B @ A ) )
              | ~ ( in @ SY1848 @ ( sK15_B @ A ) )
              | ! [Xx: $i] :
                  ( ~ ( in @ Xx @ SY1847 )
                  | ( in @ Xx @ SY1848 ) )
              | ! [Xx: $i] :
                  ( ~ ( in @ Xx @ SY1848 )
                  | ( in @ Xx @ SY1847 ) ) )
          & ! [SY1851: $i] :
              ( ~ ( in @ SY1851 @ ( sK15_B @ A ) )
              | ! [Xx: $i] :
                  ( ~ ( in @ Xx @ SY1851 )
                  | ( in @ Xx @ A ) ) )
          & ! [SY1853: $i,SY1854: $i] :
              ( ~ ( in @ SY1853 @ A )
              | ~ ( in @ SY1854 @ A )
              | ( ( in @ ( sK16_SY1855 @ SY1854 @ SY1853 @ A ) @ ( sK15_B @ A ) )
                & ( ~ ( in @ SY1853 @ ( sK16_SY1855 @ SY1854 @ SY1853 @ A ) )
                  | ~ ( in @ SY1854 @ ( sK16_SY1855 @ SY1854 @ SY1853 @ A ) ) )
                & ( ( in @ SY1853 @ ( sK16_SY1855 @ SY1854 @ SY1853 @ A ) )
                  | ( in @ SY1854 @ ( sK16_SY1855 @ SY1854 @ SY1853 @ A ) ) ) )
              | ( SY1853 = SY1854 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[14]) ).

thf(273,plain,
    ( ( ! [SY54: $i > $o] :
          ( ! [SY56: $i] :
              ( ( ( SY54 @ ( sK20_SY57 @ SY56 @ SY54 ) )
                & ( SY56
                 != ( sK20_SY57 @ SY56 @ SY54 ) ) )
              | ~ ( SY54 @ SY56 ) )
          | ( SY54
            @ ( descr
              @ ^ [Xx: $i] : ( SY54 @ Xx ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[15]) ).

thf(274,plain,
    ( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ~ ( Xphi @ Xx )
          | ( in @ Xx
            @ ( dsetconstr @ A
              @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[16]) ).

thf(275,plain,
    ( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
          ( ~ ( in @ Xx
              @ ( dsetconstr @ A
                @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
          | ( in @ Xx @ A ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[17]) ).

thf(276,plain,
    ( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
          ( ~ ( in @ Xx
              @ ( dsetconstr @ A
                @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
          | ( Xphi @ Xx ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[18]) ).

thf(277,plain,
    ( ( ! [SY71: $i > $o] :
          ( ! [SY73: $i] :
              ( ( ( SY71 @ ( sK22_SY74 @ SY73 @ SY71 ) )
                & ( SY73
                 != ( sK22_SY74 @ SY73 @ SY71 ) ) )
              | ~ ( SY71 @ SY73 ) )
          | ( ! [SY1863: $i] :
                ( ~ ( SY71 @ SY1863 )
                | ( ( sK21_Xx @ SY71 )
                  = SY1863 ) )
            & ( SY71 @ ( sK21_Xx @ SY71 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[19]) ).

thf(278,plain,
    ( ( ! [Xphi: $o] :
          ( ! [Xx: $i] :
              ~ ( in @ Xx @ ( prop2set @ Xphi ) )
          | Xphi ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[20]) ).

thf(279,plain,
    ( ( ! [Xx: $i] :
          ~ ( in @ Xx @ emptyset )
      | ! [Xphi: $o] : Xphi )
    = $true ),
    inference(extcnf_combined,[status(esa)],[21]) ).

thf(280,plain,
    ( ( ! [Xx: $i] :
          ~ ( in @ Xx @ emptyset ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[22]) ).

thf(281,plain,
    ( ( ! [SY83: $i > $o] :
          ( ! [SY85: $i] :
              ( ( ( SY83 @ ( sK24_SY86 @ SY85 @ SY83 ) )
                & ( SY85
                 != ( sK24_SY86 @ SY85 @ SY83 ) ) )
              | ~ ( SY83 @ SY85 ) )
          | ( SY83 @ ( sK23_Xx @ SY83 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[24]) ).

thf(282,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( in @ ( sK26_Xx @ B @ A ) @ A )
            & ~ ( in @ ( sK26_Xx @ B @ A ) @ B ) )
          | ( ( in @ ( sK25_Xx @ B @ A ) @ B )
            & ~ ( in @ ( sK25_Xx @ B @ A ) @ A ) )
          | ( A = B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[25]) ).

thf(283,plain,
    ( ( ! [A: $i] :
          ( ( in @ ( sK27_Xx @ A ) @ A )
          | ( A = emptyset ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[26]) ).

thf(284,plain,
    ( ( ! [A: $i] :
          ( ( in @ ( sK28_Xx @ A ) @ A )
          | ( A = emptyset ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[27]) ).

thf(285,plain,
    ( ( ! [A: $i] :
          ( ! [Xphi: $i > $o,Xx: $i] :
              ( ~ ( in @ Xx @ A )
              | ~ ( Xphi @ Xx )
              | ( in @ Xx
                @ ( dsetconstr @ A
                  @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) )
          & ! [Xphi: $i > $o,Xx: $i] :
              ( ~ ( in @ Xx @ A )
              | ~ ( in @ Xx
                  @ ( dsetconstr @ A
                    @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
              | ( Xphi @ Xx ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[28]) ).

thf(286,plain,
    ( ( ! [SY100: $i] :
          ( ( SY100 = emptyset )
          | ( in @ ( sK29_Xx @ SY100 ) @ SY100 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[29]) ).

thf(287,plain,
    ( ( ! [SY102: $i,SY103: $i > $o,SY104: $i] :
          ( ~ ( in @ SY104 @ SY102 )
          | ~ ( SY103 @ SY104 )
          | ( ( dsetconstr @ SY102
              @ ^ [Xy: $i] : ( SY103 @ Xy ) )
           != emptyset ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[30]) ).

thf(288,plain,
    ( ( ! [SY106: $i] :
          ( ! [Xx: $i] :
              ~ ( in @ Xx @ SY106 )
          | ( SY106 != emptyset ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[31]) ).

thf(289,plain,
    ( ( ! [Xx: $i,A: $i,Xy: $i] :
          ( ~ ( in @ Xy @ A )
          | ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[34]) ).

thf(290,plain,
    ( ( ! [Xx: $i,A: $i,Xy: $i] :
          ( ~ ( in @ Xy @ ( setadjoin @ Xx @ A ) )
          | ( ( ( Xy = Xx )
              | ( in @ Xy @ A )
              | ! [Xphi: $o] : Xphi )
            & ( ( Xy = Xx )
              | ! [Xphi: $o] :
                  ( ~ Xphi
                  | Xphi ) )
            & ! [Xphi: $o] :
                ( ~ Xphi
                | ( in @ Xy @ A )
                | Xphi )
            & ! [Xphi: $o] :
                ( ~ Xphi
                | ~ Xphi
                | Xphi ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[35]) ).

thf(291,plain,
    ( ( ! [Xx: $i,A: $i,Xy: $i] :
          ( ~ ( in @ Xy @ ( setadjoin @ Xx @ A ) )
          | ( Xy = Xx )
          | ( in @ Xy @ A ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[36]) ).

thf(292,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( in @ ( sK30_Xx @ B @ A ) @ B )
            & ~ ( in @ ( sK30_Xx @ B @ A ) @ A ) )
          | ( in @ B @ ( powerset @ A ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[38]) ).

thf(293,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( in @ B @ ( powerset @ A ) )
          | ! [Xx: $i] :
              ( ~ ( in @ Xx @ B )
              | ( in @ Xx @ A ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[41]) ).

thf(294,plain,
    ( ( ! [A: $i,Xx: $i,B: $i] :
          ( ~ ( in @ Xx @ B )
          | ~ ( in @ B @ A )
          | ( in @ Xx @ ( setunion @ A ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[42]) ).

thf(295,plain,
    ( ( ! [A: $i,Xx: $i] :
          ( ~ ( in @ Xx @ ( setunion @ A ) )
          | ! [Xphi: $o] :
              ( ( ( in @ Xx @ ( sK31_B @ Xphi @ Xx @ A ) )
                & ( in @ ( sK31_B @ Xphi @ Xx @ A ) @ A )
                & ~ Xphi )
              | Xphi ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[43]) ).

thf(296,plain,
    ( ( ! [A: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[44]) ).

thf(297,plain,
    ( ( ! [SY139: $i > $o] :
          ( ! [SY141: $i] :
              ( ( ( SY139 @ ( sK33_SY142 @ SY141 @ SY139 ) )
                & ( SY141
                 != ( sK33_SY142 @ SY141 @ SY139 ) ) )
              | ~ ( SY139 @ SY141 ) )
          | ( ! [SY1864: $i] :
                ( ( SY1864
                 != ( sK32_Xx @ SY139 ) )
                | ( SY139 @ SY1864 ) )
            & ! [SY1865: $i] :
                ( ~ ( SY139 @ SY1865 )
                | ( SY1865
                  = ( sK32_Xx @ SY139 ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[45]) ).

thf(298,plain,
    ( ( ! [SY145: $i] :
          ( ( SY145 = emptyset )
          | ( in @ ( sK34_Xx @ SY145 ) @ SY145 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[46]) ).

thf(299,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ~ ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
          | ( Xx = Xy ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[47]) ).

thf(300,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( Xx = Xy )
          | ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[48]) ).

thf(301,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( Xx != Xy )
          | ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[49]) ).

thf(302,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ~ ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
          | ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[50]) ).

thf(303,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i] :
          ( ~ ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
          | ( Xz = Xx )
          | ( Xz = Xy ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[51]) ).

thf(304,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ! [Xx: $i] :
              ( ~ ( Xphi @ Xx )
              | ~ ( in @ Xx @ A ) )
          | ( ( dsetconstr @ A
              @ ^ [Xx: $i] : ( Xphi @ Xx ) )
           != emptyset ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[54]) ).

thf(305,plain,
    ( ( ! [Xphi: $i > $o,Xx: $i] :
          ( ~ ( in @ Xx @ emptyset )
          | ( Xphi @ Xx ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[55]) ).

thf(306,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ! [Xx: $i] :
              ( ~ ( in @ Xx @ A )
              | ( Xphi @ Xx ) )
          | ( ( in @ ( sK35_Xx @ Xphi @ A ) @ A )
            & ~ ( Xphi @ ( sK35_Xx @ Xphi @ A ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[56]) ).

thf(307,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ( ( in @ ( sK36_Xx @ Xphi @ A ) @ A )
            & ( Xphi @ ( sK36_Xx @ Xphi @ A ) ) )
          | ! [Xx: $i] :
              ( ~ ( Xphi @ Xx )
              | ~ ( in @ Xx @ A ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[57]) ).

thf(308,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ( ( Xphi @ ( sK37_Xx @ Xphi @ A ) )
            & ( in @ ( sK37_Xx @ Xphi @ A ) @ A ) )
          | ! [Xx: $i] :
              ( ~ ( in @ Xx @ A )
              | ~ ( Xphi @ Xx ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[58]) ).

thf(309,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ! [Xx: $i] :
              ( ~ ( in @ Xx @ A )
              | ( Xphi @ Xx ) )
          | ( ( in @ ( sK38_Xx @ Xphi @ A ) @ A )
            & ~ ( Xphi @ ( sK38_Xx @ Xphi @ A ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[59]) ).

thf(310,plain,
    ( ( ! [Xphi: $o] :
          ( ~ Xphi
          | ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[60]) ).

thf(311,plain,
    ( ( ! [Xphi: $o] :
          ( ~ Xphi
          | ( set2prop @ ( prop2set @ Xphi ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[61]) ).

thf(312,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ( ( Xphi @ ( sK39_Xx @ Xphi @ A ) )
            & ( in @ ( sK39_Xx @ Xphi @ A ) @ A ) )
          | ! [Xx: $i] :
              ( ~ ( in @ Xx @ A )
              | ~ ( Xphi @ Xx ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[62]) ).

thf(313,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ! [Xx: $i] :
              ( ~ ( in @ Xx @ A )
              | ( Xphi @ Xx ) )
          | ( ( in @ ( sK40_Xx @ Xphi @ A ) @ A )
            & ~ ( Xphi @ ( sK40_Xx @ Xphi @ A ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[63]) ).

thf(314,plain,
    ( ( ! [SY194: $i > $o] :
          ( ! [Xx: $i] :
              ( ( ( SY194 @ ( sK42_Xy @ Xx @ SY194 ) )
                & ( Xx
                 != ( sK42_Xy @ Xx @ SY194 ) ) )
              | ~ ( SY194 @ Xx ) )
          | ( ! [SY1866: $i] :
                ( ~ ( SY194 @ SY1866 )
                | ( ( sK41_SY198 @ SY194 )
                  = SY1866 ) )
            & ( SY194 @ ( sK41_SY198 @ SY194 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[64]) ).

thf(315,plain,
    ( ( ! [SY200: $i > $o] :
          ( ! [Xx: $i] :
              ~ ( SY200 @ Xx )
          | ( ( SY200 @ ( sK44_Xx @ SY200 ) )
            & ( SY200 @ ( sK45_SY1868 @ SY200 ) )
            & ( ( sK44_Xx @ SY200 )
             != ( sK45_SY1868 @ SY200 ) ) )
          | ( ! [SY1867: $i] :
                ( ~ ( SY200 @ SY1867 )
                | ( ( sK43_SY205 @ SY200 )
                  = SY1867 ) )
            & ( SY200 @ ( sK43_SY205 @ SY200 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[65]) ).

thf(316,plain,
    ( ( ! [SY207: $i > $o] :
          ( ! [Xx: $i] :
              ( ( ( ( sK47_Xy @ Xx @ SY207 )
                 != Xx )
                | ~ ( SY207 @ ( sK47_Xy @ Xx @ SY207 ) ) )
              & ( ( ( sK47_Xy @ Xx @ SY207 )
                  = Xx )
                | ( SY207 @ ( sK47_Xy @ Xx @ SY207 ) ) ) )
          | ( ! [SY1869: $i] :
                ( ~ ( SY207 @ SY1869 )
                | ( ( sK46_SY211 @ SY207 )
                  = SY1869 ) )
            & ( SY207 @ ( sK46_SY211 @ SY207 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[66]) ).

thf(317,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A != B )
          | ! [Xx: $i,Xy: $i] :
              ( ( Xx != Xy )
              | ~ ( in @ Xx @ A )
              | ( in @ Xy @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[67]) ).

thf(318,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A != B )
          | ( ! [Xx: $i,Xy: $i] :
                ( ( Xx != Xy )
                | ~ ( in @ Xx @ A )
                | ( in @ Xy @ B ) )
            & ! [Xx: $i,Xy: $i] :
                ( ( Xx != Xy )
                | ~ ( in @ Xy @ B )
                | ( in @ Xx @ A ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[68]) ).

thf(319,plain,
    ( ( ! [SY221: $i > $o] :
          ( ! [SY223: $i] :
              ( ( ( SY221 @ ( sK48_SY224 @ SY223 @ SY221 ) )
                & ( SY223
                 != ( sK48_SY224 @ SY223 @ SY221 ) ) )
              | ~ ( SY221 @ SY223 ) )
          | ! [Xx: $i] :
              ( ~ ( SY221 @ Xx )
              | ! [Xy: $i] :
                  ( ~ ( SY221 @ Xy )
                  | ( Xx = Xy ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[69]) ).

thf(320,plain,
    ( ( ! [SY227: $i > $o,SY228: $i > $o] :
          ( ( ( ( sK55_Xx @ SY228 @ SY227 )
              = ( sK56_SY1873 @ SY228 @ SY227 ) )
            & ( ~ ( SY227 @ ( sK55_Xx @ SY228 @ SY227 ) )
              | ~ ( SY228 @ ( sK56_SY1873 @ SY228 @ SY227 ) ) )
            & ( ( SY227 @ ( sK55_Xx @ SY228 @ SY227 ) )
              | ( SY228 @ ( sK56_SY1873 @ SY228 @ SY227 ) ) ) )
          | ! [SY232: $i] :
              ( ( ( SY227 @ ( sK54_SY233 @ SY232 @ SY228 @ SY227 ) )
                & ( SY232
                 != ( sK54_SY233 @ SY232 @ SY228 @ SY227 ) ) )
              | ~ ( SY227 @ SY232 ) )
          | ( ! [SY1872: $i] :
                ( ~ ( SY228 @ SY1872 )
                | ( ( sK53_SY235 @ SY228 @ SY227 )
                  = SY1872 ) )
            & ( SY228 @ ( sK53_SY235 @ SY228 @ SY227 ) ) ) )
      & ! [SY227: $i > $o,SY228: $i > $o] :
          ( ( ( ( sK51_Xx @ SY228 @ SY227 )
              = ( sK52_SY1871 @ SY228 @ SY227 ) )
            & ( ~ ( SY227 @ ( sK51_Xx @ SY228 @ SY227 ) )
              | ~ ( SY228 @ ( sK52_SY1871 @ SY228 @ SY227 ) ) )
            & ( ( SY227 @ ( sK51_Xx @ SY228 @ SY227 ) )
              | ( SY228 @ ( sK52_SY1871 @ SY228 @ SY227 ) ) ) )
          | ! [SY235: $i] :
              ( ( ( SY228 @ ( sK50_SY236 @ SY235 @ SY228 @ SY227 ) )
                & ( SY235
                 != ( sK50_SY236 @ SY235 @ SY228 @ SY227 ) ) )
              | ~ ( SY228 @ SY235 ) )
          | ( ! [SY1870: $i] :
                ( ~ ( SY227 @ SY1870 )
                | ( ( sK49_SY232 @ SY228 @ SY227 )
                  = SY1870 ) )
            & ( SY227 @ ( sK49_SY232 @ SY228 @ SY227 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[70]) ).

thf(321,plain,
    $true = $true,
    inference(extcnf_combined,[status(esa)],[71]) ).

thf(322,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( Xx != Xy )
          | ! [Xz: $i,Xu: $i] :
              ( ( Xz != Xu )
              | ( ( setadjoin @ Xx @ Xz )
                = ( setadjoin @ Xy @ Xu ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[72]) ).

thf(323,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A != B )
          | ( ( powerset @ A )
            = ( powerset @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[73]) ).

thf(324,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A != B )
          | ( ( setunion @ A )
            = ( setunion @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[74]) ).

thf(325,plain,
    $true = $true,
    inference(extcnf_combined,[status(esa)],[75]) ).

thf(326,plain,
    ( ( ! [SY245: $i > $o] :
          ( ! [SY247: $i] :
              ( ( ( SY245 @ ( sK57_SY248 @ SY247 @ SY245 ) )
                & ( SY247
                 != ( sK57_SY248 @ SY247 @ SY245 ) ) )
              | ~ ( SY245 @ SY247 ) )
          | ! [Xx: $i] :
              ( ~ ( SY245 @ Xx )
              | ! [Xy: $i] :
                  ( ~ ( SY245 @ Xy )
                  | ( Xx = Xy ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[76]) ).

thf(327,plain,
    ( ( ! [SY251: $i > $o,SY252: $i > $o] :
          ( ( ( ( sK60_Xx @ SY252 @ SY251 )
              = ( sK61_SY1874 @ SY252 @ SY251 ) )
            & ( ~ ( SY251 @ ( sK60_Xx @ SY252 @ SY251 ) )
              | ~ ( SY252 @ ( sK61_SY1874 @ SY252 @ SY251 ) ) )
            & ( ( SY251 @ ( sK60_Xx @ SY252 @ SY251 ) )
              | ( SY252 @ ( sK61_SY1874 @ SY252 @ SY251 ) ) ) )
          | ! [SY256: $i] :
              ( ( ( SY251 @ ( sK59_SY257 @ SY256 @ SY252 @ SY251 ) )
                & ( SY256
                 != ( sK59_SY257 @ SY256 @ SY252 @ SY251 ) ) )
              | ~ ( SY251 @ SY256 ) )
          | ! [SY259: $i] :
              ( ( ( SY252 @ ( sK58_SY260 @ SY259 @ SY252 @ SY251 ) )
                & ( SY259
                 != ( sK58_SY260 @ SY259 @ SY252 @ SY251 ) ) )
              | ~ ( SY252 @ SY259 ) )
          | ( ( descr
              @ ^ [Xx: $i] : ( SY251 @ Xx ) )
            = ( descr
              @ ^ [Xx: $i] : ( SY252 @ Xx ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[77]) ).

thf(328,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A != B )
          | ! [Xphi: $i > $o,Xpsi: $i > $o] :
              ( ( ( in @ ( sK62_Xx @ Xpsi @ Xphi @ B @ A ) @ A )
                & ( in @ ( sK63_SY1875 @ Xpsi @ Xphi @ B @ A ) @ B )
                & ( ( sK62_Xx @ Xpsi @ Xphi @ B @ A )
                  = ( sK63_SY1875 @ Xpsi @ Xphi @ B @ A ) )
                & ( ~ ( Xphi @ ( sK62_Xx @ Xpsi @ Xphi @ B @ A ) )
                  | ~ ( Xpsi @ ( sK63_SY1875 @ Xpsi @ Xphi @ B @ A ) ) )
                & ( ( Xphi @ ( sK62_Xx @ Xpsi @ Xphi @ B @ A ) )
                  | ( Xpsi @ ( sK63_SY1875 @ Xpsi @ Xphi @ B @ A ) ) ) )
              | ( ( dsetconstr @ A
                  @ ^ [Xx: $i] : ( Xphi @ Xx ) )
                = ( dsetconstr @ B
                  @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[78]) ).

thf(329,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( in @ ( sK64_Xx @ B @ A ) @ A )
            & ~ ( in @ ( sK64_Xx @ B @ A ) @ B ) )
          | ( subset @ A @ B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[79]) ).

thf(330,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A != B )
          | ( subset @ B @ A ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[80]) ).

thf(331,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A != B )
          | ( subset @ A @ B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[81]) ).

thf(332,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( in @ ( sK65_Xx @ B @ A ) @ A )
            & ~ ( in @ ( sK65_Xx @ B @ A ) @ B ) )
          | ( subset @ A @ B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[82]) ).

thf(333,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( subset @ A @ B )
          | ! [Xx: $i] :
              ( ~ ( in @ Xx @ A )
              | ( in @ Xx @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[84]) ).

thf(334,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( subset @ A @ B )
          | ! [Xx: $i] :
              ( ( in @ Xx @ B )
              | ~ ( in @ Xx @ A ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[85]) ).

thf(335,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ( in @ Xx @ B )
          | ~ ( subset @ A @ B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[86]) ).

thf(336,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( subset @ A @ B )
          | ( A != B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[87]) ).

thf(337,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ( in @ Xx @ B )
          | ( A != B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[88]) ).

thf(338,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( subset @ A @ B )
          | ! [C: $i] :
              ( ~ ( subset @ B @ C )
              | ( subset @ A @ C ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[90]) ).

thf(339,plain,
    ( ( ! [A: $i,Xx: $i,B: $i] :
          ( ~ ( subset @ A @ B )
          | ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[92]) ).

thf(340,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( subset @ A @ B )
          | ( in @ A @ ( powerset @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[93]) ).

thf(341,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( subset @ A @ B )
          | ~ ( subset @ B @ A )
          | ( A = B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[94]) ).

thf(342,plain,
    ( ( ! [A: $i] :
          ( ~ ( subset @ A @ emptyset )
          | ( A = emptyset ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[95]) ).

thf(343,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( subset @ B @ A )
          | ( in @ B @ ( powerset @ A ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[96]) ).

thf(344,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( in @ B @ ( powerset @ A ) )
          | ( subset @ B @ A ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[97]) ).

thf(345,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( subset @ A @ B )
          | ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[99]) ).

thf(346,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ( in @ Xx @ ( binunion @ A @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[102]) ).

thf(347,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ B )
          | ( in @ Xx @ ( binunion @ A @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[104]) ).

thf(348,plain,
    ( ( ! [A: $i,B: $i] :
          ( ! [Xx: $i] :
              ( ~ ( in @ Xx @ ( binunion @ A @ B ) )
              | ( in @ Xx @ A )
              | ( in @ Xx @ B )
              | ! [Xphi: $o] : Xphi )
          & ! [Xx: $i] :
              ( ~ ( in @ Xx @ ( binunion @ A @ B ) )
              | ( in @ Xx @ A )
              | ! [Xphi: $o] :
                  ( ~ Xphi
                  | Xphi ) )
          & ! [Xx: $i] :
              ( ~ ( in @ Xx @ ( binunion @ A @ B ) )
              | ! [Xphi: $o] :
                  ( ~ Xphi
                  | ( in @ Xx @ B )
                  | Xphi ) )
          & ( ! [Xx: $i] :
                ~ ( in @ Xx @ ( binunion @ A @ B ) )
            | ! [Xphi: $o] :
                ( ~ Xphi
                | ~ Xphi
                | Xphi ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[105]) ).

thf(349,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ ( binunion @ A @ B ) )
          | ( in @ Xx @ A )
          | ( in @ Xx @ B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[106]) ).

thf(350,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ~ ( in @ Xx @ B )
          | ( in @ Xx @ ( binintersect @ A @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[109]) ).

thf(351,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ~ ( subset @ C @ A )
          | ~ ( subset @ C @ B )
          | ( subset @ C @ ( binintersect @ A @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[110]) ).

thf(352,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ ( binintersect @ A @ B ) )
          | ( in @ Xx @ A ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[111]) ).

thf(353,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( subset @ A @ B )
          | ( ( binintersect @ A @ B )
            = A ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[113]) ).

thf(354,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( binintersect @ A @ B )
           != B )
          | ( subset @ B @ A ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[114]) ).

thf(355,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ ( binintersect @ A @ B ) )
          | ( in @ Xx @ B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[115]) ).

thf(356,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( in @ ( sK66_Xx @ B @ A ) @ A )
            & ( in @ ( sK66_Xx @ B @ A ) @ B ) )
          | ( ( binintersect @ A @ B )
            = emptyset ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[116]) ).

thf(357,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( subset @ B @ A )
          | ( ( binintersect @ A @ B )
            = B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[118]) ).

thf(358,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( binintersect @ A @ B )
           != A )
          | ( subset @ A @ B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[119]) ).

thf(359,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ( in @ Xx @ B )
          | ( in @ Xx @ ( setminus @ A @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[121]) ).

thf(360,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
          | ( in @ Xx @ A ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[122]) ).

thf(361,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
          | ~ ( in @ Xx @ B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[123]) ).

thf(362,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( subset @ A @ B )
          | ( ( setminus @ A @ B )
            = emptyset ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[124]) ).

thf(363,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ ( setminus @ A @ B ) )
          | ~ ( in @ Xx @ A )
          | ( in @ Xx @ B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[125]) ).

thf(364,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ ( setminus @ A @ B ) )
          | ( in @ Xx @ B )
          | ~ ( in @ Xx @ A ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[126]) ).

thf(365,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
          | ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[127]) ).

thf(366,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ B )
          | ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[128]) ).

thf(367,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( setminus @ A @ B )
           != emptyset )
          | ( subset @ A @ B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[130]) ).

thf(368,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ ( symdiff @ A @ B ) )
          | ( ( ( in @ Xx @ A )
              | ~ ( in @ Xx @ A )
              | ! [Xphi: $o] : Xphi )
            & ( ( in @ Xx @ A )
              | ( in @ Xx @ B )
              | ! [Xphi: $o] : Xphi )
            & ( ( in @ Xx @ A )
              | ! [Xphi: $o] :
                  ( ~ Xphi
                  | Xphi ) )
            & ( ~ ( in @ Xx @ B )
              | ~ ( in @ Xx @ A )
              | ! [Xphi: $o] : Xphi )
            & ( ~ ( in @ Xx @ B )
              | ( in @ Xx @ B )
              | ! [Xphi: $o] : Xphi )
            & ( ~ ( in @ Xx @ B )
              | ! [Xphi: $o] :
                  ( ~ Xphi
                  | Xphi ) )
            & ! [Xphi: $o] :
                ( ~ Xphi
                | ~ ( in @ Xx @ A )
                | Xphi )
            & ! [Xphi: $o] :
                ( ~ Xphi
                | ( in @ Xx @ B )
                | Xphi )
            & ! [Xphi: $o] :
                ( ~ Xphi
                | ~ Xphi
                | Xphi ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[131]) ).

thf(369,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ( in @ Xx @ B )
          | ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[132]) ).

thf(370,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
          | ~ ( in @ Xx @ B )
          | ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[133]) ).

thf(371,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ~ ( in @ Xx @ B )
          | ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[134]) ).

thf(372,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
          | ( in @ Xx @ B )
          | ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[135]) ).

thf(373,plain,
    ( ( ! [A: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[141]) ).

thf(374,plain,
    ( ( ! [A: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[142]) ).

thf(375,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[143]) ).

thf(376,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i] :
          ( ~ ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
          | ( Xz = Xx )
          | ( Xz = Xy ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[144]) ).

thf(377,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(extcnf_combined,[status(esa)],[145]) ).

thf(378,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(extcnf_combined,[status(esa)],[146]) ).

thf(379,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(extcnf_combined,[status(esa)],[147]) ).

thf(380,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(extcnf_combined,[status(esa)],[148]) ).

thf(381,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(extcnf_combined,[status(esa)],[149]) ).

thf(382,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ! [Xy: $i] :
              ( ~ ( in @ Xy @ B )
              | ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[150]) ).

thf(383,plain,
    ( ( ! [A: $i,B: $i,Xu: $i] :
          ( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
          | ( ( Xu
              = ( kpair @ ( sK67_Xx @ Xu @ B @ A ) @ ( sK68_SY1876 @ Xu @ B @ A ) ) )
            & ( in @ ( sK68_SY1876 @ Xu @ B @ A ) @ B )
            & ( in @ ( sK67_Xx @ Xu @ B @ A ) @ A ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[151]) ).

thf(384,plain,
    ( ( ! [A: $i,B: $i,Xu: $i] :
          ( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
          | ( iskpair @ Xu ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[152]) ).

thf(385,plain,
    ( ( ! [A: $i,Xx: $i] :
          ( ~ ( in @ Xx @ ( setunion @ A ) )
          | ( ( in @ ( sK69_X @ Xx @ A ) @ A )
            & ( in @ Xx @ ( sK69_X @ Xx @ A ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[153]) ).

thf(386,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ( ( in @ ( sK70_Xx @ Xphi @ A ) @ A )
            & ( in @ ( sK71_SY1877 @ Xphi @ A ) @ A )
            & ( Xphi @ ( sK70_Xx @ Xphi @ A ) )
            & ( Xphi @ ( sK71_SY1877 @ Xphi @ A ) )
            & ( ( sK70_Xx @ Xphi @ A )
             != ( sK71_SY1877 @ Xphi @ A ) ) )
          | ! [Xx: $i] :
              ( ~ ( Xphi @ Xx )
              | ~ ( in @ Xx @ A ) )
          | ( singleton
            @ ( dsetconstr @ A
              @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[157]) ).

thf(387,plain,
    ( ( ! [SY479: $i,SY480: $i > $o] :
          ( ~ ( singleton
              @ ( dsetconstr @ SY479
                @ ^ [SY484: $i] : ( SY480 @ SY484 ) ) )
          | ( ( SY480 @ ( sK72_Xx @ SY480 @ SY479 ) )
            & ( in @ ( sK72_Xx @ SY480 @ SY479 ) @ SY479 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[158]) ).

thf(388,plain,
    ( ( ! [SY486: $i,SY487: $i > $o,SY488: $i] :
          ( ~ ( in @ SY488 @ SY486 )
          | ~ ( SY487 @ SY488 )
          | ( ( in @ ( sK73_Xy @ SY488 @ SY487 @ SY486 ) @ SY486 )
            & ( SY487 @ ( sK73_Xy @ SY488 @ SY487 @ SY486 ) )
            & ( ( sK73_Xy @ SY488 @ SY487 @ SY486 )
             != SY488 ) )
          | ( singleton
            @ ( dsetconstr @ SY486
              @ ^ [SY493: $i] : ( SY487 @ SY493 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[159]) ).

thf(389,plain,
    ( ( ! [SY494: $i,SY495: $i > $o] :
          ( ( ( in @ ( sK74_Xx @ SY495 @ SY494 ) @ SY494 )
            & ( in @ ( sK75_SY1878 @ SY495 @ SY494 ) @ SY494 )
            & ( SY495 @ ( sK74_Xx @ SY495 @ SY494 ) )
            & ( SY495 @ ( sK75_SY1878 @ SY495 @ SY494 ) )
            & ( ( sK74_Xx @ SY495 @ SY494 )
             != ( sK75_SY1878 @ SY495 @ SY494 ) ) )
          | ! [Xx: $i] :
              ( ~ ( SY495 @ Xx )
              | ~ ( in @ Xx @ SY494 ) )
          | ( singleton
            @ ( dsetconstr @ SY494
              @ ^ [SY502: $i] : ( SY495 @ SY502 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[160]) ).

thf(390,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( ( setadjoin @ Xx @ emptyset )
           != ( setadjoin @ Xy @ emptyset ) )
          | ( Xx = Xy ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[161]) ).

thf(391,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(extcnf_combined,[status(esa)],[162]) ).

thf(392,plain,
    ( ( ! [Xu: $i] :
          ( ~ ( iskpair @ Xu )
          | ( singleton
            @ ( dsetconstr @ ( setunion @ Xu )
              @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[163]) ).

thf(393,plain,
    ( ( ! [X: $i] :
          ( ~ ( singleton @ X )
          | ( in @ ( setunion @ X ) @ X ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[164]) ).

thf(394,plain,
    ( ( ! [A: $i,B: $i,Xu: $i] :
          ( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
          | ( in @ ( kfst @ Xu ) @ A ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[166]) ).

thf(395,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(extcnf_combined,[status(esa)],[167]) ).

thf(396,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i] :
          ( ! [Xu: $i] :
              ( ( kpair @ Xx @ Xy )
             != ( kpair @ Xz @ Xu ) )
          | ( Xx = Xz ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[168]) ).

thf(397,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( Xx != Xy )
          | ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
            = ( setadjoin @ Xx @ emptyset ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[169]) ).

thf(398,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(extcnf_combined,[status(esa)],[170]) ).

thf(399,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(extcnf_combined,[status(esa)],[171]) ).

thf(400,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ! [Xz: $i] :
              ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
             != ( setadjoin @ Xz @ emptyset ) )
          | ( Xx = Xy ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[172]) ).

thf(401,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(extcnf_combined,[status(esa)],[173]) ).

thf(402,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
          ( ( ( kpair @ Xx @ Xy )
           != ( kpair @ Xz @ Xu ) )
          | ( Xy = Xu ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[174]) ).

thf(403,plain,
    ( ( ! [Xu: $i] :
          ( ~ ( iskpair @ Xu )
          | ( singleton
            @ ( dsetconstr @ ( setunion @ Xu )
              @ ^ [Xx: $i] :
                  ( Xu
                  = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[175]) ).

thf(404,plain,
    ( ( ! [Xu: $i] :
          ( ~ ( iskpair @ Xu )
          | ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
            = Xu ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[177]) ).

thf(405,plain,
    ( ( ! [A: $i,B: $i,Xu: $i] :
          ( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
          | ( in @ ( ksnd @ Xu ) @ B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[178]) ).

thf(406,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ! [Xy: $i] :
              ~ ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
          | ( in @ Xx @ A ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[179]) ).

thf(407,plain,
    ( ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
          ( ~ ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
          | ( in @ Xy @ B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[180]) ).

thf(408,plain,
    ( ( ! [A: $i] :
          ( ! [Xx: $i] :
              ~ ( in @ Xx @ A )
          | ! [B: $i,Xy: $i] :
              ~ ( in @ Xy @ B )
          | $true ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[181]) ).

thf(409,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ! [Xy: $i] :
              ( ~ ( in @ Xy @ B )
              | ( ( kfst @ ( kpair @ Xx @ Xy ) )
                = Xx ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[182]) ).

thf(410,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ! [Xy: $i] :
              ( ~ ( in @ Xy @ B )
              | ( ( ksnd @ ( kpair @ Xx @ Xy ) )
                = Xy ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[183]) ).

thf(411,plain,
    ( ( ! [A: $i,B: $i,Xu: $i] :
          ( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
          | ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
            = Xu ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[184]) ).

thf(412,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(extcnf_combined,[status(esa)],[185]) ).

thf(413,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(extcnf_combined,[status(esa)],[188]) ).

thf(414,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(extcnf_combined,[status(esa)],[189]) ).

thf(415,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(extcnf_combined,[status(esa)],[190]) ).

thf(416,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(extcnf_combined,[status(esa)],[191]) ).

thf(417,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(extcnf_combined,[status(esa)],[192]) ).

thf(418,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(extcnf_combined,[status(esa)],[193]) ).

thf(419,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(extcnf_combined,[status(esa)],[194]) ).

thf(420,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ~ ( in @ Xf @ ( funcSet @ A @ B ) )
          | ( func @ A @ B @ Xf ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[195]) ).

thf(421,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(extcnf_combined,[status(esa)],[196]) ).

thf(422,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ~ ( func @ A @ B @ Xf )
          | ( in @ Xf @ ( funcSet @ A @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[197]) ).

thf(423,plain,
    ( ( ! [A: $i,B: $i,Xf: $i > $i] :
          ( ( ( in @ ( sK76_Xx @ Xf @ B @ A ) @ A )
            & ~ ( in @ ( Xf @ ( sK76_Xx @ Xf @ B @ A ) ) @ B ) )
          | ( func @ A @ B
            @ ( dpsetconstr @ A @ B
              @ ^ [Xx: $i,Xy: $i] :
                  ( ( Xf @ Xx )
                  = Xy ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[198]) ).

thf(424,plain,
    ( ( ! [A: $i,B: $i,Xf: $i > $i] :
          ( ( ( in @ ( sK77_Xx @ Xf @ B @ A ) @ A )
            & ~ ( in @ ( Xf @ ( sK77_Xx @ Xf @ B @ A ) ) @ B ) )
          | ( func @ A @ B
            @ ( lam @ A @ B
              @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[199]) ).

thf(425,plain,
    ( ( ! [A: $i,B: $i,Xf: $i > $i] :
          ( ( ( in @ ( sK78_Xx @ Xf @ B @ A ) @ A )
            & ~ ( in @ ( Xf @ ( sK78_Xx @ Xf @ B @ A ) ) @ B ) )
          | ( in
            @ ( lam @ A @ B
              @ ^ [Xx: $i] : ( Xf @ Xx ) )
            @ ( funcSet @ A @ B ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[200]) ).

thf(426,plain,
    ( ( ! [SY662: $i,SY663: $i,SY664: $i] :
          ( ~ ( subset @ SY664 @ ( cartprod @ SY662 @ SY663 ) )
          | ! [Xphi: $i > $o] :
              ( ( ( in @ ( sK79_Xx @ Xphi @ SY664 @ SY663 @ SY662 ) @ SY662 )
                & ( in @ ( sK80_SY1879 @ Xphi @ SY664 @ SY663 @ SY662 ) @ SY663 )
                & ( in @ ( kpair @ ( sK79_Xx @ Xphi @ SY664 @ SY663 @ SY662 ) @ ( sK80_SY1879 @ Xphi @ SY664 @ SY663 @ SY662 ) ) @ SY664 )
                & ~ ( Xphi @ ( kpair @ ( sK79_Xx @ Xphi @ SY664 @ SY663 @ SY662 ) @ ( sK80_SY1879 @ Xphi @ SY664 @ SY663 @ SY662 ) ) ) )
              | ! [Xx: $i] :
                  ( ~ ( in @ Xx @ SY664 )
                  | ( Xphi @ Xx ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[201]) ).

thf(427,plain,
    ( ( ! [SY672: $i,SY673: $i,SY674: $i] :
          ( ~ ( subset @ SY674 @ ( cartprod @ SY672 @ SY673 ) )
          | ! [Xphi: $i > $o] :
              ( ( ( in @ ( sK81_Xx @ Xphi @ SY674 @ SY673 @ SY672 ) @ SY672 )
                & ( in @ ( sK82_SY1880 @ Xphi @ SY674 @ SY673 @ SY672 ) @ SY673 )
                & ( in @ ( kpair @ ( sK81_Xx @ Xphi @ SY674 @ SY673 @ SY672 ) @ ( sK82_SY1880 @ Xphi @ SY674 @ SY673 @ SY672 ) ) @ SY674 )
                & ~ ( Xphi @ ( kpair @ ( sK81_Xx @ Xphi @ SY674 @ SY673 @ SY672 ) @ ( sK82_SY1880 @ Xphi @ SY674 @ SY673 @ SY672 ) ) ) )
              | ! [Xx: $i] :
                  ( ~ ( in @ Xx @ SY674 )
                  | ( Xphi @ Xx ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[202]) ).

thf(428,plain,
    ( ( ! [SY682: $i,SY683: $i > $o] :
          ( ~ ( singleton
              @ ( dsetconstr @ SY682
                @ ^ [SY687: $i] : ( SY683 @ SY687 ) ) )
          | ! [Xx: $i] :
              ( ~ ( in @ Xx @ SY682 )
              | ! [Xy: $i] :
                  ( ~ ( in @ Xy @ SY682 )
                  | ~ ( SY683 @ Xx )
                  | ~ ( SY683 @ Xy )
                  | ( Xx = Xy ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[203]) ).

thf(429,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(extcnf_combined,[status(esa)],[204]) ).

thf(430,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(extcnf_combined,[status(esa)],[205]) ).

thf(431,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(extcnf_combined,[status(esa)],[206]) ).

thf(432,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ~ ( func @ A @ B @ Xf )
          | ! [Xg: $i] :
              ( ~ ( func @ A @ B @ Xg )
              | ( ( in @ ( sK83_Xx @ Xg @ Xf @ B @ A ) @ A )
                & ( ( ap @ A @ B @ Xf @ ( sK83_Xx @ Xg @ Xf @ B @ A ) )
                 != ( ap @ A @ B @ Xg @ ( sK83_Xx @ Xg @ Xf @ B @ A ) ) ) )
              | ! [Xx: $i] :
                  ( ~ ( in @ Xx @ A )
                  | ! [Xy: $i] :
                      ( ~ ( in @ Xy @ B )
                      | ~ ( in @ ( kpair @ Xx @ Xy ) @ Xg )
                      | ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[207]) ).

thf(433,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(extcnf_combined,[status(esa)],[208]) ).

thf(434,plain,
    ( ( ! [SY715: $i,SY716: $i,SY717: $i] :
          ( ~ ( subset @ SY717 @ ( cartprod @ SY715 @ SY716 ) )
          | ! [SY721: $i] :
              ( ~ ( subset @ SY721 @ ( cartprod @ SY715 @ SY716 ) )
              | ( ( in @ ( sK84_Xx @ SY721 @ SY717 @ SY716 @ SY715 ) @ SY715 )
                & ( in @ ( sK85_SY1881 @ SY721 @ SY717 @ SY716 @ SY715 ) @ SY716 )
                & ( in @ ( kpair @ ( sK84_Xx @ SY721 @ SY717 @ SY716 @ SY715 ) @ ( sK85_SY1881 @ SY721 @ SY717 @ SY716 @ SY715 ) ) @ SY717 )
                & ~ ( in @ ( kpair @ ( sK84_Xx @ SY721 @ SY717 @ SY716 @ SY715 ) @ ( sK85_SY1881 @ SY721 @ SY717 @ SY716 @ SY715 ) ) @ SY721 ) )
              | ( subset @ SY717 @ SY721 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[209]) ).

thf(435,plain,
    ( ( ! [SY727: $i,SY728: $i,SY729: $i] :
          ( ~ ( subset @ SY729 @ ( cartprod @ SY727 @ SY728 ) )
          | ! [SY733: $i] :
              ( ~ ( subset @ SY733 @ ( cartprod @ SY727 @ SY728 ) )
              | ( ( in @ ( sK88_Xx @ SY733 @ SY729 @ SY728 @ SY727 ) @ SY727 )
                & ( in @ ( sK89_SY1883 @ SY733 @ SY729 @ SY728 @ SY727 ) @ SY728 )
                & ( in @ ( kpair @ ( sK88_Xx @ SY733 @ SY729 @ SY728 @ SY727 ) @ ( sK89_SY1883 @ SY733 @ SY729 @ SY728 @ SY727 ) ) @ SY729 )
                & ~ ( in @ ( kpair @ ( sK88_Xx @ SY733 @ SY729 @ SY728 @ SY727 ) @ ( sK89_SY1883 @ SY733 @ SY729 @ SY728 @ SY727 ) ) @ SY733 ) )
              | ( ( in @ ( sK86_Xx @ SY733 @ SY729 @ SY728 @ SY727 ) @ SY727 )
                & ( in @ ( sK87_SY1882 @ SY733 @ SY729 @ SY728 @ SY727 ) @ SY728 )
                & ( in @ ( kpair @ ( sK86_Xx @ SY733 @ SY729 @ SY728 @ SY727 ) @ ( sK87_SY1882 @ SY733 @ SY729 @ SY728 @ SY727 ) ) @ SY733 )
                & ~ ( in @ ( kpair @ ( sK86_Xx @ SY733 @ SY729 @ SY728 @ SY727 ) @ ( sK87_SY1882 @ SY733 @ SY729 @ SY728 @ SY727 ) ) @ SY729 ) )
              | ( SY729 = SY733 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[210]) ).

thf(436,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ~ ( func @ A @ B @ Xf )
          | ! [Xg: $i] :
              ( ~ ( func @ A @ B @ Xg )
              | ( ( in @ ( sK90_Xx @ Xg @ Xf @ B @ A ) @ A )
                & ( ( ap @ A @ B @ Xf @ ( sK90_Xx @ Xg @ Xf @ B @ A ) )
                 != ( ap @ A @ B @ Xg @ ( sK90_Xx @ Xg @ Xf @ B @ A ) ) ) )
              | ( Xf = Xg ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[211]) ).

thf(437,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ~ ( in @ Xf @ ( funcSet @ A @ B ) )
          | ! [Xg: $i] :
              ( ~ ( in @ Xg @ ( funcSet @ A @ B ) )
              | ( ( in @ ( sK91_Xx @ Xg @ Xf @ B @ A ) @ A )
                & ( ( ap @ A @ B @ Xf @ ( sK91_Xx @ Xg @ Xf @ B @ A ) )
                 != ( ap @ A @ B @ Xg @ ( sK91_Xx @ Xg @ Xf @ B @ A ) ) ) )
              | ( Xf = Xg ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[212]) ).

thf(438,plain,
    ( ( ! [A: $i] :
          ( ! [B: $i,Xf: $i] :
              ~ ( in @ Xf @ ( funcSet @ A @ B ) )
          | ! [Xx: $i] :
              ~ ( in @ Xx @ A )
          | $true ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[213]) ).

thf(439,plain,
    ( ( ! [A: $i] :
          ( ! [B: $i,Xf: $i] :
              ~ ( func @ A @ B @ Xf )
          | ! [Xx: $i] :
              ~ ( in @ Xx @ A )
          | $true ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[214]) ).

thf(440,plain,
    ( ( ! [A: $i,B: $i,Xf: $i > $i] :
          ( ( ( in @ ( sK92_Xx @ Xf @ B @ A ) @ A )
            & ~ ( in @ ( Xf @ ( sK92_Xx @ Xf @ B @ A ) ) @ B ) )
          | ! [Xx: $i] :
              ( ~ ( in @ Xx @ A )
              | ( ( ap @ A @ B
                  @ ( lam @ A @ B
                    @ ^ [Xy: $i] : ( Xf @ Xy ) )
                  @ Xx )
                = ( Xf @ Xx ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[215]) ).

thf(441,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ~ ( func @ A @ B @ Xf )
          | ( ( lam @ A @ B
              @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
            = Xf ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[216]) ).

thf(442,plain,
    ( ( ! [A: $i] :
          ( ! [B: $i,Xf: $i > $i] :
              ( ( in @ ( sK93_Xx @ Xf @ B @ A ) @ A )
              & ~ ( in @ ( Xf @ ( sK93_Xx @ Xf @ B @ A ) ) @ B ) )
          | $true ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[217]) ).

thf(443,plain,
    ( ( ! [A: $i,B: $i,Xf: $i > $i] :
          ( ( ( in @ ( sK94_Xx @ Xf @ B @ A ) @ A )
            & ~ ( in @ ( Xf @ ( sK94_Xx @ Xf @ B @ A ) ) @ B ) )
          | ! [Xx: $i] :
              ( ~ ( in @ Xx @ A )
              | ( ( ap @ A @ B
                  @ ( lam @ A @ B
                    @ ^ [Xy: $i] : ( Xf @ Xy ) )
                  @ Xx )
                = ( Xf @ Xx ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[218]) ).

thf(444,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(extcnf_combined,[status(esa)],[219]) ).

thf(445,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(extcnf_combined,[status(esa)],[220]) ).

thf(446,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(extcnf_combined,[status(esa)],[221]) ).

thf(447,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(extcnf_combined,[status(esa)],[222]) ).

thf(448,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(extcnf_combined,[status(esa)],[223]) ).

thf(449,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(extcnf_combined,[status(esa)],[224]) ).

thf(450,plain,
    ( ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ! [Xy: $i] :
              ( ~ ( in @ Xy @ A )
              | ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[225]) ).

thf(451,plain,
    ( ( ! [X: $i] :
          ( ~ ( singleton @ X )
          | ! [Xx: $i] :
              ( ~ ( in @ Xx @ X )
              | ( ( setunion @ X )
                = Xx ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[226]) ).

thf(452,plain,
    ( ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ! [Xy: $i] :
              ( ~ ( in @ Xy @ A )
              | ~ Xphi
              | ( ( if @ A @ Xphi @ Xx @ Xy )
                = Xx ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[227]) ).

thf(453,plain,
    ( ( ! [A: $i,Xphi: $o,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ! [Xy: $i] :
              ( ~ ( in @ Xy @ A )
              | Xphi
              | ( ( if @ A @ Xphi @ Xx @ Xy )
                = Xy ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[228]) ).

thf(454,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(extcnf_combined,[status(esa)],[229]) ).

thf(455,plain,
    ( ( ! [A: $i,X: $i] :
          ( ~ ( in @ X @ ( powerset @ A ) )
          | ! [Y: $i] :
              ( ~ ( in @ Y @ ( powerset @ A ) )
              | ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[230]) ).

thf(456,plain,
    ( ( ! [A: $i,X: $i] :
          ( ~ ( in @ X @ ( powerset @ A ) )
          | ! [Y: $i] :
              ( ~ ( in @ Y @ ( powerset @ A ) )
              | ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[231]) ).

thf(457,plain,
    ( ( ! [A: $i,X: $i] :
          ( ~ ( in @ X @ ( powerset @ A ) )
          | ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[232]) ).

thf(458,plain,
    ( ( ! [A: $i,X: $i] :
          ( ~ ( in @ X @ ( powerset @ A ) )
          | ! [Y: $i] :
              ( ~ ( in @ Y @ ( powerset @ A ) )
              | ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[233]) ).

thf(459,plain,
    ( ( ! [A: $i,X: $i] :
          ( ~ ( in @ X @ ( powerset @ A ) )
          | ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[234]) ).

thf(460,plain,
    ( ( ! [A: $i,X: $i] :
          ( ~ ( in @ X @ ( powerset @ A ) )
          | ! [Y: $i] :
              ( ~ ( in @ Y @ ( powerset @ A ) )
              | ( ( in @ ( sK96_Xx @ Y @ X @ A ) @ A )
                & ( in @ ( sK96_Xx @ Y @ X @ A ) @ X )
                & ~ ( in @ ( sK96_Xx @ Y @ X @ A ) @ Y ) )
              | ( ( in @ ( sK95_Xx @ Y @ X @ A ) @ A )
                & ( in @ ( sK95_Xx @ Y @ X @ A ) @ Y )
                & ~ ( in @ ( sK95_Xx @ Y @ X @ A ) @ X ) )
              | ( X = Y ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[235]) ).

thf(461,plain,
    ( ( ! [A: $i,X: $i] :
          ( ~ ( in @ X @ ( powerset @ A ) )
          | ! [Y: $i] :
              ( ~ ( in @ Y @ ( powerset @ A ) )
              | ( ( in @ ( sK97_Xx @ Y @ X @ A ) @ A )
                & ( in @ ( sK97_Xx @ Y @ X @ A ) @ X )
                & ~ ( in @ ( sK97_Xx @ Y @ X @ A ) @ Y ) )
              | ( subset @ X @ Y ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[236]) ).

thf(462,plain,
    ( ( ! [A: $i,X: $i] :
          ( ~ ( in @ X @ ( powerset @ A ) )
          | ! [Y: $i] :
              ( ~ ( in @ Y @ ( powerset @ A ) )
              | ( ( in @ ( sK98_Xx @ Y @ X @ A ) @ A )
                & ( in @ ( sK98_Xx @ Y @ X @ A ) @ X )
                & ~ ( in @ ( sK98_Xx @ Y @ X @ A ) @ Y ) )
              | ( in @ X @ ( powerset @ Y ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[237]) ).

thf(463,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(extcnf_combined,[status(esa)],[238]) ).

thf(464,plain,
    ( ( ! [A: $i,X: $i] :
          ( ~ ( in @ X @ ( powerset @ A ) )
          | ! [Xx: $i] :
              ( ~ ( in @ Xx @ A )
              | ~ ( in @ Xx @ X )
              | ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[239]) ).

thf(465,plain,
    ( ( ! [A: $i,X: $i] :
          ( ~ ( in @ X @ ( powerset @ A ) )
          | ! [Xx: $i] :
              ( ~ ( in @ Xx @ A )
              | ( in @ Xx @ ( setminus @ A @ X ) )
              | ( in @ Xx @ X ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[240]) ).

thf(466,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(extcnf_combined,[status(esa)],[241]) ).

thf(467,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(extcnf_combined,[status(esa)],[242]) ).

thf(468,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(extcnf_combined,[status(esa)],[243]) ).

thf(469,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(extcnf_combined,[status(esa)],[244]) ).

thf(470,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(extcnf_combined,[status(esa)],[245]) ).

thf(471,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(extcnf_combined,[status(esa)],[246]) ).

thf(472,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(extcnf_combined,[status(esa)],[247]) ).

thf(473,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(extcnf_combined,[status(esa)],[248]) ).

thf(474,plain,
    ( ( ! [A: $i,X: $i] :
          ( ~ ( in @ X @ ( powerset @ A ) )
          | ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[249]) ).

thf(475,plain,
    ( ( ! [A: $i,X: $i] :
          ( ~ ( in @ X @ ( powerset @ A ) )
          | ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[250]) ).

thf(476,plain,
    ( ( ! [A: $i,X: $i] :
          ( ~ ( in @ X @ ( powerset @ A ) )
          | ( X
            = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[251]) ).

thf(477,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(extcnf_combined,[status(esa)],[252]) ).

thf(478,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(extcnf_combined,[status(esa)],[253]) ).

thf(479,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(extcnf_combined,[status(esa)],[254]) ).

thf(480,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(extcnf_combined,[status(esa)],[255]) ).

thf(481,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(extcnf_combined,[status(esa)],[256]) ).

thf(482,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(extcnf_combined,[status(esa)],[257]) ).

thf(483,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(extcnf_combined,[status(esa)],[258]) ).

thf(484,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(extcnf_combined,[status(esa)],[259]) ).

thf(485,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(extcnf_combined,[status(esa)],[260]) ).

thf(486,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)],[485]) ).

thf(487,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)],[484]) ).

thf(488,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)],[483]) ).

thf(489,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)],[482]) ).

thf(490,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)],[481]) ).

thf(491,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)],[480]) ).

thf(492,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)],[479]) ).

thf(493,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)],[478]) ).

thf(494,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)],[477]) ).

thf(495,plain,
    ( ( ! [A: $i,X: $i] :
          ( ~ ( in @ X @ ( powerset @ A ) )
          | ( X
            = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[476]) ).

thf(496,plain,
    ( ( ! [A: $i,X: $i] :
          ( ~ ( in @ X @ ( powerset @ A ) )
          | ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[475]) ).

thf(497,plain,
    ( ( ! [A: $i,X: $i] :
          ( ~ ( in @ X @ ( powerset @ A ) )
          | ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[474]) ).

thf(498,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)],[473]) ).

thf(499,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)],[472]) ).

thf(500,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)],[471]) ).

thf(501,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)],[470]) ).

thf(502,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)],[469]) ).

thf(503,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)],[468]) ).

thf(504,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)],[467]) ).

thf(505,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)],[466]) ).

thf(506,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)],[465]) ).

thf(507,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)],[464]) ).

thf(508,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)],[463]) ).

thf(509,plain,
    ( ( ! [A: $i,X: $i] :
          ( ~ ( in @ X @ ( powerset @ A ) )
          | ! [Y: $i] :
              ( ~ ( in @ Y @ ( powerset @ A ) )
              | ( ( in @ ( sK98_Xx @ Y @ X @ A ) @ A )
                & ( in @ ( sK98_Xx @ Y @ X @ A ) @ X )
                & ~ ( in @ ( sK98_Xx @ Y @ X @ A ) @ Y ) )
              | ( in @ X @ ( powerset @ Y ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[462]) ).

thf(510,plain,
    ( ( ! [A: $i,X: $i] :
          ( ~ ( in @ X @ ( powerset @ A ) )
          | ! [Y: $i] :
              ( ~ ( in @ Y @ ( powerset @ A ) )
              | ( ( in @ ( sK97_Xx @ Y @ X @ A ) @ A )
                & ( in @ ( sK97_Xx @ Y @ X @ A ) @ X )
                & ~ ( in @ ( sK97_Xx @ Y @ X @ A ) @ Y ) )
              | ( subset @ X @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[461]) ).

thf(511,plain,
    ( ( ! [A: $i,X: $i] :
          ( ~ ( in @ X @ ( powerset @ A ) )
          | ! [Y: $i] :
              ( ~ ( in @ Y @ ( powerset @ A ) )
              | ( ( in @ ( sK96_Xx @ Y @ X @ A ) @ A )
                & ( in @ ( sK96_Xx @ Y @ X @ A ) @ X )
                & ~ ( in @ ( sK96_Xx @ Y @ X @ A ) @ Y ) )
              | ( ( in @ ( sK95_Xx @ Y @ X @ A ) @ A )
                & ( in @ ( sK95_Xx @ Y @ X @ A ) @ Y )
                & ~ ( in @ ( sK95_Xx @ Y @ X @ A ) @ X ) )
              | ( X = Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[460]) ).

thf(512,plain,
    ( ( ! [A: $i,X: $i] :
          ( ~ ( in @ X @ ( powerset @ A ) )
          | ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[459]) ).

thf(513,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)],[458]) ).

thf(514,plain,
    ( ( ! [A: $i,X: $i] :
          ( ~ ( in @ X @ ( powerset @ A ) )
          | ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[457]) ).

thf(515,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)],[456]) ).

thf(516,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)],[455]) ).

thf(517,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)],[454]) ).

thf(518,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)],[453]) ).

thf(519,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)],[452]) ).

thf(520,plain,
    ( ( ! [X: $i] :
          ( ~ ( singleton @ X )
          | ! [Xx: $i] :
              ( ~ ( in @ Xx @ X )
              | ( ( setunion @ X )
                = Xx ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[451]) ).

thf(521,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)],[450]) ).

thf(522,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)],[449]) ).

thf(523,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)],[448]) ).

thf(524,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)],[447]) ).

thf(525,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)],[446]) ).

thf(526,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)],[445]) ).

thf(527,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)],[444]) ).

thf(528,plain,
    ( ( ! [A: $i,B: $i,Xf: $i > $i] :
          ( ( ( in @ ( sK94_Xx @ Xf @ B @ A ) @ A )
            & ~ ( in @ ( Xf @ ( sK94_Xx @ Xf @ B @ A ) ) @ B ) )
          | ! [Xx: $i] :
              ( ~ ( in @ Xx @ A )
              | ( ( ap @ A @ B
                  @ ( lam @ A @ B
                    @ ^ [Xy: $i] : ( Xf @ Xy ) )
                  @ Xx )
                = ( Xf @ Xx ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[443]) ).

thf(529,plain,
    ( ( ! [A: $i] :
          ( ! [B: $i,Xf: $i > $i] :
              ( ( in @ ( sK93_Xx @ Xf @ B @ A ) @ A )
              & ~ ( in @ ( Xf @ ( sK93_Xx @ Xf @ B @ A ) ) @ B ) )
          | $true ) )
    = $true ),
    inference(copy,[status(thm)],[442]) ).

thf(530,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)],[441]) ).

thf(531,plain,
    ( ( ! [A: $i,B: $i,Xf: $i > $i] :
          ( ( ( in @ ( sK92_Xx @ Xf @ B @ A ) @ A )
            & ~ ( in @ ( Xf @ ( sK92_Xx @ Xf @ B @ A ) ) @ B ) )
          | ! [Xx: $i] :
              ( ~ ( in @ Xx @ A )
              | ( ( ap @ A @ B
                  @ ( lam @ A @ B
                    @ ^ [Xy: $i] : ( Xf @ Xy ) )
                  @ Xx )
                = ( Xf @ Xx ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[440]) ).

thf(532,plain,
    ( ( ! [A: $i] :
          ( ! [B: $i,Xf: $i] :
              ~ ( func @ A @ B @ Xf )
          | ! [Xx: $i] :
              ~ ( in @ Xx @ A )
          | $true ) )
    = $true ),
    inference(copy,[status(thm)],[439]) ).

thf(533,plain,
    ( ( ! [A: $i] :
          ( ! [B: $i,Xf: $i] :
              ~ ( in @ Xf @ ( funcSet @ A @ B ) )
          | ! [Xx: $i] :
              ~ ( in @ Xx @ A )
          | $true ) )
    = $true ),
    inference(copy,[status(thm)],[438]) ).

thf(534,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ~ ( in @ Xf @ ( funcSet @ A @ B ) )
          | ! [Xg: $i] :
              ( ~ ( in @ Xg @ ( funcSet @ A @ B ) )
              | ( ( in @ ( sK91_Xx @ Xg @ Xf @ B @ A ) @ A )
                & ( ( ap @ A @ B @ Xf @ ( sK91_Xx @ Xg @ Xf @ B @ A ) )
                 != ( ap @ A @ B @ Xg @ ( sK91_Xx @ Xg @ Xf @ B @ A ) ) ) )
              | ( Xf = Xg ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[437]) ).

thf(535,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ~ ( func @ A @ B @ Xf )
          | ! [Xg: $i] :
              ( ~ ( func @ A @ B @ Xg )
              | ( ( in @ ( sK90_Xx @ Xg @ Xf @ B @ A ) @ A )
                & ( ( ap @ A @ B @ Xf @ ( sK90_Xx @ Xg @ Xf @ B @ A ) )
                 != ( ap @ A @ B @ Xg @ ( sK90_Xx @ Xg @ Xf @ B @ A ) ) ) )
              | ( Xf = Xg ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[436]) ).

thf(536,plain,
    ( ( ! [SY727: $i,SY728: $i,SY729: $i] :
          ( ~ ( subset @ SY729 @ ( cartprod @ SY727 @ SY728 ) )
          | ! [SY733: $i] :
              ( ~ ( subset @ SY733 @ ( cartprod @ SY727 @ SY728 ) )
              | ( ( in @ ( sK88_Xx @ SY733 @ SY729 @ SY728 @ SY727 ) @ SY727 )
                & ( in @ ( sK89_SY1883 @ SY733 @ SY729 @ SY728 @ SY727 ) @ SY728 )
                & ( in @ ( kpair @ ( sK88_Xx @ SY733 @ SY729 @ SY728 @ SY727 ) @ ( sK89_SY1883 @ SY733 @ SY729 @ SY728 @ SY727 ) ) @ SY729 )
                & ~ ( in @ ( kpair @ ( sK88_Xx @ SY733 @ SY729 @ SY728 @ SY727 ) @ ( sK89_SY1883 @ SY733 @ SY729 @ SY728 @ SY727 ) ) @ SY733 ) )
              | ( ( in @ ( sK86_Xx @ SY733 @ SY729 @ SY728 @ SY727 ) @ SY727 )
                & ( in @ ( sK87_SY1882 @ SY733 @ SY729 @ SY728 @ SY727 ) @ SY728 )
                & ( in @ ( kpair @ ( sK86_Xx @ SY733 @ SY729 @ SY728 @ SY727 ) @ ( sK87_SY1882 @ SY733 @ SY729 @ SY728 @ SY727 ) ) @ SY733 )
                & ~ ( in @ ( kpair @ ( sK86_Xx @ SY733 @ SY729 @ SY728 @ SY727 ) @ ( sK87_SY1882 @ SY733 @ SY729 @ SY728 @ SY727 ) ) @ SY729 ) )
              | ( SY729 = SY733 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[435]) ).

thf(537,plain,
    ( ( ! [SY715: $i,SY716: $i,SY717: $i] :
          ( ~ ( subset @ SY717 @ ( cartprod @ SY715 @ SY716 ) )
          | ! [SY721: $i] :
              ( ~ ( subset @ SY721 @ ( cartprod @ SY715 @ SY716 ) )
              | ( ( in @ ( sK84_Xx @ SY721 @ SY717 @ SY716 @ SY715 ) @ SY715 )
                & ( in @ ( sK85_SY1881 @ SY721 @ SY717 @ SY716 @ SY715 ) @ SY716 )
                & ( in @ ( kpair @ ( sK84_Xx @ SY721 @ SY717 @ SY716 @ SY715 ) @ ( sK85_SY1881 @ SY721 @ SY717 @ SY716 @ SY715 ) ) @ SY717 )
                & ~ ( in @ ( kpair @ ( sK84_Xx @ SY721 @ SY717 @ SY716 @ SY715 ) @ ( sK85_SY1881 @ SY721 @ SY717 @ SY716 @ SY715 ) ) @ SY721 ) )
              | ( subset @ SY717 @ SY721 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[434]) ).

thf(538,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)],[433]) ).

thf(539,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ~ ( func @ A @ B @ Xf )
          | ! [Xg: $i] :
              ( ~ ( func @ A @ B @ Xg )
              | ( ( in @ ( sK83_Xx @ Xg @ Xf @ B @ A ) @ A )
                & ( ( ap @ A @ B @ Xf @ ( sK83_Xx @ Xg @ Xf @ B @ A ) )
                 != ( ap @ A @ B @ Xg @ ( sK83_Xx @ Xg @ Xf @ B @ A ) ) ) )
              | ! [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)],[432]) ).

thf(540,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)],[431]) ).

thf(541,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)],[430]) ).

thf(542,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)],[429]) ).

thf(543,plain,
    ( ( ! [SY682: $i,SY683: $i > $o] :
          ( ~ ( singleton
              @ ( dsetconstr @ SY682
                @ ^ [SY687: $i] : ( SY683 @ SY687 ) ) )
          | ! [Xx: $i] :
              ( ~ ( in @ Xx @ SY682 )
              | ! [Xy: $i] :
                  ( ~ ( in @ Xy @ SY682 )
                  | ~ ( SY683 @ Xx )
                  | ~ ( SY683 @ Xy )
                  | ( Xx = Xy ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[428]) ).

thf(544,plain,
    ( ( ! [SY672: $i,SY673: $i,SY674: $i] :
          ( ~ ( subset @ SY674 @ ( cartprod @ SY672 @ SY673 ) )
          | ! [Xphi: $i > $o] :
              ( ( ( in @ ( sK81_Xx @ Xphi @ SY674 @ SY673 @ SY672 ) @ SY672 )
                & ( in @ ( sK82_SY1880 @ Xphi @ SY674 @ SY673 @ SY672 ) @ SY673 )
                & ( in @ ( kpair @ ( sK81_Xx @ Xphi @ SY674 @ SY673 @ SY672 ) @ ( sK82_SY1880 @ Xphi @ SY674 @ SY673 @ SY672 ) ) @ SY674 )
                & ~ ( Xphi @ ( kpair @ ( sK81_Xx @ Xphi @ SY674 @ SY673 @ SY672 ) @ ( sK82_SY1880 @ Xphi @ SY674 @ SY673 @ SY672 ) ) ) )
              | ! [Xx: $i] :
                  ( ~ ( in @ Xx @ SY674 )
                  | ( Xphi @ Xx ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[427]) ).

thf(545,plain,
    ( ( ! [SY662: $i,SY663: $i,SY664: $i] :
          ( ~ ( subset @ SY664 @ ( cartprod @ SY662 @ SY663 ) )
          | ! [Xphi: $i > $o] :
              ( ( ( in @ ( sK79_Xx @ Xphi @ SY664 @ SY663 @ SY662 ) @ SY662 )
                & ( in @ ( sK80_SY1879 @ Xphi @ SY664 @ SY663 @ SY662 ) @ SY663 )
                & ( in @ ( kpair @ ( sK79_Xx @ Xphi @ SY664 @ SY663 @ SY662 ) @ ( sK80_SY1879 @ Xphi @ SY664 @ SY663 @ SY662 ) ) @ SY664 )
                & ~ ( Xphi @ ( kpair @ ( sK79_Xx @ Xphi @ SY664 @ SY663 @ SY662 ) @ ( sK80_SY1879 @ Xphi @ SY664 @ SY663 @ SY662 ) ) ) )
              | ! [Xx: $i] :
                  ( ~ ( in @ Xx @ SY664 )
                  | ( Xphi @ Xx ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[426]) ).

thf(546,plain,
    ( ( ! [A: $i,B: $i,Xf: $i > $i] :
          ( ( ( in @ ( sK78_Xx @ Xf @ B @ A ) @ A )
            & ~ ( in @ ( Xf @ ( sK78_Xx @ Xf @ B @ A ) ) @ B ) )
          | ( in
            @ ( lam @ A @ B
              @ ^ [Xx: $i] : ( Xf @ Xx ) )
            @ ( funcSet @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[425]) ).

thf(547,plain,
    ( ( ! [A: $i,B: $i,Xf: $i > $i] :
          ( ( ( in @ ( sK77_Xx @ Xf @ B @ A ) @ A )
            & ~ ( in @ ( Xf @ ( sK77_Xx @ Xf @ B @ A ) ) @ B ) )
          | ( func @ A @ B
            @ ( lam @ A @ B
              @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[424]) ).

thf(548,plain,
    ( ( ! [A: $i,B: $i,Xf: $i > $i] :
          ( ( ( in @ ( sK76_Xx @ Xf @ B @ A ) @ A )
            & ~ ( in @ ( Xf @ ( sK76_Xx @ Xf @ B @ A ) ) @ B ) )
          | ( func @ A @ B
            @ ( dpsetconstr @ A @ B
              @ ^ [Xx: $i,Xy: $i] :
                  ( ( Xf @ Xx )
                  = Xy ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[423]) ).

thf(549,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ~ ( func @ A @ B @ Xf )
          | ( in @ Xf @ ( funcSet @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[422]) ).

thf(550,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)],[421]) ).

thf(551,plain,
    ( ( ! [A: $i,B: $i,Xf: $i] :
          ( ~ ( in @ Xf @ ( funcSet @ A @ B ) )
          | ( func @ A @ B @ Xf ) ) )
    = $true ),
    inference(copy,[status(thm)],[420]) ).

thf(552,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)],[419]) ).

thf(553,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)],[418]) ).

thf(554,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)],[417]) ).

thf(555,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)],[416]) ).

thf(556,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)],[415]) ).

thf(557,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)],[414]) ).

thf(558,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)],[413]) ).

thf(559,plain,
    ( ( ! [SY586: $i,SY587: $i,SY588: $i > $i > $o] :
          ( subset
          @ ( dpsetconstr @ SY586 @ SY587
            @ ^ [Xx: $i,Xy: $i] : ( SY588 @ Xx @ Xy ) )
          @ ( cartprod @ SY586 @ SY587 ) ) )
    = $true ),
    inference(copy,[status(thm)],[187]) ).

thf(560,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(561,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)],[412]) ).

thf(562,plain,
    ( ( ! [A: $i,B: $i,Xu: $i] :
          ( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
          | ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
            = Xu ) ) )
    = $true ),
    inference(copy,[status(thm)],[411]) ).

thf(563,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)],[410]) ).

thf(564,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)],[409]) ).

thf(565,plain,
    ( ( ! [A: $i] :
          ( ! [Xx: $i] :
              ~ ( in @ Xx @ A )
          | ! [B: $i,Xy: $i] :
              ~ ( in @ Xy @ B )
          | $true ) )
    = $true ),
    inference(copy,[status(thm)],[408]) ).

thf(566,plain,
    ( ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
          ( ~ ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
          | ( in @ Xy @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[407]) ).

thf(567,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ! [Xy: $i] :
              ~ ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
          | ( in @ Xx @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[406]) ).

thf(568,plain,
    ( ( ! [A: $i,B: $i,Xu: $i] :
          ( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
          | ( in @ ( ksnd @ Xu ) @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[405]) ).

thf(569,plain,
    ( ( ! [Xu: $i] :
          ( ~ ( iskpair @ Xu )
          | ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
            = Xu ) ) )
    = $true ),
    inference(copy,[status(thm)],[404]) ).

thf(570,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( ksnd @ ( kpair @ Xx @ Xy ) )
          = Xy ) )
    = $true ),
    inference(copy,[status(thm)],[176]) ).

thf(571,plain,
    ( ( ! [Xu: $i] :
          ( ~ ( iskpair @ Xu )
          | ( singleton
            @ ( dsetconstr @ ( setunion @ Xu )
              @ ^ [Xx: $i] :
                  ( Xu
                  = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[403]) ).

thf(572,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
          ( ( ( kpair @ Xx @ Xy )
           != ( kpair @ Xz @ Xu ) )
          | ( Xy = Xu ) ) )
    = $true ),
    inference(copy,[status(thm)],[402]) ).

thf(573,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)],[401]) ).

thf(574,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ! [Xz: $i] :
              ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
             != ( setadjoin @ Xz @ emptyset ) )
          | ( Xx = Xy ) ) )
    = $true ),
    inference(copy,[status(thm)],[400]) ).

thf(575,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)],[399]) ).

thf(576,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)],[398]) ).

thf(577,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( Xx != Xy )
          | ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
            = ( setadjoin @ Xx @ emptyset ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[397]) ).

thf(578,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i] :
          ( ! [Xu: $i] :
              ( ( kpair @ Xx @ Xy )
             != ( kpair @ Xz @ Xu ) )
          | ( Xx = Xz ) ) )
    = $true ),
    inference(copy,[status(thm)],[396]) ).

thf(579,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)],[395]) ).

thf(580,plain,
    ( ( ! [A: $i,B: $i,Xu: $i] :
          ( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
          | ( in @ ( kfst @ Xu ) @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[394]) ).

thf(581,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( kfst @ ( kpair @ Xx @ Xy ) )
          = Xx ) )
    = $true ),
    inference(copy,[status(thm)],[165]) ).

thf(582,plain,
    ( ( ! [X: $i] :
          ( ~ ( singleton @ X )
          | ( in @ ( setunion @ X ) @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[393]) ).

thf(583,plain,
    ( ( ! [Xu: $i] :
          ( ~ ( iskpair @ Xu )
          | ( singleton
            @ ( dsetconstr @ ( setunion @ Xu )
              @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[392]) ).

thf(584,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)],[391]) ).

thf(585,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( ( setadjoin @ Xx @ emptyset )
           != ( setadjoin @ Xy @ emptyset ) )
          | ( Xx = Xy ) ) )
    = $true ),
    inference(copy,[status(thm)],[390]) ).

thf(586,plain,
    ( ( ! [SY494: $i,SY495: $i > $o] :
          ( ( ( in @ ( sK74_Xx @ SY495 @ SY494 ) @ SY494 )
            & ( in @ ( sK75_SY1878 @ SY495 @ SY494 ) @ SY494 )
            & ( SY495 @ ( sK74_Xx @ SY495 @ SY494 ) )
            & ( SY495 @ ( sK75_SY1878 @ SY495 @ SY494 ) )
            & ( ( sK74_Xx @ SY495 @ SY494 )
             != ( sK75_SY1878 @ SY495 @ SY494 ) ) )
          | ! [Xx: $i] :
              ( ~ ( SY495 @ Xx )
              | ~ ( in @ Xx @ SY494 ) )
          | ( singleton
            @ ( dsetconstr @ SY494
              @ ^ [SY502: $i] : ( SY495 @ SY502 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[389]) ).

thf(587,plain,
    ( ( ! [SY486: $i,SY487: $i > $o,SY488: $i] :
          ( ~ ( in @ SY488 @ SY486 )
          | ~ ( SY487 @ SY488 )
          | ( ( in @ ( sK73_Xy @ SY488 @ SY487 @ SY486 ) @ SY486 )
            & ( SY487 @ ( sK73_Xy @ SY488 @ SY487 @ SY486 ) )
            & ( ( sK73_Xy @ SY488 @ SY487 @ SY486 )
             != SY488 ) )
          | ( singleton
            @ ( dsetconstr @ SY486
              @ ^ [SY493: $i] : ( SY487 @ SY493 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[388]) ).

thf(588,plain,
    ( ( ! [SY479: $i,SY480: $i > $o] :
          ( ~ ( singleton
              @ ( dsetconstr @ SY479
                @ ^ [SY484: $i] : ( SY480 @ SY484 ) ) )
          | ( ( SY480 @ ( sK72_Xx @ SY480 @ SY479 ) )
            & ( in @ ( sK72_Xx @ SY480 @ SY479 ) @ SY479 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[387]) ).

thf(589,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ( ( in @ ( sK70_Xx @ Xphi @ A ) @ A )
            & ( in @ ( sK71_SY1877 @ Xphi @ A ) @ A )
            & ( Xphi @ ( sK70_Xx @ Xphi @ A ) )
            & ( Xphi @ ( sK71_SY1877 @ Xphi @ A ) )
            & ( ( sK70_Xx @ Xphi @ A )
             != ( sK71_SY1877 @ Xphi @ A ) ) )
          | ! [Xx: $i] :
              ( ~ ( Xphi @ Xx )
              | ~ ( in @ Xx @ A ) )
          | ( singleton
            @ ( dsetconstr @ A
              @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[386]) ).

thf(590,plain,
    ( ( ! [Xx: $i] :
          ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
          = Xx ) )
    = $true ),
    inference(copy,[status(thm)],[156]) ).

thf(591,plain,
    ( ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[155]) ).

thf(592,plain,
    ( ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) )
    = $true ),
    inference(copy,[status(thm)],[154]) ).

thf(593,plain,
    ( ( ! [A: $i,Xx: $i] :
          ( ~ ( in @ Xx @ ( setunion @ A ) )
          | ( ( in @ ( sK69_X @ Xx @ A ) @ A )
            & ( in @ Xx @ ( sK69_X @ Xx @ A ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[385]) ).

thf(594,plain,
    ( ( ! [A: $i,B: $i,Xu: $i] :
          ( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
          | ( iskpair @ Xu ) ) )
    = $true ),
    inference(copy,[status(thm)],[384]) ).

thf(595,plain,
    ( ( ! [A: $i,B: $i,Xu: $i] :
          ( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
          | ( ( Xu
              = ( kpair @ ( sK67_Xx @ Xu @ B @ A ) @ ( sK68_SY1876 @ Xu @ B @ A ) ) )
            & ( in @ ( sK68_SY1876 @ Xu @ B @ A ) @ B )
            & ( in @ ( sK67_Xx @ Xu @ B @ A ) @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[383]) ).

thf(596,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)],[382]) ).

thf(597,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)],[381]) ).

thf(598,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)],[380]) ).

thf(599,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)],[379]) ).

thf(600,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)],[378]) ).

thf(601,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)],[377]) ).

thf(602,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i] :
          ( ~ ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
          | ( Xz = Xx )
          | ( Xz = Xy ) ) )
    = $true ),
    inference(copy,[status(thm)],[376]) ).

thf(603,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[375]) ).

thf(604,plain,
    ( ( ! [A: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[374]) ).

thf(605,plain,
    ( ( ! [A: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[373]) ).

thf(606,plain,
    ( ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) )
    = $true ),
    inference(copy,[status(thm)],[140]) ).

thf(607,plain,
    ( ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[139]) ).

thf(608,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(609,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(610,plain,
    ( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[136]) ).

thf(611,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
          | ( in @ Xx @ B )
          | ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[372]) ).

thf(612,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ~ ( in @ Xx @ B )
          | ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[371]) ).

thf(613,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
          | ~ ( in @ Xx @ B )
          | ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[370]) ).

thf(614,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ( in @ Xx @ B )
          | ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[369]) ).

thf(615,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ ( symdiff @ A @ B ) )
          | ( ( ( in @ Xx @ A )
              | ~ ( in @ Xx @ A )
              | ! [Xphi: $o] : Xphi )
            & ( ( in @ Xx @ A )
              | ( in @ Xx @ B )
              | ! [Xphi: $o] : Xphi )
            & ( ( in @ Xx @ A )
              | ! [Xphi: $o] :
                  ( ~ Xphi
                  | Xphi ) )
            & ( ~ ( in @ Xx @ B )
              | ~ ( in @ Xx @ A )
              | ! [Xphi: $o] : Xphi )
            & ( ~ ( in @ Xx @ B )
              | ( in @ Xx @ B )
              | ! [Xphi: $o] : Xphi )
            & ( ~ ( in @ Xx @ B )
              | ! [Xphi: $o] :
                  ( ~ Xphi
                  | Xphi ) )
            & ! [Xphi: $o] :
                ( ~ Xphi
                | ~ ( in @ Xx @ A )
                | Xphi )
            & ! [Xphi: $o] :
                ( ~ Xphi
                | ( in @ Xx @ B )
                | Xphi )
            & ! [Xphi: $o] :
                ( ~ Xphi
                | ~ Xphi
                | Xphi ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[368]) ).

thf(616,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( setminus @ A @ B )
           != emptyset )
          | ( subset @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[367]) ).

thf(617,plain,
    ( ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) )
    = $true ),
    inference(copy,[status(thm)],[129]) ).

thf(618,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ B )
          | ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[366]) ).

thf(619,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
          | ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[365]) ).

thf(620,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ ( setminus @ A @ B ) )
          | ( in @ Xx @ B )
          | ~ ( in @ Xx @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[364]) ).

thf(621,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ ( setminus @ A @ B ) )
          | ~ ( in @ Xx @ A )
          | ( in @ Xx @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[363]) ).

thf(622,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( subset @ A @ B )
          | ( ( setminus @ A @ B )
            = emptyset ) ) )
    = $true ),
    inference(copy,[status(thm)],[362]) ).

thf(623,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
          | ~ ( in @ Xx @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[361]) ).

thf(624,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
          | ( in @ Xx @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[360]) ).

thf(625,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ( in @ Xx @ B )
          | ( in @ Xx @ ( setminus @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[359]) ).

thf(626,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(627,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( binintersect @ A @ B )
           != A )
          | ( subset @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[358]) ).

thf(628,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( subset @ B @ A )
          | ( ( binintersect @ A @ B )
            = B ) ) )
    = $true ),
    inference(copy,[status(thm)],[357]) ).

thf(629,plain,
    ( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) )
    = $true ),
    inference(copy,[status(thm)],[117]) ).

thf(630,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( in @ ( sK66_Xx @ B @ A ) @ A )
            & ( in @ ( sK66_Xx @ B @ A ) @ B ) )
          | ( ( binintersect @ A @ B )
            = emptyset ) ) )
    = $true ),
    inference(copy,[status(thm)],[356]) ).

thf(631,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ ( binintersect @ A @ B ) )
          | ( in @ Xx @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[355]) ).

thf(632,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( binintersect @ A @ B )
           != B )
          | ( subset @ B @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[354]) ).

thf(633,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( subset @ A @ B )
          | ( ( binintersect @ A @ B )
            = A ) ) )
    = $true ),
    inference(copy,[status(thm)],[353]) ).

thf(634,plain,
    ( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) )
    = $true ),
    inference(copy,[status(thm)],[112]) ).

thf(635,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ ( binintersect @ A @ B ) )
          | ( in @ Xx @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[352]) ).

thf(636,plain,
    ( ( ! [A: $i,B: $i,C: $i] :
          ( ~ ( subset @ C @ A )
          | ~ ( subset @ C @ B )
          | ( subset @ C @ ( binintersect @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[351]) ).

thf(637,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ~ ( in @ Xx @ B )
          | ( in @ Xx @ ( binintersect @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[350]) ).

thf(638,plain,
    ( ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[108]) ).

thf(639,plain,
    ( ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[107]) ).

thf(640,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ ( binunion @ A @ B ) )
          | ( in @ Xx @ A )
          | ( in @ Xx @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[349]) ).

thf(641,plain,
    ( ( ! [A: $i,B: $i] :
          ( ! [Xx: $i] :
              ( ~ ( in @ Xx @ ( binunion @ A @ B ) )
              | ( in @ Xx @ A )
              | ( in @ Xx @ B )
              | ! [Xphi: $o] : Xphi )
          & ! [Xx: $i] :
              ( ~ ( in @ Xx @ ( binunion @ A @ B ) )
              | ( in @ Xx @ A )
              | ! [Xphi: $o] :
                  ( ~ Xphi
                  | Xphi ) )
          & ! [Xx: $i] :
              ( ~ ( in @ Xx @ ( binunion @ A @ B ) )
              | ! [Xphi: $o] :
                  ( ~ Xphi
                  | ( in @ Xx @ B )
                  | Xphi ) )
          & ( ! [Xx: $i] :
                ~ ( in @ Xx @ ( binunion @ A @ B ) )
            | ! [Xphi: $o] :
                ( ~ Xphi
                | ~ Xphi
                | Xphi ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[348]) ).

thf(642,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ B )
          | ( in @ Xx @ ( binunion @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[347]) ).

thf(643,plain,
    ( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[103]) ).

thf(644,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ( in @ Xx @ ( binunion @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[346]) ).

thf(645,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( subset
          @ ( dsetconstr @ A
            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
          @ A ) )
    = $true ),
    inference(copy,[status(thm)],[101]) ).

thf(646,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( in
          @ ( dsetconstr @ A
            @ ^ [Xx: $i] : ( Xphi @ Xx ) )
          @ ( powerset @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[100]) ).

thf(647,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( subset @ A @ B )
          | ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[345]) ).

thf(648,plain,
    ( ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[98]) ).

thf(649,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( in @ B @ ( powerset @ A ) )
          | ( subset @ B @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[344]) ).

thf(650,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( subset @ B @ A )
          | ( in @ B @ ( powerset @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[343]) ).

thf(651,plain,
    ( ( ! [A: $i] :
          ( ~ ( subset @ A @ emptyset )
          | ( A = emptyset ) ) )
    = $true ),
    inference(copy,[status(thm)],[342]) ).

thf(652,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( subset @ A @ B )
          | ~ ( subset @ B @ A )
          | ( A = B ) ) )
    = $true ),
    inference(copy,[status(thm)],[341]) ).

thf(653,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( subset @ A @ B )
          | ( in @ A @ ( powerset @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[340]) ).

thf(654,plain,
    ( ( ! [A: $i,Xx: $i,B: $i] :
          ( ~ ( subset @ A @ B )
          | ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[339]) ).

thf(655,plain,
    ( ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[91]) ).

thf(656,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( subset @ A @ B )
          | ! [C: $i] :
              ( ~ ( subset @ B @ C )
              | ( subset @ A @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[338]) ).

thf(657,plain,
    ( ( ! [A: $i] : ( subset @ A @ A ) )
    = $true ),
    inference(copy,[status(thm)],[89]) ).

thf(658,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ( in @ Xx @ B )
          | ( A != B ) ) )
    = $true ),
    inference(copy,[status(thm)],[337]) ).

thf(659,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( subset @ A @ B )
          | ( A != B ) ) )
    = $true ),
    inference(copy,[status(thm)],[336]) ).

thf(660,plain,
    ( ( ! [A: $i,B: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ( in @ Xx @ B )
          | ~ ( subset @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[335]) ).

thf(661,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( subset @ A @ B )
          | ! [Xx: $i] :
              ( ( in @ Xx @ B )
              | ~ ( in @ Xx @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[334]) ).

thf(662,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( subset @ A @ B )
          | ! [Xx: $i] :
              ( ~ ( in @ Xx @ A )
              | ( in @ Xx @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[333]) ).

thf(663,plain,
    ( ( ! [A: $i] : ( subset @ emptyset @ A ) )
    = $true ),
    inference(copy,[status(thm)],[83]) ).

thf(664,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( in @ ( sK65_Xx @ B @ A ) @ A )
            & ~ ( in @ ( sK65_Xx @ B @ A ) @ B ) )
          | ( subset @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[332]) ).

thf(665,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A != B )
          | ( subset @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[331]) ).

thf(666,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A != B )
          | ( subset @ B @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[330]) ).

thf(667,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( in @ ( sK64_Xx @ B @ A ) @ A )
            & ~ ( in @ ( sK64_Xx @ B @ A ) @ B ) )
          | ( subset @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[329]) ).

thf(668,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A != B )
          | ! [Xphi: $i > $o,Xpsi: $i > $o] :
              ( ( ( in @ ( sK62_Xx @ Xpsi @ Xphi @ B @ A ) @ A )
                & ( in @ ( sK63_SY1875 @ Xpsi @ Xphi @ B @ A ) @ B )
                & ( ( sK62_Xx @ Xpsi @ Xphi @ B @ A )
                  = ( sK63_SY1875 @ Xpsi @ Xphi @ B @ A ) )
                & ( ~ ( Xphi @ ( sK62_Xx @ Xpsi @ Xphi @ B @ A ) )
                  | ~ ( Xpsi @ ( sK63_SY1875 @ Xpsi @ Xphi @ B @ A ) ) )
                & ( ( Xphi @ ( sK62_Xx @ Xpsi @ Xphi @ B @ A ) )
                  | ( Xpsi @ ( sK63_SY1875 @ Xpsi @ Xphi @ B @ A ) ) ) )
              | ( ( dsetconstr @ A
                  @ ^ [Xx: $i] : ( Xphi @ Xx ) )
                = ( dsetconstr @ B
                  @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[328]) ).

thf(669,plain,
    ( ( ! [SY251: $i > $o,SY252: $i > $o] :
          ( ( ( ( sK60_Xx @ SY252 @ SY251 )
              = ( sK61_SY1874 @ SY252 @ SY251 ) )
            & ( ~ ( SY251 @ ( sK60_Xx @ SY252 @ SY251 ) )
              | ~ ( SY252 @ ( sK61_SY1874 @ SY252 @ SY251 ) ) )
            & ( ( SY251 @ ( sK60_Xx @ SY252 @ SY251 ) )
              | ( SY252 @ ( sK61_SY1874 @ SY252 @ SY251 ) ) ) )
          | ! [SY256: $i] :
              ( ( ( SY251 @ ( sK59_SY257 @ SY256 @ SY252 @ SY251 ) )
                & ( SY256
                 != ( sK59_SY257 @ SY256 @ SY252 @ SY251 ) ) )
              | ~ ( SY251 @ SY256 ) )
          | ! [SY259: $i] :
              ( ( ( SY252 @ ( sK58_SY260 @ SY259 @ SY252 @ SY251 ) )
                & ( SY259
                 != ( sK58_SY260 @ SY259 @ SY252 @ SY251 ) ) )
              | ~ ( SY252 @ SY259 ) )
          | ( ( descr
              @ ^ [Xx: $i] : ( SY251 @ Xx ) )
            = ( descr
              @ ^ [Xx: $i] : ( SY252 @ Xx ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[327]) ).

thf(670,plain,
    ( ( ! [SY245: $i > $o] :
          ( ! [SY247: $i] :
              ( ( ( SY245 @ ( sK57_SY248 @ SY247 @ SY245 ) )
                & ( SY247
                 != ( sK57_SY248 @ SY247 @ SY245 ) ) )
              | ~ ( SY245 @ SY247 ) )
          | ! [Xx: $i] :
              ( ~ ( SY245 @ Xx )
              | ! [Xy: $i] :
                  ( ~ ( SY245 @ Xy )
                  | ( Xx = Xy ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[326]) ).

thf(671,plain,
    $true = $true,
    inference(copy,[status(thm)],[325]) ).

thf(672,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A != B )
          | ( ( setunion @ A )
            = ( setunion @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[324]) ).

thf(673,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A != B )
          | ( ( powerset @ A )
            = ( powerset @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[323]) ).

thf(674,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( Xx != Xy )
          | ! [Xz: $i,Xu: $i] :
              ( ( Xz != Xu )
              | ( ( setadjoin @ Xx @ Xz )
                = ( setadjoin @ Xy @ Xu ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[322]) ).

thf(675,plain,
    $true = $true,
    inference(copy,[status(thm)],[321]) ).

thf(676,plain,
    ( ( ! [SY227: $i > $o,SY228: $i > $o] :
          ( ( ( ( sK55_Xx @ SY228 @ SY227 )
              = ( sK56_SY1873 @ SY228 @ SY227 ) )
            & ( ~ ( SY227 @ ( sK55_Xx @ SY228 @ SY227 ) )
              | ~ ( SY228 @ ( sK56_SY1873 @ SY228 @ SY227 ) ) )
            & ( ( SY227 @ ( sK55_Xx @ SY228 @ SY227 ) )
              | ( SY228 @ ( sK56_SY1873 @ SY228 @ SY227 ) ) ) )
          | ! [SY232: $i] :
              ( ( ( SY227 @ ( sK54_SY233 @ SY232 @ SY228 @ SY227 ) )
                & ( SY232
                 != ( sK54_SY233 @ SY232 @ SY228 @ SY227 ) ) )
              | ~ ( SY227 @ SY232 ) )
          | ( ! [SY1872: $i] :
                ( ~ ( SY228 @ SY1872 )
                | ( ( sK53_SY235 @ SY228 @ SY227 )
                  = SY1872 ) )
            & ( SY228 @ ( sK53_SY235 @ SY228 @ SY227 ) ) ) )
      & ! [SY227: $i > $o,SY228: $i > $o] :
          ( ( ( ( sK51_Xx @ SY228 @ SY227 )
              = ( sK52_SY1871 @ SY228 @ SY227 ) )
            & ( ~ ( SY227 @ ( sK51_Xx @ SY228 @ SY227 ) )
              | ~ ( SY228 @ ( sK52_SY1871 @ SY228 @ SY227 ) ) )
            & ( ( SY227 @ ( sK51_Xx @ SY228 @ SY227 ) )
              | ( SY228 @ ( sK52_SY1871 @ SY228 @ SY227 ) ) ) )
          | ! [SY235: $i] :
              ( ( ( SY228 @ ( sK50_SY236 @ SY235 @ SY228 @ SY227 ) )
                & ( SY235
                 != ( sK50_SY236 @ SY235 @ SY228 @ SY227 ) ) )
              | ~ ( SY228 @ SY235 ) )
          | ( ! [SY1870: $i] :
                ( ~ ( SY227 @ SY1870 )
                | ( ( sK49_SY232 @ SY228 @ SY227 )
                  = SY1870 ) )
            & ( SY227 @ ( sK49_SY232 @ SY228 @ SY227 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[320]) ).

thf(677,plain,
    ( ( ! [SY221: $i > $o] :
          ( ! [SY223: $i] :
              ( ( ( SY221 @ ( sK48_SY224 @ SY223 @ SY221 ) )
                & ( SY223
                 != ( sK48_SY224 @ SY223 @ SY221 ) ) )
              | ~ ( SY221 @ SY223 ) )
          | ! [Xx: $i] :
              ( ~ ( SY221 @ Xx )
              | ! [Xy: $i] :
                  ( ~ ( SY221 @ Xy )
                  | ( Xx = Xy ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[319]) ).

thf(678,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A != B )
          | ( ! [Xx: $i,Xy: $i] :
                ( ( Xx != Xy )
                | ~ ( in @ Xx @ A )
                | ( in @ Xy @ B ) )
            & ! [Xx: $i,Xy: $i] :
                ( ( Xx != Xy )
                | ~ ( in @ Xy @ B )
                | ( in @ Xx @ A ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[318]) ).

thf(679,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A != B )
          | ! [Xx: $i,Xy: $i] :
              ( ( Xx != Xy )
              | ~ ( in @ Xx @ A )
              | ( in @ Xy @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[317]) ).

thf(680,plain,
    ( ( ! [SY207: $i > $o] :
          ( ! [Xx: $i] :
              ( ( ( ( sK47_Xy @ Xx @ SY207 )
                 != Xx )
                | ~ ( SY207 @ ( sK47_Xy @ Xx @ SY207 ) ) )
              & ( ( ( sK47_Xy @ Xx @ SY207 )
                  = Xx )
                | ( SY207 @ ( sK47_Xy @ Xx @ SY207 ) ) ) )
          | ( ! [SY1869: $i] :
                ( ~ ( SY207 @ SY1869 )
                | ( ( sK46_SY211 @ SY207 )
                  = SY1869 ) )
            & ( SY207 @ ( sK46_SY211 @ SY207 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[316]) ).

thf(681,plain,
    ( ( ! [SY200: $i > $o] :
          ( ! [Xx: $i] :
              ~ ( SY200 @ Xx )
          | ( ( SY200 @ ( sK44_Xx @ SY200 ) )
            & ( SY200 @ ( sK45_SY1868 @ SY200 ) )
            & ( ( sK44_Xx @ SY200 )
             != ( sK45_SY1868 @ SY200 ) ) )
          | ( ! [SY1867: $i] :
                ( ~ ( SY200 @ SY1867 )
                | ( ( sK43_SY205 @ SY200 )
                  = SY1867 ) )
            & ( SY200 @ ( sK43_SY205 @ SY200 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[315]) ).

thf(682,plain,
    ( ( ! [SY194: $i > $o] :
          ( ! [Xx: $i] :
              ( ( ( SY194 @ ( sK42_Xy @ Xx @ SY194 ) )
                & ( Xx
                 != ( sK42_Xy @ Xx @ SY194 ) ) )
              | ~ ( SY194 @ Xx ) )
          | ( ! [SY1866: $i] :
                ( ~ ( SY194 @ SY1866 )
                | ( ( sK41_SY198 @ SY194 )
                  = SY1866 ) )
            & ( SY194 @ ( sK41_SY198 @ SY194 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[314]) ).

thf(683,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ! [Xx: $i] :
              ( ~ ( in @ Xx @ A )
              | ( Xphi @ Xx ) )
          | ( ( in @ ( sK40_Xx @ Xphi @ A ) @ A )
            & ~ ( Xphi @ ( sK40_Xx @ Xphi @ A ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[313]) ).

thf(684,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ( ( Xphi @ ( sK39_Xx @ Xphi @ A ) )
            & ( in @ ( sK39_Xx @ Xphi @ A ) @ A ) )
          | ! [Xx: $i] :
              ( ~ ( in @ Xx @ A )
              | ~ ( Xphi @ Xx ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[312]) ).

thf(685,plain,
    ( ( ! [Xphi: $o] :
          ( ~ Xphi
          | ( set2prop @ ( prop2set @ Xphi ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[311]) ).

thf(686,plain,
    ( ( ! [Xphi: $o] :
          ( ~ Xphi
          | ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[310]) ).

thf(687,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ! [Xx: $i] :
              ( ~ ( in @ Xx @ A )
              | ( Xphi @ Xx ) )
          | ( ( in @ ( sK38_Xx @ Xphi @ A ) @ A )
            & ~ ( Xphi @ ( sK38_Xx @ Xphi @ A ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[309]) ).

thf(688,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ( ( Xphi @ ( sK37_Xx @ Xphi @ A ) )
            & ( in @ ( sK37_Xx @ Xphi @ A ) @ A ) )
          | ! [Xx: $i] :
              ( ~ ( in @ Xx @ A )
              | ~ ( Xphi @ Xx ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[308]) ).

thf(689,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ( ( in @ ( sK36_Xx @ Xphi @ A ) @ A )
            & ( Xphi @ ( sK36_Xx @ Xphi @ A ) ) )
          | ! [Xx: $i] :
              ( ~ ( Xphi @ Xx )
              | ~ ( in @ Xx @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[307]) ).

thf(690,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ! [Xx: $i] :
              ( ~ ( in @ Xx @ A )
              | ( Xphi @ Xx ) )
          | ( ( in @ ( sK35_Xx @ Xphi @ A ) @ A )
            & ~ ( Xphi @ ( sK35_Xx @ Xphi @ A ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[306]) ).

thf(691,plain,
    ( ( ! [Xphi: $i > $o,Xx: $i] :
          ( ~ ( in @ Xx @ emptyset )
          | ( Xphi @ Xx ) ) )
    = $true ),
    inference(copy,[status(thm)],[305]) ).

thf(692,plain,
    ( ( ! [A: $i,Xphi: $i > $o] :
          ( ! [Xx: $i] :
              ( ~ ( Xphi @ Xx )
              | ~ ( in @ Xx @ A ) )
          | ( ( dsetconstr @ A
              @ ^ [Xx: $i] : ( Xphi @ Xx ) )
           != emptyset ) ) )
    = $true ),
    inference(copy,[status(thm)],[304]) ).

thf(693,plain,
    ( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[53]) ).

thf(694,plain,
    ( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[52]) ).

thf(695,plain,
    ( ( ! [Xx: $i,Xy: $i,Xz: $i] :
          ( ~ ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
          | ( Xz = Xx )
          | ( Xz = Xy ) ) )
    = $true ),
    inference(copy,[status(thm)],[303]) ).

thf(696,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ~ ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
          | ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[302]) ).

thf(697,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( Xx != Xy )
          | ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[301]) ).

thf(698,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ( Xx = Xy )
          | ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[300]) ).

thf(699,plain,
    ( ( ! [Xx: $i,Xy: $i] :
          ( ~ ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
          | ( Xx = Xy ) ) )
    = $true ),
    inference(copy,[status(thm)],[299]) ).

thf(700,plain,
    ( ( ! [SY145: $i] :
          ( ( SY145 = emptyset )
          | ( in @ ( sK34_Xx @ SY145 ) @ SY145 ) ) )
    = $true ),
    inference(copy,[status(thm)],[298]) ).

thf(701,plain,
    ( ( ! [SY139: $i > $o] :
          ( ! [SY141: $i] :
              ( ( ( SY139 @ ( sK33_SY142 @ SY141 @ SY139 ) )
                & ( SY141
                 != ( sK33_SY142 @ SY141 @ SY139 ) ) )
              | ~ ( SY139 @ SY141 ) )
          | ( ! [SY1864: $i] :
                ( ( SY1864
                 != ( sK32_Xx @ SY139 ) )
                | ( SY139 @ SY1864 ) )
            & ! [SY1865: $i] :
                ( ~ ( SY139 @ SY1865 )
                | ( SY1865
                  = ( sK32_Xx @ SY139 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[297]) ).

thf(702,plain,
    ( ( ! [A: $i,Xx: $i] :
          ( ~ ( in @ Xx @ A )
          | ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[296]) ).

thf(703,plain,
    ( ( ! [A: $i,Xx: $i] :
          ( ~ ( in @ Xx @ ( setunion @ A ) )
          | ! [Xphi: $o] :
              ( ( ( in @ Xx @ ( sK31_B @ Xphi @ Xx @ A ) )
                & ( in @ ( sK31_B @ Xphi @ Xx @ A ) @ A )
                & ~ Xphi )
              | Xphi ) ) )
    = $true ),
    inference(copy,[status(thm)],[295]) ).

thf(704,plain,
    ( ( ! [A: $i,Xx: $i,B: $i] :
          ( ~ ( in @ Xx @ B )
          | ~ ( in @ B @ A )
          | ( in @ Xx @ ( setunion @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[294]) ).

thf(705,plain,
    ( ( ! [A: $i,B: $i] :
          ( ~ ( in @ B @ ( powerset @ A ) )
          | ! [Xx: $i] :
              ( ~ ( in @ Xx @ B )
              | ( in @ Xx @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[293]) ).

thf(706,plain,
    ( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[40]) ).

thf(707,plain,
    ( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[39]) ).

thf(708,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( in @ ( sK30_Xx @ B @ A ) @ B )
            & ~ ( in @ ( sK30_Xx @ B @ A ) @ A ) )
          | ( in @ B @ ( powerset @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[292]) ).

thf(709,plain,
    ( ( ! [A: $i] :
          ( ( dsetconstr @ A
            @ ^ [Xx: $i] : $true )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[37]) ).

thf(710,plain,
    ( ( ! [Xx: $i,A: $i,Xy: $i] :
          ( ~ ( in @ Xy @ ( setadjoin @ Xx @ A ) )
          | ( Xy = Xx )
          | ( in @ Xy @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[291]) ).

thf(711,plain,
    ( ( ! [Xx: $i,A: $i,Xy: $i] :
          ( ~ ( in @ Xy @ ( setadjoin @ Xx @ A ) )
          | ( ( ( Xy = Xx )
              | ( in @ Xy @ A )
              | ! [Xphi: $o] : Xphi )
            & ( ( Xy = Xx )
              | ! [Xphi: $o] :
                  ( ~ Xphi
                  | Xphi ) )
            & ! [Xphi: $o] :
                ( ~ Xphi
                | ( in @ Xy @ A )
                | Xphi )
            & ! [Xphi: $o] :
                ( ~ Xphi
                | ~ Xphi
                | Xphi ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[290]) ).

thf(712,plain,
    ( ( ! [Xx: $i,A: $i,Xy: $i] :
          ( ~ ( in @ Xy @ A )
          | ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[289]) ).

thf(713,plain,
    ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
    = $true ),
    inference(copy,[status(thm)],[33]) ).

thf(714,plain,
    ( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
    = $true ),
    inference(copy,[status(thm)],[32]) ).

thf(715,plain,
    ( ( ! [SY106: $i] :
          ( ! [Xx: $i] :
              ~ ( in @ Xx @ SY106 )
          | ( SY106 != emptyset ) ) )
    = $true ),
    inference(copy,[status(thm)],[288]) ).

thf(716,plain,
    ( ( ! [SY102: $i,SY103: $i > $o,SY104: $i] :
          ( ~ ( in @ SY104 @ SY102 )
          | ~ ( SY103 @ SY104 )
          | ( ( dsetconstr @ SY102
              @ ^ [Xy: $i] : ( SY103 @ Xy ) )
           != emptyset ) ) )
    = $true ),
    inference(copy,[status(thm)],[287]) ).

thf(717,plain,
    ( ( ! [SY100: $i] :
          ( ( SY100 = emptyset )
          | ( in @ ( sK29_Xx @ SY100 ) @ SY100 ) ) )
    = $true ),
    inference(copy,[status(thm)],[286]) ).

thf(718,plain,
    ( ( ! [A: $i] :
          ( ! [Xphi: $i > $o,Xx: $i] :
              ( ~ ( in @ Xx @ A )
              | ~ ( Xphi @ Xx )
              | ( in @ Xx
                @ ( dsetconstr @ A
                  @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) )
          & ! [Xphi: $i > $o,Xx: $i] :
              ( ~ ( in @ Xx @ A )
              | ~ ( in @ Xx
                  @ ( dsetconstr @ A
                    @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
              | ( Xphi @ Xx ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[285]) ).

thf(719,plain,
    ( ( ! [A: $i] :
          ( ( in @ ( sK28_Xx @ A ) @ A )
          | ( A = emptyset ) ) )
    = $true ),
    inference(copy,[status(thm)],[284]) ).

thf(720,plain,
    ( ( ! [A: $i] :
          ( ( in @ ( sK27_Xx @ A ) @ A )
          | ( A = emptyset ) ) )
    = $true ),
    inference(copy,[status(thm)],[283]) ).

thf(721,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( in @ ( sK26_Xx @ B @ A ) @ A )
            & ~ ( in @ ( sK26_Xx @ B @ A ) @ B ) )
          | ( ( in @ ( sK25_Xx @ B @ A ) @ B )
            & ~ ( in @ ( sK25_Xx @ B @ A ) @ A ) )
          | ( A = B ) ) )
    = $true ),
    inference(copy,[status(thm)],[282]) ).

thf(722,plain,
    ( ( ! [SY83: $i > $o] :
          ( ! [SY85: $i] :
              ( ( ( SY83 @ ( sK24_SY86 @ SY85 @ SY83 ) )
                & ( SY85
                 != ( sK24_SY86 @ SY85 @ SY83 ) ) )
              | ~ ( SY83 @ SY85 ) )
          | ( SY83 @ ( sK23_Xx @ SY83 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[281]) ).

thf(723,plain,
    ( ( ! [Xx: $i] :
          ~ ( in @ Xx @ emptyset ) )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(724,plain,
    ( ( ! [Xx: $i] :
          ~ ( in @ Xx @ emptyset ) )
    = $true ),
    inference(copy,[status(thm)],[280]) ).

thf(725,plain,
    ( ( ! [Xx: $i] :
          ~ ( in @ Xx @ emptyset )
      | ! [Xphi: $o] : Xphi )
    = $true ),
    inference(copy,[status(thm)],[279]) ).

thf(726,plain,
    ( ( ! [Xphi: $o] :
          ( ! [Xx: $i] :
              ~ ( in @ Xx @ ( prop2set @ Xphi ) )
          | Xphi ) )
    = $true ),
    inference(copy,[status(thm)],[278]) ).

thf(727,plain,
    ( ( ! [SY71: $i > $o] :
          ( ! [SY73: $i] :
              ( ( ( SY71 @ ( sK22_SY74 @ SY73 @ SY71 ) )
                & ( SY73
                 != ( sK22_SY74 @ SY73 @ SY71 ) ) )
              | ~ ( SY71 @ SY73 ) )
          | ( ! [SY1863: $i] :
                ( ~ ( SY71 @ SY1863 )
                | ( ( sK21_Xx @ SY71 )
                  = SY1863 ) )
            & ( SY71 @ ( sK21_Xx @ SY71 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[277]) ).

thf(728,plain,
    ( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
          ( ~ ( in @ Xx
              @ ( dsetconstr @ A
                @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
          | ( Xphi @ Xx ) ) )
    = $true ),
    inference(copy,[status(thm)],[276]) ).

thf(729,plain,
    ( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
          ( ~ ( in @ Xx
              @ ( dsetconstr @ A
                @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
          | ( in @ Xx @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[275]) ).

thf(730,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)],[274]) ).

thf(731,plain,
    ( ( ! [SY54: $i > $o] :
          ( ! [SY56: $i] :
              ( ( ( SY54 @ ( sK20_SY57 @ SY56 @ SY54 ) )
                & ( SY56
                 != ( sK20_SY57 @ SY56 @ SY54 ) ) )
              | ~ ( SY54 @ SY56 ) )
          | ( SY54
            @ ( descr
              @ ^ [Xx: $i] : ( SY54 @ Xx ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[273]) ).

thf(732,plain,
    ( ( ! [A: $i] :
          ( ! [SY1839: $i] :
              ( ( ( in @ ( sK19_Xx @ SY1839 @ A ) @ SY1839 )
                & ~ ( in @ ( sK19_Xx @ SY1839 @ A ) @ A ) )
              | ! [Xx: $i] :
                  ~ ( in @ Xx @ SY1839 )
              | ( ! [SY1860: $i] :
                    ( ~ ( in @ SY1860 @ ( sK15_B @ A ) )
                    | ! [SY1858: $i] :
                        ( ~ ( in @ SY1858 @ SY1860 )
                        | ( in @ SY1858 @ ( sK17_SY1842 @ SY1839 @ A ) ) )
                    | ( in @ ( sK18_SY1856 @ SY1839 @ A ) @ SY1860 ) )
                & ( in @ ( sK17_SY1842 @ SY1839 @ A ) @ ( sK15_B @ A ) )
                & ( in @ ( sK18_SY1856 @ SY1839 @ A ) @ SY1839 )
                & ! [SY1859: $i] :
                    ( ~ ( in @ SY1859 @ ( sK17_SY1842 @ SY1839 @ A ) )
                    | ~ ( in @ SY1859 @ SY1839 ) ) ) )
          & ! [SY1847: $i,SY1848: $i] :
              ( ~ ( in @ SY1847 @ ( sK15_B @ A ) )
              | ~ ( in @ SY1848 @ ( sK15_B @ A ) )
              | ! [Xx: $i] :
                  ( ~ ( in @ Xx @ SY1847 )
                  | ( in @ Xx @ SY1848 ) )
              | ! [Xx: $i] :
                  ( ~ ( in @ Xx @ SY1848 )
                  | ( in @ Xx @ SY1847 ) ) )
          & ! [SY1851: $i] :
              ( ~ ( in @ SY1851 @ ( sK15_B @ A ) )
              | ! [Xx: $i] :
                  ( ~ ( in @ Xx @ SY1851 )
                  | ( in @ Xx @ A ) ) )
          & ! [SY1853: $i,SY1854: $i] :
              ( ~ ( in @ SY1853 @ A )
              | ~ ( in @ SY1854 @ A )
              | ( ( in @ ( sK16_SY1855 @ SY1854 @ SY1853 @ A ) @ ( sK15_B @ A ) )
                & ( ~ ( in @ SY1853 @ ( sK16_SY1855 @ SY1854 @ SY1853 @ A ) )
                  | ~ ( in @ SY1854 @ ( sK16_SY1855 @ SY1854 @ SY1853 @ A ) ) )
                & ( ( in @ SY1853 @ ( sK16_SY1855 @ SY1854 @ SY1853 @ A ) )
                  | ( in @ SY1854 @ ( sK16_SY1855 @ SY1854 @ SY1853 @ A ) ) ) )
              | ( SY1853 = SY1854 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[272]) ).

thf(733,plain,
    ( ( ! [A: $i] :
          ( ! [Xx: $i] :
              ~ ( in @ Xx @ A )
          | ( ( in @ ( sK14_B @ A ) @ A )
            & ! [SY1838: $i] :
                ( ~ ( in @ SY1838 @ ( sK14_B @ A ) )
                | ~ ( in @ SY1838 @ A ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[271]) ).

thf(734,plain,
    ( ( ! [SY22: $i > $i > $o,SY23: $i] :
          ( ( ( in @ ( sK12_SY24 @ SY23 @ SY22 ) @ SY23 )
            & ! [SY1836: $i] :
                ( ( ( SY22 @ ( sK12_SY24 @ SY23 @ SY22 ) @ ( sK13_SY1837 @ SY1836 @ SY23 @ SY22 ) )
                  & ( SY1836
                   != ( sK13_SY1837 @ SY1836 @ SY23 @ SY22 ) ) )
                | ~ ( SY22 @ ( sK12_SY24 @ SY23 @ SY22 ) @ SY1836 ) ) )
          | ( ! [SY1832: $i] :
                ( ! [Xy: $i] :
                    ( ~ ( SY22 @ Xy @ SY1832 )
                    | ~ ( in @ Xy @ SY23 ) )
                | ( in @ SY1832 @ ( sK10_B @ SY23 @ SY22 ) ) )
            & ! [SY1834: $i] :
                ( ~ ( in @ SY1834 @ ( sK10_B @ SY23 @ SY22 ) )
                | ( ( SY22 @ ( sK11_Xy @ SY1834 @ SY23 @ SY22 ) @ SY1834 )
                  & ( in @ ( sK11_Xy @ SY1834 @ SY23 @ SY22 ) @ SY23 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[270]) ).

thf(735,plain,
    ( ( ! [A: $i] :
          ( ( ( in @ ( sK9_Xx @ A ) @ omega )
            & ( in @ ( sK9_Xx @ A ) @ A )
            & ~ ( in @ ( setadjoin @ ( sK9_Xx @ A ) @ ( sK9_Xx @ A ) ) @ A ) )
          | ~ ( in @ emptyset @ A )
          | ! [Xx: $i] :
              ( ~ ( in @ Xx @ omega )
              | ( in @ Xx @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[269]) ).

thf(736,plain,
    ( ( ! [Xx: $i] :
          ( ~ ( in @ Xx @ omega )
          | ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
    = $true ),
    inference(copy,[status(thm)],[268]) ).

thf(737,plain,
    ( ( in @ emptyset @ omega )
    = $true ),
    inference(copy,[status(thm)],[9]) ).

thf(738,plain,
    ( ( ! [A: $i,Xx: $i] :
          ( ! [B: $i] :
              ( ~ ( in @ Xx @ B )
              | ~ ( in @ B @ A ) )
          | ( in @ Xx @ ( setunion @ A ) ) )
      & ! [A: $i,Xx: $i] :
          ( ~ ( in @ Xx @ ( setunion @ A ) )
          | ( ( in @ Xx @ ( sK8_B @ Xx @ A ) )
            & ( in @ ( sK8_B @ Xx @ A ) @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[267]) ).

thf(739,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( in @ ( sK7_Xx @ B @ A ) @ B )
            & ~ ( in @ ( sK7_Xx @ B @ A ) @ A ) )
          | ( in @ B @ ( powerset @ A ) ) )
      & ! [A: $i,B: $i] :
          ( ~ ( in @ B @ ( powerset @ A ) )
          | ! [Xx: $i] :
              ( ~ ( in @ Xx @ B )
              | ( in @ Xx @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[266]) ).

thf(740,plain,
    ( ( ! [Xx: $i] :
          ( ! [A: $i,Xy: $i] :
              ( ~ ( in @ Xy @ ( setadjoin @ Xx @ A ) )
              | ( Xy = Xx )
              | ( in @ Xy @ A ) )
          & ! [A: $i,Xy: $i] :
              ( ( Xy != Xx )
              | ( in @ Xy @ ( setadjoin @ Xx @ A ) ) )
          & ! [A: $i,Xy: $i] :
              ( ~ ( in @ Xy @ A )
              | ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[265]) ).

thf(741,plain,
    ( ( ! [Xx: $i] :
          ~ ( in @ Xx @ emptyset ) )
    = $true ),
    inference(copy,[status(thm)],[5]) ).

thf(742,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( ( ~ ( in @ ( sK6_Xx @ B @ A ) @ A )
              | ~ ( in @ ( sK6_Xx @ B @ A ) @ B ) )
            & ( ( in @ ( sK6_Xx @ B @ A ) @ A )
              | ( in @ ( sK6_Xx @ B @ A ) @ B ) ) )
          | ( A = B ) ) )
    = $true ),
    inference(copy,[status(thm)],[264]) ).

thf(743,plain,
    ( ( ( in @ sK2_SY1822 @ ( powerset @ sK1_A ) )
      & ( in @ sK3_SY1826 @ ( powerset @ sK1_A ) )
      & ( in @ sK4_SY1829 @ ( powerset @ sK1_A ) )
      & ( in @ sK5_SY1831 @ sK1_A )
      & ( in @ sK5_SY1831 @ ( binintersect @ sK2_SY1822 @ sK3_SY1826 ) )
      & ~ ( in @ sK5_SY1831 @ ( binunion @ sK3_SY1826 @ sK4_SY1829 ) ) )
    = $true ),
    inference(copy,[status(thm)],[263]) ).

thf(744,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ~ ( ~ ( in @ ( sK97_Xx @ SX2 @ SX1 @ SX0 ) @ SX0 )
                  | ~ ~ ( ~ ( in @ ( sK97_Xx @ SX2 @ SX1 @ SX0 ) @ SX1 )
                        | ~ ~ ( in @ ( sK97_Xx @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
              | ( subset @ SX1 @ SX2 ) ) ) )
    = $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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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] :
                ( ~ ( ~ ( in @ ( sK7_Xx @ SX1 @ SX0 ) @ SX1 )
                    | ~ ~ ( in @ ( sK7_Xx @ SX1 @ SX0 ) @ SX0 ) )
                | ( in @ SX1 @ ( powerset @ SX0 ) ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
                | ! [SX2: $i] :
                    ( ~ ( in @ SX2 @ SX1 )
                    | ( in @ SX2 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[739,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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 > $o] :
          ( ! [SX1: $i] :
              ( ~ ( ~ ( SX0 @ ( sK24_SY86 @ SX1 @ SX0 ) )
                  | ~ ( ( SX1
                       != ( sK24_SY86 @ SX1 @ SX0 ) ) ) )
              | ~ ( SX0 @ SX1 ) )
          | ( SX0 @ ( sK23_Xx @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[722,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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: $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)],[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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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 > $i] :
          ( ~ ( ~ ( in @ ( sK92_Xx @ SX2 @ SX1 @ SX0 ) @ SX0 )
              | ~ ~ ( in @ ( SX2 @ ( sK92_Xx @ SX2 @ SX1 @ SX0 ) ) @ 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)],[531,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
          | ~ ( ~ ~ ( ( SX2
                     != ( kpair @ ( sK67_Xx @ SX2 @ SX1 @ SX0 ) @ ( sK68_SY1876 @ SX2 @ SX1 @ SX0 ) ) )
                    | ~ ( in @ ( sK68_SY1876 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
              | ~ ( in @ ( sK67_Xx @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[595,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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 > $o] :
          ( ! [SX1: $i] :
              ( ~ ( ~ ( SX0 @ ( sK57_SY248 @ SX1 @ SX0 ) )
                  | ~ ( ( SX1
                       != ( sK57_SY248 @ SX1 @ SX0 ) ) ) )
              | ~ ( SX0 @ SX1 ) )
          | ! [SX1: $i] :
              ( ~ ( SX0 @ SX1 )
              | ! [SX2: $i] :
                  ( ~ ( SX0 @ SX2 )
                  | ( SX1 = SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[670,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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 > $i > $o,SX1: $i] :
          ( ~ ( ~ ( in @ ( sK12_SY24 @ SX1 @ SX0 ) @ SX1 )
              | ~ ! [SX2: $i] :
                    ( ~ ( ~ ( SX0 @ ( sK12_SY24 @ SX1 @ SX0 ) @ ( sK13_SY1837 @ SX2 @ SX1 @ SX0 ) )
                        | ~ ( ( SX2
                             != ( sK13_SY1837 @ SX2 @ SX1 @ SX0 ) ) ) )
                    | ~ ( SX0 @ ( sK12_SY24 @ SX1 @ SX0 ) @ SX2 ) ) )
          | ~ ( ~ ! [SX2: $i] :
                    ( ! [SX3: $i] :
                        ( ~ ( SX0 @ SX3 @ SX2 )
                        | ~ ( in @ SX3 @ SX1 ) )
                    | ( in @ SX2 @ ( sK10_B @ SX1 @ SX0 ) ) )
              | ~ ! [SX2: $i] :
                    ( ~ ( in @ SX2 @ ( sK10_B @ SX1 @ SX0 ) )
                    | ~ ( ~ ( SX0 @ ( sK11_Xy @ SX2 @ SX1 @ SX0 ) @ SX2 )
                        | ~ ( in @ ( sK11_Xy @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[734,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
          | ~ ( ~ ~ ( ~ ( ( SX2 = SX0 )
                        | ( in @ SX2 @ SX1 )
                        | ! [SX3: $o] : SX3 )
                    | ~ ( ( SX2 = SX0 )
                        | ! [SX3: $o] :
                            ( ~ SX3
                            | SX3 ) ) )
              | ~ ~ ( ~ ! [SX3: $o] :
                          ( ~ SX3
                          | ( in @ SX2 @ SX1 )
                          | SX3 )
                    | ~ ! [SX3: $o] :
                          ( ~ SX3
                          | ~ SX3
                          | SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[711,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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] :
          ( ~ ( ~ ( in @ ( sK66_Xx @ SX1 @ SX0 ) @ SX0 )
              | ~ ( in @ ( sK66_Xx @ SX1 @ SX0 ) @ SX1 ) )
          | ( ( binintersect @ SX0 @ SX1 )
            = emptyset ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[630,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i > $o,SX2: $i] :
                  ( ~ ( in @ SX2 @ SX0 )
                  | ~ ( SX1 @ SX2 )
                  | ( in @ SX2
                    @ ( dsetconstr @ SX0
                      @ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) )
            | ~ ! [SX1: $i > $o,SX2: $i] :
                  ( ~ ( in @ SX2 @ SX0 )
                  | ~ ( in @ SX2
                      @ ( dsetconstr @ SX0
                        @ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
                  | ( SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[718,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(755,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( ~ ( in @ ( sK30_Xx @ SX1 @ SX0 ) @ SX1 )
              | ~ ~ ( in @ ( sK30_Xx @ SX1 @ SX0 ) @ SX0 ) )
          | ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[708,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(756,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ! [SX2: $i] :
              ( ~ ( in @ SX2 @ SX0 )
              | ( SX1 @ SX2 ) )
          | ~ ( ~ ( in @ ( sK40_Xx @ SX1 @ SX0 ) @ SX0 )
              | ~ ~ ( SX1 @ ( sK40_Xx @ SX1 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[683,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(757,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i > $i] :
          ( ~ ( ~ ( in @ ( sK78_Xx @ SX2 @ SX1 @ SX0 ) @ SX0 )
              | ~ ~ ( in @ ( SX2 @ ( sK78_Xx @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
          | ( in
            @ ( lam @ SX0 @ SX1
              @ ^ [SX3: $i] : ( SX2 @ SX3 ) )
            @ ( funcSet @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[546,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(758,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)],[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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(759,plain,
    ( ( ~ ( ~ ! [SX0: $i > $o,SX1: $i > $o] :
                ( ~ ( ( ( sK55_Xx @ SX1 @ SX0 )
                     != ( sK56_SY1873 @ SX1 @ SX0 ) )
                    | ~ ~ ( ~ ( ~ ( SX0 @ ( sK55_Xx @ SX1 @ SX0 ) )
                              | ~ ( SX1 @ ( sK56_SY1873 @ SX1 @ SX0 ) ) )
                          | ~ ( ( SX0 @ ( sK55_Xx @ SX1 @ SX0 ) )
                              | ( SX1 @ ( sK56_SY1873 @ SX1 @ SX0 ) ) ) ) )
                | ! [SX2: $i] :
                    ( ~ ( ~ ( SX0 @ ( sK54_SY233 @ SX2 @ SX1 @ SX0 ) )
                        | ~ ( ( SX2
                             != ( sK54_SY233 @ SX2 @ SX1 @ SX0 ) ) ) )
                    | ~ ( SX0 @ SX2 ) )
                | ~ ( ~ ! [SX2: $i] :
                          ( ~ ( SX1 @ SX2 )
                          | ( ( sK53_SY235 @ SX1 @ SX0 )
                            = SX2 ) )
                    | ~ ( SX1 @ ( sK53_SY235 @ SX1 @ SX0 ) ) ) )
          | ~ ! [SX0: $i > $o,SX1: $i > $o] :
                ( ~ ( ( ( sK51_Xx @ SX1 @ SX0 )
                     != ( sK52_SY1871 @ SX1 @ SX0 ) )
                    | ~ ~ ( ~ ( ~ ( SX0 @ ( sK51_Xx @ SX1 @ SX0 ) )
                              | ~ ( SX1 @ ( sK52_SY1871 @ SX1 @ SX0 ) ) )
                          | ~ ( ( SX0 @ ( sK51_Xx @ SX1 @ SX0 ) )
                              | ( SX1 @ ( sK52_SY1871 @ SX1 @ SX0 ) ) ) ) )
                | ! [SX2: $i] :
                    ( ~ ( ~ ( SX1 @ ( sK50_SY236 @ SX2 @ SX1 @ SX0 ) )
                        | ~ ( ( SX2
                             != ( sK50_SY236 @ SX2 @ SX1 @ SX0 ) ) ) )
                    | ~ ( SX1 @ SX2 ) )
                | ~ ( ~ ! [SX2: $i] :
                          ( ~ ( SX0 @ SX2 )
                          | ( ( sK49_SY232 @ SX1 @ SX0 )
                            = SX2 ) )
                    | ~ ( SX0 @ ( sK49_SY232 @ SX1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[676,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(760,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ( ~ ( SX1 @ ( sK39_Xx @ SX1 @ SX0 ) )
              | ~ ( in @ ( sK39_Xx @ SX1 @ SX0 ) @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ SX0 )
              | ~ ( SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[684,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(761,plain,
    ( ( ! [SX0: $i > $o] :
          ( ! [SX1: $i] :
              ( ~ ( ~ ( SX0 @ ( sK20_SY57 @ SX1 @ SX0 ) )
                  | ~ ( ( SX1
                       != ( sK20_SY57 @ SX1 @ SX0 ) ) ) )
              | ~ ( SX0 @ SX1 ) )
          | ( SX0
            @ ( descr
              @ ^ [SX1: $i] : ( SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[731,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(762,plain,
    ( ( ! [SX0: $i > $o] :
          ( ! [SX1: $i] :
              ( ~ ( ~ ( SX0 @ ( sK42_Xy @ SX1 @ SX0 ) )
                  | ~ ( ( SX1
                       != ( sK42_Xy @ SX1 @ SX0 ) ) ) )
              | ~ ( SX0 @ SX1 ) )
          | ~ ( ~ ! [SX1: $i] :
                    ( ~ ( SX0 @ SX1 )
                    | ( ( sK41_SY198 @ SX0 )
                      = SX1 ) )
              | ~ ( SX0 @ ( sK41_SY198 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[682,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(763,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i > $i] :
          ( ~ ( ~ ( in @ ( sK94_Xx @ SX2 @ SX1 @ SX0 ) @ SX0 )
              | ~ ~ ( in @ ( SX2 @ ( sK94_Xx @ SX2 @ SX1 @ SX0 ) ) @ 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)],[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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(764,plain,
    ( ( ~ ( ~ ( in @ sK2_SY1822 @ ( powerset @ sK1_A ) )
          | ~ ~ ( ~ ( in @ sK3_SY1826 @ ( powerset @ sK1_A ) )
                | ~ ~ ( ~ ( in @ sK4_SY1829 @ ( powerset @ sK1_A ) )
                      | ~ ~ ( ~ ( in @ sK5_SY1831 @ sK1_A )
                            | ~ ~ ( ~ ( in @ sK5_SY1831 @ ( binintersect @ sK2_SY1822 @ sK3_SY1826 ) )
                                  | ~ ~ ( in @ sK5_SY1831 @ ( binunion @ sK3_SY1826 @ sK4_SY1829 ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[743,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(765,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
          | ! [SX3: $i > $o] :
              ( ~ ( ~ ( in @ ( sK81_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
                  | ~ ~ ( ~ ( in @ ( sK82_SY1880 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 )
                        | ~ ~ ( ~ ( in @ ( kpair @ ( sK81_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK82_SY1880 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX2 )
                              | ~ ~ ( SX3 @ ( kpair @ ( sK81_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK82_SY1880 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
              | ! [SX4: $i] :
                  ( ~ ( in @ SX4 @ SX2 )
                  | ( SX3 @ SX4 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[544,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(766,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
          | ! [SX3: $i] :
              ( ~ ( subset @ SX3 @ ( cartprod @ SX0 @ SX1 ) )
              | ~ ( ~ ( in @ ( sK84_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
                  | ~ ~ ( ~ ( in @ ( sK85_SY1881 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 )
                        | ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK85_SY1881 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX2 )
                              | ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK85_SY1881 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX3 ) ) ) )
              | ( subset @ SX2 @ SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[537,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(767,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ( ~ ( in @ ( sK70_Xx @ SX1 @ SX0 ) @ SX0 )
              | ~ ~ ( ~ ( in @ ( sK71_SY1877 @ SX1 @ SX0 ) @ SX0 )
                    | ~ ~ ( ~ ( SX1 @ ( sK70_Xx @ SX1 @ SX0 ) )
                          | ~ ~ ( ~ ( SX1 @ ( sK71_SY1877 @ SX1 @ SX0 ) )
                                | ~ ( ( ( sK70_Xx @ SX1 @ SX0 )
                                     != ( sK71_SY1877 @ SX1 @ SX0 ) ) ) ) ) ) )
          | ! [SX2: $i] :
              ( ~ ( SX1 @ SX2 )
              | ~ ( in @ SX2 @ SX0 ) )
          | ( singleton
            @ ( dsetconstr @ SX0
              @ ^ [SX2: $i] : ( SX1 @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[589,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(768,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ~ ( ~ ! [SX2: $i,SX3: $i] :
                    ( ( SX2 != SX3 )
                    | ~ ( in @ SX2 @ SX0 )
                    | ( in @ SX3 @ SX1 ) )
              | ~ ! [SX2: $i,SX3: $i] :
                    ( ( SX2 != SX3 )
                    | ~ ( in @ SX3 @ SX1 )
                    | ( in @ SX2 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[678,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(769,plain,
    ( ( ! [SX0: $i > $o] :
          ( ! [SX1: $i] :
              ( ~ ( ~ ( SX0 @ ( sK48_SY224 @ SX1 @ SX0 ) )
                  | ~ ( ( SX1
                       != ( sK48_SY224 @ SX1 @ SX0 ) ) ) )
              | ~ ( SX0 @ SX1 ) )
          | ! [SX1: $i] :
              ( ~ ( SX0 @ SX1 )
              | ! [SX2: $i] :
                  ( ~ ( SX0 @ SX2 )
                  | ( SX1 = SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[677,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(770,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i > $i] :
          ( ~ ( ~ ( in @ ( sK77_Xx @ SX2 @ SX1 @ SX0 ) @ SX0 )
              | ~ ~ ( in @ ( SX2 @ ( sK77_Xx @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
          | ( func @ SX0 @ SX1
            @ ( lam @ SX0 @ SX1
              @ ^ [SX3: $i] : ( SX2 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[547,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(771,plain,
    ( ( ! [SX0: $i > $o,SX1: $i > $o] :
          ( ~ ( ( ( sK60_Xx @ SX1 @ SX0 )
               != ( sK61_SY1874 @ SX1 @ SX0 ) )
              | ~ ~ ( ~ ( ~ ( SX0 @ ( sK60_Xx @ SX1 @ SX0 ) )
                        | ~ ( SX1 @ ( sK61_SY1874 @ SX1 @ SX0 ) ) )
                    | ~ ( ( SX0 @ ( sK60_Xx @ SX1 @ SX0 ) )
                        | ( SX1 @ ( sK61_SY1874 @ SX1 @ SX0 ) ) ) ) )
          | ! [SX2: $i] :
              ( ~ ( ~ ( SX0 @ ( sK59_SY257 @ SX2 @ SX1 @ SX0 ) )
                  | ~ ( ( SX2
                       != ( sK59_SY257 @ SX2 @ SX1 @ SX0 ) ) ) )
              | ~ ( SX0 @ SX2 ) )
          | ! [SX2: $i] :
              ( ~ ( ~ ( SX1 @ ( sK58_SY260 @ SX2 @ SX1 @ SX0 ) )
                  | ~ ( ( SX2
                       != ( sK58_SY260 @ SX2 @ SX1 @ SX0 ) ) ) )
              | ~ ( SX1 @ SX2 ) )
          | ( ( descr
              @ ^ [SX2: $i] : ( SX0 @ SX2 ) )
            = ( descr
              @ ^ [SX2: $i] : ( SX1 @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[669,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(772,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ~ ( ~ ( in @ ( sK98_Xx @ SX2 @ SX1 @ SX0 ) @ SX0 )
                  | ~ ~ ( ~ ( in @ ( sK98_Xx @ SX2 @ SX1 @ SX0 ) @ SX1 )
                        | ~ ~ ( in @ ( sK98_Xx @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
              | ( in @ SX1 @ ( powerset @ SX2 ) ) ) ) )
    = $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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(773,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
          | ! [SX2: $o] :
              ( ~ ( ~ ( in @ SX1 @ ( sK31_B @ SX2 @ SX1 @ SX0 ) )
                  | ~ ~ ( ~ ( in @ ( sK31_B @ SX2 @ SX1 @ SX0 ) @ SX0 )
                        | ~ ~ SX2 ) )
              | SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[703,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(774,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( ~ ( in @ ( sK26_Xx @ SX1 @ SX0 ) @ SX0 )
              | ~ ~ ( in @ ( sK26_Xx @ SX1 @ SX0 ) @ SX1 ) )
          | ~ ( ~ ( in @ ( sK25_Xx @ SX1 @ SX0 ) @ SX1 )
              | ~ ~ ( in @ ( sK25_Xx @ SX1 @ SX0 ) @ SX0 ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[721,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(775,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
          | ~ ( ~ ( in @ ( sK69_X @ SX1 @ SX0 ) @ SX0 )
              | ~ ( in @ SX1 @ ( sK69_X @ SX1 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[593,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(776,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( func @ SX0 @ SX1 @ SX2 )
          | ! [SX3: $i] :
              ( ~ ( func @ SX0 @ SX1 @ SX3 )
              | ~ ( ~ ( in @ ( sK83_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
                  | ~ ( ( ( ap @ SX0 @ SX1 @ SX2 @ ( sK83_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) )
                       != ( ap @ SX0 @ SX1 @ SX3 @ ( sK83_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
              | ! [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)],[539,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(777,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
              | ~ ( ~ ( in @ ( sK96_Xx @ SX2 @ SX1 @ SX0 ) @ SX0 )
                  | ~ ~ ( ~ ( in @ ( sK96_Xx @ SX2 @ SX1 @ SX0 ) @ SX1 )
                        | ~ ~ ( in @ ( sK96_Xx @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
              | ~ ( ~ ( in @ ( sK95_Xx @ SX2 @ SX1 @ SX0 ) @ SX0 )
                  | ~ ~ ( ~ ( in @ ( sK95_Xx @ SX2 @ SX1 @ SX0 ) @ SX2 )
                        | ~ ~ ( in @ ( sK95_Xx @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
              | ( SX1 = SX2 ) ) ) )
    = $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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(778,plain,
    ( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
          ( ~ ( in @ SX2 @ SX0 )
          | ~ ( SX1 @ SX2 )
          | ~ ( ~ ( in @ ( sK73_Xy @ SX2 @ SX1 @ SX0 ) @ SX0 )
              | ~ ~ ( ~ ( SX1 @ ( sK73_Xy @ SX2 @ SX1 @ SX0 ) )
                    | ~ ( ( ( sK73_Xy @ SX2 @ SX1 @ SX0 )
                         != SX2 ) ) ) )
          | ( singleton
            @ ( dsetconstr @ SX0
              @ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[587,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(779,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) )
          | ~ ( ~ ~ ( ~ ( ( in @ SX2 @ SX0 )
                        | ~ ( in @ SX2 @ SX0 )
                        | ! [SX3: $o] : SX3 )
                    | ~ ~ ( ~ ( ( in @ SX2 @ SX0 )
                              | ( in @ SX2 @ SX1 )
                              | ! [SX3: $o] : SX3 )
                          | ~ ( ( in @ SX2 @ SX0 )
                              | ! [SX3: $o] :
                                  ( ~ SX3
                                  | SX3 ) ) ) )
              | ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SX2 @ SX1 )
                              | ~ ( in @ SX2 @ SX0 )
                              | ! [SX3: $o] : SX3 )
                          | ~ ~ ( ~ ( ~ ( in @ SX2 @ SX1 )
                                    | ( in @ SX2 @ SX1 )
                                    | ! [SX3: $o] : SX3 )
                                | ~ ( ~ ( in @ SX2 @ SX1 )
                                    | ! [SX3: $o] :
                                        ( ~ SX3
                                        | SX3 ) ) ) )
                    | ~ ~ ( ~ ! [SX3: $o] :
                                ( ~ SX3
                                | ~ ( in @ SX2 @ SX0 )
                                | SX3 )
                          | ~ ~ ( ~ ! [SX3: $o] :
                                      ( ~ SX3
                                      | ( in @ SX2 @ SX1 )
                                      | SX3 )
                                | ~ ! [SX3: $o] :
                                      ( ~ SX3
                                      | ~ SX3
                                      | SX3 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[615,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(780,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i > $i] :
          ( ~ ( ~ ( in @ ( sK76_Xx @ SX2 @ SX1 @ SX0 ) @ SX0 )
              | ~ ~ ( in @ ( SX2 @ ( sK76_Xx @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
          | ( func @ SX0 @ SX1
            @ ( dpsetconstr @ SX0 @ SX1
              @ ^ [SX3: $i,SX4: $i] :
                  ( ( SX2 @ SX3 )
                  = SX4 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[548,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(781,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
                  | ( SX2 = SX0 )
                  | ( in @ SX2 @ SX1 ) )
            | ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
                        ( ( SX2 != SX0 )
                        | ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) )
                  | ~ ! [SX1: $i,SX2: $i] :
                        ( ~ ( in @ SX2 @ SX1 )
                        | ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[740,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(782,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( ~ ( in @ ( sK65_Xx @ SX1 @ SX0 ) @ SX0 )
              | ~ ~ ( in @ ( sK65_Xx @ SX1 @ SX0 ) @ SX1 ) )
          | ( subset @ SX0 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[664,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(783,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( ~ ( ~ ( in @ ( sK6_Xx @ SX1 @ SX0 ) @ SX0 )
                  | ~ ( in @ ( sK6_Xx @ SX1 @ SX0 ) @ SX1 ) )
              | ~ ( ( in @ ( sK6_Xx @ SX1 @ SX0 ) @ SX0 )
                  | ( in @ ( sK6_Xx @ SX1 @ SX0 ) @ SX1 ) ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[742,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(784,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ~ ( ~ ! [SX2: $i] :
                        ( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
                        | ( in @ SX2 @ SX0 )
                        | ( in @ SX2 @ SX1 )
                        | ! [SX3: $o] : SX3 )
                  | ~ ! [SX2: $i] :
                        ( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
                        | ( in @ SX2 @ SX0 )
                        | ! [SX3: $o] :
                            ( ~ SX3
                            | SX3 ) ) )
            | ~ ~ ( ~ ! [SX2: $i] :
                        ( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
                        | ! [SX3: $o] :
                            ( ~ SX3
                            | ( in @ SX2 @ SX1 )
                            | SX3 ) )
                  | ~ ( ! [SX2: $i] :
                          ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
                      | ! [SX2: $o] :
                          ( ~ SX2
                          | ~ SX2
                          | SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[641,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(785,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ! [SX2: $i] :
              ( ~ ( in @ SX2 @ SX0 )
              | ( SX1 @ SX2 ) )
          | ~ ( ~ ( in @ ( sK38_Xx @ SX1 @ SX0 ) @ SX0 )
              | ~ ~ ( SX1 @ ( sK38_Xx @ SX1 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[687,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(786,plain,
    ( ( ! [SX0: $i > $o] :
          ( ! [SX1: $i] :
              ~ ( ~ ( ( ( sK47_Xy @ SX1 @ SX0 )
                     != SX1 )
                    | ~ ( SX0 @ ( sK47_Xy @ SX1 @ SX0 ) ) )
                | ~ ( ( ( sK47_Xy @ SX1 @ SX0 )
                      = SX1 )
                    | ( SX0 @ ( sK47_Xy @ SX1 @ SX0 ) ) ) )
          | ~ ( ~ ! [SX1: $i] :
                    ( ~ ( SX0 @ SX1 )
                    | ( ( sK46_SY211 @ SX0 )
                      = SX1 ) )
              | ~ ( SX0 @ ( sK46_SY211 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[680,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(787,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ( ~ ( in @ ( sK74_Xx @ SX1 @ SX0 ) @ SX0 )
              | ~ ~ ( ~ ( in @ ( sK75_SY1878 @ SX1 @ SX0 ) @ SX0 )
                    | ~ ~ ( ~ ( SX1 @ ( sK74_Xx @ SX1 @ SX0 ) )
                          | ~ ~ ( ~ ( SX1 @ ( sK75_SY1878 @ SX1 @ SX0 ) )
                                | ~ ( ( ( sK74_Xx @ SX1 @ SX0 )
                                     != ( sK75_SY1878 @ SX1 @ SX0 ) ) ) ) ) ) )
          | ! [SX2: $i] :
              ( ~ ( SX1 @ SX2 )
              | ~ ( in @ SX2 @ SX0 ) )
          | ( singleton
            @ ( dsetconstr @ SX0
              @ ^ [SX2: $i] : ( SX1 @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[586,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(788,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
          | ! [SX3: $i] :
              ( ~ ( subset @ SX3 @ ( cartprod @ SX0 @ SX1 ) )
              | ~ ( ~ ( in @ ( sK88_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
                  | ~ ~ ( ~ ( in @ ( sK89_SY1883 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 )
                        | ~ ~ ( ~ ( in @ ( kpair @ ( sK88_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK89_SY1883 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX2 )
                              | ~ ~ ( in @ ( kpair @ ( sK88_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK89_SY1883 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX3 ) ) ) )
              | ~ ( ~ ( in @ ( sK86_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
                  | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 )
                        | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK87_SY1882 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX3 )
                              | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK87_SY1882 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX2 ) ) ) )
              | ( SX2 = SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[536,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(789,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( ~ ~ ( ~ ( in @ ( sK9_Xx @ SX0 ) @ omega )
                    | ~ ( in @ ( sK9_Xx @ SX0 ) @ SX0 ) )
              | ~ ~ ( in @ ( setadjoin @ ( sK9_Xx @ SX0 ) @ ( sK9_Xx @ SX0 ) ) @ SX0 ) )
          | ~ ( in @ emptyset @ SX0 )
          | ! [SX1: $i] :
              ( ~ ( in @ SX1 @ omega )
              | ( in @ SX1 @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[735,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(790,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)],[526,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(791,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i] :
                  ( ~ ( ~ ( in @ ( sK19_Xx @ SX1 @ SX0 ) @ SX1 )
                      | ~ ~ ( in @ ( sK19_Xx @ SX1 @ SX0 ) @ SX0 ) )
                  | ! [SX2: $i] :
                      ~ ( in @ SX2 @ SX1 )
                  | ~ ( ~ ! [SX2: $i] :
                            ( ~ ( in @ SX2 @ ( sK15_B @ SX0 ) )
                            | ! [SX3: $i] :
                                ( ~ ( in @ SX3 @ SX2 )
                                | ( in @ SX3 @ ( sK17_SY1842 @ SX1 @ SX0 ) ) )
                            | ( in @ ( sK18_SY1856 @ SX1 @ SX0 ) @ SX2 ) )
                      | ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1842 @ SX1 @ SX0 ) @ ( sK15_B @ SX0 ) )
                                  | ~ ( in @ ( sK18_SY1856 @ SX1 @ SX0 ) @ SX1 ) )
                            | ~ ! [SX2: $i] :
                                  ( ~ ( in @ SX2 @ ( sK17_SY1842 @ SX1 @ SX0 ) )
                                  | ~ ( in @ SX2 @ SX1 ) ) ) ) )
            | ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
                        ( ~ ( in @ SX1 @ ( sK15_B @ SX0 ) )
                        | ~ ( in @ SX2 @ ( sK15_B @ SX0 ) )
                        | ! [SX3: $i] :
                            ( ~ ( in @ SX3 @ SX1 )
                            | ( in @ SX3 @ SX2 ) )
                        | ! [SX3: $i] :
                            ( ~ ( in @ SX3 @ SX2 )
                            | ( in @ SX3 @ SX1 ) ) )
                  | ~ ~ ( ~ ! [SX1: $i] :
                              ( ~ ( in @ SX1 @ ( sK15_B @ SX0 ) )
                              | ! [SX2: $i] :
                                  ( ~ ( in @ SX2 @ SX1 )
                                  | ( in @ SX2 @ SX0 ) ) )
                        | ~ ! [SX1: $i,SX2: $i] :
                              ( ~ ( in @ SX1 @ SX0 )
                              | ~ ( in @ SX2 @ SX0 )
                              | ~ ( ~ ( in @ ( sK16_SY1855 @ SX2 @ SX1 @ SX0 ) @ ( sK15_B @ SX0 ) )
                                  | ~ ~ ( ~ ( ~ ( in @ SX1 @ ( sK16_SY1855 @ SX2 @ SX1 @ SX0 ) )
                                            | ~ ( in @ SX2 @ ( sK16_SY1855 @ SX2 @ SX1 @ SX0 ) ) )
                                        | ~ ( ( in @ SX1 @ ( sK16_SY1855 @ SX2 @ SX1 @ SX0 ) )
                                            | ( in @ SX2 @ ( sK16_SY1855 @ SX2 @ SX1 @ SX0 ) ) ) ) )
                              | ( SX1 = SX2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[732,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(792,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ( ~ ( SX1 @ ( sK37_Xx @ SX1 @ SX0 ) )
              | ~ ( in @ ( sK37_Xx @ SX1 @ SX0 ) @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ SX0 )
              | ~ ( SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[688,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(793,plain,
    ( ( ! [SX0: $i > $o] :
          ( ! [SX1: $i] :
              ( ~ ( ~ ( SX0 @ ( sK33_SY142 @ SX1 @ SX0 ) )
                  | ~ ( ( SX1
                       != ( sK33_SY142 @ SX1 @ SX0 ) ) ) )
              | ~ ( SX0 @ SX1 ) )
          | ~ ( ~ ! [SX1: $i] :
                    ( ( SX1
                     != ( sK32_Xx @ SX0 ) )
                    | ( SX0 @ SX1 ) )
              | ~ ! [SX1: $i] :
                    ( ~ ( SX0 @ SX1 )
                    | ( SX1
                      = ( sK32_Xx @ SX0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[701,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(794,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
          | ! [SX3: $i > $o] :
              ( ~ ( ~ ( in @ ( sK79_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
                  | ~ ~ ( ~ ( in @ ( sK80_SY1879 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 )
                        | ~ ~ ( ~ ( in @ ( kpair @ ( sK79_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK80_SY1879 @ SX3 @ SX2 @ SX1 @ SX0 ) ) @ SX2 )
                              | ~ ~ ( SX3 @ ( kpair @ ( sK79_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK80_SY1879 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) )
              | ! [SX4: $i] :
                  ( ~ ( in @ SX4 @ SX2 )
                  | ( SX3 @ SX4 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[545,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(795,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ! [SX2: $i] :
              ( ~ ( in @ SX2 @ SX0 )
              | ( SX1 @ SX2 ) )
          | ~ ( ~ ( in @ ( sK35_Xx @ SX1 @ SX0 ) @ SX0 )
              | ~ ~ ( SX1 @ ( sK35_Xx @ SX1 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[690,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(796,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)],[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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(797,plain,
    ( ( ! [SX0: $i] :
          ( ! [SX1: $i] :
              ~ ( in @ SX1 @ SX0 )
          | ~ ( ~ ( in @ ( sK14_B @ SX0 ) @ SX0 )
              | ~ ! [SX1: $i] :
                    ( ~ ( in @ SX1 @ ( sK14_B @ SX0 ) )
                    | ~ ( in @ SX1 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[733,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(798,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)],[522,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(799,plain,
    ( ( ! [SX0: $i > $o] :
          ( ! [SX1: $i] :
              ~ ( SX0 @ SX1 )
          | ~ ( ~ ( SX0 @ ( sK44_Xx @ SX0 ) )
              | ~ ~ ( ~ ( SX0 @ ( sK45_SY1868 @ SX0 ) )
                    | ~ ( ( ( sK44_Xx @ SX0 )
                         != ( sK45_SY1868 @ SX0 ) ) ) ) )
          | ~ ( ~ ! [SX1: $i] :
                    ( ~ ( SX0 @ SX1 )
                    | ( ( sK43_SY205 @ SX0 )
                      = SX1 ) )
              | ~ ( SX0 @ ( sK43_SY205 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[681,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(800,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( ~ ( in @ ( sK64_Xx @ SX1 @ SX0 ) @ SX0 )
              | ~ ~ ( in @ ( sK64_Xx @ SX1 @ SX0 ) @ SX1 ) )
          | ( subset @ SX0 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[667,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(801,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ! [SX2: $i] :
                    ( ~ ( in @ SX1 @ SX2 )
                    | ~ ( in @ SX2 @ SX0 ) )
                | ( in @ SX1 @ ( setunion @ SX0 ) ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
                | ~ ( ~ ( in @ SX1 @ ( sK8_B @ SX1 @ SX0 ) )
                    | ~ ( in @ ( sK8_B @ SX1 @ SX0 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[738,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(802,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( func @ SX0 @ SX1 @ SX2 )
          | ! [SX3: $i] :
              ( ~ ( func @ SX0 @ SX1 @ SX3 )
              | ~ ( ~ ( in @ ( sK90_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
                  | ~ ( ( ( ap @ SX0 @ SX1 @ SX2 @ ( sK90_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) )
                       != ( ap @ SX0 @ SX1 @ SX3 @ ( sK90_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
              | ( SX2 = SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[535,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(803,plain,
    ( ( ! [SX0: $i] :
          ( ! [SX1: $i,SX2: $i > $i] :
              ~ ( ~ ( in @ ( sK93_Xx @ SX2 @ SX1 @ SX0 ) @ SX0 )
                | ~ ~ ( in @ ( SX2 @ ( sK93_Xx @ SX2 @ SX1 @ SX0 ) ) @ SX1 ) )
          | $true ) )
    = $true ),
    inference(unfold_def,[status(thm)],[529,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(804,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
          | ! [SX3: $i] :
              ( ~ ( in @ SX3 @ ( funcSet @ SX0 @ SX1 ) )
              | ~ ( ~ ( in @ ( sK91_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
                  | ~ ( ( ( ap @ SX0 @ SX1 @ SX2 @ ( sK91_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) )
                       != ( ap @ SX0 @ SX1 @ SX3 @ ( sK91_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) )
              | ( SX2 = SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[534,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(805,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ( ~ ( in @ ( sK36_Xx @ SX1 @ SX0 ) @ SX0 )
              | ~ ( SX1 @ ( sK36_Xx @ SX1 @ SX0 ) ) )
          | ! [SX2: $i] :
              ( ~ ( SX1 @ SX2 )
              | ~ ( in @ SX2 @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[689,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(806,plain,
    ( ( ! [SX0: $i > $o] :
          ( ! [SX1: $i] :
              ( ~ ( ~ ( SX0 @ ( sK22_SY74 @ SX1 @ SX0 ) )
                  | ~ ( ( SX1
                       != ( sK22_SY74 @ SX1 @ SX0 ) ) ) )
              | ~ ( SX0 @ SX1 ) )
          | ~ ( ~ ! [SX1: $i] :
                    ( ~ ( SX0 @ SX1 )
                    | ( ( sK21_Xx @ SX0 )
                      = SX1 ) )
              | ~ ( SX0 @ ( sK21_Xx @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[727,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(807,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ! [SX2: $i > $o,SX3: $i > $o] :
              ( ~ ( ~ ( in @ ( sK62_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
                  | ~ ~ ( ~ ( in @ ( sK63_SY1875 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 )
                        | ~ ~ ( ( ( sK62_Xx @ SX3 @ SX2 @ SX1 @ SX0 )
                               != ( sK63_SY1875 @ SX3 @ SX2 @ SX1 @ SX0 ) )
                              | ~ ~ ( ~ ( ~ ( SX2 @ ( sK62_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) )
                                        | ~ ( SX3 @ ( sK63_SY1875 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
                                    | ~ ( ( SX2 @ ( sK62_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) )
                                        | ( SX3 @ ( sK63_SY1875 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) )
              | ( ( dsetconstr @ SX0
                  @ ^ [SX4: $i] : ( SX2 @ SX4 ) )
                = ( dsetconstr @ SX1
                  @ ^ [SX4: $i] : ( SX3 @ SX4 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[668,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(808,plain,
    ( ( ! [SX0: $i,SX1: $i > $o] :
          ( ~ ( singleton
              @ ( dsetconstr @ SX0
                @ ^ [SX2: $i] : ( SX1 @ SX2 ) ) )
          | ~ ( ~ ( SX1 @ ( sK72_Xx @ SX1 @ SX0 ) )
              | ~ ( in @ ( sK72_Xx @ SX1 @ SX0 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[588,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,inCongP,inIntersectImpInUnion,inPowerset,in__Cong,infuncsetfunc,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(809,plain,
    ! [SV1: $i] :
      ( ( ! [SY1884: $i] :
            ( ~ ( in @ SY1884 @ ( powerset @ SV1 ) )
            | ! [SY1885: $i] :
                ( ~ ( in @ SY1885 @ ( powerset @ SV1 ) )
                | ! [SY1886: $i] :
                    ( ~ ( in @ SY1886 @ ( powerset @ SV1 ) )
                    | ! [SY1887: $i] :
                        ( ~ ( in @ SY1887 @ SV1 )
                        | ~ ( in @ SY1887 @ ( binintersect @ SY1884 @ SY1885 ) )
                        | ( in @ SY1887 @ ( binunion @ SY1884 @ SY1886 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[486]) ).

thf(810,plain,
    ! [SV2: $i] :
      ( ( ! [SY1888: $i] :
            ( ~ ( in @ SY1888 @ ( powerset @ SV2 ) )
            | ! [SY1889: $i] :
                ( ~ ( in @ SY1889 @ ( powerset @ SV2 ) )
                | ! [SY1890: $i] :
                    ( ~ ( in @ SY1890 @ SV2 )
                    | ( in @ SY1890 @ ( binunion @ SY1888 @ SY1889 ) )
                    | ~ ( in @ SY1890 @ SY1889 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[487]) ).

thf(811,plain,
    ! [SV3: $i] :
      ( ( ! [SY1891: $i] :
            ( ~ ( in @ SY1891 @ ( powerset @ SV3 ) )
            | ! [SY1892: $i] :
                ( ~ ( in @ SY1892 @ ( powerset @ SV3 ) )
                | ! [SY1893: $i] :
                    ( ~ ( in @ SY1893 @ SV3 )
                    | ( in @ SY1893 @ ( binunion @ SY1891 @ SY1892 ) )
                    | ~ ( in @ SY1893 @ SY1891 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[488]) ).

thf(812,plain,
    ! [SV4: $i] :
      ( ( ! [SY1894: $i] :
            ( ~ ( in @ SY1894 @ ( powerset @ SV4 ) )
            | ! [SY1895: $i] :
                ( ~ ( in @ SY1895 @ ( powerset @ SV4 ) )
                | ~ ( subset @ SY1894 @ ( setminus @ SV4 @ SY1895 ) )
                | ( subset @ SY1895 @ ( setminus @ SV4 @ SY1894 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[489]) ).

thf(813,plain,
    ! [SV5: $i] :
      ( ( ! [SY1896: $i] :
            ( ~ ( in @ SY1896 @ ( powerset @ SV5 ) )
            | ! [SY1897: $i] :
                ( ~ ( in @ SY1897 @ ( powerset @ SV5 ) )
                | ~ ( subset @ SY1896 @ ( setminus @ SV5 @ SY1897 ) )
                | ! [SY1898: $i] :
                    ( ~ ( in @ SY1898 @ SV5 )
                    | ~ ( in @ SY1898 @ SY1897 )
                    | ( in @ SY1898 @ ( setminus @ SV5 @ SY1896 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[490]) ).

thf(814,plain,
    ! [SV6: $i] :
      ( ( ! [SY1899: $i] :
            ( ~ ( in @ SY1899 @ ( powerset @ SV6 ) )
            | ! [SY1900: $i] :
                ( ~ ( in @ SY1900 @ ( powerset @ SV6 ) )
                | ( in @ ( setminus @ SV6 @ SY1899 ) @ ( powerset @ ( setminus @ SV6 @ ( binintersect @ SY1899 @ SY1900 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[491]) ).

thf(815,plain,
    ! [SV7: $i] :
      ( ( ! [SY1901: $i] :
            ( ~ ( in @ SY1901 @ ( powerset @ SV7 ) )
            | ! [SY1902: $i] :
                ( ~ ( in @ SY1902 @ ( powerset @ SV7 ) )
                | ( subset @ ( setminus @ SV7 @ SY1901 ) @ ( setminus @ SV7 @ ( binintersect @ SY1901 @ SY1902 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[492]) ).

thf(816,plain,
    ! [SV8: $i] :
      ( ( ! [SY1903: $i] :
            ( ~ ( in @ SY1903 @ ( powerset @ SV8 ) )
            | ! [SY1904: $i] :
                ( ~ ( in @ SY1904 @ ( powerset @ SV8 ) )
                | ! [SY1905: $i] :
                    ( ~ ( in @ SY1905 @ SV8 )
                    | ~ ( in @ SY1905 @ ( setminus @ SV8 @ SY1903 ) )
                    | ( in @ SY1905 @ ( setminus @ SV8 @ ( binintersect @ SY1903 @ SY1904 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[493]) ).

thf(817,plain,
    ! [SV9: $i] :
      ( ( ! [SY1906: $i] :
            ( ~ ( in @ SY1906 @ ( powerset @ SV9 ) )
            | ! [SY1907: $i] :
                ( ~ ( in @ SY1907 @ ( powerset @ SV9 ) )
                | ! [SY1908: $i] :
                    ( ~ ( in @ SY1908 @ SV9 )
                    | ~ ( in @ SY1908 @ ( setminus @ SV9 @ SY1906 ) )
                    | ~ ( in @ SY1908 @ ( binintersect @ SY1906 @ SY1907 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[494]) ).

thf(818,plain,
    ! [SV10: $i] :
      ( ( ! [SY1909: $i] :
            ( ~ ( in @ SY1909 @ ( powerset @ SV10 ) )
            | ( SY1909
              = ( setminus @ SV10 @ ( setminus @ SV10 @ SY1909 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[495]) ).

thf(819,plain,
    ! [SV11: $i] :
      ( ( ! [SY1910: $i] :
            ( ~ ( in @ SY1910 @ ( powerset @ SV11 ) )
            | ( subset @ ( setminus @ SV11 @ ( setminus @ SV11 @ SY1910 ) ) @ SY1910 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[496]) ).

thf(820,plain,
    ! [SV12: $i] :
      ( ( ! [SY1911: $i] :
            ( ~ ( in @ SY1911 @ ( powerset @ SV12 ) )
            | ( subset @ SY1911 @ ( setminus @ SV12 @ ( setminus @ SV12 @ SY1911 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[497]) ).

thf(821,plain,
    ! [SV13: $i] :
      ( ( ! [SY1912: $i] :
            ( ~ ( in @ SY1912 @ ( powerset @ SV13 ) )
            | ! [SY1913: $i] :
                ( ~ ( in @ SY1913 @ SV13 )
                | ~ ( in @ SY1913 @ ( setminus @ SV13 @ ( setminus @ SV13 @ SY1912 ) ) )
                | ( in @ SY1913 @ SY1912 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[498]) ).

thf(822,plain,
    ! [SV14: $i] :
      ( ( ! [SY1914: $i] :
            ( ~ ( in @ SY1914 @ ( powerset @ SV14 ) )
            | ! [SY1915: $i] :
                ( ~ ( in @ SY1915 @ SV14 )
                | ~ ( in @ SY1915 @ SY1914 )
                | ( in @ SY1915 @ ( setminus @ SV14 @ ( setminus @ SV14 @ SY1914 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[499]) ).

thf(823,plain,
    ! [SV15: $i] :
      ( ( ! [SY1916: $i] :
            ( ~ ( in @ SY1916 @ ( powerset @ SV15 ) )
            | ! [SY1917: $i] :
                ( ~ ( in @ SY1917 @ ( powerset @ SV15 ) )
                | ~ ( subset @ ( setminus @ SV15 @ SY1917 ) @ ( setminus @ SV15 @ SY1916 ) )
                | ( subset @ SY1916 @ SY1917 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[500]) ).

thf(824,plain,
    ! [SV16: $i] :
      ( ( ! [SY1918: $i] :
            ( ~ ( in @ SY1918 @ ( powerset @ SV16 ) )
            | ! [SY1919: $i] :
                ( ~ ( in @ SY1919 @ ( powerset @ SV16 ) )
                | ~ ( subset @ SY1918 @ SY1919 )
                | ( subset @ ( setminus @ SV16 @ SY1919 ) @ ( setminus @ SV16 @ SY1918 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[501]) ).

thf(825,plain,
    ! [SV17: $i] :
      ( ( ! [SY1920: $i] :
            ( ~ ( in @ SY1920 @ ( powerset @ SV17 ) )
            | ! [SY1921: $i] :
                ( ~ ( in @ SY1921 @ ( powerset @ SV17 ) )
                | ! [SY1922: $i] :
                    ( ~ ( in @ SY1922 @ SV17 )
                    | ~ ( subset @ SY1920 @ SY1921 )
                    | ( in @ SY1922 @ SY1921 )
                    | ~ ( in @ SY1922 @ SY1920 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[502]) ).

thf(826,plain,
    ! [SV18: $i] :
      ( ( ! [SY1923: $i] :
            ( ~ ( in @ SY1923 @ ( powerset @ SV18 ) )
            | ! [SY1924: $i] :
                ( ~ ( in @ SY1924 @ ( powerset @ SV18 ) )
                | ! [SY1925: $i] :
                    ( ~ ( in @ SY1925 @ SV18 )
                    | ~ ( subset @ SY1923 @ ( setminus @ SV18 @ SY1924 ) )
                    | ~ ( in @ SY1925 @ SY1924 )
                    | ~ ( in @ SY1925 @ SY1923 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[503]) ).

thf(827,plain,
    ! [SV19: $i] :
      ( ( ! [SY1926: $i] :
            ( ~ ( in @ SY1926 @ ( powerset @ SV19 ) )
            | ! [SY1927: $i] :
                ( ~ ( in @ SY1927 @ ( powerset @ SV19 ) )
                | ! [SY1928: $i] :
                    ( ~ ( in @ SY1928 @ SV19 )
                    | ( in @ SY1928 @ SY1927 )
                    | ~ ( in @ SY1928 @ ( binintersect @ SY1926 @ SY1927 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[504]) ).

thf(828,plain,
    ! [SV20: $i] :
      ( ( ! [SY1929: $i] :
            ( ~ ( in @ SY1929 @ ( powerset @ SV20 ) )
            | ! [SY1930: $i] :
                ( ~ ( in @ SY1930 @ ( powerset @ SV20 ) )
                | ! [SY1931: $i] :
                    ( ~ ( in @ SY1931 @ SV20 )
                    | ( in @ SY1931 @ SY1929 )
                    | ~ ( in @ SY1931 @ ( binintersect @ SY1929 @ SY1930 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[505]) ).

thf(829,plain,
    ! [SV21: $i] :
      ( ( ! [SY1932: $i] :
            ( ~ ( in @ SY1932 @ ( powerset @ SV21 ) )
            | ! [SY1933: $i] :
                ( ~ ( in @ SY1933 @ SV21 )
                | ( in @ SY1933 @ ( setminus @ SV21 @ SY1932 ) )
                | ( in @ SY1933 @ SY1932 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[506]) ).

thf(830,plain,
    ! [SV22: $i] :
      ( ( ! [SY1934: $i] :
            ( ~ ( in @ SY1934 @ ( powerset @ SV22 ) )
            | ! [SY1935: $i] :
                ( ~ ( in @ SY1935 @ SV22 )
                | ~ ( in @ SY1935 @ SY1934 )
                | ~ ( in @ SY1935 @ ( setminus @ SV22 @ SY1934 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[507]) ).

thf(831,plain,
    ! [SV23: $i] :
      ( ( ! [SY1936: $i] :
            ( ~ ( in @ SY1936 @ ( powerset @ SV23 ) )
            | ! [SY1937: $i] :
                ( ~ ( in @ SY1937 @ ( powerset @ SV23 ) )
                | ! [SY1938: $i] :
                    ( ~ ( in @ SY1938 @ SV23 )
                    | ~ ( in @ SY1936 @ ( powerset @ SY1937 ) )
                    | ~ ( in @ SY1938 @ SY1936 )
                    | ( in @ SY1938 @ SY1937 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[508]) ).

thf(832,plain,
    ! [SV24: $i] :
      ( ( ! [SY1939: $i] :
            ( ~ ( in @ SY1939 @ ( powerset @ SV24 ) )
            | ( in @ ( setminus @ SV24 @ SY1939 ) @ ( powerset @ SV24 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[512]) ).

thf(833,plain,
    ! [SV25: $i] :
      ( ( ! [SY1940: $i] :
            ( ~ ( in @ SY1940 @ ( powerset @ SV25 ) )
            | ! [SY1941: $i] :
                ( ~ ( in @ SY1941 @ ( powerset @ SV25 ) )
                | ( in @ ( setminus @ SY1940 @ SY1941 ) @ ( powerset @ SV25 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[513]) ).

thf(834,plain,
    ! [SV26: $i] :
      ( ( ! [SY1942: $i] :
            ( ~ ( in @ SY1942 @ ( powerset @ SV26 ) )
            | ( in @ ( powerset @ SY1942 ) @ ( powerset @ ( powerset @ SV26 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[514]) ).

thf(835,plain,
    ! [SV27: $i] :
      ( ( ! [SY1943: $i] :
            ( ~ ( in @ SY1943 @ ( powerset @ SV27 ) )
            | ! [SY1944: $i] :
                ( ~ ( in @ SY1944 @ ( powerset @ SV27 ) )
                | ( in @ ( binunion @ SY1943 @ SY1944 ) @ ( powerset @ SV27 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[515]) ).

thf(836,plain,
    ! [SV28: $i] :
      ( ( ! [SY1945: $i] :
            ( ~ ( in @ SY1945 @ ( powerset @ SV28 ) )
            | ! [SY1946: $i] :
                ( ~ ( in @ SY1946 @ ( powerset @ SV28 ) )
                | ( in @ ( binintersect @ SY1945 @ SY1946 ) @ ( powerset @ SV28 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[516]) ).

thf(837,plain,
    ! [SV29: $i] :
      ( ( ! [SY1947: $o,SY1948: $i] :
            ( ~ ( in @ SY1948 @ SV29 )
            | ! [SY1949: $i] :
                ( ~ ( in @ SY1949 @ SV29 )
                | ( in @ ( if @ SV29 @ SY1947 @ SY1948 @ SY1949 ) @ ( setadjoin @ SY1948 @ ( setadjoin @ SY1949 @ emptyset ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[517]) ).

thf(838,plain,
    ! [SV30: $i] :
      ( ( ! [SY1950: $o,SY1951: $i] :
            ( ~ ( in @ SY1951 @ SV30 )
            | ! [SY1952: $i] :
                ( ~ ( in @ SY1952 @ SV30 )
                | SY1950
                | ( ( if @ SV30 @ SY1950 @ SY1951 @ SY1952 )
                  = SY1952 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[518]) ).

thf(839,plain,
    ! [SV31: $i] :
      ( ( ! [SY1953: $o,SY1954: $i] :
            ( ~ ( in @ SY1954 @ SV31 )
            | ! [SY1955: $i] :
                ( ~ ( in @ SY1955 @ SV31 )
                | ~ SY1953
                | ( ( if @ SV31 @ SY1953 @ SY1954 @ SY1955 )
                  = SY1954 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[519]) ).

thf(840,plain,
    ! [SV32: $i] :
      ( ( ~ ( singleton @ SV32 )
        | ! [SY1956: $i] :
            ( ~ ( in @ SY1956 @ SV32 )
            | ( ( setunion @ SV32 )
              = SY1956 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[520]) ).

thf(841,plain,
    ! [SV33: $i] :
      ( ( ! [SY1957: $o,SY1958: $i] :
            ( ~ ( in @ SY1958 @ SV33 )
            | ! [SY1959: $i] :
                ( ~ ( in @ SY1959 @ SV33 )
                | ( in @ ( if @ SV33 @ SY1957 @ SY1958 @ SY1959 ) @ SV33 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[521]) ).

thf(842,plain,
    ! [SV34: $i] :
      ( ( ! [SY1960: $i,SY1961: $i] :
            ( ~ ( in @ SY1961 @ ( funcSet @ SV34 @ SY1960 ) )
            | ( ( lam @ SV34 @ SY1960
                @ ^ [SY1962: $i] : ( ap @ SV34 @ SY1960 @ SY1961 @ SY1962 ) )
              = SY1961 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[527]) ).

thf(843,plain,
    ! [SV35: $i] :
      ( ( ! [SY1963: $i,SY1964: $i] :
            ( ~ ( func @ SV35 @ SY1963 @ SY1964 )
            | ( ( lam @ SV35 @ SY1963
                @ ^ [SY1965: $i] : ( ap @ SV35 @ SY1963 @ SY1964 @ SY1965 ) )
              = SY1964 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[530]) ).

thf(844,plain,
    ! [SV36: $i] :
      ( ( ! [SY1966: $i,SY1967: $i] :
            ~ ( func @ SV36 @ SY1966 @ SY1967 )
        | ! [SY1968: $i] :
            ~ ( in @ SY1968 @ SV36 )
        | $true )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[532]) ).

thf(845,plain,
    ! [SV37: $i] :
      ( ( ! [SY1969: $i,SY1970: $i] :
            ~ ( in @ SY1970 @ ( funcSet @ SV37 @ SY1969 ) )
        | ! [SY1971: $i] :
            ~ ( in @ SY1971 @ SV37 )
        | $true )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[533]) ).

thf(846,plain,
    ! [SV38: $i] :
      ( ( ! [SY1972: $i,SY1973: $i] :
            ( ~ ( in @ SY1973 @ ( funcSet @ SV38 @ SY1972 ) )
            | ! [SY1974: $i] :
                ( ~ ( in @ SY1974 @ SV38 )
                | ! [SY1975: $i] :
                    ( ~ ( in @ SY1975 @ SY1972 )
                    | ~ ( in @ ( kpair @ SY1974 @ SY1975 ) @ SY1973 )
                    | ( ( ap @ SV38 @ SY1972 @ SY1973 @ SY1974 )
                      = SY1975 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[538]) ).

thf(847,plain,
    ! [SV39: $i] :
      ( ( ! [SY1976: $i,SY1977: $i] :
            ( ~ ( func @ SV39 @ SY1976 @ SY1977 )
            | ! [SY1978: $i] :
                ( ~ ( in @ SY1978 @ SV39 )
                | ! [SY1979: $i] :
                    ( ~ ( in @ SY1979 @ SY1976 )
                    | ~ ( in @ ( kpair @ SY1978 @ SY1979 ) @ SY1977 )
                    | ( ( ap @ SV39 @ SY1976 @ SY1977 @ SY1978 )
                      = SY1979 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[540]) ).

thf(848,plain,
    ! [SV40: $i] :
      ( ( ! [SY1980: $i,SY1981: $i] :
            ( ~ ( in @ SY1981 @ ( funcSet @ SV40 @ SY1980 ) )
            | ! [SY1982: $i] :
                ( ~ ( in @ SY1982 @ SV40 )
                | ( in @ ( kpair @ SY1982 @ ( ap @ SV40 @ SY1980 @ SY1981 @ SY1982 ) ) @ SY1981 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[541]) ).

thf(849,plain,
    ! [SV41: $i] :
      ( ( ! [SY1983: $i,SY1984: $i] :
            ( ~ ( func @ SV41 @ SY1983 @ SY1984 )
            | ! [SY1985: $i] :
                ( ~ ( in @ SY1985 @ SV41 )
                | ( in @ ( kpair @ SY1985 @ ( ap @ SV41 @ SY1983 @ SY1984 @ SY1985 ) ) @ SY1984 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[542]) ).

thf(850,plain,
    ! [SV42: $i] :
      ( ( ! [SY1986: $i > $o] :
            ( ~ ( singleton
                @ ( dsetconstr @ SV42
                  @ ^ [SY687: $i] : ( SY1986 @ SY687 ) ) )
            | ! [SY1988: $i] :
                ( ~ ( in @ SY1988 @ SV42 )
                | ! [SY1989: $i] :
                    ( ~ ( in @ SY1989 @ SV42 )
                    | ~ ( SY1986 @ SY1988 )
                    | ~ ( SY1986 @ SY1989 )
                    | ( SY1988 = SY1989 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[543]) ).

thf(851,plain,
    ! [SV43: $i] :
      ( ( ! [SY1990: $i,SY1991: $i] :
            ( ~ ( func @ SV43 @ SY1990 @ SY1991 )
            | ( in @ SY1991 @ ( funcSet @ SV43 @ SY1990 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[549]) ).

thf(852,plain,
    ! [SV44: $i] :
      ( ( ! [SY1992: $i,SY1993: $i] :
            ( ~ ( in @ SY1993 @ ( funcSet @ SV44 @ SY1992 ) )
            | ! [SY1994: $i] :
                ( ~ ( in @ SY1994 @ SV44 )
                | ( in @ ( ap @ SV44 @ SY1992 @ SY1993 @ SY1994 ) @ SY1992 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[550]) ).

thf(853,plain,
    ! [SV45: $i] :
      ( ( ! [SY1995: $i,SY1996: $i] :
            ( ~ ( in @ SY1996 @ ( funcSet @ SV45 @ SY1995 ) )
            | ( func @ SV45 @ SY1995 @ SY1996 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[551]) ).

thf(854,plain,
    ! [SV46: $i] :
      ( ( ! [SY1997: $i,SY1998: $i] :
            ( ~ ( func @ SV46 @ SY1997 @ SY1998 )
            | ! [SY1999: $i] :
                ( ~ ( in @ SY1999 @ SV46 )
                | ( in @ ( ap @ SV46 @ SY1997 @ SY1998 @ SY1999 ) @ SY1997 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[552]) ).

thf(855,plain,
    ! [SV47: $i] :
      ( ( ! [SY2000: $i,SY2001: $i] :
            ( ~ ( func @ SV47 @ SY2000 @ SY2001 )
            | ! [SY2002: $i] :
                ( ~ ( in @ SY2002 @ SV47 )
                | ( in
                  @ ( setunion
                    @ ( dsetconstr @ SY2000
                      @ ^ [Xy: $i] : ( in @ ( kpair @ SY2002 @ Xy ) @ SY2001 ) ) )
                  @ SY2000 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[553]) ).

thf(856,plain,
    ! [SV48: $i] :
      ( ( ! [SY2004: $i,SY2005: $i] :
            ( ~ ( func @ SV48 @ SY2004 @ SY2005 )
            | ! [SY2006: $i] :
                ( ~ ( in @ SY2006 @ SV48 )
                | ( singleton
                  @ ( dsetconstr @ SY2004
                    @ ^ [Xy: $i] : ( in @ ( kpair @ SY2006 @ Xy ) @ SY2005 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[554]) ).

thf(857,plain,
    ! [SV49: $i] :
      ( ( ! [SY2008: $i,SY2009: $i > $i > $o,SY2010: $i,SY2011: $i] :
            ( ~ ( in @ ( kpair @ SY2010 @ SY2011 )
                @ ( dpsetconstr @ SV49 @ SY2008
                  @ ^ [Xz: $i,Xu: $i] : ( SY2009 @ Xz @ Xu ) ) )
            | ( SY2009 @ SY2010 @ SY2011 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[555]) ).

thf(858,plain,
    ! [SV50: $i] :
      ( ( ! [SY2014: $i,SY2015: $i > $i > $o,SY2016: $i,SY2017: $i] :
            ( ~ ( in @ ( kpair @ SY2016 @ SY2017 )
                @ ( dpsetconstr @ SV50 @ SY2014
                  @ ^ [Xz: $i,Xu: $i] : ( SY2015 @ Xz @ Xu ) ) )
            | ( in @ SY2017 @ SY2014 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[556]) ).

thf(859,plain,
    ! [SV51: $i] :
      ( ( ! [SY2020: $i,SY2021: $i > $i > $o,SY2022: $i] :
            ( ! [SY2023: $i] :
                ~ ( in @ ( kpair @ SY2022 @ SY2023 )
                  @ ( dpsetconstr @ SV51 @ SY2020
                    @ ^ [Xz: $i,Xu: $i] : ( SY2021 @ Xz @ Xu ) ) )
            | ( in @ SY2022 @ SV51 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[557]) ).

thf(860,plain,
    ! [SV52: $i] :
      ( ( ! [SY2026: $i,SY2027: $i > $i > $o,SY2028: $i] :
            ( ~ ( in @ SY2028 @ SV52 )
            | ! [SY2029: $i] :
                ( ~ ( in @ SY2029 @ SY2026 )
                | ~ ( in @ ( kpair @ SY2028 @ SY2029 )
                    @ ( dpsetconstr @ SV52 @ SY2026
                      @ ^ [Xz: $i,Xu: $i] : ( SY2027 @ Xz @ Xu ) ) )
                | ( SY2027 @ SY2028 @ SY2029 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[558]) ).

thf(861,plain,
    ! [SV53: $i] :
      ( ( ! [SY2032: $i,SY2033: $i > $i > $o] :
            ( subset
            @ ( dpsetconstr @ SV53 @ SY2032
              @ ^ [Xx: $i,Xy: $i] : ( SY2033 @ Xx @ Xy ) )
            @ ( cartprod @ SV53 @ SY2032 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[559]) ).

thf(862,plain,
    ! [SV54: $i] :
      ( ( ! [SY2036: $i,SY2037: $i > $i > $o] :
            ( subset
            @ ( dpsetconstr @ SV54 @ SY2036
              @ ^ [Xx: $i,Xy: $i] : ( SY2037 @ Xx @ Xy ) )
            @ ( cartprod @ SV54 @ SY2036 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[560]) ).

thf(863,plain,
    ! [SV55: $i] :
      ( ( ! [SY2040: $i,SY2041: $i > $i > $o,SY2042: $i] :
            ( ~ ( in @ SY2042 @ SV55 )
            | ! [SY2043: $i] :
                ( ~ ( in @ SY2043 @ SY2040 )
                | ~ ( SY2041 @ SY2042 @ SY2043 )
                | ( in @ ( kpair @ SY2042 @ SY2043 )
                  @ ( dpsetconstr @ SV55 @ SY2040
                    @ ^ [Xz: $i,Xu: $i] : ( SY2041 @ Xz @ Xu ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[561]) ).

thf(864,plain,
    ! [SV56: $i] :
      ( ( ! [SY2046: $i,SY2047: $i] :
            ( ~ ( in @ SY2047 @ ( cartprod @ SV56 @ SY2046 ) )
            | ( ( kpair @ ( kfst @ SY2047 ) @ ( ksnd @ SY2047 ) )
              = SY2047 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[562]) ).

thf(865,plain,
    ! [SV57: $i] :
      ( ( ! [SY2048: $i,SY2049: $i] :
            ( ~ ( in @ SY2049 @ SV57 )
            | ! [Xy: $i] :
                ( ~ ( in @ Xy @ SY2048 )
                | ( ( ksnd @ ( kpair @ SY2049 @ Xy ) )
                  = Xy ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[563]) ).

thf(866,plain,
    ! [SV58: $i] :
      ( ( ! [SY2051: $i,SY2052: $i] :
            ( ~ ( in @ SY2052 @ SV58 )
            | ! [Xy: $i] :
                ( ~ ( in @ Xy @ SY2051 )
                | ( ( kfst @ ( kpair @ SY2052 @ Xy ) )
                  = SY2052 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[564]) ).

thf(867,plain,
    ! [SV59: $i] :
      ( ( ! [SY2054: $i] :
            ~ ( in @ SY2054 @ SV59 )
        | ! [B: $i,Xy: $i] :
            ~ ( in @ Xy @ B )
        | $true )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[565]) ).

thf(868,plain,
    ! [SV60: $i] :
      ( ( ! [SY2057: $i,SY2058: $i,SY2059: $i] :
            ( ~ ( in @ ( kpair @ SY2058 @ SY2059 ) @ ( cartprod @ SV60 @ SY2057 ) )
            | ( in @ SY2059 @ SY2057 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[566]) ).

thf(869,plain,
    ! [SV61: $i] :
      ( ( ! [SY2060: $i,SY2061: $i] :
            ( ! [SY2062: $i] :
                ~ ( in @ ( kpair @ SY2061 @ SY2062 ) @ ( cartprod @ SV61 @ SY2060 ) )
            | ( in @ SY2061 @ SV61 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[567]) ).

thf(870,plain,
    ! [SV62: $i] :
      ( ( ! [SY2063: $i,SY2064: $i] :
            ( ~ ( in @ SY2064 @ ( cartprod @ SV62 @ SY2063 ) )
            | ( in @ ( ksnd @ SY2064 ) @ SY2063 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[568]) ).

thf(871,plain,
    ! [SV63: $i] :
      ( ( ~ ( iskpair @ SV63 )
        | ( ( kpair @ ( kfst @ SV63 ) @ ( ksnd @ SV63 ) )
          = SV63 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[569]) ).

thf(872,plain,
    ! [SV64: $i] :
      ( ( ! [SY2065: $i] :
            ( ( ksnd @ ( kpair @ SV64 @ SY2065 ) )
            = SY2065 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[570]) ).

thf(873,plain,
    ! [SV65: $i] :
      ( ( ~ ( iskpair @ SV65 )
        | ( singleton
          @ ( dsetconstr @ ( setunion @ SV65 )
            @ ^ [SY2066: $i] :
                ( SV65
                = ( kpair @ ( kfst @ SV65 ) @ SY2066 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[571]) ).

thf(874,plain,
    ! [SV66: $i] :
      ( ( ! [SY2067: $i,SY2068: $i,SY2069: $i] :
            ( ( ( kpair @ SV66 @ SY2067 )
             != ( kpair @ SY2068 @ SY2069 ) )
            | ( SY2067 = SY2069 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[572]) ).

thf(875,plain,
    ! [SV67: $i] :
      ( ( ! [SY2070: $i,SY2071: $i,SY2072: $i] :
            ( ( ( setadjoin @ ( setadjoin @ SV67 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV67 @ ( setadjoin @ SY2070 @ emptyset ) ) @ emptyset ) )
             != ( setadjoin @ ( setadjoin @ SY2071 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2071 @ ( setadjoin @ SY2072 @ emptyset ) ) @ emptyset ) ) )
            | ( SY2070 = SY2072 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[573]) ).

thf(876,plain,
    ! [SV68: $i] :
      ( ( ! [SY2073: $i] :
            ( ! [SY2074: $i] :
                ( ( setadjoin @ SV68 @ ( setadjoin @ SY2073 @ emptyset ) )
               != ( setadjoin @ SY2074 @ emptyset ) )
            | ( SV68 = SY2073 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[574]) ).

thf(877,plain,
    ! [SV69: $i] :
      ( ( ! [SY2075: $i,SY2076: $i,SY2077: $i] :
            ( ( ( setadjoin @ ( setadjoin @ SV69 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV69 @ ( setadjoin @ SY2075 @ emptyset ) ) @ emptyset ) )
             != ( setadjoin @ ( setadjoin @ SY2076 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2076 @ ( setadjoin @ SY2077 @ emptyset ) ) @ emptyset ) ) )
            | ( SY2076 != SY2077 )
            | ( SY2075 = SY2077 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[575]) ).

thf(878,plain,
    ! [SV70: $i] :
      ( ( ! [SY2078: $i] :
            ( ( SV70 != SY2078 )
            | ( ( setadjoin @ ( setadjoin @ SV70 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV70 @ ( setadjoin @ SY2078 @ emptyset ) ) @ emptyset ) )
              = ( setadjoin @ ( setadjoin @ SV70 @ emptyset ) @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[576]) ).

thf(879,plain,
    ! [SV71: $i] :
      ( ( ! [SY2079: $i] :
            ( ( SV71 != SY2079 )
            | ( ( setadjoin @ SV71 @ ( setadjoin @ SY2079 @ emptyset ) )
              = ( setadjoin @ SV71 @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[577]) ).

thf(880,plain,
    ! [SV72: $i] :
      ( ( ! [SY2080: $i,SY2081: $i] :
            ( ! [SY2082: $i] :
                ( ( kpair @ SV72 @ SY2080 )
               != ( kpair @ SY2081 @ SY2082 ) )
            | ( SV72 = SY2081 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[578]) ).

thf(881,plain,
    ! [SV73: $i] :
      ( ( ! [SY2083: $i,SY2084: $i] :
            ( ! [SY2085: $i] :
                ( ( setadjoin @ ( setadjoin @ SV73 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV73 @ ( setadjoin @ SY2083 @ emptyset ) ) @ emptyset ) )
               != ( setadjoin @ ( setadjoin @ SY2084 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2084 @ ( setadjoin @ SY2085 @ emptyset ) ) @ emptyset ) ) )
            | ( SV73 = SY2084 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[579]) ).

thf(882,plain,
    ! [SV74: $i] :
      ( ( ! [SY2086: $i,SY2087: $i] :
            ( ~ ( in @ SY2087 @ ( cartprod @ SV74 @ SY2086 ) )
            | ( in @ ( kfst @ SY2087 ) @ SV74 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[580]) ).

thf(883,plain,
    ! [SV75: $i] :
      ( ( ! [SY2088: $i] :
            ( ( kfst @ ( kpair @ SV75 @ SY2088 ) )
            = SV75 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[581]) ).

thf(884,plain,
    ! [SV76: $i] :
      ( ( ~ ( singleton @ SV76 )
        | ( in @ ( setunion @ SV76 ) @ SV76 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[582]) ).

thf(885,plain,
    ! [SV77: $i] :
      ( ( ~ ( iskpair @ SV77 )
        | ( singleton
          @ ( dsetconstr @ ( setunion @ SV77 )
            @ ^ [SY2089: $i] : ( in @ ( setadjoin @ SY2089 @ emptyset ) @ SV77 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[583]) ).

thf(886,plain,
    ! [SV78: $i] :
      ( ( ! [SY2090: $i,SY2091: $i] :
            ( ~ ( in @ ( setadjoin @ SY2091 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV78 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV78 @ ( setadjoin @ SY2090 @ emptyset ) ) @ emptyset ) ) )
            | ( SV78 = SY2091 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[584]) ).

thf(887,plain,
    ! [SV79: $i] :
      ( ( ! [SY2092: $i] :
            ( ( ( setadjoin @ SV79 @ emptyset )
             != ( setadjoin @ SY2092 @ emptyset ) )
            | ( SV79 = SY2092 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[585]) ).

thf(888,plain,
    ! [SV80: $i] :
      ( ( ( setunion @ ( setadjoin @ SV80 @ emptyset ) )
        = SV80 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[590]) ).

thf(889,plain,
    ! [SV81: $i] :
      ( ( subset @ SV81 @ ( setunion @ ( setadjoin @ SV81 @ emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[591]) ).

thf(890,plain,
    ! [SV82: $i] :
      ( ( subset @ ( setunion @ ( setadjoin @ SV82 @ emptyset ) ) @ SV82 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[592]) ).

thf(891,plain,
    ! [SV83: $i] :
      ( ( ! [SY2093: $i,SY2094: $i] :
            ( ~ ( in @ SY2094 @ ( cartprod @ SV83 @ SY2093 ) )
            | ( iskpair @ SY2094 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[594]) ).

thf(892,plain,
    ! [SV84: $i] :
      ( ( ! [SY2095: $i,SY2096: $i] :
            ( ~ ( in @ SY2096 @ SV84 )
            | ! [SY2097: $i] :
                ( ~ ( in @ SY2097 @ SY2095 )
                | ( in @ ( kpair @ SY2096 @ SY2097 ) @ ( cartprod @ SV84 @ SY2095 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[596]) ).

thf(893,plain,
    ! [SV85: $i] :
      ( ( ! [SY2098: $i,SY2099: $i] :
            ( ~ ( in @ SY2099 @ SV85 )
            | ! [SY2100: $i] :
                ( ~ ( in @ SY2100 @ SY2098 )
                | ( in @ ( kpair @ SY2099 @ SY2100 ) @ ( powerset @ ( powerset @ ( binunion @ SV85 @ SY2098 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[597]) ).

thf(894,plain,
    ! [SV86: $i] :
      ( ( ! [SY2101: $i,SY2102: $i] :
            ( ~ ( in @ SY2102 @ SV86 )
            | ! [SY2103: $i] :
                ( ~ ( in @ SY2103 @ SY2101 )
                | ( in @ ( setadjoin @ ( setadjoin @ SY2102 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2102 @ ( setadjoin @ SY2103 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV86 @ SY2101 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[598]) ).

thf(895,plain,
    ! [SV87: $i] :
      ( ( ! [SY2104: $i,SY2105: $i] :
            ( ~ ( in @ SY2105 @ SV87 )
            | ! [SY2106: $i] :
                ( ~ ( in @ SY2106 @ SY2104 )
                | ( subset @ ( setadjoin @ ( setadjoin @ SY2105 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2105 @ ( setadjoin @ SY2106 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV87 @ SY2104 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[599]) ).

thf(896,plain,
    ! [SV88: $i] :
      ( ( ! [SY2107: $i,SY2108: $i] :
            ( ~ ( in @ SY2108 @ SV88 )
            | ! [SY2109: $i] :
                ( ~ ( in @ SY2109 @ SY2107 )
                | ( in @ ( setadjoin @ SY2108 @ ( setadjoin @ SY2109 @ emptyset ) ) @ ( powerset @ ( binunion @ SV88 @ SY2107 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[600]) ).

thf(897,plain,
    ! [SV89: $i] :
      ( ( ! [SY2110: $i,SY2111: $i] :
            ( ~ ( in @ SY2111 @ SV89 )
            | ! [SY2112: $i] :
                ( ~ ( in @ SY2112 @ SY2110 )
                | ( subset @ ( setadjoin @ SY2111 @ ( setadjoin @ SY2112 @ emptyset ) ) @ ( binunion @ SV89 @ SY2110 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[601]) ).

thf(898,plain,
    ! [SV90: $i] :
      ( ( ! [SY2113: $i,SY2114: $i] :
            ( ~ ( in @ SY2114 @ ( setadjoin @ SV90 @ ( setadjoin @ SY2113 @ emptyset ) ) )
            | ( SY2114 = SV90 )
            | ( SY2114 = SY2113 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[602]) ).

thf(899,plain,
    ! [SV91: $i] :
      ( ( ! [SY2115: $i,SY2116: $i] :
            ( ~ ( in @ SY2116 @ SV91 )
            | ( in @ ( setadjoin @ SY2116 @ emptyset ) @ ( powerset @ ( binunion @ SV91 @ SY2115 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[603]) ).

thf(900,plain,
    ! [SV92: $i] :
      ( ( ! [SY2117: $i] :
            ( ~ ( in @ SY2117 @ SV92 )
            | ( in @ ( setadjoin @ SY2117 @ emptyset ) @ ( powerset @ SV92 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[604]) ).

thf(901,plain,
    ! [SV93: $i] :
      ( ( ! [SY2118: $i] :
            ( ~ ( in @ SY2118 @ SV93 )
            | ( subset @ ( setadjoin @ SY2118 @ emptyset ) @ SV93 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[605]) ).

thf(902,plain,
    ! [SV94: $i] :
      ( ( ! [SY2119: $i] : ( iskpair @ ( kpair @ SV94 @ SY2119 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[606]) ).

thf(903,plain,
    ! [SV95: $i] :
      ( ( ! [SY2120: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ SV95 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV95 @ ( setadjoin @ SY2120 @ emptyset ) ) @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[607]) ).

thf(904,plain,
    ! [SV96: $i] :
      ( ( ! [SY2121: $i] : ( in @ SY2121 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV96 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV96 @ ( setadjoin @ SY2121 @ emptyset ) ) @ emptyset ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[608]) ).

thf(905,plain,
    ! [SV97: $i] :
      ( ( ! [SY2122: $i] : ( in @ SV97 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV97 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV97 @ ( setadjoin @ SY2122 @ emptyset ) ) @ emptyset ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[609]) ).

thf(906,plain,
    ! [SV98: $i] :
      ( ( ! [SY2123: $i] : ( in @ SY2123 @ ( setadjoin @ SV98 @ ( setadjoin @ SY2123 @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[610]) ).

thf(907,plain,
    ! [SV99: $i] :
      ( ( ! [SY2124: $i,SY2125: $i] :
            ( ( in @ SY2125 @ SV99 )
            | ( in @ SY2125 @ SY2124 )
            | ~ ( in @ SY2125 @ ( symdiff @ SV99 @ SY2124 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[611]) ).

thf(908,plain,
    ! [SV100: $i] :
      ( ( ! [SY2126: $i,SY2127: $i] :
            ( ~ ( in @ SY2127 @ SV100 )
            | ~ ( in @ SY2127 @ SY2126 )
            | ~ ( in @ SY2127 @ ( symdiff @ SV100 @ SY2126 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[612]) ).

thf(909,plain,
    ! [SV101: $i] :
      ( ( ! [SY2128: $i,SY2129: $i] :
            ( ( in @ SY2129 @ SV101 )
            | ~ ( in @ SY2129 @ SY2128 )
            | ( in @ SY2129 @ ( symdiff @ SV101 @ SY2128 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[613]) ).

thf(910,plain,
    ! [SV102: $i] :
      ( ( ! [SY2130: $i,SY2131: $i] :
            ( ~ ( in @ SY2131 @ SV102 )
            | ( in @ SY2131 @ SY2130 )
            | ( in @ SY2131 @ ( symdiff @ SV102 @ SY2130 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[614]) ).

thf(911,plain,
    ! [SV103: $i] :
      ( ( ! [SY2132: $i] :
            ( ( ( setminus @ SV103 @ SY2132 )
             != emptyset )
            | ( subset @ SV103 @ SY2132 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[616]) ).

thf(912,plain,
    ! [SV104: $i] :
      ( ( ! [SY2133: $i] : ( subset @ ( setminus @ SV104 @ SY2133 ) @ SV104 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[617]) ).

thf(913,plain,
    ! [SV105: $i] :
      ( ( ! [SY2134: $i,SY2135: $i] :
            ( ~ ( in @ SY2135 @ SY2134 )
            | ~ ( in @ SY2135 @ ( setminus @ SV105 @ SY2134 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[618]) ).

thf(914,plain,
    ! [SV106: $i] :
      ( ( ! [SY2136: $i,SY2137: $i] :
            ( ( in @ SY2137 @ SV106 )
            | ~ ( in @ SY2137 @ ( setminus @ SV106 @ SY2136 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[619]) ).

thf(915,plain,
    ! [SV107: $i] :
      ( ( ! [SY2138: $i,SY2139: $i] :
            ( ( in @ SY2139 @ ( setminus @ SV107 @ SY2138 ) )
            | ( in @ SY2139 @ SY2138 )
            | ~ ( in @ SY2139 @ SV107 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[620]) ).

thf(916,plain,
    ! [SV108: $i] :
      ( ( ! [SY2140: $i,SY2141: $i] :
            ( ( in @ SY2141 @ ( setminus @ SV108 @ SY2140 ) )
            | ~ ( in @ SY2141 @ SV108 )
            | ( in @ SY2141 @ SY2140 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[621]) ).

thf(917,plain,
    ! [SV109: $i] :
      ( ( ! [SY2142: $i] :
            ( ~ ( subset @ SV109 @ SY2142 )
            | ( ( setminus @ SV109 @ SY2142 )
              = emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[622]) ).

thf(918,plain,
    ! [SV110: $i] :
      ( ( ! [SY2143: $i,SY2144: $i] :
            ( ~ ( in @ SY2144 @ ( setminus @ SV110 @ SY2143 ) )
            | ~ ( in @ SY2144 @ SY2143 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[623]) ).

thf(919,plain,
    ! [SV111: $i] :
      ( ( ! [SY2145: $i,SY2146: $i] :
            ( ~ ( in @ SY2146 @ ( setminus @ SV111 @ SY2145 ) )
            | ( in @ SY2146 @ SV111 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[624]) ).

thf(920,plain,
    ! [SV112: $i] :
      ( ( ! [SY2147: $i,SY2148: $i] :
            ( ~ ( in @ SY2148 @ SV112 )
            | ( in @ SY2148 @ SY2147 )
            | ( in @ SY2148 @ ( setminus @ SV112 @ SY2147 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[625]) ).

thf(921,plain,
    ! [SV113: $i] :
      ( ( ! [SY2149: $i,SY2150: $i] :
            ( ( binintersect @ SV113 @ ( binunion @ SY2149 @ SY2150 ) )
            = ( binunion @ ( binintersect @ SV113 @ SY2149 ) @ ( binintersect @ SV113 @ SY2150 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[626]) ).

thf(922,plain,
    ! [SV114: $i] :
      ( ( ! [SY2151: $i] :
            ( ( ( binintersect @ SV114 @ SY2151 )
             != SV114 )
            | ( subset @ SV114 @ SY2151 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[627]) ).

thf(923,plain,
    ! [SV115: $i] :
      ( ( ! [SY2152: $i] :
            ( ~ ( subset @ SY2152 @ SV115 )
            | ( ( binintersect @ SV115 @ SY2152 )
              = SY2152 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[628]) ).

thf(924,plain,
    ! [SV116: $i] :
      ( ( ! [SY2153: $i] : ( subset @ ( binintersect @ SV116 @ SY2153 ) @ SY2153 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[629]) ).

thf(925,plain,
    ! [SV117: $i] :
      ( ( ! [SY2154: $i,SY2155: $i] :
            ( ~ ( in @ SY2155 @ ( binintersect @ SV117 @ SY2154 ) )
            | ( in @ SY2155 @ SY2154 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[631]) ).

thf(926,plain,
    ! [SV118: $i] :
      ( ( ! [SY2156: $i] :
            ( ( ( binintersect @ SV118 @ SY2156 )
             != SY2156 )
            | ( subset @ SY2156 @ SV118 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[632]) ).

thf(927,plain,
    ! [SV119: $i] :
      ( ( ! [SY2157: $i] :
            ( ~ ( subset @ SV119 @ SY2157 )
            | ( ( binintersect @ SV119 @ SY2157 )
              = SV119 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[633]) ).

thf(928,plain,
    ! [SV120: $i] :
      ( ( ! [SY2158: $i] : ( subset @ ( binintersect @ SV120 @ SY2158 ) @ SV120 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[634]) ).

thf(929,plain,
    ! [SV121: $i] :
      ( ( ! [SY2159: $i,SY2160: $i] :
            ( ~ ( in @ SY2160 @ ( binintersect @ SV121 @ SY2159 ) )
            | ( in @ SY2160 @ SV121 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[635]) ).

thf(930,plain,
    ! [SV122: $i] :
      ( ( ! [SY2161: $i,SY2162: $i] :
            ( ~ ( subset @ SY2162 @ SV122 )
            | ~ ( subset @ SY2162 @ SY2161 )
            | ( subset @ SY2162 @ ( binintersect @ SV122 @ SY2161 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[636]) ).

thf(931,plain,
    ! [SV123: $i] :
      ( ( ! [SY2163: $i,SY2164: $i] :
            ( ~ ( in @ SY2164 @ SV123 )
            | ~ ( in @ SY2164 @ SY2163 )
            | ( in @ SY2164 @ ( binintersect @ SV123 @ SY2163 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[637]) ).

thf(932,plain,
    ! [SV124: $i] :
      ( ( ! [SY2165: $i] : ( subset @ SY2165 @ ( binunion @ SV124 @ SY2165 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[638]) ).

thf(933,plain,
    ! [SV125: $i] :
      ( ( ! [SY2166: $i] : ( subset @ SV125 @ ( binunion @ SV125 @ SY2166 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[639]) ).

thf(934,plain,
    ! [SV126: $i] :
      ( ( ! [SY2167: $i,SY2168: $i] :
            ( ~ ( in @ SY2168 @ ( binunion @ SV126 @ SY2167 ) )
            | ( in @ SY2168 @ SV126 )
            | ( in @ SY2168 @ SY2167 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[640]) ).

thf(935,plain,
    ! [SV127: $i] :
      ( ( ! [SY2169: $i,SY2170: $i] :
            ( ~ ( in @ SY2170 @ SY2169 )
            | ( in @ SY2170 @ ( binunion @ SV127 @ SY2169 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[642]) ).

thf(936,plain,
    ! [SV128: $i] :
      ( ( ! [SY2171: $i] : ( in @ SY2171 @ ( setadjoin @ SV128 @ ( setadjoin @ SY2171 @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[643]) ).

thf(937,plain,
    ! [SV129: $i] :
      ( ( ! [SY2172: $i,SY2173: $i] :
            ( ~ ( in @ SY2173 @ SV129 )
            | ( in @ SY2173 @ ( binunion @ SV129 @ SY2172 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[644]) ).

thf(938,plain,
    ! [SV130: $i] :
      ( ( ! [SY2174: $i > $o] :
            ( subset
            @ ( dsetconstr @ SV130
              @ ^ [Xx: $i] : ( SY2174 @ Xx ) )
            @ SV130 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[645]) ).

thf(939,plain,
    ! [SV131: $i] :
      ( ( ! [SY2176: $i > $o] :
            ( in
            @ ( dsetconstr @ SV131
              @ ^ [Xx: $i] : ( SY2176 @ Xx ) )
            @ ( powerset @ SV131 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[646]) ).

thf(940,plain,
    ! [SV132: $i] :
      ( ( ! [SY2178: $i] :
            ( ~ ( subset @ SV132 @ SY2178 )
            | ( subset @ ( powerset @ SV132 ) @ ( powerset @ SY2178 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[647]) ).

thf(941,plain,
    ! [SV133: $i] :
      ( ( in @ SV133 @ ( powerset @ SV133 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[648]) ).

thf(942,plain,
    ! [SV134: $i] :
      ( ( ! [SY2179: $i] :
            ( ~ ( in @ SY2179 @ ( powerset @ SV134 ) )
            | ( subset @ SY2179 @ SV134 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[649]) ).

thf(943,plain,
    ! [SV135: $i] :
      ( ( ! [SY2180: $i] :
            ( ~ ( subset @ SY2180 @ SV135 )
            | ( in @ SY2180 @ ( powerset @ SV135 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[650]) ).

thf(944,plain,
    ! [SV136: $i] :
      ( ( ~ ( subset @ SV136 @ emptyset )
        | ( SV136 = emptyset ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[651]) ).

thf(945,plain,
    ! [SV137: $i] :
      ( ( ! [SY2181: $i] :
            ( ~ ( subset @ SV137 @ SY2181 )
            | ~ ( subset @ SY2181 @ SV137 )
            | ( SV137 = SY2181 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[652]) ).

thf(946,plain,
    ! [SV138: $i] :
      ( ( ! [SY2182: $i] :
            ( ~ ( subset @ SV138 @ SY2182 )
            | ( in @ SV138 @ ( powerset @ SY2182 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[653]) ).

thf(947,plain,
    ! [SV139: $i] :
      ( ( ! [SY2183: $i,SY2184: $i] :
            ( ~ ( subset @ SV139 @ SY2184 )
            | ( subset @ SV139 @ ( setadjoin @ SY2183 @ SY2184 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[654]) ).

thf(948,plain,
    ! [SV140: $i] :
      ( ( ! [SY2185: $i] : ( subset @ SY2185 @ ( setadjoin @ SV140 @ SY2185 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[655]) ).

thf(949,plain,
    ! [SV141: $i] :
      ( ( ! [SY2186: $i] :
            ( ~ ( subset @ SV141 @ SY2186 )
            | ! [SY2187: $i] :
                ( ~ ( subset @ SY2186 @ SY2187 )
                | ( subset @ SV141 @ SY2187 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[656]) ).

thf(950,plain,
    ! [SV142: $i] :
      ( ( subset @ SV142 @ SV142 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[657]) ).

thf(951,plain,
    ! [SV143: $i] :
      ( ( ! [SY2188: $i,SY2189: $i] :
            ( ~ ( in @ SY2189 @ SV143 )
            | ( in @ SY2189 @ SY2188 )
            | ( SV143 != SY2188 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[658]) ).

thf(952,plain,
    ! [SV144: $i] :
      ( ( ! [SY2190: $i] :
            ( ( subset @ SV144 @ SY2190 )
            | ( SV144 != SY2190 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[659]) ).

thf(953,plain,
    ! [SV145: $i] :
      ( ( ! [SY2191: $i,SY2192: $i] :
            ( ~ ( in @ SY2192 @ SV145 )
            | ( in @ SY2192 @ SY2191 )
            | ~ ( subset @ SV145 @ SY2191 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[660]) ).

thf(954,plain,
    ! [SV146: $i] :
      ( ( ! [SY2193: $i] :
            ( ~ ( subset @ SV146 @ SY2193 )
            | ! [SY2194: $i] :
                ( ( in @ SY2194 @ SY2193 )
                | ~ ( in @ SY2194 @ SV146 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[661]) ).

thf(955,plain,
    ! [SV147: $i] :
      ( ( ! [SY2195: $i] :
            ( ~ ( subset @ SV147 @ SY2195 )
            | ! [SY2196: $i] :
                ( ~ ( in @ SY2196 @ SV147 )
                | ( in @ SY2196 @ SY2195 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[662]) ).

thf(956,plain,
    ! [SV148: $i] :
      ( ( subset @ emptyset @ SV148 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[663]) ).

thf(957,plain,
    ! [SV149: $i] :
      ( ( ! [SY2197: $i] :
            ( ( SV149 != SY2197 )
            | ( subset @ SV149 @ SY2197 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[665]) ).

thf(958,plain,
    ! [SV150: $i] :
      ( ( ! [SY2198: $i] :
            ( ( SV150 != SY2198 )
            | ( subset @ SY2198 @ SV150 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[666]) ).

thf(959,plain,
    ! [SV151: $i] :
      ( ( ! [SY2199: $i] :
            ( ( SV151 != SY2199 )
            | ( ( setunion @ SV151 )
              = ( setunion @ SY2199 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[672]) ).

thf(960,plain,
    ! [SV152: $i] :
      ( ( ! [SY2200: $i] :
            ( ( SV152 != SY2200 )
            | ( ( powerset @ SV152 )
              = ( powerset @ SY2200 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[673]) ).

thf(961,plain,
    ! [SV153: $i] :
      ( ( ! [SY2201: $i] :
            ( ( SV153 != SY2201 )
            | ! [SY2202: $i,SY2203: $i] :
                ( ( SY2202 != SY2203 )
                | ( ( setadjoin @ SV153 @ SY2202 )
                  = ( setadjoin @ SY2201 @ SY2203 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[674]) ).

thf(962,plain,
    ! [SV154: $i] :
      ( ( ! [SY2204: $i] :
            ( ( SV154 != SY2204 )
            | ! [SY2205: $i,SY2206: $i] :
                ( ( SY2205 != SY2206 )
                | ~ ( in @ SY2205 @ SV154 )
                | ( in @ SY2206 @ SY2204 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[679]) ).

thf(963,plain,
    ! [SV155: $o] :
      ( ( ~ SV155
        | ( set2prop @ ( prop2set @ SV155 ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[685]) ).

thf(964,plain,
    ( ( ~ $true
      | ( set2prop @ ( prop2set @ $true ) ) )
    = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[685]) ).

thf(965,plain,
    ( ( ~ $false
      | ( set2prop @ ( prop2set @ $false ) ) )
    = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[685]) ).

thf(966,plain,
    ! [SV156: $o] :
      ( ( ~ SV156
        | ( in @ emptyset @ ( prop2set @ SV156 ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[686]) ).

thf(967,plain,
    ( ( ~ $true
      | ( in @ emptyset @ ( prop2set @ $true ) ) )
    = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[686]) ).

thf(968,plain,
    ( ( ~ $false
      | ( in @ emptyset @ ( prop2set @ $false ) ) )
    = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[686]) ).

thf(969,plain,
    ! [SV157: $i > $o] :
      ( ( ! [SY2207: $i] :
            ( ~ ( in @ SY2207 @ emptyset )
            | ( SV157 @ SY2207 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[691]) ).

thf(970,plain,
    ! [SV158: $i] :
      ( ( ! [SY2208: $i > $o] :
            ( ! [SY2209: $i] :
                ( ~ ( SY2208 @ SY2209 )
                | ~ ( in @ SY2209 @ SV158 ) )
            | ( ( dsetconstr @ SV158
                @ ^ [Xx: $i] : ( SY2208 @ Xx ) )
             != emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[692]) ).

thf(971,plain,
    ! [SV159: $i] :
      ( ( ! [SY2211: $i] : ( in @ SY2211 @ ( setadjoin @ SV159 @ ( setadjoin @ SY2211 @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[693]) ).

thf(972,plain,
    ! [SV160: $i] :
      ( ( ! [SY2212: $i] : ( in @ SV160 @ ( setadjoin @ SV160 @ ( setadjoin @ SY2212 @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[694]) ).

thf(973,plain,
    ! [SV161: $i] :
      ( ( ! [SY2213: $i,SY2214: $i] :
            ( ~ ( in @ SY2214 @ ( setadjoin @ SV161 @ ( setadjoin @ SY2213 @ emptyset ) ) )
            | ( SY2214 = SV161 )
            | ( SY2214 = SY2213 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[695]) ).

thf(974,plain,
    ! [SV162: $i] :
      ( ( ! [SY2215: $i] :
            ( ~ ( in @ SV162 @ ( setadjoin @ SY2215 @ emptyset ) )
            | ( in @ SY2215 @ ( setadjoin @ SV162 @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[696]) ).

thf(975,plain,
    ! [SV163: $i] :
      ( ( ! [SY2216: $i] :
            ( ( SV163 != SY2216 )
            | ( in @ SV163 @ ( setadjoin @ SY2216 @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[697]) ).

thf(976,plain,
    ! [SV164: $i] :
      ( ( ! [SY2217: $i] :
            ( ( SV164 = SY2217 )
            | ~ ( in @ SY2217 @ ( setadjoin @ SV164 @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[698]) ).

thf(977,plain,
    ! [SV165: $i] :
      ( ( ! [SY2218: $i] :
            ( ~ ( in @ SV165 @ ( setadjoin @ SY2218 @ emptyset ) )
            | ( SV165 = SY2218 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[699]) ).

thf(978,plain,
    ! [SV166: $i] :
      ( ( ( SV166 = emptyset )
        | ( in @ ( sK34_Xx @ SV166 ) @ SV166 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[700]) ).

thf(979,plain,
    ! [SV167: $i] :
      ( ( ! [SY2219: $i] :
            ( ~ ( in @ SY2219 @ SV167 )
            | ( in @ SY2219 @ ( powerset @ ( setunion @ SV167 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[702]) ).

thf(980,plain,
    ! [SV168: $i] :
      ( ( ! [SY2220: $i,SY2221: $i] :
            ( ~ ( in @ SY2220 @ SY2221 )
            | ~ ( in @ SY2221 @ SV168 )
            | ( in @ SY2220 @ ( setunion @ SV168 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[704]) ).

thf(981,plain,
    ! [SV169: $i] :
      ( ( ! [SY2222: $i] :
            ( ~ ( in @ SY2222 @ ( powerset @ SV169 ) )
            | ! [SY2223: $i] :
                ( ~ ( in @ SY2223 @ SY2222 )
                | ( in @ SY2223 @ SV169 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[705]) ).

thf(982,plain,
    ! [SV170: $i] :
      ( ( in @ emptyset @ ( powerset @ SV170 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[706]) ).

thf(983,plain,
    ! [SV171: $i] :
      ( ( in @ emptyset @ ( powerset @ SV171 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[707]) ).

thf(984,plain,
    ! [SV172: $i] :
      ( ( ( dsetconstr @ SV172
          @ ^ [Xx: $i] : $true )
        = SV172 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[709]) ).

thf(985,plain,
    ! [SV173: $i] :
      ( ( ! [SY2225: $i,SY2226: $i] :
            ( ~ ( in @ SY2226 @ ( setadjoin @ SV173 @ SY2225 ) )
            | ( SY2226 = SV173 )
            | ( in @ SY2226 @ SY2225 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[710]) ).

thf(986,plain,
    ! [SV174: $i] :
      ( ( ! [SY2227: $i,SY2228: $i] :
            ( ~ ( in @ SY2228 @ SY2227 )
            | ( in @ SY2228 @ ( setadjoin @ SV174 @ SY2227 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[712]) ).

thf(987,plain,
    ! [SV175: $i] :
      ( ( ! [SY2229: $i] : ( in @ SV175 @ ( setadjoin @ SV175 @ SY2229 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[714]) ).

thf(988,plain,
    ! [SV176: $i] :
      ( ( ! [SY2230: $i] :
            ~ ( in @ SY2230 @ SV176 )
        | ( SV176 != emptyset ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[715]) ).

thf(989,plain,
    ! [SV177: $i] :
      ( ( ! [SY2231: $i > $o,SY2232: $i] :
            ( ~ ( in @ SY2232 @ SV177 )
            | ~ ( SY2231 @ SY2232 )
            | ( ( dsetconstr @ SV177
                @ ^ [Xy: $i] : ( SY2231 @ Xy ) )
             != emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[716]) ).

thf(990,plain,
    ! [SV178: $i] :
      ( ( ( SV178 = emptyset )
        | ( in @ ( sK29_Xx @ SV178 ) @ SV178 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[717]) ).

thf(991,plain,
    ! [SV179: $i] :
      ( ( ( in @ ( sK28_Xx @ SV179 ) @ SV179 )
        | ( SV179 = emptyset ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[719]) ).

thf(992,plain,
    ! [SV180: $i] :
      ( ( ( in @ ( sK27_Xx @ SV180 ) @ SV180 )
        | ( SV180 = emptyset ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[720]) ).

thf(993,plain,
    ! [SV181: $i] :
      ( ( ~ ( in @ SV181 @ emptyset ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[723]) ).

thf(994,plain,
    ! [SV182: $i] :
      ( ( ~ ( in @ SV182 @ emptyset ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[724]) ).

thf(995,plain,
    ( ( ( ! [Xx: $i] :
            ~ ( in @ Xx @ emptyset ) )
      = $true )
    | ( ( ! [Xphi: $o] : Xphi )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[725]) ).

thf(996,plain,
    ! [SV183: $o] :
      ( ( ! [SY2234: $i] :
            ~ ( in @ SY2234 @ ( prop2set @ SV183 ) )
        | SV183 )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[726]) ).

thf(997,plain,
    ( ( ! [SX0: $i] :
          ~ ( in @ SX0 @ ( prop2set @ $true ) )
      | $true )
    = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[726]) ).

thf(998,plain,
    ( ( ! [SX0: $i] :
          ~ ( in @ SX0 @ ( prop2set @ $false ) )
      | $false )
    = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[726]) ).

thf(999,plain,
    ! [SV184: $i] :
      ( ( ! [SY2235: $i > $o,SY2236: $i] :
            ( ~ ( in @ SY2236
                @ ( dsetconstr @ SV184
                  @ ^ [Xy: $i] : ( SY2235 @ Xy ) ) )
            | ( SY2235 @ SY2236 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[728]) ).

thf(1000,plain,
    ! [SV185: $i] :
      ( ( ! [SY2238: $i > $o,SY2239: $i] :
            ( ~ ( in @ SY2239
                @ ( dsetconstr @ SV185
                  @ ^ [Xy: $i] : ( SY2238 @ Xy ) ) )
            | ( in @ SY2239 @ SV185 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[729]) ).

thf(1001,plain,
    ! [SV186: $i] :
      ( ( ! [SY2241: $i > $o,SY2242: $i] :
            ( ~ ( in @ SY2242 @ SV186 )
            | ~ ( SY2241 @ SY2242 )
            | ( in @ SY2242
              @ ( dsetconstr @ SV186
                @ ^ [Xy: $i] : ( SY2241 @ Xy ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[730]) ).

thf(1002,plain,
    ! [SV187: $i] :
      ( ( ~ ( in @ SV187 @ omega )
        | ( in @ ( setadjoin @ SV187 @ SV187 ) @ omega ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[736]) ).

thf(1003,plain,
    ! [SV188: $i] :
      ( ( ~ ( in @ SV188 @ emptyset ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[741]) ).

thf(1004,plain,
    ! [SV189: $i] :
      ( ( ! [SY2244: $i] :
            ( ~ ( in @ SY2244 @ ( powerset @ SV189 ) )
            | ! [SY2245: $i] :
                ( ~ ( in @ SY2245 @ ( powerset @ SV189 ) )
                | ~ ( ~ ( in @ ( sK97_Xx @ SY2245 @ SY2244 @ SV189 ) @ SV189 )
                    | ~ ~ ( ~ ( in @ ( sK97_Xx @ SY2245 @ SY2244 @ SV189 ) @ SY2244 )
                          | ~ ~ ( in @ ( sK97_Xx @ SY2245 @ SY2244 @ SV189 ) @ SY2245 ) ) )
                | ( subset @ SY2244 @ SY2245 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[744]) ).

thf(1005,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( ~ ( in @ ( sK7_Xx @ SX1 @ SX0 ) @ SX1 )
                | ~ ~ ( in @ ( sK7_Xx @ SX1 @ SX0 ) @ SX0 ) )
            | ( in @ SX1 @ ( powerset @ SX0 ) ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
            | ! [SX2: $i] :
                ( ~ ( in @ SX2 @ SX1 )
                | ( in @ SX2 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[745]) ).

thf(1006,plain,
    ! [SV190: $i > $o] :
      ( ( ! [SY2246: $i] :
            ( ~ ( ~ ( SV190 @ ( sK24_SY86 @ SY2246 @ SV190 ) )
                | ~ ( ( SY2246
                     != ( sK24_SY86 @ SY2246 @ SV190 ) ) ) )
            | ~ ( SV190 @ SY2246 ) )
        | ( SV190 @ ( sK23_Xx @ SV190 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[746]) ).

thf(1007,plain,
    ! [SV191: $i] :
      ( ( ! [SY2247: $o,SY2248: $i] :
            ( ~ ( in @ SY2248 @ SV191 )
            | ! [SY2249: $i] :
                ( ~ ( in @ SY2249 @ SV191 )
                | ~ SY2247
                | ( in @ SY2248
                  @ ( dsetconstr @ SV191
                    @ ^ [SX4: $i] :
                        ( ~ ( ~ SY2247
                            | ( SX4 != SY2248 ) )
                        | ~ ( ~ ~ SY2247
                            | ( SX4 != SY2249 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[747]) ).

thf(1008,plain,
    ! [SV192: $i] :
      ( ( ! [SY2251: $i,SY2252: $i > $i] :
            ( ~ ( ~ ( in @ ( sK92_Xx @ SY2252 @ SY2251 @ SV192 ) @ SV192 )
                | ~ ~ ( in @ ( SY2252 @ ( sK92_Xx @ SY2252 @ SY2251 @ SV192 ) ) @ SY2251 ) )
            | ! [SY2253: $i] :
                ( ~ ( in @ SY2253 @ SV192 )
                | ( ( ap @ SV192 @ SY2251
                    @ ( lam @ SV192 @ SY2251
                      @ ^ [SX4: $i] : ( SY2252 @ SX4 ) )
                    @ SY2253 )
                  = ( SY2252 @ SY2253 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[748]) ).

thf(1009,plain,
    ! [SV193: $i] :
      ( ( ! [SY2255: $i,SY2256: $i] :
            ( ~ ( in @ SY2256 @ ( cartprod @ SV193 @ SY2255 ) )
            | ~ ( ~ ~ ( ( SY2256
                       != ( kpair @ ( sK67_Xx @ SY2256 @ SY2255 @ SV193 ) @ ( sK68_SY1876 @ SY2256 @ SY2255 @ SV193 ) ) )
                      | ~ ( in @ ( sK68_SY1876 @ SY2256 @ SY2255 @ SV193 ) @ SY2255 ) )
                | ~ ( in @ ( sK67_Xx @ SY2256 @ SY2255 @ SV193 ) @ SV193 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[749]) ).

thf(1010,plain,
    ! [SV194: $i > $o] :
      ( ( ! [SY2257: $i] :
            ( ~ ( ~ ( SV194 @ ( sK57_SY248 @ SY2257 @ SV194 ) )
                | ~ ( ( SY2257
                     != ( sK57_SY248 @ SY2257 @ SV194 ) ) ) )
            | ~ ( SV194 @ SY2257 ) )
        | ! [SY2258: $i] :
            ( ~ ( SV194 @ SY2258 )
            | ! [SY2259: $i] :
                ( ~ ( SV194 @ SY2259 )
                | ( SY2258 = SY2259 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[750]) ).

thf(1011,plain,
    ! [SV195: $i > $i > $o] :
      ( ( ! [SY2260: $i] :
            ( ~ ( ~ ( in @ ( sK12_SY24 @ SY2260 @ SV195 ) @ SY2260 )
                | ~ ! [SY2261: $i] :
                      ( ~ ( ~ ( SV195 @ ( sK12_SY24 @ SY2260 @ SV195 ) @ ( sK13_SY1837 @ SY2261 @ SY2260 @ SV195 ) )
                          | ~ ( ( SY2261
                               != ( sK13_SY1837 @ SY2261 @ SY2260 @ SV195 ) ) ) )
                      | ~ ( SV195 @ ( sK12_SY24 @ SY2260 @ SV195 ) @ SY2261 ) ) )
            | ~ ( ~ ! [SY2262: $i] :
                      ( ! [SY2263: $i] :
                          ( ~ ( SV195 @ SY2263 @ SY2262 )
                          | ~ ( in @ SY2263 @ SY2260 ) )
                      | ( in @ SY2262 @ ( sK10_B @ SY2260 @ SV195 ) ) )
                | ~ ! [SY2264: $i] :
                      ( ~ ( in @ SY2264 @ ( sK10_B @ SY2260 @ SV195 ) )
                      | ~ ( ~ ( SV195 @ ( sK11_Xy @ SY2264 @ SY2260 @ SV195 ) @ SY2264 )
                          | ~ ( in @ ( sK11_Xy @ SY2264 @ SY2260 @ SV195 ) @ SY2260 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[751]) ).

thf(1012,plain,
    ! [SV196: $i] :
      ( ( ! [SY2265: $i,SY2266: $i] :
            ( ~ ( in @ SY2266 @ ( setadjoin @ SV196 @ SY2265 ) )
            | ~ ( ~ ~ ( ~ ( ( SY2266 = SV196 )
                          | ( in @ SY2266 @ SY2265 )
                          | ! [SX3: $o] : SX3 )
                      | ~ ( ( SY2266 = SV196 )
                          | ! [SX3: $o] :
                              ( ~ SX3
                              | SX3 ) ) )
                | ~ ~ ( ~ ! [SX3: $o] :
                            ( ~ SX3
                            | ( in @ SY2266 @ SY2265 )
                            | SX3 )
                      | ~ ! [SX3: $o] :
                            ( ~ SX3
                            | ~ SX3
                            | SX3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[752]) ).

thf(1013,plain,
    ! [SV197: $i] :
      ( ( ! [SY2271: $i] :
            ( ~ ( ~ ( in @ ( sK66_Xx @ SY2271 @ SV197 ) @ SV197 )
                | ~ ( in @ ( sK66_Xx @ SY2271 @ SV197 ) @ SY2271 ) )
            | ( ( binintersect @ SV197 @ SY2271 )
              = emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[753]) ).

thf(1014,plain,
    ! [SV198: $i] :
      ( ( ~ ( ~ ! [SY2272: $i > $o,SY2273: $i] :
                  ( ~ ( in @ SY2273 @ SV198 )
                  | ~ ( SY2272 @ SY2273 )
                  | ( in @ SY2273
                    @ ( dsetconstr @ SV198
                      @ ^ [SX3: $i] : ( SY2272 @ SX3 ) ) ) )
            | ~ ! [SY2275: $i > $o,SY2276: $i] :
                  ( ~ ( in @ SY2276 @ SV198 )
                  | ~ ( in @ SY2276
                      @ ( dsetconstr @ SV198
                        @ ^ [SX3: $i] : ( SY2275 @ SX3 ) ) )
                  | ( SY2275 @ SY2276 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[754]) ).

thf(1015,plain,
    ! [SV199: $i] :
      ( ( ! [SY2278: $i] :
            ( ~ ( ~ ( in @ ( sK30_Xx @ SY2278 @ SV199 ) @ SY2278 )
                | ~ ~ ( in @ ( sK30_Xx @ SY2278 @ SV199 ) @ SV199 ) )
            | ( in @ SY2278 @ ( powerset @ SV199 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[755]) ).

thf(1016,plain,
    ! [SV200: $i] :
      ( ( ! [SY2279: $i > $o] :
            ( ! [SY2280: $i] :
                ( ~ ( in @ SY2280 @ SV200 )
                | ( SY2279 @ SY2280 ) )
            | ~ ( ~ ( in @ ( sK40_Xx @ SY2279 @ SV200 ) @ SV200 )
                | ~ ~ ( SY2279 @ ( sK40_Xx @ SY2279 @ SV200 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[756]) ).

thf(1017,plain,
    ! [SV201: $i] :
      ( ( ! [SY2281: $i,SY2282: $i > $i] :
            ( ~ ( ~ ( in @ ( sK78_Xx @ SY2282 @ SY2281 @ SV201 ) @ SV201 )
                | ~ ~ ( in @ ( SY2282 @ ( sK78_Xx @ SY2282 @ SY2281 @ SV201 ) ) @ SY2281 ) )
            | ( in
              @ ( lam @ SV201 @ SY2281
                @ ^ [SX3: $i] : ( SY2282 @ SX3 ) )
              @ ( funcSet @ SV201 @ SY2281 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[757]) ).

thf(1018,plain,
    ! [SV202: $i] :
      ( ( ! [SY2284: $o,SY2285: $i] :
            ( ~ ( in @ SY2285 @ SV202 )
            | ! [SY2286: $i] :
                ( ~ ( in @ SY2286 @ SV202 )
                | SY2284
                | ( ( dsetconstr @ SV202
                    @ ^ [SX4: $i] :
                        ( ~ ( ~ SY2284
                            | ( SX4 != SY2285 ) )
                        | ~ ( ~ ~ SY2284
                            | ( SX4 != SY2286 ) ) ) )
                  = ( setadjoin @ SY2286 @ emptyset ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[758]) ).

thf(1019,plain,
    ( ( ~ ! [SX0: $i > $o,SX1: $i > $o] :
            ( ~ ( ( ( sK55_Xx @ SX1 @ SX0 )
                 != ( sK56_SY1873 @ SX1 @ SX0 ) )
                | ~ ~ ( ~ ( ~ ( SX0 @ ( sK55_Xx @ SX1 @ SX0 ) )
                          | ~ ( SX1 @ ( sK56_SY1873 @ SX1 @ SX0 ) ) )
                      | ~ ( ( SX0 @ ( sK55_Xx @ SX1 @ SX0 ) )
                          | ( SX1 @ ( sK56_SY1873 @ SX1 @ SX0 ) ) ) ) )
            | ! [SX2: $i] :
                ( ~ ( ~ ( SX0 @ ( sK54_SY233 @ SX2 @ SX1 @ SX0 ) )
                    | ~ ( ( SX2
                         != ( sK54_SY233 @ SX2 @ SX1 @ SX0 ) ) ) )
                | ~ ( SX0 @ SX2 ) )
            | ~ ( ~ ! [SX2: $i] :
                      ( ~ ( SX1 @ SX2 )
                      | ( ( sK53_SY235 @ SX1 @ SX0 )
                        = SX2 ) )
                | ~ ( SX1 @ ( sK53_SY235 @ SX1 @ SX0 ) ) ) )
      | ~ ! [SX0: $i > $o,SX1: $i > $o] :
            ( ~ ( ( ( sK51_Xx @ SX1 @ SX0 )
                 != ( sK52_SY1871 @ SX1 @ SX0 ) )
                | ~ ~ ( ~ ( ~ ( SX0 @ ( sK51_Xx @ SX1 @ SX0 ) )
                          | ~ ( SX1 @ ( sK52_SY1871 @ SX1 @ SX0 ) ) )
                      | ~ ( ( SX0 @ ( sK51_Xx @ SX1 @ SX0 ) )
                          | ( SX1 @ ( sK52_SY1871 @ SX1 @ SX0 ) ) ) ) )
            | ! [SX2: $i] :
                ( ~ ( ~ ( SX1 @ ( sK50_SY236 @ SX2 @ SX1 @ SX0 ) )
                    | ~ ( ( SX2
                         != ( sK50_SY236 @ SX2 @ SX1 @ SX0 ) ) ) )
                | ~ ( SX1 @ SX2 ) )
            | ~ ( ~ ! [SX2: $i] :
                      ( ~ ( SX0 @ SX2 )
                      | ( ( sK49_SY232 @ SX1 @ SX0 )
                        = SX2 ) )
                | ~ ( SX0 @ ( sK49_SY232 @ SX1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[759]) ).

thf(1020,plain,
    ! [SV203: $i] :
      ( ( ! [SY2288: $i > $o] :
            ( ~ ( ~ ( SY2288 @ ( sK39_Xx @ SY2288 @ SV203 ) )
                | ~ ( in @ ( sK39_Xx @ SY2288 @ SV203 ) @ SV203 ) )
            | ! [SY2289: $i] :
                ( ~ ( in @ SY2289 @ SV203 )
                | ~ ( SY2288 @ SY2289 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[760]) ).

thf(1021,plain,
    ! [SV204: $i > $o] :
      ( ( ! [SY2290: $i] :
            ( ~ ( ~ ( SV204 @ ( sK20_SY57 @ SY2290 @ SV204 ) )
                | ~ ( ( SY2290
                     != ( sK20_SY57 @ SY2290 @ SV204 ) ) ) )
            | ~ ( SV204 @ SY2290 ) )
        | ( SV204
          @ ( descr
            @ ^ [SY2291: $i] : ( SV204 @ SY2291 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[761]) ).

thf(1022,plain,
    ! [SV205: $i > $o] :
      ( ( ! [SY2292: $i] :
            ( ~ ( ~ ( SV205 @ ( sK42_Xy @ SY2292 @ SV205 ) )
                | ~ ( ( SY2292
                     != ( sK42_Xy @ SY2292 @ SV205 ) ) ) )
            | ~ ( SV205 @ SY2292 ) )
        | ~ ( ~ ! [SY2293: $i] :
                  ( ~ ( SV205 @ SY2293 )
                  | ( ( sK41_SY198 @ SV205 )
                    = SY2293 ) )
            | ~ ( SV205 @ ( sK41_SY198 @ SV205 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[762]) ).

thf(1023,plain,
    ! [SV206: $i] :
      ( ( ! [SY2294: $i,SY2295: $i > $i] :
            ( ~ ( ~ ( in @ ( sK94_Xx @ SY2295 @ SY2294 @ SV206 ) @ SV206 )
                | ~ ~ ( in @ ( SY2295 @ ( sK94_Xx @ SY2295 @ SY2294 @ SV206 ) ) @ SY2294 ) )
            | ! [SY2296: $i] :
                ( ~ ( in @ SY2296 @ SV206 )
                | ( ( ap @ SV206 @ SY2294
                    @ ( lam @ SV206 @ SY2294
                      @ ^ [SX4: $i] : ( SY2295 @ SX4 ) )
                    @ SY2296 )
                  = ( SY2295 @ SY2296 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[763]) ).

thf(1024,plain,
    ( ( ~ ( in @ sK2_SY1822 @ ( powerset @ sK1_A ) )
      | ~ ~ ( ~ ( in @ sK3_SY1826 @ ( powerset @ sK1_A ) )
            | ~ ~ ( ~ ( in @ sK4_SY1829 @ ( powerset @ sK1_A ) )
                  | ~ ~ ( ~ ( in @ sK5_SY1831 @ sK1_A )
                        | ~ ~ ( ~ ( in @ sK5_SY1831 @ ( binintersect @ sK2_SY1822 @ sK3_SY1826 ) )
                              | ~ ~ ( in @ sK5_SY1831 @ ( binunion @ sK3_SY1826 @ sK4_SY1829 ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[764]) ).

thf(1025,plain,
    ! [SV207: $i] :
      ( ( ! [SY2298: $i,SY2299: $i] :
            ( ~ ( subset @ SY2299 @ ( cartprod @ SV207 @ SY2298 ) )
            | ! [SY2300: $i > $o] :
                ( ~ ( ~ ( in @ ( sK81_Xx @ SY2300 @ SY2299 @ SY2298 @ SV207 ) @ SV207 )
                    | ~ ~ ( ~ ( in @ ( sK82_SY1880 @ SY2300 @ SY2299 @ SY2298 @ SV207 ) @ SY2298 )
                          | ~ ~ ( ~ ( in @ ( kpair @ ( sK81_Xx @ SY2300 @ SY2299 @ SY2298 @ SV207 ) @ ( sK82_SY1880 @ SY2300 @ SY2299 @ SY2298 @ SV207 ) ) @ SY2299 )
                                | ~ ~ ( SY2300 @ ( kpair @ ( sK81_Xx @ SY2300 @ SY2299 @ SY2298 @ SV207 ) @ ( sK82_SY1880 @ SY2300 @ SY2299 @ SY2298 @ SV207 ) ) ) ) ) )
                | ! [SX4: $i] :
                    ( ~ ( in @ SX4 @ SY2299 )
                    | ( SY2300 @ SX4 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[765]) ).

thf(1026,plain,
    ! [SV208: $i] :
      ( ( ! [SY2302: $i,SY2303: $i] :
            ( ~ ( subset @ SY2303 @ ( cartprod @ SV208 @ SY2302 ) )
            | ! [SY2304: $i] :
                ( ~ ( subset @ SY2304 @ ( cartprod @ SV208 @ SY2302 ) )
                | ~ ( ~ ( in @ ( sK84_Xx @ SY2304 @ SY2303 @ SY2302 @ SV208 ) @ SV208 )
                    | ~ ~ ( ~ ( in @ ( sK85_SY1881 @ SY2304 @ SY2303 @ SY2302 @ SV208 ) @ SY2302 )
                          | ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SY2304 @ SY2303 @ SY2302 @ SV208 ) @ ( sK85_SY1881 @ SY2304 @ SY2303 @ SY2302 @ SV208 ) ) @ SY2303 )
                                | ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SY2304 @ SY2303 @ SY2302 @ SV208 ) @ ( sK85_SY1881 @ SY2304 @ SY2303 @ SY2302 @ SV208 ) ) @ SY2304 ) ) ) )
                | ( subset @ SY2303 @ SY2304 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[766]) ).

thf(1027,plain,
    ! [SV209: $i] :
      ( ( ! [SY2305: $i > $o] :
            ( ~ ( ~ ( in @ ( sK70_Xx @ SY2305 @ SV209 ) @ SV209 )
                | ~ ~ ( ~ ( in @ ( sK71_SY1877 @ SY2305 @ SV209 ) @ SV209 )
                      | ~ ~ ( ~ ( SY2305 @ ( sK70_Xx @ SY2305 @ SV209 ) )
                            | ~ ~ ( ~ ( SY2305 @ ( sK71_SY1877 @ SY2305 @ SV209 ) )
                                  | ~ ( ( ( sK70_Xx @ SY2305 @ SV209 )
                                       != ( sK71_SY1877 @ SY2305 @ SV209 ) ) ) ) ) ) )
            | ! [SY2306: $i] :
                ( ~ ( SY2305 @ SY2306 )
                | ~ ( in @ SY2306 @ SV209 ) )
            | ( singleton
              @ ( dsetconstr @ SV209
                @ ^ [SX2: $i] : ( SY2305 @ SX2 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[767]) ).

thf(1028,plain,
    ! [SV210: $i] :
      ( ( ! [SY2308: $i] :
            ( ( SV210 != SY2308 )
            | ~ ( ~ ! [SY2309: $i,SY2310: $i] :
                      ( ( SY2309 != SY2310 )
                      | ~ ( in @ SY2309 @ SV210 )
                      | ( in @ SY2310 @ SY2308 ) )
                | ~ ! [SY2311: $i,SY2312: $i] :
                      ( ( SY2311 != SY2312 )
                      | ~ ( in @ SY2312 @ SY2308 )
                      | ( in @ SY2311 @ SV210 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[768]) ).

thf(1029,plain,
    ! [SV211: $i > $o] :
      ( ( ! [SY2313: $i] :
            ( ~ ( ~ ( SV211 @ ( sK48_SY224 @ SY2313 @ SV211 ) )
                | ~ ( ( SY2313
                     != ( sK48_SY224 @ SY2313 @ SV211 ) ) ) )
            | ~ ( SV211 @ SY2313 ) )
        | ! [SY2314: $i] :
            ( ~ ( SV211 @ SY2314 )
            | ! [SY2315: $i] :
                ( ~ ( SV211 @ SY2315 )
                | ( SY2314 = SY2315 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[769]) ).

thf(1030,plain,
    ! [SV212: $i] :
      ( ( ! [SY2316: $i,SY2317: $i > $i] :
            ( ~ ( ~ ( in @ ( sK77_Xx @ SY2317 @ SY2316 @ SV212 ) @ SV212 )
                | ~ ~ ( in @ ( SY2317 @ ( sK77_Xx @ SY2317 @ SY2316 @ SV212 ) ) @ SY2316 ) )
            | ( func @ SV212 @ SY2316
              @ ( lam @ SV212 @ SY2316
                @ ^ [SX3: $i] : ( SY2317 @ SX3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[770]) ).

thf(1031,plain,
    ! [SV213: $i > $o] :
      ( ( ! [SY2319: $i > $o] :
            ( ~ ( ( ( sK60_Xx @ SY2319 @ SV213 )
                 != ( sK61_SY1874 @ SY2319 @ SV213 ) )
                | ~ ~ ( ~ ( ~ ( SV213 @ ( sK60_Xx @ SY2319 @ SV213 ) )
                          | ~ ( SY2319 @ ( sK61_SY1874 @ SY2319 @ SV213 ) ) )
                      | ~ ( ( SV213 @ ( sK60_Xx @ SY2319 @ SV213 ) )
                          | ( SY2319 @ ( sK61_SY1874 @ SY2319 @ SV213 ) ) ) ) )
            | ! [SY2320: $i] :
                ( ~ ( ~ ( SV213 @ ( sK59_SY257 @ SY2320 @ SY2319 @ SV213 ) )
                    | ~ ( ( SY2320
                         != ( sK59_SY257 @ SY2320 @ SY2319 @ SV213 ) ) ) )
                | ~ ( SV213 @ SY2320 ) )
            | ! [SY2321: $i] :
                ( ~ ( ~ ( SY2319 @ ( sK58_SY260 @ SY2321 @ SY2319 @ SV213 ) )
                    | ~ ( ( SY2321
                         != ( sK58_SY260 @ SY2321 @ SY2319 @ SV213 ) ) ) )
                | ~ ( SY2319 @ SY2321 ) )
            | ( ( descr
                @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
              = ( descr
                @ ^ [SX2: $i] : ( SY2319 @ SX2 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[771]) ).

thf(1032,plain,
    ! [SV214: $i] :
      ( ( ! [SY2324: $i] :
            ( ~ ( in @ SY2324 @ ( powerset @ SV214 ) )
            | ! [SY2325: $i] :
                ( ~ ( in @ SY2325 @ ( powerset @ SV214 ) )
                | ~ ( ~ ( in @ ( sK98_Xx @ SY2325 @ SY2324 @ SV214 ) @ SV214 )
                    | ~ ~ ( ~ ( in @ ( sK98_Xx @ SY2325 @ SY2324 @ SV214 ) @ SY2324 )
                          | ~ ~ ( in @ ( sK98_Xx @ SY2325 @ SY2324 @ SV214 ) @ SY2325 ) ) )
                | ( in @ SY2324 @ ( powerset @ SY2325 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[772]) ).

thf(1033,plain,
    ! [SV215: $i] :
      ( ( ! [SY2326: $i] :
            ( ~ ( in @ SY2326 @ ( setunion @ SV215 ) )
            | ! [SY2327: $o] :
                ( ~ ( ~ ( in @ SY2326 @ ( sK31_B @ SY2327 @ SY2326 @ SV215 ) )
                    | ~ ~ ( ~ ( in @ ( sK31_B @ SY2327 @ SY2326 @ SV215 ) @ SV215 )
                          | ~ ~ SY2327 ) )
                | SY2327 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[773]) ).

thf(1034,plain,
    ! [SV216: $i] :
      ( ( ! [SY2328: $i] :
            ( ~ ( ~ ( in @ ( sK26_Xx @ SY2328 @ SV216 ) @ SV216 )
                | ~ ~ ( in @ ( sK26_Xx @ SY2328 @ SV216 ) @ SY2328 ) )
            | ~ ( ~ ( in @ ( sK25_Xx @ SY2328 @ SV216 ) @ SY2328 )
                | ~ ~ ( in @ ( sK25_Xx @ SY2328 @ SV216 ) @ SV216 ) )
            | ( SV216 = SY2328 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[774]) ).

thf(1035,plain,
    ! [SV217: $i] :
      ( ( ! [SY2329: $i] :
            ( ~ ( in @ SY2329 @ ( setunion @ SV217 ) )
            | ~ ( ~ ( in @ ( sK69_X @ SY2329 @ SV217 ) @ SV217 )
                | ~ ( in @ SY2329 @ ( sK69_X @ SY2329 @ SV217 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[775]) ).

thf(1036,plain,
    ! [SV218: $i] :
      ( ( ! [SY2330: $i,SY2331: $i] :
            ( ~ ( func @ SV218 @ SY2330 @ SY2331 )
            | ! [SY2332: $i] :
                ( ~ ( func @ SV218 @ SY2330 @ SY2332 )
                | ~ ( ~ ( in @ ( sK83_Xx @ SY2332 @ SY2331 @ SY2330 @ SV218 ) @ SV218 )
                    | ~ ( ( ( ap @ SV218 @ SY2330 @ SY2331 @ ( sK83_Xx @ SY2332 @ SY2331 @ SY2330 @ SV218 ) )
                         != ( ap @ SV218 @ SY2330 @ SY2332 @ ( sK83_Xx @ SY2332 @ SY2331 @ SY2330 @ SV218 ) ) ) ) )
                | ! [SY2333: $i] :
                    ( ~ ( in @ SY2333 @ SV218 )
                    | ! [SX5: $i] :
                        ( ~ ( in @ SX5 @ SY2330 )
                        | ~ ( in @ ( kpair @ SY2333 @ SX5 ) @ SY2332 )
                        | ( in @ ( kpair @ SY2333 @ SX5 ) @ SY2331 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[776]) ).

thf(1037,plain,
    ! [SV219: $i] :
      ( ( ! [SY2335: $i] :
            ( ~ ( in @ SY2335 @ ( powerset @ SV219 ) )
            | ! [SY2336: $i] :
                ( ~ ( in @ SY2336 @ ( powerset @ SV219 ) )
                | ~ ( ~ ( in @ ( sK96_Xx @ SY2336 @ SY2335 @ SV219 ) @ SV219 )
                    | ~ ~ ( ~ ( in @ ( sK96_Xx @ SY2336 @ SY2335 @ SV219 ) @ SY2335 )
                          | ~ ~ ( in @ ( sK96_Xx @ SY2336 @ SY2335 @ SV219 ) @ SY2336 ) ) )
                | ~ ( ~ ( in @ ( sK95_Xx @ SY2336 @ SY2335 @ SV219 ) @ SV219 )
                    | ~ ~ ( ~ ( in @ ( sK95_Xx @ SY2336 @ SY2335 @ SV219 ) @ SY2336 )
                          | ~ ~ ( in @ ( sK95_Xx @ SY2336 @ SY2335 @ SV219 ) @ SY2335 ) ) )
                | ( SY2335 = SY2336 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[777]) ).

thf(1038,plain,
    ! [SV220: $i] :
      ( ( ! [SY2337: $i > $o,SY2338: $i] :
            ( ~ ( in @ SY2338 @ SV220 )
            | ~ ( SY2337 @ SY2338 )
            | ~ ( ~ ( in @ ( sK73_Xy @ SY2338 @ SY2337 @ SV220 ) @ SV220 )
                | ~ ~ ( ~ ( SY2337 @ ( sK73_Xy @ SY2338 @ SY2337 @ SV220 ) )
                      | ~ ( ( ( sK73_Xy @ SY2338 @ SY2337 @ SV220 )
                           != SY2338 ) ) ) )
            | ( singleton
              @ ( dsetconstr @ SV220
                @ ^ [SX3: $i] : ( SY2337 @ SX3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[778]) ).

thf(1039,plain,
    ! [SV221: $i] :
      ( ( ! [SY2340: $i,SY2341: $i] :
            ( ~ ( in @ SY2341 @ ( symdiff @ SV221 @ SY2340 ) )
            | ~ ( ~ ~ ( ~ ( ( in @ SY2341 @ SV221 )
                          | ~ ( in @ SY2341 @ SV221 )
                          | ! [SX3: $o] : SX3 )
                      | ~ ~ ( ~ ( ( in @ SY2341 @ SV221 )
                                | ( in @ SY2341 @ SY2340 )
                                | ! [SX3: $o] : SX3 )
                            | ~ ( ( in @ SY2341 @ SV221 )
                                | ! [SX3: $o] :
                                    ( ~ SX3
                                    | SX3 ) ) ) )
                | ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SY2341 @ SY2340 )
                                | ~ ( in @ SY2341 @ SV221 )
                                | ! [SX3: $o] : SX3 )
                            | ~ ~ ( ~ ( ~ ( in @ SY2341 @ SY2340 )
                                      | ( in @ SY2341 @ SY2340 )
                                      | ! [SX3: $o] : SX3 )
                                  | ~ ( ~ ( in @ SY2341 @ SY2340 )
                                      | ! [SX3: $o] :
                                          ( ~ SX3
                                          | SX3 ) ) ) )
                      | ~ ~ ( ~ ! [SY2348: $o] :
                                  ( ~ SY2348
                                  | ~ ( in @ SY2341 @ SV221 )
                                  | SY2348 )
                            | ~ ~ ( ~ ! [SX3: $o] :
                                        ( ~ SX3
                                        | ( in @ SY2341 @ SY2340 )
                                        | SX3 )
                                  | ~ ! [SX3: $o] :
                                        ( ~ SX3
                                        | ~ SX3
                                        | SX3 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[779]) ).

thf(1040,plain,
    ! [SV222: $i] :
      ( ( ! [SY2351: $i,SY2352: $i > $i] :
            ( ~ ( ~ ( in @ ( sK76_Xx @ SY2352 @ SY2351 @ SV222 ) @ SV222 )
                | ~ ~ ( in @ ( SY2352 @ ( sK76_Xx @ SY2352 @ SY2351 @ SV222 ) ) @ SY2351 ) )
            | ( func @ SV222 @ SY2351
              @ ( dpsetconstr @ SV222 @ SY2351
                @ ^ [SX3: $i,SX4: $i] :
                    ( ( SY2352 @ SX3 )
                    = SX4 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[780]) ).

thf(1041,plain,
    ! [SV223: $i] :
      ( ( ~ ( ~ ! [SY2355: $i,SY2356: $i] :
                  ( ~ ( in @ SY2356 @ ( setadjoin @ SV223 @ SY2355 ) )
                  | ( SY2356 = SV223 )
                  | ( in @ SY2356 @ SY2355 ) )
            | ~ ~ ( ~ ! [SY2357: $i,SY2358: $i] :
                        ( ( SY2358 != SV223 )
                        | ( in @ SY2358 @ ( setadjoin @ SV223 @ SY2357 ) ) )
                  | ~ ! [SY2359: $i,SY2360: $i] :
                        ( ~ ( in @ SY2360 @ SY2359 )
                        | ( in @ SY2360 @ ( setadjoin @ SV223 @ SY2359 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[781]) ).

thf(1042,plain,
    ! [SV224: $i] :
      ( ( ! [SY2361: $i] :
            ( ~ ( ~ ( in @ ( sK65_Xx @ SY2361 @ SV224 ) @ SV224 )
                | ~ ~ ( in @ ( sK65_Xx @ SY2361 @ SV224 ) @ SY2361 ) )
            | ( subset @ SV224 @ SY2361 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[782]) ).

thf(1043,plain,
    ! [SV225: $i] :
      ( ( ! [SY2362: $i] :
            ( ~ ( ~ ( ~ ( in @ ( sK6_Xx @ SY2362 @ SV225 ) @ SV225 )
                    | ~ ( in @ ( sK6_Xx @ SY2362 @ SV225 ) @ SY2362 ) )
                | ~ ( ( in @ ( sK6_Xx @ SY2362 @ SV225 ) @ SV225 )
                    | ( in @ ( sK6_Xx @ SY2362 @ SV225 ) @ SY2362 ) ) )
            | ( SV225 = SY2362 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[783]) ).

thf(1044,plain,
    ! [SV226: $i] :
      ( ( ! [SY2363: $i] :
            ~ ( ~ ~ ( ~ ! [SY2364: $i] :
                          ( ~ ( in @ SY2364 @ ( binunion @ SV226 @ SY2363 ) )
                          | ( in @ SY2364 @ SV226 )
                          | ( in @ SY2364 @ SY2363 )
                          | ! [SX3: $o] : SX3 )
                    | ~ ! [SY2366: $i] :
                          ( ~ ( in @ SY2366 @ ( binunion @ SV226 @ SY2363 ) )
                          | ( in @ SY2366 @ SV226 )
                          | ! [SX3: $o] :
                              ( ~ SX3
                              | SX3 ) ) )
              | ~ ~ ( ~ ! [SY2368: $i] :
                          ( ~ ( in @ SY2368 @ ( binunion @ SV226 @ SY2363 ) )
                          | ! [SX3: $o] :
                              ( ~ SX3
                              | ( in @ SY2368 @ SY2363 )
                              | SX3 ) )
                    | ~ ( ! [SY2370: $i] :
                            ~ ( in @ SY2370 @ ( binunion @ SV226 @ SY2363 ) )
                        | ! [SX2: $o] :
                            ( ~ SX2
                            | ~ SX2
                            | SX2 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[784]) ).

thf(1045,plain,
    ! [SV227: $i] :
      ( ( ! [SY2372: $i > $o] :
            ( ! [SY2373: $i] :
                ( ~ ( in @ SY2373 @ SV227 )
                | ( SY2372 @ SY2373 ) )
            | ~ ( ~ ( in @ ( sK38_Xx @ SY2372 @ SV227 ) @ SV227 )
                | ~ ~ ( SY2372 @ ( sK38_Xx @ SY2372 @ SV227 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[785]) ).

thf(1046,plain,
    ! [SV228: $i > $o] :
      ( ( ! [SY2374: $i] :
            ~ ( ~ ( ( ( sK47_Xy @ SY2374 @ SV228 )
                   != SY2374 )
                  | ~ ( SV228 @ ( sK47_Xy @ SY2374 @ SV228 ) ) )
              | ~ ( ( ( sK47_Xy @ SY2374 @ SV228 )
                    = SY2374 )
                  | ( SV228 @ ( sK47_Xy @ SY2374 @ SV228 ) ) ) )
        | ~ ( ~ ! [SY2375: $i] :
                  ( ~ ( SV228 @ SY2375 )
                  | ( ( sK46_SY211 @ SV228 )
                    = SY2375 ) )
            | ~ ( SV228 @ ( sK46_SY211 @ SV228 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[786]) ).

thf(1047,plain,
    ! [SV229: $i] :
      ( ( ! [SY2376: $i > $o] :
            ( ~ ( ~ ( in @ ( sK74_Xx @ SY2376 @ SV229 ) @ SV229 )
                | ~ ~ ( ~ ( in @ ( sK75_SY1878 @ SY2376 @ SV229 ) @ SV229 )
                      | ~ ~ ( ~ ( SY2376 @ ( sK74_Xx @ SY2376 @ SV229 ) )
                            | ~ ~ ( ~ ( SY2376 @ ( sK75_SY1878 @ SY2376 @ SV229 ) )
                                  | ~ ( ( ( sK74_Xx @ SY2376 @ SV229 )
                                       != ( sK75_SY1878 @ SY2376 @ SV229 ) ) ) ) ) ) )
            | ! [SY2377: $i] :
                ( ~ ( SY2376 @ SY2377 )
                | ~ ( in @ SY2377 @ SV229 ) )
            | ( singleton
              @ ( dsetconstr @ SV229
                @ ^ [SX2: $i] : ( SY2376 @ SX2 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[787]) ).

thf(1048,plain,
    ! [SV230: $i] :
      ( ( ! [SY2379: $i,SY2380: $i] :
            ( ~ ( subset @ SY2380 @ ( cartprod @ SV230 @ SY2379 ) )
            | ! [SY2381: $i] :
                ( ~ ( subset @ SY2381 @ ( cartprod @ SV230 @ SY2379 ) )
                | ~ ( ~ ( in @ ( sK88_Xx @ SY2381 @ SY2380 @ SY2379 @ SV230 ) @ SV230 )
                    | ~ ~ ( ~ ( in @ ( sK89_SY1883 @ SY2381 @ SY2380 @ SY2379 @ SV230 ) @ SY2379 )
                          | ~ ~ ( ~ ( in @ ( kpair @ ( sK88_Xx @ SY2381 @ SY2380 @ SY2379 @ SV230 ) @ ( sK89_SY1883 @ SY2381 @ SY2380 @ SY2379 @ SV230 ) ) @ SY2380 )
                                | ~ ~ ( in @ ( kpair @ ( sK88_Xx @ SY2381 @ SY2380 @ SY2379 @ SV230 ) @ ( sK89_SY1883 @ SY2381 @ SY2380 @ SY2379 @ SV230 ) ) @ SY2381 ) ) ) )
                | ~ ( ~ ( in @ ( sK86_Xx @ SY2381 @ SY2380 @ SY2379 @ SV230 ) @ SV230 )
                    | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SY2381 @ SY2380 @ SY2379 @ SV230 ) @ SY2379 )
                          | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SY2381 @ SY2380 @ SY2379 @ SV230 ) @ ( sK87_SY1882 @ SY2381 @ SY2380 @ SY2379 @ SV230 ) ) @ SY2381 )
                                | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SY2381 @ SY2380 @ SY2379 @ SV230 ) @ ( sK87_SY1882 @ SY2381 @ SY2380 @ SY2379 @ SV230 ) ) @ SY2380 ) ) ) )
                | ( SY2380 = SY2381 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[788]) ).

thf(1049,plain,
    ! [SV231: $i] :
      ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_Xx @ SV231 ) @ omega )
                  | ~ ( in @ ( sK9_Xx @ SV231 ) @ SV231 ) )
            | ~ ~ ( in @ ( setadjoin @ ( sK9_Xx @ SV231 ) @ ( sK9_Xx @ SV231 ) ) @ SV231 ) )
        | ~ ( in @ emptyset @ SV231 )
        | ! [SY2382: $i] :
            ( ~ ( in @ SY2382 @ omega )
            | ( in @ SY2382 @ SV231 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[789]) ).

thf(1050,plain,
    ! [SV232: $i] :
      ( ( ! [SY2383: $o,SY2384: $i] :
            ( ~ ( in @ SY2384 @ SV232 )
            | ! [SY2385: $i] :
                ( ~ ( in @ SY2385 @ SV232 )
                | SY2383
                | ( in @ SY2385
                  @ ( dsetconstr @ SV232
                    @ ^ [SX4: $i] :
                        ( ~ ( ~ SY2383
                            | ( SX4 != SY2384 ) )
                        | ~ ( ~ ~ SY2383
                            | ( SX4 != SY2385 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[790]) ).

thf(1051,plain,
    ! [SV233: $i] :
      ( ( ~ ( ~ ! [SY2387: $i] :
                  ( ~ ( ~ ( in @ ( sK19_Xx @ SY2387 @ SV233 ) @ SY2387 )
                      | ~ ~ ( in @ ( sK19_Xx @ SY2387 @ SV233 ) @ SV233 ) )
                  | ! [SX2: $i] :
                      ~ ( in @ SX2 @ SY2387 )
                  | ~ ( ~ ! [SY2389: $i] :
                            ( ~ ( in @ SY2389 @ ( sK15_B @ SV233 ) )
                            | ! [SY2390: $i] :
                                ( ~ ( in @ SY2390 @ SY2389 )
                                | ( in @ SY2390 @ ( sK17_SY1842 @ SY2387 @ SV233 ) ) )
                            | ( in @ ( sK18_SY1856 @ SY2387 @ SV233 ) @ SY2389 ) )
                      | ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1842 @ SY2387 @ SV233 ) @ ( sK15_B @ SV233 ) )
                                  | ~ ( in @ ( sK18_SY1856 @ SY2387 @ SV233 ) @ SY2387 ) )
                            | ~ ! [SY2391: $i] :
                                  ( ~ ( in @ SY2391 @ ( sK17_SY1842 @ SY2387 @ SV233 ) )
                                  | ~ ( in @ SY2391 @ SY2387 ) ) ) ) )
            | ~ ~ ( ~ ! [SY2392: $i,SY2393: $i] :
                        ( ~ ( in @ SY2392 @ ( sK15_B @ SV233 ) )
                        | ~ ( in @ SY2393 @ ( sK15_B @ SV233 ) )
                        | ! [SX3: $i] :
                            ( ~ ( in @ SX3 @ SY2392 )
                            | ( in @ SX3 @ SY2393 ) )
                        | ! [SX3: $i] :
                            ( ~ ( in @ SX3 @ SY2393 )
                            | ( in @ SX3 @ SY2392 ) ) )
                  | ~ ~ ( ~ ! [SY2396: $i] :
                              ( ~ ( in @ SY2396 @ ( sK15_B @ SV233 ) )
                              | ! [SY2397: $i] :
                                  ( ~ ( in @ SY2397 @ SY2396 )
                                  | ( in @ SY2397 @ SV233 ) ) )
                        | ~ ! [SY2398: $i,SY2399: $i] :
                              ( ~ ( in @ SY2398 @ SV233 )
                              | ~ ( in @ SY2399 @ SV233 )
                              | ~ ( ~ ( in @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) @ ( sK15_B @ SV233 ) )
                                  | ~ ~ ( ~ ( ~ ( in @ SY2398 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) )
                                            | ~ ( in @ SY2399 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) ) )
                                        | ~ ( ( in @ SY2398 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) )
                                            | ( in @ SY2399 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) ) ) ) )
                              | ( SY2398 = SY2399 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[791]) ).

thf(1052,plain,
    ! [SV234: $i] :
      ( ( ! [SY2400: $i > $o] :
            ( ~ ( ~ ( SY2400 @ ( sK37_Xx @ SY2400 @ SV234 ) )
                | ~ ( in @ ( sK37_Xx @ SY2400 @ SV234 ) @ SV234 ) )
            | ! [SY2401: $i] :
                ( ~ ( in @ SY2401 @ SV234 )
                | ~ ( SY2400 @ SY2401 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[792]) ).

thf(1053,plain,
    ! [SV235: $i > $o] :
      ( ( ! [SY2402: $i] :
            ( ~ ( ~ ( SV235 @ ( sK33_SY142 @ SY2402 @ SV235 ) )
                | ~ ( ( SY2402
                     != ( sK33_SY142 @ SY2402 @ SV235 ) ) ) )
            | ~ ( SV235 @ SY2402 ) )
        | ~ ( ~ ! [SY2403: $i] :
                  ( ( SY2403
                   != ( sK32_Xx @ SV235 ) )
                  | ( SV235 @ SY2403 ) )
            | ~ ! [SY2404: $i] :
                  ( ~ ( SV235 @ SY2404 )
                  | ( SY2404
                    = ( sK32_Xx @ SV235 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[793]) ).

thf(1054,plain,
    ! [SV236: $i] :
      ( ( ! [SY2405: $i,SY2406: $i] :
            ( ~ ( subset @ SY2406 @ ( cartprod @ SV236 @ SY2405 ) )
            | ! [SY2407: $i > $o] :
                ( ~ ( ~ ( in @ ( sK79_Xx @ SY2407 @ SY2406 @ SY2405 @ SV236 ) @ SV236 )
                    | ~ ~ ( ~ ( in @ ( sK80_SY1879 @ SY2407 @ SY2406 @ SY2405 @ SV236 ) @ SY2405 )
                          | ~ ~ ( ~ ( in @ ( kpair @ ( sK79_Xx @ SY2407 @ SY2406 @ SY2405 @ SV236 ) @ ( sK80_SY1879 @ SY2407 @ SY2406 @ SY2405 @ SV236 ) ) @ SY2406 )
                                | ~ ~ ( SY2407 @ ( kpair @ ( sK79_Xx @ SY2407 @ SY2406 @ SY2405 @ SV236 ) @ ( sK80_SY1879 @ SY2407 @ SY2406 @ SY2405 @ SV236 ) ) ) ) ) )
                | ! [SX4: $i] :
                    ( ~ ( in @ SX4 @ SY2406 )
                    | ( SY2407 @ SX4 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[794]) ).

thf(1055,plain,
    ! [SV237: $i] :
      ( ( ! [SY2409: $i > $o] :
            ( ! [SY2410: $i] :
                ( ~ ( in @ SY2410 @ SV237 )
                | ( SY2409 @ SY2410 ) )
            | ~ ( ~ ( in @ ( sK35_Xx @ SY2409 @ SV237 ) @ SV237 )
                | ~ ~ ( SY2409 @ ( sK35_Xx @ SY2409 @ SV237 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[795]) ).

thf(1056,plain,
    ! [SV238: $i] :
      ( ( ! [SY2411: $o,SY2412: $i] :
            ( ~ ( in @ SY2412 @ SV238 )
            | ! [SY2413: $i] :
                ( ~ ( in @ SY2413 @ SV238 )
                | ~ SY2411
                | ( ( dsetconstr @ SV238
                    @ ^ [SX4: $i] :
                        ( ~ ( ~ SY2411
                            | ( SX4 != SY2412 ) )
                        | ~ ( ~ ~ SY2411
                            | ( SX4 != SY2413 ) ) ) )
                  = ( setadjoin @ SY2412 @ emptyset ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[796]) ).

thf(1057,plain,
    ! [SV239: $i] :
      ( ( ! [SY2415: $i] :
            ~ ( in @ SY2415 @ SV239 )
        | ~ ( ~ ( in @ ( sK14_B @ SV239 ) @ SV239 )
            | ~ ! [SY2416: $i] :
                  ( ~ ( in @ SY2416 @ ( sK14_B @ SV239 ) )
                  | ~ ( in @ SY2416 @ SV239 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[797]) ).

thf(1058,plain,
    ! [SV240: $i] :
      ( ( ! [SY2417: $o,SY2418: $i] :
            ( ~ ( in @ SY2418 @ SV240 )
            | ! [SY2419: $i] :
                ( ~ ( in @ SY2419 @ SV240 )
                | ( singleton
                  @ ( dsetconstr @ SV240
                    @ ^ [SX4: $i] :
                        ( ~ ( ~ SY2417
                            | ( SX4 != SY2418 ) )
                        | ~ ( ~ ~ SY2417
                            | ( SX4 != SY2419 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[798]) ).

thf(1059,plain,
    ! [SV241: $i > $o] :
      ( ( ! [SY2421: $i] :
            ~ ( SV241 @ SY2421 )
        | ~ ( ~ ( SV241 @ ( sK44_Xx @ SV241 ) )
            | ~ ~ ( ~ ( SV241 @ ( sK45_SY1868 @ SV241 ) )
                  | ~ ( ( ( sK44_Xx @ SV241 )
                       != ( sK45_SY1868 @ SV241 ) ) ) ) )
        | ~ ( ~ ! [SY2422: $i] :
                  ( ~ ( SV241 @ SY2422 )
                  | ( ( sK43_SY205 @ SV241 )
                    = SY2422 ) )
            | ~ ( SV241 @ ( sK43_SY205 @ SV241 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[799]) ).

thf(1060,plain,
    ! [SV242: $i] :
      ( ( ! [SY2423: $i] :
            ( ~ ( ~ ( in @ ( sK64_Xx @ SY2423 @ SV242 ) @ SV242 )
                | ~ ~ ( in @ ( sK64_Xx @ SY2423 @ SV242 ) @ SY2423 ) )
            | ( subset @ SV242 @ SY2423 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[800]) ).

thf(1061,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ! [SX2: $i] :
                ( ~ ( in @ SX1 @ SX2 )
                | ~ ( in @ SX2 @ SX0 ) )
            | ( in @ SX1 @ ( setunion @ SX0 ) ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
            | ~ ( ~ ( in @ SX1 @ ( sK8_B @ SX1 @ SX0 ) )
                | ~ ( in @ ( sK8_B @ SX1 @ SX0 ) @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[801]) ).

thf(1062,plain,
    ! [SV243: $i] :
      ( ( ! [SY2424: $i,SY2425: $i] :
            ( ~ ( func @ SV243 @ SY2424 @ SY2425 )
            | ! [SY2426: $i] :
                ( ~ ( func @ SV243 @ SY2424 @ SY2426 )
                | ~ ( ~ ( in @ ( sK90_Xx @ SY2426 @ SY2425 @ SY2424 @ SV243 ) @ SV243 )
                    | ~ ( ( ( ap @ SV243 @ SY2424 @ SY2425 @ ( sK90_Xx @ SY2426 @ SY2425 @ SY2424 @ SV243 ) )
                         != ( ap @ SV243 @ SY2424 @ SY2426 @ ( sK90_Xx @ SY2426 @ SY2425 @ SY2424 @ SV243 ) ) ) ) )
                | ( SY2425 = SY2426 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[802]) ).

thf(1063,plain,
    ! [SV244: $i] :
      ( ( ! [SY2427: $i,SY2428: $i > $i] :
            ~ ( ~ ( in @ ( sK93_Xx @ SY2428 @ SY2427 @ SV244 ) @ SV244 )
              | ~ ~ ( in @ ( SY2428 @ ( sK93_Xx @ SY2428 @ SY2427 @ SV244 ) ) @ SY2427 ) )
        | $true )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[803]) ).

thf(1064,plain,
    ! [SV245: $i] :
      ( ( ! [SY2429: $i,SY2430: $i] :
            ( ~ ( in @ SY2430 @ ( funcSet @ SV245 @ SY2429 ) )
            | ! [SY2431: $i] :
                ( ~ ( in @ SY2431 @ ( funcSet @ SV245 @ SY2429 ) )
                | ~ ( ~ ( in @ ( sK91_Xx @ SY2431 @ SY2430 @ SY2429 @ SV245 ) @ SV245 )
                    | ~ ( ( ( ap @ SV245 @ SY2429 @ SY2430 @ ( sK91_Xx @ SY2431 @ SY2430 @ SY2429 @ SV245 ) )
                         != ( ap @ SV245 @ SY2429 @ SY2431 @ ( sK91_Xx @ SY2431 @ SY2430 @ SY2429 @ SV245 ) ) ) ) )
                | ( SY2430 = SY2431 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[804]) ).

thf(1065,plain,
    ! [SV246: $i] :
      ( ( ! [SY2432: $i > $o] :
            ( ~ ( ~ ( in @ ( sK36_Xx @ SY2432 @ SV246 ) @ SV246 )
                | ~ ( SY2432 @ ( sK36_Xx @ SY2432 @ SV246 ) ) )
            | ! [SY2433: $i] :
                ( ~ ( SY2432 @ SY2433 )
                | ~ ( in @ SY2433 @ SV246 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[805]) ).

thf(1066,plain,
    ! [SV247: $i > $o] :
      ( ( ! [SY2434: $i] :
            ( ~ ( ~ ( SV247 @ ( sK22_SY74 @ SY2434 @ SV247 ) )
                | ~ ( ( SY2434
                     != ( sK22_SY74 @ SY2434 @ SV247 ) ) ) )
            | ~ ( SV247 @ SY2434 ) )
        | ~ ( ~ ! [SY2435: $i] :
                  ( ~ ( SV247 @ SY2435 )
                  | ( ( sK21_Xx @ SV247 )
                    = SY2435 ) )
            | ~ ( SV247 @ ( sK21_Xx @ SV247 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[806]) ).

thf(1067,plain,
    ! [SV248: $i] :
      ( ( ! [SY2436: $i] :
            ( ( SV248 != SY2436 )
            | ! [SY2437: $i > $o,SY2438: $i > $o] :
                ( ~ ( ~ ( in @ ( sK62_Xx @ SY2438 @ SY2437 @ SY2436 @ SV248 ) @ SV248 )
                    | ~ ~ ( ~ ( in @ ( sK63_SY1875 @ SY2438 @ SY2437 @ SY2436 @ SV248 ) @ SY2436 )
                          | ~ ~ ( ( ( sK62_Xx @ SY2438 @ SY2437 @ SY2436 @ SV248 )
                                 != ( sK63_SY1875 @ SY2438 @ SY2437 @ SY2436 @ SV248 ) )
                                | ~ ~ ( ~ ( ~ ( SY2437 @ ( sK62_Xx @ SY2438 @ SY2437 @ SY2436 @ SV248 ) )
                                          | ~ ( SY2438 @ ( sK63_SY1875 @ SY2438 @ SY2437 @ SY2436 @ SV248 ) ) )
                                      | ~ ( ( SY2437 @ ( sK62_Xx @ SY2438 @ SY2437 @ SY2436 @ SV248 ) )
                                          | ( SY2438 @ ( sK63_SY1875 @ SY2438 @ SY2437 @ SY2436 @ SV248 ) ) ) ) ) ) )
                | ( ( dsetconstr @ SV248
                    @ ^ [SX4: $i] : ( SY2437 @ SX4 ) )
                  = ( dsetconstr @ SY2436
                    @ ^ [SX4: $i] : ( SY2438 @ SX4 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[807]) ).

thf(1068,plain,
    ! [SV249: $i] :
      ( ( ! [SY2441: $i > $o] :
            ( ~ ( singleton
                @ ( dsetconstr @ SV249
                  @ ^ [SX2: $i] : ( SY2441 @ SX2 ) ) )
            | ~ ( ~ ( SY2441 @ ( sK72_Xx @ SY2441 @ SV249 ) )
                | ~ ( in @ ( sK72_Xx @ SY2441 @ SV249 ) @ SV249 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[808]) ).

thf(1069,plain,
    ! [SV1: $i,SV250: $i] :
      ( ( ~ ( in @ SV250 @ ( powerset @ SV1 ) )
        | ! [SY2443: $i] :
            ( ~ ( in @ SY2443 @ ( powerset @ SV1 ) )
            | ! [SY2444: $i] :
                ( ~ ( in @ SY2444 @ ( powerset @ SV1 ) )
                | ! [SY2445: $i] :
                    ( ~ ( in @ SY2445 @ SV1 )
                    | ~ ( in @ SY2445 @ ( binintersect @ SV250 @ SY2443 ) )
                    | ( in @ SY2445 @ ( binunion @ SV250 @ SY2444 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[809]) ).

thf(1070,plain,
    ! [SV2: $i,SV251: $i] :
      ( ( ~ ( in @ SV251 @ ( powerset @ SV2 ) )
        | ! [SY2446: $i] :
            ( ~ ( in @ SY2446 @ ( powerset @ SV2 ) )
            | ! [SY2447: $i] :
                ( ~ ( in @ SY2447 @ SV2 )
                | ( in @ SY2447 @ ( binunion @ SV251 @ SY2446 ) )
                | ~ ( in @ SY2447 @ SY2446 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[810]) ).

thf(1071,plain,
    ! [SV3: $i,SV252: $i] :
      ( ( ~ ( in @ SV252 @ ( powerset @ SV3 ) )
        | ! [SY2448: $i] :
            ( ~ ( in @ SY2448 @ ( powerset @ SV3 ) )
            | ! [SY2449: $i] :
                ( ~ ( in @ SY2449 @ SV3 )
                | ( in @ SY2449 @ ( binunion @ SV252 @ SY2448 ) )
                | ~ ( in @ SY2449 @ SV252 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[811]) ).

thf(1072,plain,
    ! [SV4: $i,SV253: $i] :
      ( ( ~ ( in @ SV253 @ ( powerset @ SV4 ) )
        | ! [SY2450: $i] :
            ( ~ ( in @ SY2450 @ ( powerset @ SV4 ) )
            | ~ ( subset @ SV253 @ ( setminus @ SV4 @ SY2450 ) )
            | ( subset @ SY2450 @ ( setminus @ SV4 @ SV253 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[812]) ).

thf(1073,plain,
    ! [SV5: $i,SV254: $i] :
      ( ( ~ ( in @ SV254 @ ( powerset @ SV5 ) )
        | ! [SY2451: $i] :
            ( ~ ( in @ SY2451 @ ( powerset @ SV5 ) )
            | ~ ( subset @ SV254 @ ( setminus @ SV5 @ SY2451 ) )
            | ! [SY2452: $i] :
                ( ~ ( in @ SY2452 @ SV5 )
                | ~ ( in @ SY2452 @ SY2451 )
                | ( in @ SY2452 @ ( setminus @ SV5 @ SV254 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[813]) ).

thf(1074,plain,
    ! [SV6: $i,SV255: $i] :
      ( ( ~ ( in @ SV255 @ ( powerset @ SV6 ) )
        | ! [SY2453: $i] :
            ( ~ ( in @ SY2453 @ ( powerset @ SV6 ) )
            | ( in @ ( setminus @ SV6 @ SV255 ) @ ( powerset @ ( setminus @ SV6 @ ( binintersect @ SV255 @ SY2453 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[814]) ).

thf(1075,plain,
    ! [SV7: $i,SV256: $i] :
      ( ( ~ ( in @ SV256 @ ( powerset @ SV7 ) )
        | ! [SY2454: $i] :
            ( ~ ( in @ SY2454 @ ( powerset @ SV7 ) )
            | ( subset @ ( setminus @ SV7 @ SV256 ) @ ( setminus @ SV7 @ ( binintersect @ SV256 @ SY2454 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[815]) ).

thf(1076,plain,
    ! [SV8: $i,SV257: $i] :
      ( ( ~ ( in @ SV257 @ ( powerset @ SV8 ) )
        | ! [SY2455: $i] :
            ( ~ ( in @ SY2455 @ ( powerset @ SV8 ) )
            | ! [SY2456: $i] :
                ( ~ ( in @ SY2456 @ SV8 )
                | ~ ( in @ SY2456 @ ( setminus @ SV8 @ SV257 ) )
                | ( in @ SY2456 @ ( setminus @ SV8 @ ( binintersect @ SV257 @ SY2455 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[816]) ).

thf(1077,plain,
    ! [SV9: $i,SV258: $i] :
      ( ( ~ ( in @ SV258 @ ( powerset @ SV9 ) )
        | ! [SY2457: $i] :
            ( ~ ( in @ SY2457 @ ( powerset @ SV9 ) )
            | ! [SY2458: $i] :
                ( ~ ( in @ SY2458 @ SV9 )
                | ~ ( in @ SY2458 @ ( setminus @ SV9 @ SV258 ) )
                | ~ ( in @ SY2458 @ ( binintersect @ SV258 @ SY2457 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[817]) ).

thf(1078,plain,
    ! [SV10: $i,SV259: $i] :
      ( ( ~ ( in @ SV259 @ ( powerset @ SV10 ) )
        | ( SV259
          = ( setminus @ SV10 @ ( setminus @ SV10 @ SV259 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[818]) ).

thf(1079,plain,
    ! [SV11: $i,SV260: $i] :
      ( ( ~ ( in @ SV260 @ ( powerset @ SV11 ) )
        | ( subset @ ( setminus @ SV11 @ ( setminus @ SV11 @ SV260 ) ) @ SV260 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[819]) ).

thf(1080,plain,
    ! [SV12: $i,SV261: $i] :
      ( ( ~ ( in @ SV261 @ ( powerset @ SV12 ) )
        | ( subset @ SV261 @ ( setminus @ SV12 @ ( setminus @ SV12 @ SV261 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[820]) ).

thf(1081,plain,
    ! [SV13: $i,SV262: $i] :
      ( ( ~ ( in @ SV262 @ ( powerset @ SV13 ) )
        | ! [SY2459: $i] :
            ( ~ ( in @ SY2459 @ SV13 )
            | ~ ( in @ SY2459 @ ( setminus @ SV13 @ ( setminus @ SV13 @ SV262 ) ) )
            | ( in @ SY2459 @ SV262 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[821]) ).

thf(1082,plain,
    ! [SV14: $i,SV263: $i] :
      ( ( ~ ( in @ SV263 @ ( powerset @ SV14 ) )
        | ! [SY2460: $i] :
            ( ~ ( in @ SY2460 @ SV14 )
            | ~ ( in @ SY2460 @ SV263 )
            | ( in @ SY2460 @ ( setminus @ SV14 @ ( setminus @ SV14 @ SV263 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[822]) ).

thf(1083,plain,
    ! [SV15: $i,SV264: $i] :
      ( ( ~ ( in @ SV264 @ ( powerset @ SV15 ) )
        | ! [SY2461: $i] :
            ( ~ ( in @ SY2461 @ ( powerset @ SV15 ) )
            | ~ ( subset @ ( setminus @ SV15 @ SY2461 ) @ ( setminus @ SV15 @ SV264 ) )
            | ( subset @ SV264 @ SY2461 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[823]) ).

thf(1084,plain,
    ! [SV16: $i,SV265: $i] :
      ( ( ~ ( in @ SV265 @ ( powerset @ SV16 ) )
        | ! [SY2462: $i] :
            ( ~ ( in @ SY2462 @ ( powerset @ SV16 ) )
            | ~ ( subset @ SV265 @ SY2462 )
            | ( subset @ ( setminus @ SV16 @ SY2462 ) @ ( setminus @ SV16 @ SV265 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[824]) ).

thf(1085,plain,
    ! [SV17: $i,SV266: $i] :
      ( ( ~ ( in @ SV266 @ ( powerset @ SV17 ) )
        | ! [SY2463: $i] :
            ( ~ ( in @ SY2463 @ ( powerset @ SV17 ) )
            | ! [SY2464: $i] :
                ( ~ ( in @ SY2464 @ SV17 )
                | ~ ( subset @ SV266 @ SY2463 )
                | ( in @ SY2464 @ SY2463 )
                | ~ ( in @ SY2464 @ SV266 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[825]) ).

thf(1086,plain,
    ! [SV18: $i,SV267: $i] :
      ( ( ~ ( in @ SV267 @ ( powerset @ SV18 ) )
        | ! [SY2465: $i] :
            ( ~ ( in @ SY2465 @ ( powerset @ SV18 ) )
            | ! [SY2466: $i] :
                ( ~ ( in @ SY2466 @ SV18 )
                | ~ ( subset @ SV267 @ ( setminus @ SV18 @ SY2465 ) )
                | ~ ( in @ SY2466 @ SY2465 )
                | ~ ( in @ SY2466 @ SV267 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[826]) ).

thf(1087,plain,
    ! [SV19: $i,SV268: $i] :
      ( ( ~ ( in @ SV268 @ ( powerset @ SV19 ) )
        | ! [SY2467: $i] :
            ( ~ ( in @ SY2467 @ ( powerset @ SV19 ) )
            | ! [SY2468: $i] :
                ( ~ ( in @ SY2468 @ SV19 )
                | ( in @ SY2468 @ SY2467 )
                | ~ ( in @ SY2468 @ ( binintersect @ SV268 @ SY2467 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[827]) ).

thf(1088,plain,
    ! [SV20: $i,SV269: $i] :
      ( ( ~ ( in @ SV269 @ ( powerset @ SV20 ) )
        | ! [SY2469: $i] :
            ( ~ ( in @ SY2469 @ ( powerset @ SV20 ) )
            | ! [SY2470: $i] :
                ( ~ ( in @ SY2470 @ SV20 )
                | ( in @ SY2470 @ SV269 )
                | ~ ( in @ SY2470 @ ( binintersect @ SV269 @ SY2469 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[828]) ).

thf(1089,plain,
    ! [SV21: $i,SV270: $i] :
      ( ( ~ ( in @ SV270 @ ( powerset @ SV21 ) )
        | ! [SY2471: $i] :
            ( ~ ( in @ SY2471 @ SV21 )
            | ( in @ SY2471 @ ( setminus @ SV21 @ SV270 ) )
            | ( in @ SY2471 @ SV270 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[829]) ).

thf(1090,plain,
    ! [SV22: $i,SV271: $i] :
      ( ( ~ ( in @ SV271 @ ( powerset @ SV22 ) )
        | ! [SY2472: $i] :
            ( ~ ( in @ SY2472 @ SV22 )
            | ~ ( in @ SY2472 @ SV271 )
            | ~ ( in @ SY2472 @ ( setminus @ SV22 @ SV271 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[830]) ).

thf(1091,plain,
    ! [SV23: $i,SV272: $i] :
      ( ( ~ ( in @ SV272 @ ( powerset @ SV23 ) )
        | ! [SY2473: $i] :
            ( ~ ( in @ SY2473 @ ( powerset @ SV23 ) )
            | ! [SY2474: $i] :
                ( ~ ( in @ SY2474 @ SV23 )
                | ~ ( in @ SV272 @ ( powerset @ SY2473 ) )
                | ~ ( in @ SY2474 @ SV272 )
                | ( in @ SY2474 @ SY2473 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[831]) ).

thf(1092,plain,
    ! [SV24: $i,SV273: $i] :
      ( ( ~ ( in @ SV273 @ ( powerset @ SV24 ) )
        | ( in @ ( setminus @ SV24 @ SV273 ) @ ( powerset @ SV24 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[832]) ).

thf(1093,plain,
    ! [SV25: $i,SV274: $i] :
      ( ( ~ ( in @ SV274 @ ( powerset @ SV25 ) )
        | ! [SY2475: $i] :
            ( ~ ( in @ SY2475 @ ( powerset @ SV25 ) )
            | ( in @ ( setminus @ SV274 @ SY2475 ) @ ( powerset @ SV25 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[833]) ).

thf(1094,plain,
    ! [SV26: $i,SV275: $i] :
      ( ( ~ ( in @ SV275 @ ( powerset @ SV26 ) )
        | ( in @ ( powerset @ SV275 ) @ ( powerset @ ( powerset @ SV26 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[834]) ).

thf(1095,plain,
    ! [SV27: $i,SV276: $i] :
      ( ( ~ ( in @ SV276 @ ( powerset @ SV27 ) )
        | ! [SY2476: $i] :
            ( ~ ( in @ SY2476 @ ( powerset @ SV27 ) )
            | ( in @ ( binunion @ SV276 @ SY2476 ) @ ( powerset @ SV27 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[835]) ).

thf(1096,plain,
    ! [SV28: $i,SV277: $i] :
      ( ( ~ ( in @ SV277 @ ( powerset @ SV28 ) )
        | ! [SY2477: $i] :
            ( ~ ( in @ SY2477 @ ( powerset @ SV28 ) )
            | ( in @ ( binintersect @ SV277 @ SY2477 ) @ ( powerset @ SV28 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[836]) ).

thf(1097,plain,
    ! [SV278: $o,SV29: $i] :
      ( ( ! [SY2478: $i] :
            ( ~ ( in @ SY2478 @ SV29 )
            | ! [SY2479: $i] :
                ( ~ ( in @ SY2479 @ SV29 )
                | ( in @ ( if @ SV29 @ SV278 @ SY2478 @ SY2479 ) @ ( setadjoin @ SY2478 @ ( setadjoin @ SY2479 @ emptyset ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[837]) ).

thf(1098,plain,
    ! [SV29: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV29 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV29 )
                | ( in @ ( if @ SV29 @ $true @ SX0 @ SX1 ) @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[837]) ).

thf(1099,plain,
    ! [SV29: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV29 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV29 )
                | ( in @ ( if @ SV29 @ $false @ SX0 @ SX1 ) @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[837]) ).

thf(1100,plain,
    ! [SV279: $o,SV30: $i] :
      ( ( ! [SY2480: $i] :
            ( ~ ( in @ SY2480 @ SV30 )
            | ! [SY2481: $i] :
                ( ~ ( in @ SY2481 @ SV30 )
                | SV279
                | ( ( if @ SV30 @ SV279 @ SY2480 @ SY2481 )
                  = SY2481 ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[838]) ).

thf(1101,plain,
    ! [SV30: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV30 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV30 )
                | $true
                | ( ( if @ SV30 @ $true @ SX0 @ SX1 )
                  = SX1 ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[838]) ).

thf(1102,plain,
    ! [SV30: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV30 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV30 )
                | $false
                | ( ( if @ SV30 @ $false @ SX0 @ SX1 )
                  = SX1 ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[838]) ).

thf(1103,plain,
    ! [SV280: $o,SV31: $i] :
      ( ( ! [SY2482: $i] :
            ( ~ ( in @ SY2482 @ SV31 )
            | ! [SY2483: $i] :
                ( ~ ( in @ SY2483 @ SV31 )
                | ~ SV280
                | ( ( if @ SV31 @ SV280 @ SY2482 @ SY2483 )
                  = SY2482 ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[839]) ).

thf(1104,plain,
    ! [SV31: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV31 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV31 )
                | ~ $true
                | ( ( if @ SV31 @ $true @ SX0 @ SX1 )
                  = SX0 ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[839]) ).

thf(1105,plain,
    ! [SV31: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV31 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV31 )
                | ~ $false
                | ( ( if @ SV31 @ $false @ SX0 @ SX1 )
                  = SX0 ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[839]) ).

thf(1106,plain,
    ! [SV32: $i] :
      ( ( ( ~ ( singleton @ SV32 ) )
        = $true )
      | ( ( ! [SY1956: $i] :
              ( ~ ( in @ SY1956 @ SV32 )
              | ( ( setunion @ SV32 )
                = SY1956 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[840]) ).

thf(1107,plain,
    ! [SV281: $o,SV33: $i] :
      ( ( ! [SY2484: $i] :
            ( ~ ( in @ SY2484 @ SV33 )
            | ! [SY2485: $i] :
                ( ~ ( in @ SY2485 @ SV33 )
                | ( in @ ( if @ SV33 @ SV281 @ SY2484 @ SY2485 ) @ SV33 ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[841]) ).

thf(1108,plain,
    ! [SV33: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV33 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV33 )
                | ( in @ ( if @ SV33 @ $true @ SX0 @ SX1 ) @ SV33 ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[841]) ).

thf(1109,plain,
    ! [SV33: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV33 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV33 )
                | ( in @ ( if @ SV33 @ $false @ SX0 @ SX1 ) @ SV33 ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[841]) ).

thf(1110,plain,
    ! [SV282: $i,SV34: $i] :
      ( ( ! [SY2486: $i] :
            ( ~ ( in @ SY2486 @ ( funcSet @ SV34 @ SV282 ) )
            | ( ( lam @ SV34 @ SV282
                @ ^ [SY2487: $i] : ( ap @ SV34 @ SV282 @ SY2486 @ SY2487 ) )
              = SY2486 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[842]) ).

thf(1111,plain,
    ! [SV283: $i,SV35: $i] :
      ( ( ! [SY2488: $i] :
            ( ~ ( func @ SV35 @ SV283 @ SY2488 )
            | ( ( lam @ SV35 @ SV283
                @ ^ [SY2489: $i] : ( ap @ SV35 @ SV283 @ SY2488 @ SY2489 ) )
              = SY2488 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[843]) ).

thf(1112,plain,
    ! [SV36: $i] :
      ( ( ( ! [SY1966: $i,SY1967: $i] :
              ~ ( func @ SV36 @ SY1966 @ SY1967 ) )
        = $true )
      | ( ( ! [SY1968: $i] :
              ~ ( in @ SY1968 @ SV36 )
          | $true )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[844]) ).

thf(1113,plain,
    ! [SV37: $i] :
      ( ( ( ! [SY1969: $i,SY1970: $i] :
              ~ ( in @ SY1970 @ ( funcSet @ SV37 @ SY1969 ) ) )
        = $true )
      | ( ( ! [SY1971: $i] :
              ~ ( in @ SY1971 @ SV37 )
          | $true )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[845]) ).

thf(1114,plain,
    ! [SV284: $i,SV38: $i] :
      ( ( ! [SY2490: $i] :
            ( ~ ( in @ SY2490 @ ( funcSet @ SV38 @ SV284 ) )
            | ! [SY2491: $i] :
                ( ~ ( in @ SY2491 @ SV38 )
                | ! [SY2492: $i] :
                    ( ~ ( in @ SY2492 @ SV284 )
                    | ~ ( in @ ( kpair @ SY2491 @ SY2492 ) @ SY2490 )
                    | ( ( ap @ SV38 @ SV284 @ SY2490 @ SY2491 )
                      = SY2492 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[846]) ).

thf(1115,plain,
    ! [SV285: $i,SV39: $i] :
      ( ( ! [SY2493: $i] :
            ( ~ ( func @ SV39 @ SV285 @ SY2493 )
            | ! [SY2494: $i] :
                ( ~ ( in @ SY2494 @ SV39 )
                | ! [SY2495: $i] :
                    ( ~ ( in @ SY2495 @ SV285 )
                    | ~ ( in @ ( kpair @ SY2494 @ SY2495 ) @ SY2493 )
                    | ( ( ap @ SV39 @ SV285 @ SY2493 @ SY2494 )
                      = SY2495 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[847]) ).

thf(1116,plain,
    ! [SV286: $i,SV40: $i] :
      ( ( ! [SY2496: $i] :
            ( ~ ( in @ SY2496 @ ( funcSet @ SV40 @ SV286 ) )
            | ! [SY2497: $i] :
                ( ~ ( in @ SY2497 @ SV40 )
                | ( in @ ( kpair @ SY2497 @ ( ap @ SV40 @ SV286 @ SY2496 @ SY2497 ) ) @ SY2496 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[848]) ).

thf(1117,plain,
    ! [SV287: $i,SV41: $i] :
      ( ( ! [SY2498: $i] :
            ( ~ ( func @ SV41 @ SV287 @ SY2498 )
            | ! [SY2499: $i] :
                ( ~ ( in @ SY2499 @ SV41 )
                | ( in @ ( kpair @ SY2499 @ ( ap @ SV41 @ SV287 @ SY2498 @ SY2499 ) ) @ SY2498 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[849]) ).

thf(1118,plain,
    ! [SV288: $i > $o,SV42: $i] :
      ( ( ~ ( singleton
            @ ( dsetconstr @ SV42
              @ ^ [SY2500: $i] : ( SV288 @ SY2500 ) ) )
        | ! [SY2501: $i] :
            ( ~ ( in @ SY2501 @ SV42 )
            | ! [SY2502: $i] :
                ( ~ ( in @ SY2502 @ SV42 )
                | ~ ( SV288 @ SY2501 )
                | ~ ( SV288 @ SY2502 )
                | ( SY2501 = SY2502 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[850]) ).

thf(1119,plain,
    ! [SV289: $i,SV43: $i] :
      ( ( ! [SY2503: $i] :
            ( ~ ( func @ SV43 @ SV289 @ SY2503 )
            | ( in @ SY2503 @ ( funcSet @ SV43 @ SV289 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[851]) ).

thf(1120,plain,
    ! [SV290: $i,SV44: $i] :
      ( ( ! [SY2504: $i] :
            ( ~ ( in @ SY2504 @ ( funcSet @ SV44 @ SV290 ) )
            | ! [SY2505: $i] :
                ( ~ ( in @ SY2505 @ SV44 )
                | ( in @ ( ap @ SV44 @ SV290 @ SY2504 @ SY2505 ) @ SV290 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[852]) ).

thf(1121,plain,
    ! [SV291: $i,SV45: $i] :
      ( ( ! [SY2506: $i] :
            ( ~ ( in @ SY2506 @ ( funcSet @ SV45 @ SV291 ) )
            | ( func @ SV45 @ SV291 @ SY2506 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[853]) ).

thf(1122,plain,
    ! [SV292: $i,SV46: $i] :
      ( ( ! [SY2507: $i] :
            ( ~ ( func @ SV46 @ SV292 @ SY2507 )
            | ! [SY2508: $i] :
                ( ~ ( in @ SY2508 @ SV46 )
                | ( in @ ( ap @ SV46 @ SV292 @ SY2507 @ SY2508 ) @ SV292 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[854]) ).

thf(1123,plain,
    ! [SV293: $i,SV47: $i] :
      ( ( ! [SY2509: $i] :
            ( ~ ( func @ SV47 @ SV293 @ SY2509 )
            | ! [SY2510: $i] :
                ( ~ ( in @ SY2510 @ SV47 )
                | ( in
                  @ ( setunion
                    @ ( dsetconstr @ SV293
                      @ ^ [Xy: $i] : ( in @ ( kpair @ SY2510 @ Xy ) @ SY2509 ) ) )
                  @ SV293 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[855]) ).

thf(1124,plain,
    ! [SV294: $i,SV48: $i] :
      ( ( ! [SY2512: $i] :
            ( ~ ( func @ SV48 @ SV294 @ SY2512 )
            | ! [SY2513: $i] :
                ( ~ ( in @ SY2513 @ SV48 )
                | ( singleton
                  @ ( dsetconstr @ SV294
                    @ ^ [Xy: $i] : ( in @ ( kpair @ SY2513 @ Xy ) @ SY2512 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[856]) ).

thf(1125,plain,
    ! [SV295: $i,SV49: $i] :
      ( ( ! [SY2515: $i > $i > $o,SY2516: $i,SY2517: $i] :
            ( ~ ( in @ ( kpair @ SY2516 @ SY2517 )
                @ ( dpsetconstr @ SV49 @ SV295
                  @ ^ [Xz: $i,Xu: $i] : ( SY2515 @ Xz @ Xu ) ) )
            | ( SY2515 @ SY2516 @ SY2517 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[857]) ).

thf(1126,plain,
    ! [SV296: $i,SV50: $i] :
      ( ( ! [SY2520: $i > $i > $o,SY2521: $i,SY2522: $i] :
            ( ~ ( in @ ( kpair @ SY2521 @ SY2522 )
                @ ( dpsetconstr @ SV50 @ SV296
                  @ ^ [Xz: $i,Xu: $i] : ( SY2520 @ Xz @ Xu ) ) )
            | ( in @ SY2522 @ SV296 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[858]) ).

thf(1127,plain,
    ! [SV297: $i,SV51: $i] :
      ( ( ! [SY2525: $i > $i > $o,SY2526: $i] :
            ( ! [SY2527: $i] :
                ~ ( in @ ( kpair @ SY2526 @ SY2527 )
                  @ ( dpsetconstr @ SV51 @ SV297
                    @ ^ [Xz: $i,Xu: $i] : ( SY2525 @ Xz @ Xu ) ) )
            | ( in @ SY2526 @ SV51 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[859]) ).

thf(1128,plain,
    ! [SV298: $i,SV52: $i] :
      ( ( ! [SY2530: $i > $i > $o,SY2531: $i] :
            ( ~ ( in @ SY2531 @ SV52 )
            | ! [SY2532: $i] :
                ( ~ ( in @ SY2532 @ SV298 )
                | ~ ( in @ ( kpair @ SY2531 @ SY2532 )
                    @ ( dpsetconstr @ SV52 @ SV298
                      @ ^ [Xz: $i,Xu: $i] : ( SY2530 @ Xz @ Xu ) ) )
                | ( SY2530 @ SY2531 @ SY2532 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[860]) ).

thf(1129,plain,
    ! [SV299: $i,SV53: $i] :
      ( ( ! [SY2535: $i > $i > $o] :
            ( subset
            @ ( dpsetconstr @ SV53 @ SV299
              @ ^ [Xx: $i,Xy: $i] : ( SY2535 @ Xx @ Xy ) )
            @ ( cartprod @ SV53 @ SV299 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[861]) ).

thf(1130,plain,
    ! [SV300: $i,SV54: $i] :
      ( ( ! [SY2538: $i > $i > $o] :
            ( subset
            @ ( dpsetconstr @ SV54 @ SV300
              @ ^ [Xx: $i,Xy: $i] : ( SY2538 @ Xx @ Xy ) )
            @ ( cartprod @ SV54 @ SV300 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[862]) ).

thf(1131,plain,
    ! [SV301: $i,SV55: $i] :
      ( ( ! [SY2541: $i > $i > $o,SY2542: $i] :
            ( ~ ( in @ SY2542 @ SV55 )
            | ! [SY2543: $i] :
                ( ~ ( in @ SY2543 @ SV301 )
                | ~ ( SY2541 @ SY2542 @ SY2543 )
                | ( in @ ( kpair @ SY2542 @ SY2543 )
                  @ ( dpsetconstr @ SV55 @ SV301
                    @ ^ [Xz: $i,Xu: $i] : ( SY2541 @ Xz @ Xu ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[863]) ).

thf(1132,plain,
    ! [SV302: $i,SV56: $i] :
      ( ( ! [SY2546: $i] :
            ( ~ ( in @ SY2546 @ ( cartprod @ SV56 @ SV302 ) )
            | ( ( kpair @ ( kfst @ SY2546 ) @ ( ksnd @ SY2546 ) )
              = SY2546 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[864]) ).

thf(1133,plain,
    ! [SV303: $i,SV57: $i] :
      ( ( ! [SY2547: $i] :
            ( ~ ( in @ SY2547 @ SV57 )
            | ! [SY2548: $i] :
                ( ~ ( in @ SY2548 @ SV303 )
                | ( ( ksnd @ ( kpair @ SY2547 @ SY2548 ) )
                  = SY2548 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[865]) ).

thf(1134,plain,
    ! [SV304: $i,SV58: $i] :
      ( ( ! [SY2549: $i] :
            ( ~ ( in @ SY2549 @ SV58 )
            | ! [SY2550: $i] :
                ( ~ ( in @ SY2550 @ SV304 )
                | ( ( kfst @ ( kpair @ SY2549 @ SY2550 ) )
                  = SY2549 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[866]) ).

thf(1135,plain,
    ! [SV59: $i] :
      ( ( ( ! [SY2054: $i] :
              ~ ( in @ SY2054 @ SV59 ) )
        = $true )
      | ( ( ! [B: $i,Xy: $i] :
              ~ ( in @ Xy @ B )
          | $true )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[867]) ).

thf(1136,plain,
    ! [SV305: $i,SV60: $i] :
      ( ( ! [SY2551: $i,SY2552: $i] :
            ( ~ ( in @ ( kpair @ SY2551 @ SY2552 ) @ ( cartprod @ SV60 @ SV305 ) )
            | ( in @ SY2552 @ SV305 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[868]) ).

thf(1137,plain,
    ! [SV306: $i,SV61: $i] :
      ( ( ! [SY2553: $i] :
            ( ! [SY2554: $i] :
                ~ ( in @ ( kpair @ SY2553 @ SY2554 ) @ ( cartprod @ SV61 @ SV306 ) )
            | ( in @ SY2553 @ SV61 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[869]) ).

thf(1138,plain,
    ! [SV307: $i,SV62: $i] :
      ( ( ! [SY2555: $i] :
            ( ~ ( in @ SY2555 @ ( cartprod @ SV62 @ SV307 ) )
            | ( in @ ( ksnd @ SY2555 ) @ SV307 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[870]) ).

thf(1139,plain,
    ! [SV63: $i] :
      ( ( ( ~ ( iskpair @ SV63 ) )
        = $true )
      | ( ( ( kpair @ ( kfst @ SV63 ) @ ( ksnd @ SV63 ) )
          = SV63 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[871]) ).

thf(1140,plain,
    ! [SV308: $i,SV64: $i] :
      ( ( ( ksnd @ ( kpair @ SV64 @ SV308 ) )
        = SV308 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[872]) ).

thf(1141,plain,
    ! [SV65: $i] :
      ( ( ( ~ ( iskpair @ SV65 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ ( setunion @ SV65 )
            @ ^ [SY2066: $i] :
                ( SV65
                = ( kpair @ ( kfst @ SV65 ) @ SY2066 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[873]) ).

thf(1142,plain,
    ! [SV309: $i,SV66: $i] :
      ( ( ! [SY2556: $i,SY2557: $i] :
            ( ( ( kpair @ SV66 @ SV309 )
             != ( kpair @ SY2556 @ SY2557 ) )
            | ( SV309 = SY2557 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[874]) ).

thf(1143,plain,
    ! [SV310: $i,SV67: $i] :
      ( ( ! [SY2558: $i,SY2559: $i] :
            ( ( ( setadjoin @ ( setadjoin @ SV67 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV67 @ ( setadjoin @ SV310 @ emptyset ) ) @ emptyset ) )
             != ( setadjoin @ ( setadjoin @ SY2558 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2558 @ ( setadjoin @ SY2559 @ emptyset ) ) @ emptyset ) ) )
            | ( SV310 = SY2559 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[875]) ).

thf(1144,plain,
    ! [SV311: $i,SV68: $i] :
      ( ( ! [SY2560: $i] :
            ( ( setadjoin @ SV68 @ ( setadjoin @ SV311 @ emptyset ) )
           != ( setadjoin @ SY2560 @ emptyset ) )
        | ( SV68 = SV311 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[876]) ).

thf(1145,plain,
    ! [SV312: $i,SV69: $i] :
      ( ( ! [SY2561: $i,SY2562: $i] :
            ( ( ( setadjoin @ ( setadjoin @ SV69 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV69 @ ( setadjoin @ SV312 @ emptyset ) ) @ emptyset ) )
             != ( setadjoin @ ( setadjoin @ SY2561 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2561 @ ( setadjoin @ SY2562 @ emptyset ) ) @ emptyset ) ) )
            | ( SY2561 != SY2562 )
            | ( SV312 = SY2562 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[877]) ).

thf(1146,plain,
    ! [SV313: $i,SV70: $i] :
      ( ( ( SV70 != SV313 )
        | ( ( setadjoin @ ( setadjoin @ SV70 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV70 @ ( setadjoin @ SV313 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ SV70 @ emptyset ) @ emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[878]) ).

thf(1147,plain,
    ! [SV314: $i,SV71: $i] :
      ( ( ( SV71 != SV314 )
        | ( ( setadjoin @ SV71 @ ( setadjoin @ SV314 @ emptyset ) )
          = ( setadjoin @ SV71 @ emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[879]) ).

thf(1148,plain,
    ! [SV315: $i,SV72: $i] :
      ( ( ! [SY2563: $i] :
            ( ! [SY2564: $i] :
                ( ( kpair @ SV72 @ SV315 )
               != ( kpair @ SY2563 @ SY2564 ) )
            | ( SV72 = SY2563 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[880]) ).

thf(1149,plain,
    ! [SV316: $i,SV73: $i] :
      ( ( ! [SY2565: $i] :
            ( ! [SY2566: $i] :
                ( ( setadjoin @ ( setadjoin @ SV73 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV73 @ ( setadjoin @ SV316 @ emptyset ) ) @ emptyset ) )
               != ( setadjoin @ ( setadjoin @ SY2565 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2565 @ ( setadjoin @ SY2566 @ emptyset ) ) @ emptyset ) ) )
            | ( SV73 = SY2565 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[881]) ).

thf(1150,plain,
    ! [SV317: $i,SV74: $i] :
      ( ( ! [SY2567: $i] :
            ( ~ ( in @ SY2567 @ ( cartprod @ SV74 @ SV317 ) )
            | ( in @ ( kfst @ SY2567 ) @ SV74 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[882]) ).

thf(1151,plain,
    ! [SV318: $i,SV75: $i] :
      ( ( ( kfst @ ( kpair @ SV75 @ SV318 ) )
        = SV75 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[883]) ).

thf(1152,plain,
    ! [SV76: $i] :
      ( ( ( ~ ( singleton @ SV76 ) )
        = $true )
      | ( ( in @ ( setunion @ SV76 ) @ SV76 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[884]) ).

thf(1153,plain,
    ! [SV77: $i] :
      ( ( ( ~ ( iskpair @ SV77 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ ( setunion @ SV77 )
            @ ^ [SY2089: $i] : ( in @ ( setadjoin @ SY2089 @ emptyset ) @ SV77 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[885]) ).

thf(1154,plain,
    ! [SV319: $i,SV78: $i] :
      ( ( ! [SY2568: $i] :
            ( ~ ( in @ ( setadjoin @ SY2568 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV78 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV78 @ ( setadjoin @ SV319 @ emptyset ) ) @ emptyset ) ) )
            | ( SV78 = SY2568 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[886]) ).

thf(1155,plain,
    ! [SV320: $i,SV79: $i] :
      ( ( ( ( setadjoin @ SV79 @ emptyset )
         != ( setadjoin @ SV320 @ emptyset ) )
        | ( SV79 = SV320 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[887]) ).

thf(1156,plain,
    ! [SV321: $i,SV83: $i] :
      ( ( ! [SY2569: $i] :
            ( ~ ( in @ SY2569 @ ( cartprod @ SV83 @ SV321 ) )
            | ( iskpair @ SY2569 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[891]) ).

thf(1157,plain,
    ! [SV322: $i,SV84: $i] :
      ( ( ! [SY2570: $i] :
            ( ~ ( in @ SY2570 @ SV84 )
            | ! [SY2571: $i] :
                ( ~ ( in @ SY2571 @ SV322 )
                | ( in @ ( kpair @ SY2570 @ SY2571 ) @ ( cartprod @ SV84 @ SV322 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[892]) ).

thf(1158,plain,
    ! [SV323: $i,SV85: $i] :
      ( ( ! [SY2572: $i] :
            ( ~ ( in @ SY2572 @ SV85 )
            | ! [SY2573: $i] :
                ( ~ ( in @ SY2573 @ SV323 )
                | ( in @ ( kpair @ SY2572 @ SY2573 ) @ ( powerset @ ( powerset @ ( binunion @ SV85 @ SV323 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[893]) ).

thf(1159,plain,
    ! [SV324: $i,SV86: $i] :
      ( ( ! [SY2574: $i] :
            ( ~ ( in @ SY2574 @ SV86 )
            | ! [SY2575: $i] :
                ( ~ ( in @ SY2575 @ SV324 )
                | ( in @ ( setadjoin @ ( setadjoin @ SY2574 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2574 @ ( setadjoin @ SY2575 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV86 @ SV324 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[894]) ).

thf(1160,plain,
    ! [SV325: $i,SV87: $i] :
      ( ( ! [SY2576: $i] :
            ( ~ ( in @ SY2576 @ SV87 )
            | ! [SY2577: $i] :
                ( ~ ( in @ SY2577 @ SV325 )
                | ( subset @ ( setadjoin @ ( setadjoin @ SY2576 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2576 @ ( setadjoin @ SY2577 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV87 @ SV325 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[895]) ).

thf(1161,plain,
    ! [SV326: $i,SV88: $i] :
      ( ( ! [SY2578: $i] :
            ( ~ ( in @ SY2578 @ SV88 )
            | ! [SY2579: $i] :
                ( ~ ( in @ SY2579 @ SV326 )
                | ( in @ ( setadjoin @ SY2578 @ ( setadjoin @ SY2579 @ emptyset ) ) @ ( powerset @ ( binunion @ SV88 @ SV326 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[896]) ).

thf(1162,plain,
    ! [SV327: $i,SV89: $i] :
      ( ( ! [SY2580: $i] :
            ( ~ ( in @ SY2580 @ SV89 )
            | ! [SY2581: $i] :
                ( ~ ( in @ SY2581 @ SV327 )
                | ( subset @ ( setadjoin @ SY2580 @ ( setadjoin @ SY2581 @ emptyset ) ) @ ( binunion @ SV89 @ SV327 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[897]) ).

thf(1163,plain,
    ! [SV328: $i,SV90: $i] :
      ( ( ! [SY2582: $i] :
            ( ~ ( in @ SY2582 @ ( setadjoin @ SV90 @ ( setadjoin @ SV328 @ emptyset ) ) )
            | ( SY2582 = SV90 )
            | ( SY2582 = SV328 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[898]) ).

thf(1164,plain,
    ! [SV329: $i,SV91: $i] :
      ( ( ! [SY2583: $i] :
            ( ~ ( in @ SY2583 @ SV91 )
            | ( in @ ( setadjoin @ SY2583 @ emptyset ) @ ( powerset @ ( binunion @ SV91 @ SV329 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[899]) ).

thf(1165,plain,
    ! [SV92: $i,SV330: $i] :
      ( ( ~ ( in @ SV330 @ SV92 )
        | ( in @ ( setadjoin @ SV330 @ emptyset ) @ ( powerset @ SV92 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[900]) ).

thf(1166,plain,
    ! [SV93: $i,SV331: $i] :
      ( ( ~ ( in @ SV331 @ SV93 )
        | ( subset @ ( setadjoin @ SV331 @ emptyset ) @ SV93 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[901]) ).

thf(1167,plain,
    ! [SV332: $i,SV94: $i] :
      ( ( iskpair @ ( kpair @ SV94 @ SV332 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[902]) ).

thf(1168,plain,
    ! [SV333: $i,SV95: $i] :
      ( ( iskpair @ ( setadjoin @ ( setadjoin @ SV95 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV95 @ ( setadjoin @ SV333 @ emptyset ) ) @ emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[903]) ).

thf(1169,plain,
    ! [SV96: $i,SV334: $i] :
      ( ( in @ SV334 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV96 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV96 @ ( setadjoin @ SV334 @ emptyset ) ) @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[904]) ).

thf(1170,plain,
    ! [SV335: $i,SV97: $i] :
      ( ( in @ SV97 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV97 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV97 @ ( setadjoin @ SV335 @ emptyset ) ) @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[905]) ).

thf(1171,plain,
    ! [SV98: $i,SV336: $i] :
      ( ( in @ SV336 @ ( setadjoin @ SV98 @ ( setadjoin @ SV336 @ emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[906]) ).

thf(1172,plain,
    ! [SV337: $i,SV99: $i] :
      ( ( ! [SY2584: $i] :
            ( ( in @ SY2584 @ SV99 )
            | ( in @ SY2584 @ SV337 )
            | ~ ( in @ SY2584 @ ( symdiff @ SV99 @ SV337 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[907]) ).

thf(1173,plain,
    ! [SV338: $i,SV100: $i] :
      ( ( ! [SY2585: $i] :
            ( ~ ( in @ SY2585 @ SV100 )
            | ~ ( in @ SY2585 @ SV338 )
            | ~ ( in @ SY2585 @ ( symdiff @ SV100 @ SV338 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[908]) ).

thf(1174,plain,
    ! [SV339: $i,SV101: $i] :
      ( ( ! [SY2586: $i] :
            ( ( in @ SY2586 @ SV101 )
            | ~ ( in @ SY2586 @ SV339 )
            | ( in @ SY2586 @ ( symdiff @ SV101 @ SV339 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[909]) ).

thf(1175,plain,
    ! [SV340: $i,SV102: $i] :
      ( ( ! [SY2587: $i] :
            ( ~ ( in @ SY2587 @ SV102 )
            | ( in @ SY2587 @ SV340 )
            | ( in @ SY2587 @ ( symdiff @ SV102 @ SV340 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[910]) ).

thf(1176,plain,
    ! [SV341: $i,SV103: $i] :
      ( ( ( ( setminus @ SV103 @ SV341 )
         != emptyset )
        | ( subset @ SV103 @ SV341 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[911]) ).

thf(1177,plain,
    ! [SV342: $i,SV104: $i] :
      ( ( subset @ ( setminus @ SV104 @ SV342 ) @ SV104 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[912]) ).

thf(1178,plain,
    ! [SV105: $i,SV343: $i] :
      ( ( ! [SY2588: $i] :
            ( ~ ( in @ SY2588 @ SV343 )
            | ~ ( in @ SY2588 @ ( setminus @ SV105 @ SV343 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[913]) ).

thf(1179,plain,
    ! [SV344: $i,SV106: $i] :
      ( ( ! [SY2589: $i] :
            ( ( in @ SY2589 @ SV106 )
            | ~ ( in @ SY2589 @ ( setminus @ SV106 @ SV344 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[914]) ).

thf(1180,plain,
    ! [SV345: $i,SV107: $i] :
      ( ( ! [SY2590: $i] :
            ( ( in @ SY2590 @ ( setminus @ SV107 @ SV345 ) )
            | ( in @ SY2590 @ SV345 )
            | ~ ( in @ SY2590 @ SV107 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[915]) ).

thf(1181,plain,
    ! [SV346: $i,SV108: $i] :
      ( ( ! [SY2591: $i] :
            ( ( in @ SY2591 @ ( setminus @ SV108 @ SV346 ) )
            | ~ ( in @ SY2591 @ SV108 )
            | ( in @ SY2591 @ SV346 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[916]) ).

thf(1182,plain,
    ! [SV347: $i,SV109: $i] :
      ( ( ~ ( subset @ SV109 @ SV347 )
        | ( ( setminus @ SV109 @ SV347 )
          = emptyset ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[917]) ).

thf(1183,plain,
    ! [SV348: $i,SV110: $i] :
      ( ( ! [SY2592: $i] :
            ( ~ ( in @ SY2592 @ ( setminus @ SV110 @ SV348 ) )
            | ~ ( in @ SY2592 @ SV348 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[918]) ).

thf(1184,plain,
    ! [SV349: $i,SV111: $i] :
      ( ( ! [SY2593: $i] :
            ( ~ ( in @ SY2593 @ ( setminus @ SV111 @ SV349 ) )
            | ( in @ SY2593 @ SV111 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[919]) ).

thf(1185,plain,
    ! [SV350: $i,SV112: $i] :
      ( ( ! [SY2594: $i] :
            ( ~ ( in @ SY2594 @ SV112 )
            | ( in @ SY2594 @ SV350 )
            | ( in @ SY2594 @ ( setminus @ SV112 @ SV350 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[920]) ).

thf(1186,plain,
    ! [SV351: $i,SV113: $i] :
      ( ( ! [SY2595: $i] :
            ( ( binintersect @ SV113 @ ( binunion @ SV351 @ SY2595 ) )
            = ( binunion @ ( binintersect @ SV113 @ SV351 ) @ ( binintersect @ SV113 @ SY2595 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[921]) ).

thf(1187,plain,
    ! [SV352: $i,SV114: $i] :
      ( ( ( ( binintersect @ SV114 @ SV352 )
         != SV114 )
        | ( subset @ SV114 @ SV352 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[922]) ).

thf(1188,plain,
    ! [SV115: $i,SV353: $i] :
      ( ( ~ ( subset @ SV353 @ SV115 )
        | ( ( binintersect @ SV115 @ SV353 )
          = SV353 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[923]) ).

thf(1189,plain,
    ! [SV354: $i,SV116: $i] :
      ( ( subset @ ( binintersect @ SV116 @ SV354 ) @ SV354 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[924]) ).

thf(1190,plain,
    ! [SV355: $i,SV117: $i] :
      ( ( ! [SY2596: $i] :
            ( ~ ( in @ SY2596 @ ( binintersect @ SV117 @ SV355 ) )
            | ( in @ SY2596 @ SV355 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[925]) ).

thf(1191,plain,
    ! [SV356: $i,SV118: $i] :
      ( ( ( ( binintersect @ SV118 @ SV356 )
         != SV356 )
        | ( subset @ SV356 @ SV118 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[926]) ).

thf(1192,plain,
    ! [SV357: $i,SV119: $i] :
      ( ( ~ ( subset @ SV119 @ SV357 )
        | ( ( binintersect @ SV119 @ SV357 )
          = SV119 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[927]) ).

thf(1193,plain,
    ! [SV358: $i,SV120: $i] :
      ( ( subset @ ( binintersect @ SV120 @ SV358 ) @ SV120 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[928]) ).

thf(1194,plain,
    ! [SV359: $i,SV121: $i] :
      ( ( ! [SY2597: $i] :
            ( ~ ( in @ SY2597 @ ( binintersect @ SV121 @ SV359 ) )
            | ( in @ SY2597 @ SV121 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[929]) ).

thf(1195,plain,
    ! [SV360: $i,SV122: $i] :
      ( ( ! [SY2598: $i] :
            ( ~ ( subset @ SY2598 @ SV122 )
            | ~ ( subset @ SY2598 @ SV360 )
            | ( subset @ SY2598 @ ( binintersect @ SV122 @ SV360 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[930]) ).

thf(1196,plain,
    ! [SV361: $i,SV123: $i] :
      ( ( ! [SY2599: $i] :
            ( ~ ( in @ SY2599 @ SV123 )
            | ~ ( in @ SY2599 @ SV361 )
            | ( in @ SY2599 @ ( binintersect @ SV123 @ SV361 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[931]) ).

thf(1197,plain,
    ! [SV124: $i,SV362: $i] :
      ( ( subset @ SV362 @ ( binunion @ SV124 @ SV362 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[932]) ).

thf(1198,plain,
    ! [SV363: $i,SV125: $i] :
      ( ( subset @ SV125 @ ( binunion @ SV125 @ SV363 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[933]) ).

thf(1199,plain,
    ! [SV364: $i,SV126: $i] :
      ( ( ! [SY2600: $i] :
            ( ~ ( in @ SY2600 @ ( binunion @ SV126 @ SV364 ) )
            | ( in @ SY2600 @ SV126 )
            | ( in @ SY2600 @ SV364 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[934]) ).

thf(1200,plain,
    ! [SV127: $i,SV365: $i] :
      ( ( ! [SY2601: $i] :
            ( ~ ( in @ SY2601 @ SV365 )
            | ( in @ SY2601 @ ( binunion @ SV127 @ SV365 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[935]) ).

thf(1201,plain,
    ! [SV128: $i,SV366: $i] :
      ( ( in @ SV366 @ ( setadjoin @ SV128 @ ( setadjoin @ SV366 @ emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[936]) ).

thf(1202,plain,
    ! [SV367: $i,SV129: $i] :
      ( ( ! [SY2602: $i] :
            ( ~ ( in @ SY2602 @ SV129 )
            | ( in @ SY2602 @ ( binunion @ SV129 @ SV367 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[937]) ).

thf(1203,plain,
    ! [SV368: $i > $o,SV130: $i] :
      ( ( subset
        @ ( dsetconstr @ SV130
          @ ^ [SY2603: $i] : ( SV368 @ SY2603 ) )
        @ SV130 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[938]) ).

thf(1204,plain,
    ! [SV369: $i > $o,SV131: $i] :
      ( ( in
        @ ( dsetconstr @ SV131
          @ ^ [SY2604: $i] : ( SV369 @ SY2604 ) )
        @ ( powerset @ SV131 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[939]) ).

thf(1205,plain,
    ! [SV370: $i,SV132: $i] :
      ( ( ~ ( subset @ SV132 @ SV370 )
        | ( subset @ ( powerset @ SV132 ) @ ( powerset @ SV370 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[940]) ).

thf(1206,plain,
    ! [SV134: $i,SV371: $i] :
      ( ( ~ ( in @ SV371 @ ( powerset @ SV134 ) )
        | ( subset @ SV371 @ SV134 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[942]) ).

thf(1207,plain,
    ! [SV135: $i,SV372: $i] :
      ( ( ~ ( subset @ SV372 @ SV135 )
        | ( in @ SV372 @ ( powerset @ SV135 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[943]) ).

thf(1208,plain,
    ! [SV136: $i] :
      ( ( ( ~ ( subset @ SV136 @ emptyset ) )
        = $true )
      | ( ( SV136 = emptyset )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[944]) ).

thf(1209,plain,
    ! [SV373: $i,SV137: $i] :
      ( ( ~ ( subset @ SV137 @ SV373 )
        | ~ ( subset @ SV373 @ SV137 )
        | ( SV137 = SV373 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[945]) ).

thf(1210,plain,
    ! [SV374: $i,SV138: $i] :
      ( ( ~ ( subset @ SV138 @ SV374 )
        | ( in @ SV138 @ ( powerset @ SV374 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[946]) ).

thf(1211,plain,
    ! [SV375: $i,SV139: $i] :
      ( ( ! [SY2605: $i] :
            ( ~ ( subset @ SV139 @ SY2605 )
            | ( subset @ SV139 @ ( setadjoin @ SV375 @ SY2605 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[947]) ).

thf(1212,plain,
    ! [SV140: $i,SV376: $i] :
      ( ( subset @ SV376 @ ( setadjoin @ SV140 @ SV376 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[948]) ).

thf(1213,plain,
    ! [SV377: $i,SV141: $i] :
      ( ( ~ ( subset @ SV141 @ SV377 )
        | ! [SY2606: $i] :
            ( ~ ( subset @ SV377 @ SY2606 )
            | ( subset @ SV141 @ SY2606 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[949]) ).

thf(1214,plain,
    ! [SV378: $i,SV143: $i] :
      ( ( ! [SY2607: $i] :
            ( ~ ( in @ SY2607 @ SV143 )
            | ( in @ SY2607 @ SV378 )
            | ( SV143 != SV378 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[951]) ).

thf(1215,plain,
    ! [SV379: $i,SV144: $i] :
      ( ( ( subset @ SV144 @ SV379 )
        | ( SV144 != SV379 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[952]) ).

thf(1216,plain,
    ! [SV380: $i,SV145: $i] :
      ( ( ! [SY2608: $i] :
            ( ~ ( in @ SY2608 @ SV145 )
            | ( in @ SY2608 @ SV380 )
            | ~ ( subset @ SV145 @ SV380 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[953]) ).

thf(1217,plain,
    ! [SV381: $i,SV146: $i] :
      ( ( ~ ( subset @ SV146 @ SV381 )
        | ! [SY2609: $i] :
            ( ( in @ SY2609 @ SV381 )
            | ~ ( in @ SY2609 @ SV146 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[954]) ).

thf(1218,plain,
    ! [SV382: $i,SV147: $i] :
      ( ( ~ ( subset @ SV147 @ SV382 )
        | ! [SY2610: $i] :
            ( ~ ( in @ SY2610 @ SV147 )
            | ( in @ SY2610 @ SV382 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[955]) ).

thf(1219,plain,
    ! [SV383: $i,SV149: $i] :
      ( ( ( SV149 != SV383 )
        | ( subset @ SV149 @ SV383 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[957]) ).

thf(1220,plain,
    ! [SV384: $i,SV150: $i] :
      ( ( ( SV150 != SV384 )
        | ( subset @ SV384 @ SV150 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[958]) ).

thf(1221,plain,
    ! [SV385: $i,SV151: $i] :
      ( ( ( SV151 != SV385 )
        | ( ( setunion @ SV151 )
          = ( setunion @ SV385 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[959]) ).

thf(1222,plain,
    ! [SV386: $i,SV152: $i] :
      ( ( ( SV152 != SV386 )
        | ( ( powerset @ SV152 )
          = ( powerset @ SV386 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[960]) ).

thf(1223,plain,
    ! [SV387: $i,SV153: $i] :
      ( ( ( SV153 != SV387 )
        | ! [SY2611: $i,SY2612: $i] :
            ( ( SY2611 != SY2612 )
            | ( ( setadjoin @ SV153 @ SY2611 )
              = ( setadjoin @ SV387 @ SY2612 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[961]) ).

thf(1224,plain,
    ! [SV388: $i,SV154: $i] :
      ( ( ( SV154 != SV388 )
        | ! [SY2613: $i,SY2614: $i] :
            ( ( SY2613 != SY2614 )
            | ~ ( in @ SY2613 @ SV154 )
            | ( in @ SY2614 @ SV388 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[962]) ).

thf(1225,plain,
    ! [SV155: $o] :
      ( ( ( ~ SV155 ) = $true )
      | ( ( set2prop @ ( prop2set @ SV155 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[963]) ).

thf(1226,plain,
    ( ( ( ~ $true ) = $true )
    | ( ( set2prop @ ( prop2set @ $true ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[964]) ).

thf(1227,plain,
    ( ( ( ~ $false ) = $true )
    | ( ( set2prop @ ( prop2set @ $false ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[965]) ).

thf(1228,plain,
    ! [SV156: $o] :
      ( ( ( ~ SV156 ) = $true )
      | ( ( in @ emptyset @ ( prop2set @ SV156 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[966]) ).

thf(1229,plain,
    ( ( ( ~ $true ) = $true )
    | ( ( in @ emptyset @ ( prop2set @ $true ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[967]) ).

thf(1230,plain,
    ( ( ( ~ $false ) = $true )
    | ( ( in @ emptyset @ ( prop2set @ $false ) )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[968]) ).

thf(1231,plain,
    ! [SV157: $i > $o,SV389: $i] :
      ( ( ~ ( in @ SV389 @ emptyset )
        | ( SV157 @ SV389 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[969]) ).

thf(1232,plain,
    ! [SV158: $i,SV390: $i > $o] :
      ( ( ! [SY2615: $i] :
            ( ~ ( SV390 @ SY2615 )
            | ~ ( in @ SY2615 @ SV158 ) )
        | ( ( dsetconstr @ SV158
            @ ^ [SY2616: $i] : ( SV390 @ SY2616 ) )
         != emptyset ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[970]) ).

thf(1233,plain,
    ! [SV159: $i,SV391: $i] :
      ( ( in @ SV391 @ ( setadjoin @ SV159 @ ( setadjoin @ SV391 @ emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[971]) ).

thf(1234,plain,
    ! [SV392: $i,SV160: $i] :
      ( ( in @ SV160 @ ( setadjoin @ SV160 @ ( setadjoin @ SV392 @ emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[972]) ).

thf(1235,plain,
    ! [SV393: $i,SV161: $i] :
      ( ( ! [SY2617: $i] :
            ( ~ ( in @ SY2617 @ ( setadjoin @ SV161 @ ( setadjoin @ SV393 @ emptyset ) ) )
            | ( SY2617 = SV161 )
            | ( SY2617 = SV393 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[973]) ).

thf(1236,plain,
    ! [SV394: $i,SV162: $i] :
      ( ( ~ ( in @ SV162 @ ( setadjoin @ SV394 @ emptyset ) )
        | ( in @ SV394 @ ( setadjoin @ SV162 @ emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[974]) ).

thf(1237,plain,
    ! [SV395: $i,SV163: $i] :
      ( ( ( SV163 != SV395 )
        | ( in @ SV163 @ ( setadjoin @ SV395 @ emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[975]) ).

thf(1238,plain,
    ! [SV396: $i,SV164: $i] :
      ( ( ( SV164 = SV396 )
        | ~ ( in @ SV396 @ ( setadjoin @ SV164 @ emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[976]) ).

thf(1239,plain,
    ! [SV397: $i,SV165: $i] :
      ( ( ~ ( in @ SV165 @ ( setadjoin @ SV397 @ emptyset ) )
        | ( SV165 = SV397 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[977]) ).

thf(1240,plain,
    ! [SV166: $i] :
      ( ( ( SV166 = emptyset )
        = $true )
      | ( ( in @ ( sK34_Xx @ SV166 ) @ SV166 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[978]) ).

thf(1241,plain,
    ! [SV167: $i,SV398: $i] :
      ( ( ~ ( in @ SV398 @ SV167 )
        | ( in @ SV398 @ ( powerset @ ( setunion @ SV167 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[979]) ).

thf(1242,plain,
    ! [SV168: $i,SV399: $i] :
      ( ( ! [SY2618: $i] :
            ( ~ ( in @ SV399 @ SY2618 )
            | ~ ( in @ SY2618 @ SV168 )
            | ( in @ SV399 @ ( setunion @ SV168 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[980]) ).

thf(1243,plain,
    ! [SV169: $i,SV400: $i] :
      ( ( ~ ( in @ SV400 @ ( powerset @ SV169 ) )
        | ! [SY2619: $i] :
            ( ~ ( in @ SY2619 @ SV400 )
            | ( in @ SY2619 @ SV169 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[981]) ).

thf(1244,plain,
    ! [SV401: $i,SV173: $i] :
      ( ( ! [SY2620: $i] :
            ( ~ ( in @ SY2620 @ ( setadjoin @ SV173 @ SV401 ) )
            | ( SY2620 = SV173 )
            | ( in @ SY2620 @ SV401 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[985]) ).

thf(1245,plain,
    ! [SV174: $i,SV402: $i] :
      ( ( ! [SY2621: $i] :
            ( ~ ( in @ SY2621 @ SV402 )
            | ( in @ SY2621 @ ( setadjoin @ SV174 @ SV402 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[986]) ).

thf(1246,plain,
    ! [SV403: $i,SV175: $i] :
      ( ( in @ SV175 @ ( setadjoin @ SV175 @ SV403 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[987]) ).

thf(1247,plain,
    ! [SV176: $i] :
      ( ( ( ! [SY2230: $i] :
              ~ ( in @ SY2230 @ SV176 ) )
        = $true )
      | ( ( SV176 != emptyset )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[988]) ).

thf(1248,plain,
    ! [SV404: $i > $o,SV177: $i] :
      ( ( ! [SY2622: $i] :
            ( ~ ( in @ SY2622 @ SV177 )
            | ~ ( SV404 @ SY2622 )
            | ( ( dsetconstr @ SV177
                @ ^ [SY2623: $i] : ( SV404 @ SY2623 ) )
             != emptyset ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[989]) ).

thf(1249,plain,
    ! [SV178: $i] :
      ( ( ( SV178 = emptyset )
        = $true )
      | ( ( in @ ( sK29_Xx @ SV178 ) @ SV178 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[990]) ).

thf(1250,plain,
    ! [SV179: $i] :
      ( ( ( in @ ( sK28_Xx @ SV179 ) @ SV179 )
        = $true )
      | ( ( SV179 = emptyset )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[991]) ).

thf(1251,plain,
    ! [SV180: $i] :
      ( ( ( in @ ( sK27_Xx @ SV180 ) @ SV180 )
        = $true )
      | ( ( SV180 = emptyset )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[992]) ).

thf(1252,plain,
    ! [SV181: $i] :
      ( ( in @ SV181 @ emptyset )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[993]) ).

thf(1253,plain,
    ! [SV182: $i] :
      ( ( in @ SV182 @ emptyset )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[994]) ).

thf(1254,plain,
    ! [SV405: $i] :
      ( ( ( ~ ( in @ SV405 @ emptyset ) )
        = $true )
      | ( ( ! [Xphi: $o] : Xphi )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[995]) ).

thf(1255,plain,
    ! [SV183: $o] :
      ( ( ( ! [SY2234: $i] :
              ~ ( in @ SY2234 @ ( prop2set @ SV183 ) ) )
        = $true )
      | ( SV183 = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[996]) ).

thf(1256,plain,
    ( ( ( ! [SX0: $i] :
            ~ ( in @ SX0 @ ( prop2set @ $true ) ) )
      = $true )
    | ( $true = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[997]) ).

thf(1257,plain,
    ( ( ( ! [SX0: $i] :
            ~ ( in @ SX0 @ ( prop2set @ $false ) ) )
      = $true )
    | ( $false = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[998]) ).

thf(1258,plain,
    ! [SV406: $i > $o,SV184: $i] :
      ( ( ! [SY2624: $i] :
            ( ~ ( in @ SY2624
                @ ( dsetconstr @ SV184
                  @ ^ [SY2625: $i] : ( SV406 @ SY2625 ) ) )
            | ( SV406 @ SY2624 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[999]) ).

thf(1259,plain,
    ! [SV407: $i > $o,SV185: $i] :
      ( ( ! [SY2626: $i] :
            ( ~ ( in @ SY2626
                @ ( dsetconstr @ SV185
                  @ ^ [SY2627: $i] : ( SV407 @ SY2627 ) ) )
            | ( in @ SY2626 @ SV185 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1000]) ).

thf(1260,plain,
    ! [SV408: $i > $o,SV186: $i] :
      ( ( ! [SY2628: $i] :
            ( ~ ( in @ SY2628 @ SV186 )
            | ~ ( SV408 @ SY2628 )
            | ( in @ SY2628
              @ ( dsetconstr @ SV186
                @ ^ [SY2629: $i] : ( SV408 @ SY2629 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1001]) ).

thf(1261,plain,
    ! [SV187: $i] :
      ( ( ( ~ ( in @ SV187 @ omega ) )
        = $true )
      | ( ( in @ ( setadjoin @ SV187 @ SV187 ) @ omega )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1002]) ).

thf(1262,plain,
    ! [SV188: $i] :
      ( ( in @ SV188 @ emptyset )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1003]) ).

thf(1263,plain,
    ! [SV189: $i,SV409: $i] :
      ( ( ~ ( in @ SV409 @ ( powerset @ SV189 ) )
        | ! [SY2630: $i] :
            ( ~ ( in @ SY2630 @ ( powerset @ SV189 ) )
            | ~ ( ~ ( in @ ( sK97_Xx @ SY2630 @ SV409 @ SV189 ) @ SV189 )
                | ~ ~ ( ~ ( in @ ( sK97_Xx @ SY2630 @ SV409 @ SV189 ) @ SV409 )
                      | ~ ~ ( in @ ( sK97_Xx @ SY2630 @ SV409 @ SV189 ) @ SY2630 ) ) )
            | ( subset @ SV409 @ SY2630 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1004]) ).

thf(1264,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( ~ ( in @ ( sK7_Xx @ SX1 @ SX0 ) @ SX1 )
                | ~ ~ ( in @ ( sK7_Xx @ SX1 @ SX0 ) @ SX0 ) )
            | ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1005]) ).

thf(1265,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
            | ! [SX2: $i] :
                ( ~ ( in @ SX2 @ SX1 )
                | ( in @ SX2 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1005]) ).

thf(1266,plain,
    ! [SV190: $i > $o] :
      ( ( ( ! [SY2246: $i] :
              ( ~ ( ~ ( SV190 @ ( sK24_SY86 @ SY2246 @ SV190 ) )
                  | ~ ( ( SY2246
                       != ( sK24_SY86 @ SY2246 @ SV190 ) ) ) )
              | ~ ( SV190 @ SY2246 ) ) )
        = $true )
      | ( ( SV190 @ ( sK23_Xx @ SV190 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1006]) ).

thf(1267,plain,
    ! [SV410: $o,SV191: $i] :
      ( ( ! [SY2631: $i] :
            ( ~ ( in @ SY2631 @ SV191 )
            | ! [SY2632: $i] :
                ( ~ ( in @ SY2632 @ SV191 )
                | ~ SV410
                | ( in @ SY2631
                  @ ( dsetconstr @ SV191
                    @ ^ [SY2633: $i] :
                        ( ~ ( ~ SV410
                            | ( SY2633 != SY2631 ) )
                        | ~ ( ~ ~ SV410
                            | ( SY2633 != SY2632 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[1007]) ).

thf(1268,plain,
    ! [SV191: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV191 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV191 )
                | ~ $true
                | ( in @ SX0
                  @ ( dsetconstr @ SV191
                    @ ^ [SX2: $i] :
                        ( ~ ( ~ $true
                            | ( SX2 != SX0 ) )
                        | ~ ( ~ ~ $true
                            | ( SX2 != SX1 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[1007]) ).

thf(1269,plain,
    ! [SV191: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV191 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV191 )
                | ~ $false
                | ( in @ SX0
                  @ ( dsetconstr @ SV191
                    @ ^ [SX2: $i] :
                        ( ~ ( ~ $false
                            | ( SX2 != SX0 ) )
                        | ~ ( ~ ~ $false
                            | ( SX2 != SX1 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[1007]) ).

thf(1270,plain,
    ! [SV192: $i,SV411: $i] :
      ( ( ! [SY2634: $i > $i] :
            ( ~ ( ~ ( in @ ( sK92_Xx @ SY2634 @ SV411 @ SV192 ) @ SV192 )
                | ~ ~ ( in @ ( SY2634 @ ( sK92_Xx @ SY2634 @ SV411 @ SV192 ) ) @ SV411 ) )
            | ! [SY2635: $i] :
                ( ~ ( in @ SY2635 @ SV192 )
                | ( ( ap @ SV192 @ SV411
                    @ ( lam @ SV192 @ SV411
                      @ ^ [SX4: $i] : ( SY2634 @ SX4 ) )
                    @ SY2635 )
                  = ( SY2634 @ SY2635 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1008]) ).

thf(1271,plain,
    ! [SV412: $i,SV193: $i] :
      ( ( ! [SY2637: $i] :
            ( ~ ( in @ SY2637 @ ( cartprod @ SV193 @ SV412 ) )
            | ~ ( ~ ~ ( ( SY2637
                       != ( kpair @ ( sK67_Xx @ SY2637 @ SV412 @ SV193 ) @ ( sK68_SY1876 @ SY2637 @ SV412 @ SV193 ) ) )
                      | ~ ( in @ ( sK68_SY1876 @ SY2637 @ SV412 @ SV193 ) @ SV412 ) )
                | ~ ( in @ ( sK67_Xx @ SY2637 @ SV412 @ SV193 ) @ SV193 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1009]) ).

thf(1272,plain,
    ! [SV194: $i > $o] :
      ( ( ( ! [SY2257: $i] :
              ( ~ ( ~ ( SV194 @ ( sK57_SY248 @ SY2257 @ SV194 ) )
                  | ~ ( ( SY2257
                       != ( sK57_SY248 @ SY2257 @ SV194 ) ) ) )
              | ~ ( SV194 @ SY2257 ) ) )
        = $true )
      | ( ( ! [SY2258: $i] :
              ( ~ ( SV194 @ SY2258 )
              | ! [SY2259: $i] :
                  ( ~ ( SV194 @ SY2259 )
                  | ( SY2258 = SY2259 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1010]) ).

thf(1273,plain,
    ! [SV195: $i > $i > $o,SV413: $i] :
      ( ( ~ ( ~ ( in @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV413 )
            | ~ ! [SY2638: $i] :
                  ( ~ ( ~ ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SY2638 @ SV413 @ SV195 ) )
                      | ~ ( ( SY2638
                           != ( sK13_SY1837 @ SY2638 @ SV413 @ SV195 ) ) ) )
                  | ~ ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SY2638 ) ) )
        | ~ ( ~ ! [SY2639: $i] :
                  ( ! [SY2640: $i] :
                      ( ~ ( SV195 @ SY2640 @ SY2639 )
                      | ~ ( in @ SY2640 @ SV413 ) )
                  | ( in @ SY2639 @ ( sK10_B @ SV413 @ SV195 ) ) )
            | ~ ! [SY2641: $i] :
                  ( ~ ( in @ SY2641 @ ( sK10_B @ SV413 @ SV195 ) )
                  | ~ ( ~ ( SV195 @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SY2641 )
                      | ~ ( in @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SV413 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1011]) ).

thf(1274,plain,
    ! [SV414: $i,SV196: $i] :
      ( ( ! [SY2642: $i] :
            ( ~ ( in @ SY2642 @ ( setadjoin @ SV196 @ SV414 ) )
            | ~ ( ~ ~ ( ~ ( ( SY2642 = SV196 )
                          | ( in @ SY2642 @ SV414 )
                          | ! [SX3: $o] : SX3 )
                      | ~ ( ( SY2642 = SV196 )
                          | ! [SX3: $o] :
                              ( ~ SX3
                              | SX3 ) ) )
                | ~ ~ ( ~ ! [SY2645: $o] :
                            ( ~ SY2645
                            | ( in @ SY2642 @ SV414 )
                            | SY2645 )
                      | ~ ! [SX3: $o] :
                            ( ~ SX3
                            | ~ SX3
                            | SX3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1012]) ).

thf(1275,plain,
    ! [SV197: $i,SV415: $i] :
      ( ( ~ ( ~ ( in @ ( sK66_Xx @ SV415 @ SV197 ) @ SV197 )
            | ~ ( in @ ( sK66_Xx @ SV415 @ SV197 ) @ SV415 ) )
        | ( ( binintersect @ SV197 @ SV415 )
          = emptyset ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1013]) ).

thf(1276,plain,
    ! [SV198: $i] :
      ( ( ~ ! [SY2272: $i > $o,SY2273: $i] :
              ( ~ ( in @ SY2273 @ SV198 )
              | ~ ( SY2272 @ SY2273 )
              | ( in @ SY2273
                @ ( dsetconstr @ SV198
                  @ ^ [SX3: $i] : ( SY2272 @ SX3 ) ) ) )
        | ~ ! [SY2275: $i > $o,SY2276: $i] :
              ( ~ ( in @ SY2276 @ SV198 )
              | ~ ( in @ SY2276
                  @ ( dsetconstr @ SV198
                    @ ^ [SX3: $i] : ( SY2275 @ SX3 ) ) )
              | ( SY2275 @ SY2276 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1014]) ).

thf(1277,plain,
    ! [SV199: $i,SV416: $i] :
      ( ( ~ ( ~ ( in @ ( sK30_Xx @ SV416 @ SV199 ) @ SV416 )
            | ~ ~ ( in @ ( sK30_Xx @ SV416 @ SV199 ) @ SV199 ) )
        | ( in @ SV416 @ ( powerset @ SV199 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1015]) ).

thf(1278,plain,
    ! [SV417: $i > $o,SV200: $i] :
      ( ( ! [SY2647: $i] :
            ( ~ ( in @ SY2647 @ SV200 )
            | ( SV417 @ SY2647 ) )
        | ~ ( ~ ( in @ ( sK40_Xx @ SV417 @ SV200 ) @ SV200 )
            | ~ ~ ( SV417 @ ( sK40_Xx @ SV417 @ SV200 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1016]) ).

thf(1279,plain,
    ! [SV201: $i,SV418: $i] :
      ( ( ! [SY2648: $i > $i] :
            ( ~ ( ~ ( in @ ( sK78_Xx @ SY2648 @ SV418 @ SV201 ) @ SV201 )
                | ~ ~ ( in @ ( SY2648 @ ( sK78_Xx @ SY2648 @ SV418 @ SV201 ) ) @ SV418 ) )
            | ( in
              @ ( lam @ SV201 @ SV418
                @ ^ [SX3: $i] : ( SY2648 @ SX3 ) )
              @ ( funcSet @ SV201 @ SV418 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1017]) ).

thf(1280,plain,
    ! [SV419: $o,SV202: $i] :
      ( ( ! [SY2650: $i] :
            ( ~ ( in @ SY2650 @ SV202 )
            | ! [SY2651: $i] :
                ( ~ ( in @ SY2651 @ SV202 )
                | SV419
                | ( ( dsetconstr @ SV202
                    @ ^ [SY2652: $i] :
                        ( ~ ( ~ SV419
                            | ( SY2652 != SY2650 ) )
                        | ~ ( ~ ~ SV419
                            | ( SY2652 != SY2651 ) ) ) )
                  = ( setadjoin @ SY2651 @ emptyset ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[1018]) ).

thf(1281,plain,
    ! [SV202: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV202 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV202 )
                | $true
                | ( ( dsetconstr @ SV202
                    @ ^ [SX2: $i] :
                        ( ~ ( ~ $true
                            | ( SX2 != SX0 ) )
                        | ~ ( ~ ~ $true
                            | ( SX2 != SX1 ) ) ) )
                  = ( setadjoin @ SX1 @ emptyset ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[1018]) ).

thf(1282,plain,
    ! [SV202: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV202 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV202 )
                | $false
                | ( ( dsetconstr @ SV202
                    @ ^ [SX2: $i] :
                        ( ~ ( ~ $false
                            | ( SX2 != SX0 ) )
                        | ~ ( ~ ~ $false
                            | ( SX2 != SX1 ) ) ) )
                  = ( setadjoin @ SX1 @ emptyset ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[1018]) ).

thf(1283,plain,
    ( ( ~ ! [SX0: $i > $o,SX1: $i > $o] :
            ( ~ ( ( ( sK55_Xx @ SX1 @ SX0 )
                 != ( sK56_SY1873 @ SX1 @ SX0 ) )
                | ~ ~ ( ~ ( ~ ( SX0 @ ( sK55_Xx @ SX1 @ SX0 ) )
                          | ~ ( SX1 @ ( sK56_SY1873 @ SX1 @ SX0 ) ) )
                      | ~ ( ( SX0 @ ( sK55_Xx @ SX1 @ SX0 ) )
                          | ( SX1 @ ( sK56_SY1873 @ SX1 @ SX0 ) ) ) ) )
            | ! [SX2: $i] :
                ( ~ ( ~ ( SX0 @ ( sK54_SY233 @ SX2 @ SX1 @ SX0 ) )
                    | ~ ( ( SX2
                         != ( sK54_SY233 @ SX2 @ SX1 @ SX0 ) ) ) )
                | ~ ( SX0 @ SX2 ) )
            | ~ ( ~ ! [SX2: $i] :
                      ( ~ ( SX1 @ SX2 )
                      | ( ( sK53_SY235 @ SX1 @ SX0 )
                        = SX2 ) )
                | ~ ( SX1 @ ( sK53_SY235 @ SX1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1019]) ).

thf(1284,plain,
    ( ( ~ ! [SX0: $i > $o,SX1: $i > $o] :
            ( ~ ( ( ( sK51_Xx @ SX1 @ SX0 )
                 != ( sK52_SY1871 @ SX1 @ SX0 ) )
                | ~ ~ ( ~ ( ~ ( SX0 @ ( sK51_Xx @ SX1 @ SX0 ) )
                          | ~ ( SX1 @ ( sK52_SY1871 @ SX1 @ SX0 ) ) )
                      | ~ ( ( SX0 @ ( sK51_Xx @ SX1 @ SX0 ) )
                          | ( SX1 @ ( sK52_SY1871 @ SX1 @ SX0 ) ) ) ) )
            | ! [SX2: $i] :
                ( ~ ( ~ ( SX1 @ ( sK50_SY236 @ SX2 @ SX1 @ SX0 ) )
                    | ~ ( ( SX2
                         != ( sK50_SY236 @ SX2 @ SX1 @ SX0 ) ) ) )
                | ~ ( SX1 @ SX2 ) )
            | ~ ( ~ ! [SX2: $i] :
                      ( ~ ( SX0 @ SX2 )
                      | ( ( sK49_SY232 @ SX1 @ SX0 )
                        = SX2 ) )
                | ~ ( SX0 @ ( sK49_SY232 @ SX1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1019]) ).

thf(1285,plain,
    ! [SV203: $i,SV420: $i > $o] :
      ( ( ~ ( ~ ( SV420 @ ( sK39_Xx @ SV420 @ SV203 ) )
            | ~ ( in @ ( sK39_Xx @ SV420 @ SV203 ) @ SV203 ) )
        | ! [SY2653: $i] :
            ( ~ ( in @ SY2653 @ SV203 )
            | ~ ( SV420 @ SY2653 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1020]) ).

thf(1286,plain,
    ! [SV204: $i > $o] :
      ( ( ( ! [SY2290: $i] :
              ( ~ ( ~ ( SV204 @ ( sK20_SY57 @ SY2290 @ SV204 ) )
                  | ~ ( ( SY2290
                       != ( sK20_SY57 @ SY2290 @ SV204 ) ) ) )
              | ~ ( SV204 @ SY2290 ) ) )
        = $true )
      | ( ( SV204
          @ ( descr
            @ ^ [SY2291: $i] : ( SV204 @ SY2291 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1021]) ).

thf(1287,plain,
    ! [SV205: $i > $o] :
      ( ( ( ! [SY2292: $i] :
              ( ~ ( ~ ( SV205 @ ( sK42_Xy @ SY2292 @ SV205 ) )
                  | ~ ( ( SY2292
                       != ( sK42_Xy @ SY2292 @ SV205 ) ) ) )
              | ~ ( SV205 @ SY2292 ) ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2293: $i] :
                    ( ~ ( SV205 @ SY2293 )
                    | ( ( sK41_SY198 @ SV205 )
                      = SY2293 ) )
              | ~ ( SV205 @ ( sK41_SY198 @ SV205 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1022]) ).

thf(1288,plain,
    ! [SV206: $i,SV421: $i] :
      ( ( ! [SY2654: $i > $i] :
            ( ~ ( ~ ( in @ ( sK94_Xx @ SY2654 @ SV421 @ SV206 ) @ SV206 )
                | ~ ~ ( in @ ( SY2654 @ ( sK94_Xx @ SY2654 @ SV421 @ SV206 ) ) @ SV421 ) )
            | ! [SY2655: $i] :
                ( ~ ( in @ SY2655 @ SV206 )
                | ( ( ap @ SV206 @ SV421
                    @ ( lam @ SV206 @ SV421
                      @ ^ [SX4: $i] : ( SY2654 @ SX4 ) )
                    @ SY2655 )
                  = ( SY2654 @ SY2655 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1023]) ).

thf(1289,plain,
    ( ( ~ ( in @ sK2_SY1822 @ ( powerset @ sK1_A ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1024]) ).

thf(1290,plain,
    ( ( ~ ~ ( ~ ( in @ sK3_SY1826 @ ( powerset @ sK1_A ) )
            | ~ ~ ( ~ ( in @ sK4_SY1829 @ ( powerset @ sK1_A ) )
                  | ~ ~ ( ~ ( in @ sK5_SY1831 @ sK1_A )
                        | ~ ~ ( ~ ( in @ sK5_SY1831 @ ( binintersect @ sK2_SY1822 @ sK3_SY1826 ) )
                              | ~ ~ ( in @ sK5_SY1831 @ ( binunion @ sK3_SY1826 @ sK4_SY1829 ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1024]) ).

thf(1291,plain,
    ! [SV422: $i,SV207: $i] :
      ( ( ! [SY2657: $i] :
            ( ~ ( subset @ SY2657 @ ( cartprod @ SV207 @ SV422 ) )
            | ! [SY2658: $i > $o] :
                ( ~ ( ~ ( in @ ( sK81_Xx @ SY2658 @ SY2657 @ SV422 @ SV207 ) @ SV207 )
                    | ~ ~ ( ~ ( in @ ( sK82_SY1880 @ SY2658 @ SY2657 @ SV422 @ SV207 ) @ SV422 )
                          | ~ ~ ( ~ ( in @ ( kpair @ ( sK81_Xx @ SY2658 @ SY2657 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SY2658 @ SY2657 @ SV422 @ SV207 ) ) @ SY2657 )
                                | ~ ~ ( SY2658 @ ( kpair @ ( sK81_Xx @ SY2658 @ SY2657 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SY2658 @ SY2657 @ SV422 @ SV207 ) ) ) ) ) )
                | ! [SX4: $i] :
                    ( ~ ( in @ SX4 @ SY2657 )
                    | ( SY2658 @ SX4 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1025]) ).

thf(1292,plain,
    ! [SV423: $i,SV208: $i] :
      ( ( ! [SY2660: $i] :
            ( ~ ( subset @ SY2660 @ ( cartprod @ SV208 @ SV423 ) )
            | ! [SY2661: $i] :
                ( ~ ( subset @ SY2661 @ ( cartprod @ SV208 @ SV423 ) )
                | ~ ( ~ ( in @ ( sK84_Xx @ SY2661 @ SY2660 @ SV423 @ SV208 ) @ SV208 )
                    | ~ ~ ( ~ ( in @ ( sK85_SY1881 @ SY2661 @ SY2660 @ SV423 @ SV208 ) @ SV423 )
                          | ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SY2661 @ SY2660 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SY2661 @ SY2660 @ SV423 @ SV208 ) ) @ SY2660 )
                                | ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SY2661 @ SY2660 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SY2661 @ SY2660 @ SV423 @ SV208 ) ) @ SY2661 ) ) ) )
                | ( subset @ SY2660 @ SY2661 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1026]) ).

thf(1293,plain,
    ! [SV209: $i,SV424: $i > $o] :
      ( ( ~ ( ~ ( in @ ( sK70_Xx @ SV424 @ SV209 ) @ SV209 )
            | ~ ~ ( ~ ( in @ ( sK71_SY1877 @ SV424 @ SV209 ) @ SV209 )
                  | ~ ~ ( ~ ( SV424 @ ( sK70_Xx @ SV424 @ SV209 ) )
                        | ~ ~ ( ~ ( SV424 @ ( sK71_SY1877 @ SV424 @ SV209 ) )
                              | ~ ( ( ( sK70_Xx @ SV424 @ SV209 )
                                   != ( sK71_SY1877 @ SV424 @ SV209 ) ) ) ) ) ) )
        | ! [SY2662: $i] :
            ( ~ ( SV424 @ SY2662 )
            | ~ ( in @ SY2662 @ SV209 ) )
        | ( singleton
          @ ( dsetconstr @ SV209
            @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1027]) ).

thf(1294,plain,
    ! [SV425: $i,SV210: $i] :
      ( ( ( SV210 != SV425 )
        | ~ ( ~ ! [SY2664: $i,SY2665: $i] :
                  ( ( SY2664 != SY2665 )
                  | ~ ( in @ SY2664 @ SV210 )
                  | ( in @ SY2665 @ SV425 ) )
            | ~ ! [SY2666: $i,SY2667: $i] :
                  ( ( SY2666 != SY2667 )
                  | ~ ( in @ SY2667 @ SV425 )
                  | ( in @ SY2666 @ SV210 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1028]) ).

thf(1295,plain,
    ! [SV211: $i > $o] :
      ( ( ( ! [SY2313: $i] :
              ( ~ ( ~ ( SV211 @ ( sK48_SY224 @ SY2313 @ SV211 ) )
                  | ~ ( ( SY2313
                       != ( sK48_SY224 @ SY2313 @ SV211 ) ) ) )
              | ~ ( SV211 @ SY2313 ) ) )
        = $true )
      | ( ( ! [SY2314: $i] :
              ( ~ ( SV211 @ SY2314 )
              | ! [SY2315: $i] :
                  ( ~ ( SV211 @ SY2315 )
                  | ( SY2314 = SY2315 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1029]) ).

thf(1296,plain,
    ! [SV212: $i,SV426: $i] :
      ( ( ! [SY2668: $i > $i] :
            ( ~ ( ~ ( in @ ( sK77_Xx @ SY2668 @ SV426 @ SV212 ) @ SV212 )
                | ~ ~ ( in @ ( SY2668 @ ( sK77_Xx @ SY2668 @ SV426 @ SV212 ) ) @ SV426 ) )
            | ( func @ SV212 @ SV426
              @ ( lam @ SV212 @ SV426
                @ ^ [SX3: $i] : ( SY2668 @ SX3 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1030]) ).

thf(1297,plain,
    ! [SV213: $i > $o,SV427: $i > $o] :
      ( ( ~ ( ( ( sK60_Xx @ SV427 @ SV213 )
             != ( sK61_SY1874 @ SV427 @ SV213 ) )
            | ~ ~ ( ~ ( ~ ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
                      | ~ ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) ) )
                  | ~ ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
                      | ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) ) ) ) )
        | ! [SY2670: $i] :
            ( ~ ( ~ ( SV213 @ ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) )
                | ~ ( ( SY2670
                     != ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) ) ) )
            | ~ ( SV213 @ SY2670 ) )
        | ! [SY2671: $i] :
            ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                | ~ ( ( SY2671
                     != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
            | ~ ( SV427 @ SY2671 ) )
        | ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1031]) ).

thf(1298,plain,
    ! [SV214: $i,SV428: $i] :
      ( ( ~ ( in @ SV428 @ ( powerset @ SV214 ) )
        | ! [SY2674: $i] :
            ( ~ ( in @ SY2674 @ ( powerset @ SV214 ) )
            | ~ ( ~ ( in @ ( sK98_Xx @ SY2674 @ SV428 @ SV214 ) @ SV214 )
                | ~ ~ ( ~ ( in @ ( sK98_Xx @ SY2674 @ SV428 @ SV214 ) @ SV428 )
                      | ~ ~ ( in @ ( sK98_Xx @ SY2674 @ SV428 @ SV214 ) @ SY2674 ) ) )
            | ( in @ SV428 @ ( powerset @ SY2674 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1032]) ).

thf(1299,plain,
    ! [SV215: $i,SV429: $i] :
      ( ( ~ ( in @ SV429 @ ( setunion @ SV215 ) )
        | ! [SY2675: $o] :
            ( ~ ( ~ ( in @ SV429 @ ( sK31_B @ SY2675 @ SV429 @ SV215 ) )
                | ~ ~ ( ~ ( in @ ( sK31_B @ SY2675 @ SV429 @ SV215 ) @ SV215 )
                      | ~ ~ SY2675 ) )
            | SY2675 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1033]) ).

thf(1300,plain,
    ! [SV216: $i,SV430: $i] :
      ( ( ~ ( ~ ( in @ ( sK26_Xx @ SV430 @ SV216 ) @ SV216 )
            | ~ ~ ( in @ ( sK26_Xx @ SV430 @ SV216 ) @ SV430 ) )
        | ~ ( ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV430 )
            | ~ ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV216 ) )
        | ( SV216 = SV430 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1034]) ).

thf(1301,plain,
    ! [SV217: $i,SV431: $i] :
      ( ( ~ ( in @ SV431 @ ( setunion @ SV217 ) )
        | ~ ( ~ ( in @ ( sK69_X @ SV431 @ SV217 ) @ SV217 )
            | ~ ( in @ SV431 @ ( sK69_X @ SV431 @ SV217 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1035]) ).

thf(1302,plain,
    ! [SV432: $i,SV218: $i] :
      ( ( ! [SY2676: $i] :
            ( ~ ( func @ SV218 @ SV432 @ SY2676 )
            | ! [SY2677: $i] :
                ( ~ ( func @ SV218 @ SV432 @ SY2677 )
                | ~ ( ~ ( in @ ( sK83_Xx @ SY2677 @ SY2676 @ SV432 @ SV218 ) @ SV218 )
                    | ~ ( ( ( ap @ SV218 @ SV432 @ SY2676 @ ( sK83_Xx @ SY2677 @ SY2676 @ SV432 @ SV218 ) )
                         != ( ap @ SV218 @ SV432 @ SY2677 @ ( sK83_Xx @ SY2677 @ SY2676 @ SV432 @ SV218 ) ) ) ) )
                | ! [SY2678: $i] :
                    ( ~ ( in @ SY2678 @ SV218 )
                    | ! [SY2679: $i] :
                        ( ~ ( in @ SY2679 @ SV432 )
                        | ~ ( in @ ( kpair @ SY2678 @ SY2679 ) @ SY2677 )
                        | ( in @ ( kpair @ SY2678 @ SY2679 ) @ SY2676 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1036]) ).

thf(1303,plain,
    ! [SV219: $i,SV433: $i] :
      ( ( ~ ( in @ SV433 @ ( powerset @ SV219 ) )
        | ! [SY2680: $i] :
            ( ~ ( in @ SY2680 @ ( powerset @ SV219 ) )
            | ~ ( ~ ( in @ ( sK96_Xx @ SY2680 @ SV433 @ SV219 ) @ SV219 )
                | ~ ~ ( ~ ( in @ ( sK96_Xx @ SY2680 @ SV433 @ SV219 ) @ SV433 )
                      | ~ ~ ( in @ ( sK96_Xx @ SY2680 @ SV433 @ SV219 ) @ SY2680 ) ) )
            | ~ ( ~ ( in @ ( sK95_Xx @ SY2680 @ SV433 @ SV219 ) @ SV219 )
                | ~ ~ ( ~ ( in @ ( sK95_Xx @ SY2680 @ SV433 @ SV219 ) @ SY2680 )
                      | ~ ~ ( in @ ( sK95_Xx @ SY2680 @ SV433 @ SV219 ) @ SV433 ) ) )
            | ( SV433 = SY2680 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1037]) ).

thf(1304,plain,
    ! [SV434: $i > $o,SV220: $i] :
      ( ( ! [SY2681: $i] :
            ( ~ ( in @ SY2681 @ SV220 )
            | ~ ( SV434 @ SY2681 )
            | ~ ( ~ ( in @ ( sK73_Xy @ SY2681 @ SV434 @ SV220 ) @ SV220 )
                | ~ ~ ( ~ ( SV434 @ ( sK73_Xy @ SY2681 @ SV434 @ SV220 ) )
                      | ~ ( ( ( sK73_Xy @ SY2681 @ SV434 @ SV220 )
                           != SY2681 ) ) ) )
            | ( singleton
              @ ( dsetconstr @ SV220
                @ ^ [SY2682: $i] : ( SV434 @ SY2682 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1038]) ).

thf(1305,plain,
    ! [SV435: $i,SV221: $i] :
      ( ( ! [SY2683: $i] :
            ( ~ ( in @ SY2683 @ ( symdiff @ SV221 @ SV435 ) )
            | ~ ( ~ ~ ( ~ ( ( in @ SY2683 @ SV221 )
                          | ~ ( in @ SY2683 @ SV221 )
                          | ! [SX3: $o] : SX3 )
                      | ~ ~ ( ~ ( ( in @ SY2683 @ SV221 )
                                | ( in @ SY2683 @ SV435 )
                                | ! [SX3: $o] : SX3 )
                            | ~ ( ( in @ SY2683 @ SV221 )
                                | ! [SX3: $o] :
                                    ( ~ SX3
                                    | SX3 ) ) ) )
                | ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SY2683 @ SV435 )
                                | ~ ( in @ SY2683 @ SV221 )
                                | ! [SX3: $o] : SX3 )
                            | ~ ~ ( ~ ( ~ ( in @ SY2683 @ SV435 )
                                      | ( in @ SY2683 @ SV435 )
                                      | ! [SX3: $o] : SX3 )
                                  | ~ ( ~ ( in @ SY2683 @ SV435 )
                                      | ! [SX3: $o] :
                                          ( ~ SX3
                                          | SX3 ) ) ) )
                      | ~ ~ ( ~ ! [SY2348: $o] :
                                  ( ~ SY2348
                                  | ~ ( in @ SY2683 @ SV221 )
                                  | SY2348 )
                            | ~ ~ ( ~ ! [SY2691: $o] :
                                        ( ~ SY2691
                                        | ( in @ SY2683 @ SV435 )
                                        | SY2691 )
                                  | ~ ! [SX3: $o] :
                                        ( ~ SX3
                                        | ~ SX3
                                        | SX3 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1039]) ).

thf(1306,plain,
    ! [SV222: $i,SV436: $i] :
      ( ( ! [SY2693: $i > $i] :
            ( ~ ( ~ ( in @ ( sK76_Xx @ SY2693 @ SV436 @ SV222 ) @ SV222 )
                | ~ ~ ( in @ ( SY2693 @ ( sK76_Xx @ SY2693 @ SV436 @ SV222 ) ) @ SV436 ) )
            | ( func @ SV222 @ SV436
              @ ( dpsetconstr @ SV222 @ SV436
                @ ^ [SX3: $i,SX4: $i] :
                    ( ( SY2693 @ SX3 )
                    = SX4 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1040]) ).

thf(1307,plain,
    ! [SV223: $i] :
      ( ( ~ ! [SY2355: $i,SY2356: $i] :
              ( ~ ( in @ SY2356 @ ( setadjoin @ SV223 @ SY2355 ) )
              | ( SY2356 = SV223 )
              | ( in @ SY2356 @ SY2355 ) )
        | ~ ~ ( ~ ! [SY2357: $i,SY2358: $i] :
                    ( ( SY2358 != SV223 )
                    | ( in @ SY2358 @ ( setadjoin @ SV223 @ SY2357 ) ) )
              | ~ ! [SY2359: $i,SY2360: $i] :
                    ( ~ ( in @ SY2360 @ SY2359 )
                    | ( in @ SY2360 @ ( setadjoin @ SV223 @ SY2359 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1041]) ).

thf(1308,plain,
    ! [SV224: $i,SV437: $i] :
      ( ( ~ ( ~ ( in @ ( sK65_Xx @ SV437 @ SV224 ) @ SV224 )
            | ~ ~ ( in @ ( sK65_Xx @ SV437 @ SV224 ) @ SV437 ) )
        | ( subset @ SV224 @ SV437 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1042]) ).

thf(1309,plain,
    ! [SV225: $i,SV438: $i] :
      ( ( ~ ( ~ ( ~ ( in @ ( sK6_Xx @ SV438 @ SV225 ) @ SV225 )
                | ~ ( in @ ( sK6_Xx @ SV438 @ SV225 ) @ SV438 ) )
            | ~ ( ( in @ ( sK6_Xx @ SV438 @ SV225 ) @ SV225 )
                | ( in @ ( sK6_Xx @ SV438 @ SV225 ) @ SV438 ) ) )
        | ( SV225 = SV438 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1043]) ).

thf(1310,plain,
    ! [SV439: $i,SV226: $i] :
      ( ( ~ ( ~ ~ ( ~ ! [SY2696: $i] :
                        ( ~ ( in @ SY2696 @ ( binunion @ SV226 @ SV439 ) )
                        | ( in @ SY2696 @ SV226 )
                        | ( in @ SY2696 @ SV439 )
                        | ! [SX3: $o] : SX3 )
                  | ~ ! [SY2698: $i] :
                        ( ~ ( in @ SY2698 @ ( binunion @ SV226 @ SV439 ) )
                        | ( in @ SY2698 @ SV226 )
                        | ! [SX3: $o] :
                            ( ~ SX3
                            | SX3 ) ) )
            | ~ ~ ( ~ ! [SY2700: $i] :
                        ( ~ ( in @ SY2700 @ ( binunion @ SV226 @ SV439 ) )
                        | ! [SY2701: $o] :
                            ( ~ SY2701
                            | ( in @ SY2700 @ SV439 )
                            | SY2701 ) )
                  | ~ ( ! [SY2702: $i] :
                          ~ ( in @ SY2702 @ ( binunion @ SV226 @ SV439 ) )
                      | ! [SX2: $o] :
                          ( ~ SX2
                          | ~ SX2
                          | SX2 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1044]) ).

thf(1311,plain,
    ! [SV440: $i > $o,SV227: $i] :
      ( ( ! [SY2704: $i] :
            ( ~ ( in @ SY2704 @ SV227 )
            | ( SV440 @ SY2704 ) )
        | ~ ( ~ ( in @ ( sK38_Xx @ SV440 @ SV227 ) @ SV227 )
            | ~ ~ ( SV440 @ ( sK38_Xx @ SV440 @ SV227 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1045]) ).

thf(1312,plain,
    ! [SV228: $i > $o] :
      ( ( ( ! [SY2374: $i] :
              ~ ( ~ ( ( ( sK47_Xy @ SY2374 @ SV228 )
                     != SY2374 )
                    | ~ ( SV228 @ ( sK47_Xy @ SY2374 @ SV228 ) ) )
                | ~ ( ( ( sK47_Xy @ SY2374 @ SV228 )
                      = SY2374 )
                    | ( SV228 @ ( sK47_Xy @ SY2374 @ SV228 ) ) ) ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2375: $i] :
                    ( ~ ( SV228 @ SY2375 )
                    | ( ( sK46_SY211 @ SV228 )
                      = SY2375 ) )
              | ~ ( SV228 @ ( sK46_SY211 @ SV228 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1046]) ).

thf(1313,plain,
    ! [SV229: $i,SV441: $i > $o] :
      ( ( ~ ( ~ ( in @ ( sK74_Xx @ SV441 @ SV229 ) @ SV229 )
            | ~ ~ ( ~ ( in @ ( sK75_SY1878 @ SV441 @ SV229 ) @ SV229 )
                  | ~ ~ ( ~ ( SV441 @ ( sK74_Xx @ SV441 @ SV229 ) )
                        | ~ ~ ( ~ ( SV441 @ ( sK75_SY1878 @ SV441 @ SV229 ) )
                              | ~ ( ( ( sK74_Xx @ SV441 @ SV229 )
                                   != ( sK75_SY1878 @ SV441 @ SV229 ) ) ) ) ) ) )
        | ! [SY2705: $i] :
            ( ~ ( SV441 @ SY2705 )
            | ~ ( in @ SY2705 @ SV229 ) )
        | ( singleton
          @ ( dsetconstr @ SV229
            @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1047]) ).

thf(1314,plain,
    ! [SV442: $i,SV230: $i] :
      ( ( ! [SY2707: $i] :
            ( ~ ( subset @ SY2707 @ ( cartprod @ SV230 @ SV442 ) )
            | ! [SY2708: $i] :
                ( ~ ( subset @ SY2708 @ ( cartprod @ SV230 @ SV442 ) )
                | ~ ( ~ ( in @ ( sK88_Xx @ SY2708 @ SY2707 @ SV442 @ SV230 ) @ SV230 )
                    | ~ ~ ( ~ ( in @ ( sK89_SY1883 @ SY2708 @ SY2707 @ SV442 @ SV230 ) @ SV442 )
                          | ~ ~ ( ~ ( in @ ( kpair @ ( sK88_Xx @ SY2708 @ SY2707 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SY2708 @ SY2707 @ SV442 @ SV230 ) ) @ SY2707 )
                                | ~ ~ ( in @ ( kpair @ ( sK88_Xx @ SY2708 @ SY2707 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SY2708 @ SY2707 @ SV442 @ SV230 ) ) @ SY2708 ) ) ) )
                | ~ ( ~ ( in @ ( sK86_Xx @ SY2708 @ SY2707 @ SV442 @ SV230 ) @ SV230 )
                    | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SY2708 @ SY2707 @ SV442 @ SV230 ) @ SV442 )
                          | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SY2708 @ SY2707 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SY2708 @ SY2707 @ SV442 @ SV230 ) ) @ SY2708 )
                                | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SY2708 @ SY2707 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SY2708 @ SY2707 @ SV442 @ SV230 ) ) @ SY2707 ) ) ) )
                | ( SY2707 = SY2708 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1048]) ).

thf(1315,plain,
    ! [SV231: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_Xx @ SV231 ) @ omega )
                    | ~ ( in @ ( sK9_Xx @ SV231 ) @ SV231 ) )
              | ~ ~ ( in @ ( setadjoin @ ( sK9_Xx @ SV231 ) @ ( sK9_Xx @ SV231 ) ) @ SV231 ) )
          | ~ ( in @ emptyset @ SV231 ) )
        = $true )
      | ( ( ! [SY2382: $i] :
              ( ~ ( in @ SY2382 @ omega )
              | ( in @ SY2382 @ SV231 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1049]) ).

thf(1316,plain,
    ! [SV443: $o,SV232: $i] :
      ( ( ! [SY2709: $i] :
            ( ~ ( in @ SY2709 @ SV232 )
            | ! [SY2710: $i] :
                ( ~ ( in @ SY2710 @ SV232 )
                | SV443
                | ( in @ SY2710
                  @ ( dsetconstr @ SV232
                    @ ^ [SY2711: $i] :
                        ( ~ ( ~ SV443
                            | ( SY2711 != SY2709 ) )
                        | ~ ( ~ ~ SV443
                            | ( SY2711 != SY2710 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[1050]) ).

thf(1317,plain,
    ! [SV232: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV232 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV232 )
                | $true
                | ( in @ SX1
                  @ ( dsetconstr @ SV232
                    @ ^ [SX2: $i] :
                        ( ~ ( ~ $true
                            | ( SX2 != SX0 ) )
                        | ~ ( ~ ~ $true
                            | ( SX2 != SX1 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[1050]) ).

thf(1318,plain,
    ! [SV232: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV232 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV232 )
                | $false
                | ( in @ SX1
                  @ ( dsetconstr @ SV232
                    @ ^ [SX2: $i] :
                        ( ~ ( ~ $false
                            | ( SX2 != SX0 ) )
                        | ~ ( ~ ~ $false
                            | ( SX2 != SX1 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[1050]) ).

thf(1319,plain,
    ! [SV233: $i] :
      ( ( ~ ! [SY2387: $i] :
              ( ~ ( ~ ( in @ ( sK19_Xx @ SY2387 @ SV233 ) @ SY2387 )
                  | ~ ~ ( in @ ( sK19_Xx @ SY2387 @ SV233 ) @ SV233 ) )
              | ! [SX2: $i] :
                  ~ ( in @ SX2 @ SY2387 )
              | ~ ( ~ ! [SY2389: $i] :
                        ( ~ ( in @ SY2389 @ ( sK15_B @ SV233 ) )
                        | ! [SY2390: $i] :
                            ( ~ ( in @ SY2390 @ SY2389 )
                            | ( in @ SY2390 @ ( sK17_SY1842 @ SY2387 @ SV233 ) ) )
                        | ( in @ ( sK18_SY1856 @ SY2387 @ SV233 ) @ SY2389 ) )
                  | ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1842 @ SY2387 @ SV233 ) @ ( sK15_B @ SV233 ) )
                              | ~ ( in @ ( sK18_SY1856 @ SY2387 @ SV233 ) @ SY2387 ) )
                        | ~ ! [SY2391: $i] :
                              ( ~ ( in @ SY2391 @ ( sK17_SY1842 @ SY2387 @ SV233 ) )
                              | ~ ( in @ SY2391 @ SY2387 ) ) ) ) )
        | ~ ~ ( ~ ! [SY2392: $i,SY2393: $i] :
                    ( ~ ( in @ SY2392 @ ( sK15_B @ SV233 ) )
                    | ~ ( in @ SY2393 @ ( sK15_B @ SV233 ) )
                    | ! [SX3: $i] :
                        ( ~ ( in @ SX3 @ SY2392 )
                        | ( in @ SX3 @ SY2393 ) )
                    | ! [SX3: $i] :
                        ( ~ ( in @ SX3 @ SY2393 )
                        | ( in @ SX3 @ SY2392 ) ) )
              | ~ ~ ( ~ ! [SY2396: $i] :
                          ( ~ ( in @ SY2396 @ ( sK15_B @ SV233 ) )
                          | ! [SY2397: $i] :
                              ( ~ ( in @ SY2397 @ SY2396 )
                              | ( in @ SY2397 @ SV233 ) ) )
                    | ~ ! [SY2398: $i,SY2399: $i] :
                          ( ~ ( in @ SY2398 @ SV233 )
                          | ~ ( in @ SY2399 @ SV233 )
                          | ~ ( ~ ( in @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) @ ( sK15_B @ SV233 ) )
                              | ~ ~ ( ~ ( ~ ( in @ SY2398 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) )
                                        | ~ ( in @ SY2399 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) ) )
                                    | ~ ( ( in @ SY2398 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) )
                                        | ( in @ SY2399 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) ) ) ) )
                          | ( SY2398 = SY2399 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1051]) ).

thf(1320,plain,
    ! [SV234: $i,SV444: $i > $o] :
      ( ( ~ ( ~ ( SV444 @ ( sK37_Xx @ SV444 @ SV234 ) )
            | ~ ( in @ ( sK37_Xx @ SV444 @ SV234 ) @ SV234 ) )
        | ! [SY2712: $i] :
            ( ~ ( in @ SY2712 @ SV234 )
            | ~ ( SV444 @ SY2712 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1052]) ).

thf(1321,plain,
    ! [SV235: $i > $o] :
      ( ( ( ! [SY2402: $i] :
              ( ~ ( ~ ( SV235 @ ( sK33_SY142 @ SY2402 @ SV235 ) )
                  | ~ ( ( SY2402
                       != ( sK33_SY142 @ SY2402 @ SV235 ) ) ) )
              | ~ ( SV235 @ SY2402 ) ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2403: $i] :
                    ( ( SY2403
                     != ( sK32_Xx @ SV235 ) )
                    | ( SV235 @ SY2403 ) )
              | ~ ! [SY2404: $i] :
                    ( ~ ( SV235 @ SY2404 )
                    | ( SY2404
                      = ( sK32_Xx @ SV235 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1053]) ).

thf(1322,plain,
    ! [SV445: $i,SV236: $i] :
      ( ( ! [SY2713: $i] :
            ( ~ ( subset @ SY2713 @ ( cartprod @ SV236 @ SV445 ) )
            | ! [SY2714: $i > $o] :
                ( ~ ( ~ ( in @ ( sK79_Xx @ SY2714 @ SY2713 @ SV445 @ SV236 ) @ SV236 )
                    | ~ ~ ( ~ ( in @ ( sK80_SY1879 @ SY2714 @ SY2713 @ SV445 @ SV236 ) @ SV445 )
                          | ~ ~ ( ~ ( in @ ( kpair @ ( sK79_Xx @ SY2714 @ SY2713 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SY2714 @ SY2713 @ SV445 @ SV236 ) ) @ SY2713 )
                                | ~ ~ ( SY2714 @ ( kpair @ ( sK79_Xx @ SY2714 @ SY2713 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SY2714 @ SY2713 @ SV445 @ SV236 ) ) ) ) ) )
                | ! [SX4: $i] :
                    ( ~ ( in @ SX4 @ SY2713 )
                    | ( SY2714 @ SX4 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1054]) ).

thf(1323,plain,
    ! [SV446: $i > $o,SV237: $i] :
      ( ( ! [SY2716: $i] :
            ( ~ ( in @ SY2716 @ SV237 )
            | ( SV446 @ SY2716 ) )
        | ~ ( ~ ( in @ ( sK35_Xx @ SV446 @ SV237 ) @ SV237 )
            | ~ ~ ( SV446 @ ( sK35_Xx @ SV446 @ SV237 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1055]) ).

thf(1324,plain,
    ! [SV447: $o,SV238: $i] :
      ( ( ! [SY2717: $i] :
            ( ~ ( in @ SY2717 @ SV238 )
            | ! [SY2718: $i] :
                ( ~ ( in @ SY2718 @ SV238 )
                | ~ SV447
                | ( ( dsetconstr @ SV238
                    @ ^ [SY2719: $i] :
                        ( ~ ( ~ SV447
                            | ( SY2719 != SY2717 ) )
                        | ~ ( ~ ~ SV447
                            | ( SY2719 != SY2718 ) ) ) )
                  = ( setadjoin @ SY2717 @ emptyset ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[1056]) ).

thf(1325,plain,
    ! [SV238: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV238 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV238 )
                | ~ $true
                | ( ( dsetconstr @ SV238
                    @ ^ [SX2: $i] :
                        ( ~ ( ~ $true
                            | ( SX2 != SX0 ) )
                        | ~ ( ~ ~ $true
                            | ( SX2 != SX1 ) ) ) )
                  = ( setadjoin @ SX0 @ emptyset ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[1056]) ).

thf(1326,plain,
    ! [SV238: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV238 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV238 )
                | ~ $false
                | ( ( dsetconstr @ SV238
                    @ ^ [SX2: $i] :
                        ( ~ ( ~ $false
                            | ( SX2 != SX0 ) )
                        | ~ ( ~ ~ $false
                            | ( SX2 != SX1 ) ) ) )
                  = ( setadjoin @ SX0 @ emptyset ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[1056]) ).

thf(1327,plain,
    ! [SV239: $i] :
      ( ( ( ! [SY2415: $i] :
              ~ ( in @ SY2415 @ SV239 ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK14_B @ SV239 ) @ SV239 )
              | ~ ! [SY2416: $i] :
                    ( ~ ( in @ SY2416 @ ( sK14_B @ SV239 ) )
                    | ~ ( in @ SY2416 @ SV239 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1057]) ).

thf(1328,plain,
    ! [SV448: $o,SV240: $i] :
      ( ( ! [SY2720: $i] :
            ( ~ ( in @ SY2720 @ SV240 )
            | ! [SY2721: $i] :
                ( ~ ( in @ SY2721 @ SV240 )
                | ( singleton
                  @ ( dsetconstr @ SV240
                    @ ^ [SY2722: $i] :
                        ( ~ ( ~ SV448
                            | ( SY2722 != SY2720 ) )
                        | ~ ( ~ ~ SV448
                            | ( SY2722 != SY2721 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[1058]) ).

thf(1329,plain,
    ! [SV240: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV240 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV240 )
                | ( singleton
                  @ ( dsetconstr @ SV240
                    @ ^ [SX2: $i] :
                        ( ~ ( ~ $true
                            | ( SX2 != SX0 ) )
                        | ~ ( ~ ~ $true
                            | ( SX2 != SX1 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[1058]) ).

thf(1330,plain,
    ! [SV240: $i] :
      ( ( ! [SX0: $i] :
            ( ~ ( in @ SX0 @ SV240 )
            | ! [SX1: $i] :
                ( ~ ( in @ SX1 @ SV240 )
                | ( singleton
                  @ ( dsetconstr @ SV240
                    @ ^ [SX2: $i] :
                        ( ~ ( ~ $false
                            | ( SX2 != SX0 ) )
                        | ~ ( ~ ~ $false
                            | ( SX2 != SX1 ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[1058]) ).

thf(1331,plain,
    ! [SV241: $i > $o] :
      ( ( ( ! [SY2421: $i] :
              ~ ( SV241 @ SY2421 ) )
        = $true )
      | ( ( ~ ( ~ ( SV241 @ ( sK44_Xx @ SV241 ) )
              | ~ ~ ( ~ ( SV241 @ ( sK45_SY1868 @ SV241 ) )
                    | ~ ( ( ( sK44_Xx @ SV241 )
                         != ( sK45_SY1868 @ SV241 ) ) ) ) )
          | ~ ( ~ ! [SY2422: $i] :
                    ( ~ ( SV241 @ SY2422 )
                    | ( ( sK43_SY205 @ SV241 )
                      = SY2422 ) )
              | ~ ( SV241 @ ( sK43_SY205 @ SV241 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1059]) ).

thf(1332,plain,
    ! [SV242: $i,SV449: $i] :
      ( ( ~ ( ~ ( in @ ( sK64_Xx @ SV449 @ SV242 ) @ SV242 )
            | ~ ~ ( in @ ( sK64_Xx @ SV449 @ SV242 ) @ SV449 ) )
        | ( subset @ SV242 @ SV449 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1060]) ).

thf(1333,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ! [SX2: $i] :
                ( ~ ( in @ SX1 @ SX2 )
                | ~ ( in @ SX2 @ SX0 ) )
            | ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1061]) ).

thf(1334,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
            | ~ ( ~ ( in @ SX1 @ ( sK8_B @ SX1 @ SX0 ) )
                | ~ ( in @ ( sK8_B @ SX1 @ SX0 ) @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1061]) ).

thf(1335,plain,
    ! [SV450: $i,SV243: $i] :
      ( ( ! [SY2723: $i] :
            ( ~ ( func @ SV243 @ SV450 @ SY2723 )
            | ! [SY2724: $i] :
                ( ~ ( func @ SV243 @ SV450 @ SY2724 )
                | ~ ( ~ ( in @ ( sK90_Xx @ SY2724 @ SY2723 @ SV450 @ SV243 ) @ SV243 )
                    | ~ ( ( ( ap @ SV243 @ SV450 @ SY2723 @ ( sK90_Xx @ SY2724 @ SY2723 @ SV450 @ SV243 ) )
                         != ( ap @ SV243 @ SV450 @ SY2724 @ ( sK90_Xx @ SY2724 @ SY2723 @ SV450 @ SV243 ) ) ) ) )
                | ( SY2723 = SY2724 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1062]) ).

thf(1336,plain,
    ! [SV244: $i] :
      ( ( ( ! [SY2427: $i,SY2428: $i > $i] :
              ~ ( ~ ( in @ ( sK93_Xx @ SY2428 @ SY2427 @ SV244 ) @ SV244 )
                | ~ ~ ( in @ ( SY2428 @ ( sK93_Xx @ SY2428 @ SY2427 @ SV244 ) ) @ SY2427 ) ) )
        = $true )
      | ( $true = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1063]) ).

thf(1337,plain,
    ! [SV451: $i,SV245: $i] :
      ( ( ! [SY2725: $i] :
            ( ~ ( in @ SY2725 @ ( funcSet @ SV245 @ SV451 ) )
            | ! [SY2726: $i] :
                ( ~ ( in @ SY2726 @ ( funcSet @ SV245 @ SV451 ) )
                | ~ ( ~ ( in @ ( sK91_Xx @ SY2726 @ SY2725 @ SV451 @ SV245 ) @ SV245 )
                    | ~ ( ( ( ap @ SV245 @ SV451 @ SY2725 @ ( sK91_Xx @ SY2726 @ SY2725 @ SV451 @ SV245 ) )
                         != ( ap @ SV245 @ SV451 @ SY2726 @ ( sK91_Xx @ SY2726 @ SY2725 @ SV451 @ SV245 ) ) ) ) )
                | ( SY2725 = SY2726 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1064]) ).

thf(1338,plain,
    ! [SV246: $i,SV452: $i > $o] :
      ( ( ~ ( ~ ( in @ ( sK36_Xx @ SV452 @ SV246 ) @ SV246 )
            | ~ ( SV452 @ ( sK36_Xx @ SV452 @ SV246 ) ) )
        | ! [SY2727: $i] :
            ( ~ ( SV452 @ SY2727 )
            | ~ ( in @ SY2727 @ SV246 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1065]) ).

thf(1339,plain,
    ! [SV247: $i > $o] :
      ( ( ( ! [SY2434: $i] :
              ( ~ ( ~ ( SV247 @ ( sK22_SY74 @ SY2434 @ SV247 ) )
                  | ~ ( ( SY2434
                       != ( sK22_SY74 @ SY2434 @ SV247 ) ) ) )
              | ~ ( SV247 @ SY2434 ) ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2435: $i] :
                    ( ~ ( SV247 @ SY2435 )
                    | ( ( sK21_Xx @ SV247 )
                      = SY2435 ) )
              | ~ ( SV247 @ ( sK21_Xx @ SV247 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1066]) ).

thf(1340,plain,
    ! [SV453: $i,SV248: $i] :
      ( ( ( SV248 != SV453 )
        | ! [SY2728: $i > $o,SY2729: $i > $o] :
            ( ~ ( ~ ( in @ ( sK62_Xx @ SY2729 @ SY2728 @ SV453 @ SV248 ) @ SV248 )
                | ~ ~ ( ~ ( in @ ( sK63_SY1875 @ SY2729 @ SY2728 @ SV453 @ SV248 ) @ SV453 )
                      | ~ ~ ( ( ( sK62_Xx @ SY2729 @ SY2728 @ SV453 @ SV248 )
                             != ( sK63_SY1875 @ SY2729 @ SY2728 @ SV453 @ SV248 ) )
                            | ~ ~ ( ~ ( ~ ( SY2728 @ ( sK62_Xx @ SY2729 @ SY2728 @ SV453 @ SV248 ) )
                                      | ~ ( SY2729 @ ( sK63_SY1875 @ SY2729 @ SY2728 @ SV453 @ SV248 ) ) )
                                  | ~ ( ( SY2728 @ ( sK62_Xx @ SY2729 @ SY2728 @ SV453 @ SV248 ) )
                                      | ( SY2729 @ ( sK63_SY1875 @ SY2729 @ SY2728 @ SV453 @ SV248 ) ) ) ) ) ) )
            | ( ( dsetconstr @ SV248
                @ ^ [SX4: $i] : ( SY2728 @ SX4 ) )
              = ( dsetconstr @ SV453
                @ ^ [SX4: $i] : ( SY2729 @ SX4 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1067]) ).

thf(1341,plain,
    ! [SV454: $i > $o,SV249: $i] :
      ( ( ~ ( singleton
            @ ( dsetconstr @ SV249
              @ ^ [SY2732: $i] : ( SV454 @ SY2732 ) ) )
        | ~ ( ~ ( SV454 @ ( sK72_Xx @ SV454 @ SV249 ) )
            | ~ ( in @ ( sK72_Xx @ SV454 @ SV249 ) @ SV249 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1068]) ).

thf(1342,plain,
    ! [SV1: $i,SV250: $i] :
      ( ( ( ~ ( in @ SV250 @ ( powerset @ SV1 ) ) )
        = $true )
      | ( ( ! [SY2443: $i] :
              ( ~ ( in @ SY2443 @ ( powerset @ SV1 ) )
              | ! [SY2444: $i] :
                  ( ~ ( in @ SY2444 @ ( powerset @ SV1 ) )
                  | ! [SY2445: $i] :
                      ( ~ ( in @ SY2445 @ SV1 )
                      | ~ ( in @ SY2445 @ ( binintersect @ SV250 @ SY2443 ) )
                      | ( in @ SY2445 @ ( binunion @ SV250 @ SY2444 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1069]) ).

thf(1343,plain,
    ! [SV2: $i,SV251: $i] :
      ( ( ( ~ ( in @ SV251 @ ( powerset @ SV2 ) ) )
        = $true )
      | ( ( ! [SY2446: $i] :
              ( ~ ( in @ SY2446 @ ( powerset @ SV2 ) )
              | ! [SY2447: $i] :
                  ( ~ ( in @ SY2447 @ SV2 )
                  | ( in @ SY2447 @ ( binunion @ SV251 @ SY2446 ) )
                  | ~ ( in @ SY2447 @ SY2446 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1070]) ).

thf(1344,plain,
    ! [SV3: $i,SV252: $i] :
      ( ( ( ~ ( in @ SV252 @ ( powerset @ SV3 ) ) )
        = $true )
      | ( ( ! [SY2448: $i] :
              ( ~ ( in @ SY2448 @ ( powerset @ SV3 ) )
              | ! [SY2449: $i] :
                  ( ~ ( in @ SY2449 @ SV3 )
                  | ( in @ SY2449 @ ( binunion @ SV252 @ SY2448 ) )
                  | ~ ( in @ SY2449 @ SV252 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1071]) ).

thf(1345,plain,
    ! [SV4: $i,SV253: $i] :
      ( ( ( ~ ( in @ SV253 @ ( powerset @ SV4 ) ) )
        = $true )
      | ( ( ! [SY2450: $i] :
              ( ~ ( in @ SY2450 @ ( powerset @ SV4 ) )
              | ~ ( subset @ SV253 @ ( setminus @ SV4 @ SY2450 ) )
              | ( subset @ SY2450 @ ( setminus @ SV4 @ SV253 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1072]) ).

thf(1346,plain,
    ! [SV5: $i,SV254: $i] :
      ( ( ( ~ ( in @ SV254 @ ( powerset @ SV5 ) ) )
        = $true )
      | ( ( ! [SY2451: $i] :
              ( ~ ( in @ SY2451 @ ( powerset @ SV5 ) )
              | ~ ( subset @ SV254 @ ( setminus @ SV5 @ SY2451 ) )
              | ! [SY2452: $i] :
                  ( ~ ( in @ SY2452 @ SV5 )
                  | ~ ( in @ SY2452 @ SY2451 )
                  | ( in @ SY2452 @ ( setminus @ SV5 @ SV254 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1073]) ).

thf(1347,plain,
    ! [SV6: $i,SV255: $i] :
      ( ( ( ~ ( in @ SV255 @ ( powerset @ SV6 ) ) )
        = $true )
      | ( ( ! [SY2453: $i] :
              ( ~ ( in @ SY2453 @ ( powerset @ SV6 ) )
              | ( in @ ( setminus @ SV6 @ SV255 ) @ ( powerset @ ( setminus @ SV6 @ ( binintersect @ SV255 @ SY2453 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1074]) ).

thf(1348,plain,
    ! [SV7: $i,SV256: $i] :
      ( ( ( ~ ( in @ SV256 @ ( powerset @ SV7 ) ) )
        = $true )
      | ( ( ! [SY2454: $i] :
              ( ~ ( in @ SY2454 @ ( powerset @ SV7 ) )
              | ( subset @ ( setminus @ SV7 @ SV256 ) @ ( setminus @ SV7 @ ( binintersect @ SV256 @ SY2454 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1075]) ).

thf(1349,plain,
    ! [SV8: $i,SV257: $i] :
      ( ( ( ~ ( in @ SV257 @ ( powerset @ SV8 ) ) )
        = $true )
      | ( ( ! [SY2455: $i] :
              ( ~ ( in @ SY2455 @ ( powerset @ SV8 ) )
              | ! [SY2456: $i] :
                  ( ~ ( in @ SY2456 @ SV8 )
                  | ~ ( in @ SY2456 @ ( setminus @ SV8 @ SV257 ) )
                  | ( in @ SY2456 @ ( setminus @ SV8 @ ( binintersect @ SV257 @ SY2455 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1076]) ).

thf(1350,plain,
    ! [SV9: $i,SV258: $i] :
      ( ( ( ~ ( in @ SV258 @ ( powerset @ SV9 ) ) )
        = $true )
      | ( ( ! [SY2457: $i] :
              ( ~ ( in @ SY2457 @ ( powerset @ SV9 ) )
              | ! [SY2458: $i] :
                  ( ~ ( in @ SY2458 @ SV9 )
                  | ~ ( in @ SY2458 @ ( setminus @ SV9 @ SV258 ) )
                  | ~ ( in @ SY2458 @ ( binintersect @ SV258 @ SY2457 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1077]) ).

thf(1351,plain,
    ! [SV10: $i,SV259: $i] :
      ( ( ( ~ ( in @ SV259 @ ( powerset @ SV10 ) ) )
        = $true )
      | ( ( SV259
          = ( setminus @ SV10 @ ( setminus @ SV10 @ SV259 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1078]) ).

thf(1352,plain,
    ! [SV11: $i,SV260: $i] :
      ( ( ( ~ ( in @ SV260 @ ( powerset @ SV11 ) ) )
        = $true )
      | ( ( subset @ ( setminus @ SV11 @ ( setminus @ SV11 @ SV260 ) ) @ SV260 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1079]) ).

thf(1353,plain,
    ! [SV12: $i,SV261: $i] :
      ( ( ( ~ ( in @ SV261 @ ( powerset @ SV12 ) ) )
        = $true )
      | ( ( subset @ SV261 @ ( setminus @ SV12 @ ( setminus @ SV12 @ SV261 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1080]) ).

thf(1354,plain,
    ! [SV13: $i,SV262: $i] :
      ( ( ( ~ ( in @ SV262 @ ( powerset @ SV13 ) ) )
        = $true )
      | ( ( ! [SY2459: $i] :
              ( ~ ( in @ SY2459 @ SV13 )
              | ~ ( in @ SY2459 @ ( setminus @ SV13 @ ( setminus @ SV13 @ SV262 ) ) )
              | ( in @ SY2459 @ SV262 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1081]) ).

thf(1355,plain,
    ! [SV14: $i,SV263: $i] :
      ( ( ( ~ ( in @ SV263 @ ( powerset @ SV14 ) ) )
        = $true )
      | ( ( ! [SY2460: $i] :
              ( ~ ( in @ SY2460 @ SV14 )
              | ~ ( in @ SY2460 @ SV263 )
              | ( in @ SY2460 @ ( setminus @ SV14 @ ( setminus @ SV14 @ SV263 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1082]) ).

thf(1356,plain,
    ! [SV15: $i,SV264: $i] :
      ( ( ( ~ ( in @ SV264 @ ( powerset @ SV15 ) ) )
        = $true )
      | ( ( ! [SY2461: $i] :
              ( ~ ( in @ SY2461 @ ( powerset @ SV15 ) )
              | ~ ( subset @ ( setminus @ SV15 @ SY2461 ) @ ( setminus @ SV15 @ SV264 ) )
              | ( subset @ SV264 @ SY2461 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1083]) ).

thf(1357,plain,
    ! [SV16: $i,SV265: $i] :
      ( ( ( ~ ( in @ SV265 @ ( powerset @ SV16 ) ) )
        = $true )
      | ( ( ! [SY2462: $i] :
              ( ~ ( in @ SY2462 @ ( powerset @ SV16 ) )
              | ~ ( subset @ SV265 @ SY2462 )
              | ( subset @ ( setminus @ SV16 @ SY2462 ) @ ( setminus @ SV16 @ SV265 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1084]) ).

thf(1358,plain,
    ! [SV17: $i,SV266: $i] :
      ( ( ( ~ ( in @ SV266 @ ( powerset @ SV17 ) ) )
        = $true )
      | ( ( ! [SY2463: $i] :
              ( ~ ( in @ SY2463 @ ( powerset @ SV17 ) )
              | ! [SY2464: $i] :
                  ( ~ ( in @ SY2464 @ SV17 )
                  | ~ ( subset @ SV266 @ SY2463 )
                  | ( in @ SY2464 @ SY2463 )
                  | ~ ( in @ SY2464 @ SV266 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1085]) ).

thf(1359,plain,
    ! [SV18: $i,SV267: $i] :
      ( ( ( ~ ( in @ SV267 @ ( powerset @ SV18 ) ) )
        = $true )
      | ( ( ! [SY2465: $i] :
              ( ~ ( in @ SY2465 @ ( powerset @ SV18 ) )
              | ! [SY2466: $i] :
                  ( ~ ( in @ SY2466 @ SV18 )
                  | ~ ( subset @ SV267 @ ( setminus @ SV18 @ SY2465 ) )
                  | ~ ( in @ SY2466 @ SY2465 )
                  | ~ ( in @ SY2466 @ SV267 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1086]) ).

thf(1360,plain,
    ! [SV19: $i,SV268: $i] :
      ( ( ( ~ ( in @ SV268 @ ( powerset @ SV19 ) ) )
        = $true )
      | ( ( ! [SY2467: $i] :
              ( ~ ( in @ SY2467 @ ( powerset @ SV19 ) )
              | ! [SY2468: $i] :
                  ( ~ ( in @ SY2468 @ SV19 )
                  | ( in @ SY2468 @ SY2467 )
                  | ~ ( in @ SY2468 @ ( binintersect @ SV268 @ SY2467 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1087]) ).

thf(1361,plain,
    ! [SV20: $i,SV269: $i] :
      ( ( ( ~ ( in @ SV269 @ ( powerset @ SV20 ) ) )
        = $true )
      | ( ( ! [SY2469: $i] :
              ( ~ ( in @ SY2469 @ ( powerset @ SV20 ) )
              | ! [SY2470: $i] :
                  ( ~ ( in @ SY2470 @ SV20 )
                  | ( in @ SY2470 @ SV269 )
                  | ~ ( in @ SY2470 @ ( binintersect @ SV269 @ SY2469 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1088]) ).

thf(1362,plain,
    ! [SV21: $i,SV270: $i] :
      ( ( ( ~ ( in @ SV270 @ ( powerset @ SV21 ) ) )
        = $true )
      | ( ( ! [SY2471: $i] :
              ( ~ ( in @ SY2471 @ SV21 )
              | ( in @ SY2471 @ ( setminus @ SV21 @ SV270 ) )
              | ( in @ SY2471 @ SV270 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1089]) ).

thf(1363,plain,
    ! [SV22: $i,SV271: $i] :
      ( ( ( ~ ( in @ SV271 @ ( powerset @ SV22 ) ) )
        = $true )
      | ( ( ! [SY2472: $i] :
              ( ~ ( in @ SY2472 @ SV22 )
              | ~ ( in @ SY2472 @ SV271 )
              | ~ ( in @ SY2472 @ ( setminus @ SV22 @ SV271 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1090]) ).

thf(1364,plain,
    ! [SV23: $i,SV272: $i] :
      ( ( ( ~ ( in @ SV272 @ ( powerset @ SV23 ) ) )
        = $true )
      | ( ( ! [SY2473: $i] :
              ( ~ ( in @ SY2473 @ ( powerset @ SV23 ) )
              | ! [SY2474: $i] :
                  ( ~ ( in @ SY2474 @ SV23 )
                  | ~ ( in @ SV272 @ ( powerset @ SY2473 ) )
                  | ~ ( in @ SY2474 @ SV272 )
                  | ( in @ SY2474 @ SY2473 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1091]) ).

thf(1365,plain,
    ! [SV24: $i,SV273: $i] :
      ( ( ( ~ ( in @ SV273 @ ( powerset @ SV24 ) ) )
        = $true )
      | ( ( in @ ( setminus @ SV24 @ SV273 ) @ ( powerset @ SV24 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1092]) ).

thf(1366,plain,
    ! [SV25: $i,SV274: $i] :
      ( ( ( ~ ( in @ SV274 @ ( powerset @ SV25 ) ) )
        = $true )
      | ( ( ! [SY2475: $i] :
              ( ~ ( in @ SY2475 @ ( powerset @ SV25 ) )
              | ( in @ ( setminus @ SV274 @ SY2475 ) @ ( powerset @ SV25 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1093]) ).

thf(1367,plain,
    ! [SV26: $i,SV275: $i] :
      ( ( ( ~ ( in @ SV275 @ ( powerset @ SV26 ) ) )
        = $true )
      | ( ( in @ ( powerset @ SV275 ) @ ( powerset @ ( powerset @ SV26 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1094]) ).

thf(1368,plain,
    ! [SV27: $i,SV276: $i] :
      ( ( ( ~ ( in @ SV276 @ ( powerset @ SV27 ) ) )
        = $true )
      | ( ( ! [SY2476: $i] :
              ( ~ ( in @ SY2476 @ ( powerset @ SV27 ) )
              | ( in @ ( binunion @ SV276 @ SY2476 ) @ ( powerset @ SV27 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1095]) ).

thf(1369,plain,
    ! [SV28: $i,SV277: $i] :
      ( ( ( ~ ( in @ SV277 @ ( powerset @ SV28 ) ) )
        = $true )
      | ( ( ! [SY2477: $i] :
              ( ~ ( in @ SY2477 @ ( powerset @ SV28 ) )
              | ( in @ ( binintersect @ SV277 @ SY2477 ) @ ( powerset @ SV28 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1096]) ).

thf(1370,plain,
    ! [SV278: $o,SV29: $i,SV455: $i] :
      ( ( ~ ( in @ SV455 @ SV29 )
        | ! [SY2733: $i] :
            ( ~ ( in @ SY2733 @ SV29 )
            | ( in @ ( if @ SV29 @ SV278 @ SV455 @ SY2733 ) @ ( setadjoin @ SV455 @ ( setadjoin @ SY2733 @ emptyset ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1097]) ).

thf(1371,plain,
    ! [SV29: $i,SV456: $i] :
      ( ( ~ ( in @ SV456 @ SV29 )
        | ! [SY2734: $i] :
            ( ~ ( in @ SY2734 @ SV29 )
            | ( in @ ( if @ SV29 @ $true @ SV456 @ SY2734 ) @ ( setadjoin @ SV456 @ ( setadjoin @ SY2734 @ emptyset ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1098]) ).

thf(1372,plain,
    ! [SV29: $i,SV457: $i] :
      ( ( ~ ( in @ SV457 @ SV29 )
        | ! [SY2735: $i] :
            ( ~ ( in @ SY2735 @ SV29 )
            | ( in @ ( if @ SV29 @ $false @ SV457 @ SY2735 ) @ ( setadjoin @ SV457 @ ( setadjoin @ SY2735 @ emptyset ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1099]) ).

thf(1373,plain,
    ! [SV279: $o,SV30: $i,SV458: $i] :
      ( ( ~ ( in @ SV458 @ SV30 )
        | ! [SY2736: $i] :
            ( ~ ( in @ SY2736 @ SV30 )
            | SV279
            | ( ( if @ SV30 @ SV279 @ SV458 @ SY2736 )
              = SY2736 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1100]) ).

thf(1374,plain,
    ! [SV30: $i,SV459: $i] :
      ( ( ~ ( in @ SV459 @ SV30 )
        | ! [SY2737: $i] :
            ( ~ ( in @ SY2737 @ SV30 )
            | $true
            | ( ( if @ SV30 @ $true @ SV459 @ SY2737 )
              = SY2737 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1101]) ).

thf(1375,plain,
    ! [SV30: $i,SV460: $i] :
      ( ( ~ ( in @ SV460 @ SV30 )
        | ! [SY2738: $i] :
            ( ~ ( in @ SY2738 @ SV30 )
            | $false
            | ( ( if @ SV30 @ $false @ SV460 @ SY2738 )
              = SY2738 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1102]) ).

thf(1376,plain,
    ! [SV280: $o,SV31: $i,SV461: $i] :
      ( ( ~ ( in @ SV461 @ SV31 )
        | ! [SY2739: $i] :
            ( ~ ( in @ SY2739 @ SV31 )
            | ~ SV280
            | ( ( if @ SV31 @ SV280 @ SV461 @ SY2739 )
              = SV461 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1103]) ).

thf(1377,plain,
    ! [SV31: $i,SV462: $i] :
      ( ( ~ ( in @ SV462 @ SV31 )
        | ! [SY2740: $i] :
            ( ~ ( in @ SY2740 @ SV31 )
            | ~ $true
            | ( ( if @ SV31 @ $true @ SV462 @ SY2740 )
              = SV462 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1104]) ).

thf(1378,plain,
    ! [SV31: $i,SV463: $i] :
      ( ( ~ ( in @ SV463 @ SV31 )
        | ! [SY2741: $i] :
            ( ~ ( in @ SY2741 @ SV31 )
            | ~ $false
            | ( ( if @ SV31 @ $false @ SV463 @ SY2741 )
              = SV463 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1105]) ).

thf(1379,plain,
    ! [SV32: $i] :
      ( ( ( singleton @ SV32 )
        = $false )
      | ( ( ! [SY1956: $i] :
              ( ~ ( in @ SY1956 @ SV32 )
              | ( ( setunion @ SV32 )
                = SY1956 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1106]) ).

thf(1380,plain,
    ! [SV281: $o,SV33: $i,SV464: $i] :
      ( ( ~ ( in @ SV464 @ SV33 )
        | ! [SY2742: $i] :
            ( ~ ( in @ SY2742 @ SV33 )
            | ( in @ ( if @ SV33 @ SV281 @ SV464 @ SY2742 ) @ SV33 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1107]) ).

thf(1381,plain,
    ! [SV33: $i,SV465: $i] :
      ( ( ~ ( in @ SV465 @ SV33 )
        | ! [SY2743: $i] :
            ( ~ ( in @ SY2743 @ SV33 )
            | ( in @ ( if @ SV33 @ $true @ SV465 @ SY2743 ) @ SV33 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1108]) ).

thf(1382,plain,
    ! [SV33: $i,SV466: $i] :
      ( ( ~ ( in @ SV466 @ SV33 )
        | ! [SY2744: $i] :
            ( ~ ( in @ SY2744 @ SV33 )
            | ( in @ ( if @ SV33 @ $false @ SV466 @ SY2744 ) @ SV33 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1109]) ).

thf(1383,plain,
    ! [SV282: $i,SV34: $i,SV467: $i] :
      ( ( ~ ( in @ SV467 @ ( funcSet @ SV34 @ SV282 ) )
        | ( ( lam @ SV34 @ SV282
            @ ^ [SY2745: $i] : ( ap @ SV34 @ SV282 @ SV467 @ SY2745 ) )
          = SV467 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1110]) ).

thf(1384,plain,
    ! [SV468: $i,SV283: $i,SV35: $i] :
      ( ( ~ ( func @ SV35 @ SV283 @ SV468 )
        | ( ( lam @ SV35 @ SV283
            @ ^ [SY2746: $i] : ( ap @ SV35 @ SV283 @ SV468 @ SY2746 ) )
          = SV468 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1111]) ).

thf(1385,plain,
    ! [SV469: $i,SV36: $i] :
      ( ( ( ! [SY2747: $i] :
              ~ ( func @ SV36 @ SV469 @ SY2747 ) )
        = $true )
      | ( ( ! [SY1968: $i] :
              ~ ( in @ SY1968 @ SV36 )
          | $true )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1112]) ).

thf(1386,plain,
    ! [SV470: $i,SV37: $i] :
      ( ( ( ! [SY2748: $i] :
              ~ ( in @ SY2748 @ ( funcSet @ SV37 @ SV470 ) ) )
        = $true )
      | ( ( ! [SY1971: $i] :
              ~ ( in @ SY1971 @ SV37 )
          | $true )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1113]) ).

thf(1387,plain,
    ! [SV284: $i,SV38: $i,SV471: $i] :
      ( ( ~ ( in @ SV471 @ ( funcSet @ SV38 @ SV284 ) )
        | ! [SY2749: $i] :
            ( ~ ( in @ SY2749 @ SV38 )
            | ! [SY2750: $i] :
                ( ~ ( in @ SY2750 @ SV284 )
                | ~ ( in @ ( kpair @ SY2749 @ SY2750 ) @ SV471 )
                | ( ( ap @ SV38 @ SV284 @ SV471 @ SY2749 )
                  = SY2750 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1114]) ).

thf(1388,plain,
    ! [SV472: $i,SV285: $i,SV39: $i] :
      ( ( ~ ( func @ SV39 @ SV285 @ SV472 )
        | ! [SY2751: $i] :
            ( ~ ( in @ SY2751 @ SV39 )
            | ! [SY2752: $i] :
                ( ~ ( in @ SY2752 @ SV285 )
                | ~ ( in @ ( kpair @ SY2751 @ SY2752 ) @ SV472 )
                | ( ( ap @ SV39 @ SV285 @ SV472 @ SY2751 )
                  = SY2752 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1115]) ).

thf(1389,plain,
    ! [SV286: $i,SV40: $i,SV473: $i] :
      ( ( ~ ( in @ SV473 @ ( funcSet @ SV40 @ SV286 ) )
        | ! [SY2753: $i] :
            ( ~ ( in @ SY2753 @ SV40 )
            | ( in @ ( kpair @ SY2753 @ ( ap @ SV40 @ SV286 @ SV473 @ SY2753 ) ) @ SV473 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1116]) ).

thf(1390,plain,
    ! [SV474: $i,SV287: $i,SV41: $i] :
      ( ( ~ ( func @ SV41 @ SV287 @ SV474 )
        | ! [SY2754: $i] :
            ( ~ ( in @ SY2754 @ SV41 )
            | ( in @ ( kpair @ SY2754 @ ( ap @ SV41 @ SV287 @ SV474 @ SY2754 ) ) @ SV474 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1117]) ).

thf(1391,plain,
    ! [SV288: $i > $o,SV42: $i] :
      ( ( ( ~ ( singleton
              @ ( dsetconstr @ SV42
                @ ^ [SY2500: $i] : ( SV288 @ SY2500 ) ) ) )
        = $true )
      | ( ( ! [SY2501: $i] :
              ( ~ ( in @ SY2501 @ SV42 )
              | ! [SY2502: $i] :
                  ( ~ ( in @ SY2502 @ SV42 )
                  | ~ ( SV288 @ SY2501 )
                  | ~ ( SV288 @ SY2502 )
                  | ( SY2501 = SY2502 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1118]) ).

thf(1392,plain,
    ! [SV475: $i,SV289: $i,SV43: $i] :
      ( ( ~ ( func @ SV43 @ SV289 @ SV475 )
        | ( in @ SV475 @ ( funcSet @ SV43 @ SV289 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1119]) ).

thf(1393,plain,
    ! [SV290: $i,SV44: $i,SV476: $i] :
      ( ( ~ ( in @ SV476 @ ( funcSet @ SV44 @ SV290 ) )
        | ! [SY2755: $i] :
            ( ~ ( in @ SY2755 @ SV44 )
            | ( in @ ( ap @ SV44 @ SV290 @ SV476 @ SY2755 ) @ SV290 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1120]) ).

thf(1394,plain,
    ! [SV291: $i,SV45: $i,SV477: $i] :
      ( ( ~ ( in @ SV477 @ ( funcSet @ SV45 @ SV291 ) )
        | ( func @ SV45 @ SV291 @ SV477 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1121]) ).

thf(1395,plain,
    ! [SV478: $i,SV292: $i,SV46: $i] :
      ( ( ~ ( func @ SV46 @ SV292 @ SV478 )
        | ! [SY2756: $i] :
            ( ~ ( in @ SY2756 @ SV46 )
            | ( in @ ( ap @ SV46 @ SV292 @ SV478 @ SY2756 ) @ SV292 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1122]) ).

thf(1396,plain,
    ! [SV479: $i,SV293: $i,SV47: $i] :
      ( ( ~ ( func @ SV47 @ SV293 @ SV479 )
        | ! [SY2757: $i] :
            ( ~ ( in @ SY2757 @ SV47 )
            | ( in
              @ ( setunion
                @ ( dsetconstr @ SV293
                  @ ^ [SY2758: $i] : ( in @ ( kpair @ SY2757 @ SY2758 ) @ SV479 ) ) )
              @ SV293 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1123]) ).

thf(1397,plain,
    ! [SV480: $i,SV294: $i,SV48: $i] :
      ( ( ~ ( func @ SV48 @ SV294 @ SV480 )
        | ! [SY2759: $i] :
            ( ~ ( in @ SY2759 @ SV48 )
            | ( singleton
              @ ( dsetconstr @ SV294
                @ ^ [SY2760: $i] : ( in @ ( kpair @ SY2759 @ SY2760 ) @ SV480 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1124]) ).

thf(1398,plain,
    ! [SV481: $i > $i > $o,SV295: $i,SV49: $i] :
      ( ( ! [SY2761: $i,SY2762: $i] :
            ( ~ ( in @ ( kpair @ SY2761 @ SY2762 )
                @ ( dpsetconstr @ SV49 @ SV295
                  @ ^ [SY2763: $i,SY2764: $i] : ( SV481 @ SY2763 @ SY2764 ) ) )
            | ( SV481 @ SY2761 @ SY2762 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1125]) ).

thf(1399,plain,
    ! [SV482: $i > $i > $o,SV296: $i,SV50: $i] :
      ( ( ! [SY2765: $i,SY2766: $i] :
            ( ~ ( in @ ( kpair @ SY2765 @ SY2766 )
                @ ( dpsetconstr @ SV50 @ SV296
                  @ ^ [SY2767: $i,SY2768: $i] : ( SV482 @ SY2767 @ SY2768 ) ) )
            | ( in @ SY2766 @ SV296 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1126]) ).

thf(1400,plain,
    ! [SV483: $i > $i > $o,SV297: $i,SV51: $i] :
      ( ( ! [SY2769: $i] :
            ( ! [SY2770: $i] :
                ~ ( in @ ( kpair @ SY2769 @ SY2770 )
                  @ ( dpsetconstr @ SV51 @ SV297
                    @ ^ [SY2771: $i,SY2772: $i] : ( SV483 @ SY2771 @ SY2772 ) ) )
            | ( in @ SY2769 @ SV51 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1127]) ).

thf(1401,plain,
    ! [SV484: $i > $i > $o,SV298: $i,SV52: $i] :
      ( ( ! [SY2773: $i] :
            ( ~ ( in @ SY2773 @ SV52 )
            | ! [SY2774: $i] :
                ( ~ ( in @ SY2774 @ SV298 )
                | ~ ( in @ ( kpair @ SY2773 @ SY2774 )
                    @ ( dpsetconstr @ SV52 @ SV298
                      @ ^ [SY2775: $i,SY2776: $i] : ( SV484 @ SY2775 @ SY2776 ) ) )
                | ( SV484 @ SY2773 @ SY2774 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1128]) ).

thf(1402,plain,
    ! [SV485: $i > $i > $o,SV299: $i,SV53: $i] :
      ( ( subset
        @ ( dpsetconstr @ SV53 @ SV299
          @ ^ [SY2777: $i,SY2778: $i] : ( SV485 @ SY2777 @ SY2778 ) )
        @ ( cartprod @ SV53 @ SV299 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1129]) ).

thf(1403,plain,
    ! [SV486: $i > $i > $o,SV300: $i,SV54: $i] :
      ( ( subset
        @ ( dpsetconstr @ SV54 @ SV300
          @ ^ [SY2779: $i,SY2780: $i] : ( SV486 @ SY2779 @ SY2780 ) )
        @ ( cartprod @ SV54 @ SV300 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1130]) ).

thf(1404,plain,
    ! [SV487: $i > $i > $o,SV301: $i,SV55: $i] :
      ( ( ! [SY2781: $i] :
            ( ~ ( in @ SY2781 @ SV55 )
            | ! [SY2782: $i] :
                ( ~ ( in @ SY2782 @ SV301 )
                | ~ ( SV487 @ SY2781 @ SY2782 )
                | ( in @ ( kpair @ SY2781 @ SY2782 )
                  @ ( dpsetconstr @ SV55 @ SV301
                    @ ^ [SY2783: $i,SY2784: $i] : ( SV487 @ SY2783 @ SY2784 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1131]) ).

thf(1405,plain,
    ! [SV302: $i,SV56: $i,SV488: $i] :
      ( ( ~ ( in @ SV488 @ ( cartprod @ SV56 @ SV302 ) )
        | ( ( kpair @ ( kfst @ SV488 ) @ ( ksnd @ SV488 ) )
          = SV488 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1132]) ).

thf(1406,plain,
    ! [SV303: $i,SV57: $i,SV489: $i] :
      ( ( ~ ( in @ SV489 @ SV57 )
        | ! [SY2785: $i] :
            ( ~ ( in @ SY2785 @ SV303 )
            | ( ( ksnd @ ( kpair @ SV489 @ SY2785 ) )
              = SY2785 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1133]) ).

thf(1407,plain,
    ! [SV304: $i,SV58: $i,SV490: $i] :
      ( ( ~ ( in @ SV490 @ SV58 )
        | ! [SY2786: $i] :
            ( ~ ( in @ SY2786 @ SV304 )
            | ( ( kfst @ ( kpair @ SV490 @ SY2786 ) )
              = SV490 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1134]) ).

thf(1408,plain,
    ! [SV59: $i,SV491: $i] :
      ( ( ( ~ ( in @ SV491 @ SV59 ) )
        = $true )
      | ( ( ! [B: $i,Xy: $i] :
              ~ ( in @ Xy @ B )
          | $true )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1135]) ).

thf(1409,plain,
    ! [SV305: $i,SV60: $i,SV492: $i] :
      ( ( ! [SY2787: $i] :
            ( ~ ( in @ ( kpair @ SV492 @ SY2787 ) @ ( cartprod @ SV60 @ SV305 ) )
            | ( in @ SY2787 @ SV305 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1136]) ).

thf(1410,plain,
    ! [SV306: $i,SV61: $i,SV493: $i] :
      ( ( ! [SY2788: $i] :
            ~ ( in @ ( kpair @ SV493 @ SY2788 ) @ ( cartprod @ SV61 @ SV306 ) )
        | ( in @ SV493 @ SV61 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1137]) ).

thf(1411,plain,
    ! [SV307: $i,SV62: $i,SV494: $i] :
      ( ( ~ ( in @ SV494 @ ( cartprod @ SV62 @ SV307 ) )
        | ( in @ ( ksnd @ SV494 ) @ SV307 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1138]) ).

thf(1412,plain,
    ! [SV63: $i] :
      ( ( ( iskpair @ SV63 )
        = $false )
      | ( ( ( kpair @ ( kfst @ SV63 ) @ ( ksnd @ SV63 ) )
          = SV63 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1139]) ).

thf(1413,plain,
    ! [SV65: $i] :
      ( ( ( iskpair @ SV65 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ ( setunion @ SV65 )
            @ ^ [SY2066: $i] :
                ( SV65
                = ( kpair @ ( kfst @ SV65 ) @ SY2066 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1141]) ).

thf(1414,plain,
    ! [SV495: $i,SV309: $i,SV66: $i] :
      ( ( ! [SY2789: $i] :
            ( ( ( kpair @ SV66 @ SV309 )
             != ( kpair @ SV495 @ SY2789 ) )
            | ( SV309 = SY2789 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1142]) ).

thf(1415,plain,
    ! [SV496: $i,SV310: $i,SV67: $i] :
      ( ( ! [SY2790: $i] :
            ( ( ( setadjoin @ ( setadjoin @ SV67 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV67 @ ( setadjoin @ SV310 @ emptyset ) ) @ emptyset ) )
             != ( setadjoin @ ( setadjoin @ SV496 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV496 @ ( setadjoin @ SY2790 @ emptyset ) ) @ emptyset ) ) )
            | ( SV310 = SY2790 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1143]) ).

thf(1416,plain,
    ! [SV311: $i,SV68: $i] :
      ( ( ( ! [SY2560: $i] :
              ( ( setadjoin @ SV68 @ ( setadjoin @ SV311 @ emptyset ) )
             != ( setadjoin @ SY2560 @ emptyset ) ) )
        = $true )
      | ( ( SV68 = SV311 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1144]) ).

thf(1417,plain,
    ! [SV497: $i,SV312: $i,SV69: $i] :
      ( ( ! [SY2791: $i] :
            ( ( ( setadjoin @ ( setadjoin @ SV69 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV69 @ ( setadjoin @ SV312 @ emptyset ) ) @ emptyset ) )
             != ( setadjoin @ ( setadjoin @ SV497 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV497 @ ( setadjoin @ SY2791 @ emptyset ) ) @ emptyset ) ) )
            | ( SV497 != SY2791 )
            | ( SV312 = SY2791 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1145]) ).

thf(1418,plain,
    ! [SV313: $i,SV70: $i] :
      ( ( ( SV70 != SV313 )
        = $true )
      | ( ( ( setadjoin @ ( setadjoin @ SV70 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV70 @ ( setadjoin @ SV313 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ SV70 @ emptyset ) @ emptyset ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1146]) ).

thf(1419,plain,
    ! [SV314: $i,SV71: $i] :
      ( ( ( SV71 != SV314 )
        = $true )
      | ( ( ( setadjoin @ SV71 @ ( setadjoin @ SV314 @ emptyset ) )
          = ( setadjoin @ SV71 @ emptyset ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1147]) ).

thf(1420,plain,
    ! [SV498: $i,SV315: $i,SV72: $i] :
      ( ( ! [SY2792: $i] :
            ( ( kpair @ SV72 @ SV315 )
           != ( kpair @ SV498 @ SY2792 ) )
        | ( SV72 = SV498 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1148]) ).

thf(1421,plain,
    ! [SV499: $i,SV316: $i,SV73: $i] :
      ( ( ! [SY2793: $i] :
            ( ( setadjoin @ ( setadjoin @ SV73 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV73 @ ( setadjoin @ SV316 @ emptyset ) ) @ emptyset ) )
           != ( setadjoin @ ( setadjoin @ SV499 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV499 @ ( setadjoin @ SY2793 @ emptyset ) ) @ emptyset ) ) )
        | ( SV73 = SV499 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1149]) ).

thf(1422,plain,
    ! [SV317: $i,SV74: $i,SV500: $i] :
      ( ( ~ ( in @ SV500 @ ( cartprod @ SV74 @ SV317 ) )
        | ( in @ ( kfst @ SV500 ) @ SV74 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1150]) ).

thf(1423,plain,
    ! [SV76: $i] :
      ( ( ( singleton @ SV76 )
        = $false )
      | ( ( in @ ( setunion @ SV76 ) @ SV76 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1152]) ).

thf(1424,plain,
    ! [SV77: $i] :
      ( ( ( iskpair @ SV77 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ ( setunion @ SV77 )
            @ ^ [SY2089: $i] : ( in @ ( setadjoin @ SY2089 @ emptyset ) @ SV77 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1153]) ).

thf(1425,plain,
    ! [SV319: $i,SV78: $i,SV501: $i] :
      ( ( ~ ( in @ ( setadjoin @ SV501 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV78 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV78 @ ( setadjoin @ SV319 @ emptyset ) ) @ emptyset ) ) )
        | ( SV78 = SV501 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1154]) ).

thf(1426,plain,
    ! [SV320: $i,SV79: $i] :
      ( ( ( ( setadjoin @ SV79 @ emptyset )
         != ( setadjoin @ SV320 @ emptyset ) )
        = $true )
      | ( ( SV79 = SV320 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1155]) ).

thf(1427,plain,
    ! [SV321: $i,SV83: $i,SV502: $i] :
      ( ( ~ ( in @ SV502 @ ( cartprod @ SV83 @ SV321 ) )
        | ( iskpair @ SV502 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1156]) ).

thf(1428,plain,
    ! [SV322: $i,SV84: $i,SV503: $i] :
      ( ( ~ ( in @ SV503 @ SV84 )
        | ! [SY2794: $i] :
            ( ~ ( in @ SY2794 @ SV322 )
            | ( in @ ( kpair @ SV503 @ SY2794 ) @ ( cartprod @ SV84 @ SV322 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1157]) ).

thf(1429,plain,
    ! [SV323: $i,SV85: $i,SV504: $i] :
      ( ( ~ ( in @ SV504 @ SV85 )
        | ! [SY2795: $i] :
            ( ~ ( in @ SY2795 @ SV323 )
            | ( in @ ( kpair @ SV504 @ SY2795 ) @ ( powerset @ ( powerset @ ( binunion @ SV85 @ SV323 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1158]) ).

thf(1430,plain,
    ! [SV324: $i,SV86: $i,SV505: $i] :
      ( ( ~ ( in @ SV505 @ SV86 )
        | ! [SY2796: $i] :
            ( ~ ( in @ SY2796 @ SV324 )
            | ( in @ ( setadjoin @ ( setadjoin @ SV505 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV505 @ ( setadjoin @ SY2796 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV86 @ SV324 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1159]) ).

thf(1431,plain,
    ! [SV325: $i,SV87: $i,SV506: $i] :
      ( ( ~ ( in @ SV506 @ SV87 )
        | ! [SY2797: $i] :
            ( ~ ( in @ SY2797 @ SV325 )
            | ( subset @ ( setadjoin @ ( setadjoin @ SV506 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV506 @ ( setadjoin @ SY2797 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV87 @ SV325 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1160]) ).

thf(1432,plain,
    ! [SV326: $i,SV88: $i,SV507: $i] :
      ( ( ~ ( in @ SV507 @ SV88 )
        | ! [SY2798: $i] :
            ( ~ ( in @ SY2798 @ SV326 )
            | ( in @ ( setadjoin @ SV507 @ ( setadjoin @ SY2798 @ emptyset ) ) @ ( powerset @ ( binunion @ SV88 @ SV326 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1161]) ).

thf(1433,plain,
    ! [SV327: $i,SV89: $i,SV508: $i] :
      ( ( ~ ( in @ SV508 @ SV89 )
        | ! [SY2799: $i] :
            ( ~ ( in @ SY2799 @ SV327 )
            | ( subset @ ( setadjoin @ SV508 @ ( setadjoin @ SY2799 @ emptyset ) ) @ ( binunion @ SV89 @ SV327 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1162]) ).

thf(1434,plain,
    ! [SV328: $i,SV90: $i,SV509: $i] :
      ( ( ~ ( in @ SV509 @ ( setadjoin @ SV90 @ ( setadjoin @ SV328 @ emptyset ) ) )
        | ( SV509 = SV90 )
        | ( SV509 = SV328 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1163]) ).

thf(1435,plain,
    ! [SV329: $i,SV91: $i,SV510: $i] :
      ( ( ~ ( in @ SV510 @ SV91 )
        | ( in @ ( setadjoin @ SV510 @ emptyset ) @ ( powerset @ ( binunion @ SV91 @ SV329 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1164]) ).

thf(1436,plain,
    ! [SV92: $i,SV330: $i] :
      ( ( ( ~ ( in @ SV330 @ SV92 ) )
        = $true )
      | ( ( in @ ( setadjoin @ SV330 @ emptyset ) @ ( powerset @ SV92 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1165]) ).

thf(1437,plain,
    ! [SV93: $i,SV331: $i] :
      ( ( ( ~ ( in @ SV331 @ SV93 ) )
        = $true )
      | ( ( subset @ ( setadjoin @ SV331 @ emptyset ) @ SV93 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1166]) ).

thf(1438,plain,
    ! [SV337: $i,SV99: $i,SV511: $i] :
      ( ( ( in @ SV511 @ SV99 )
        | ( in @ SV511 @ SV337 )
        | ~ ( in @ SV511 @ ( symdiff @ SV99 @ SV337 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1172]) ).

thf(1439,plain,
    ! [SV338: $i,SV100: $i,SV512: $i] :
      ( ( ~ ( in @ SV512 @ SV100 )
        | ~ ( in @ SV512 @ SV338 )
        | ~ ( in @ SV512 @ ( symdiff @ SV100 @ SV338 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1173]) ).

thf(1440,plain,
    ! [SV339: $i,SV101: $i,SV513: $i] :
      ( ( ( in @ SV513 @ SV101 )
        | ~ ( in @ SV513 @ SV339 )
        | ( in @ SV513 @ ( symdiff @ SV101 @ SV339 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1174]) ).

thf(1441,plain,
    ! [SV340: $i,SV102: $i,SV514: $i] :
      ( ( ~ ( in @ SV514 @ SV102 )
        | ( in @ SV514 @ SV340 )
        | ( in @ SV514 @ ( symdiff @ SV102 @ SV340 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1175]) ).

thf(1442,plain,
    ! [SV341: $i,SV103: $i] :
      ( ( ( ( setminus @ SV103 @ SV341 )
         != emptyset )
        = $true )
      | ( ( subset @ SV103 @ SV341 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1176]) ).

thf(1443,plain,
    ! [SV105: $i,SV343: $i,SV515: $i] :
      ( ( ~ ( in @ SV515 @ SV343 )
        | ~ ( in @ SV515 @ ( setminus @ SV105 @ SV343 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1178]) ).

thf(1444,plain,
    ! [SV344: $i,SV106: $i,SV516: $i] :
      ( ( ( in @ SV516 @ SV106 )
        | ~ ( in @ SV516 @ ( setminus @ SV106 @ SV344 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1179]) ).

thf(1445,plain,
    ! [SV345: $i,SV107: $i,SV517: $i] :
      ( ( ( in @ SV517 @ ( setminus @ SV107 @ SV345 ) )
        | ( in @ SV517 @ SV345 )
        | ~ ( in @ SV517 @ SV107 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1180]) ).

thf(1446,plain,
    ! [SV346: $i,SV108: $i,SV518: $i] :
      ( ( ( in @ SV518 @ ( setminus @ SV108 @ SV346 ) )
        | ~ ( in @ SV518 @ SV108 )
        | ( in @ SV518 @ SV346 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1181]) ).

thf(1447,plain,
    ! [SV347: $i,SV109: $i] :
      ( ( ( ~ ( subset @ SV109 @ SV347 ) )
        = $true )
      | ( ( ( setminus @ SV109 @ SV347 )
          = emptyset )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1182]) ).

thf(1448,plain,
    ! [SV348: $i,SV110: $i,SV519: $i] :
      ( ( ~ ( in @ SV519 @ ( setminus @ SV110 @ SV348 ) )
        | ~ ( in @ SV519 @ SV348 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1183]) ).

thf(1449,plain,
    ! [SV349: $i,SV111: $i,SV520: $i] :
      ( ( ~ ( in @ SV520 @ ( setminus @ SV111 @ SV349 ) )
        | ( in @ SV520 @ SV111 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1184]) ).

thf(1450,plain,
    ! [SV350: $i,SV112: $i,SV521: $i] :
      ( ( ~ ( in @ SV521 @ SV112 )
        | ( in @ SV521 @ SV350 )
        | ( in @ SV521 @ ( setminus @ SV112 @ SV350 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1185]) ).

thf(1451,plain,
    ! [SV522: $i,SV351: $i,SV113: $i] :
      ( ( ( binintersect @ SV113 @ ( binunion @ SV351 @ SV522 ) )
        = ( binunion @ ( binintersect @ SV113 @ SV351 ) @ ( binintersect @ SV113 @ SV522 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1186]) ).

thf(1452,plain,
    ! [SV352: $i,SV114: $i] :
      ( ( ( ( binintersect @ SV114 @ SV352 )
         != SV114 )
        = $true )
      | ( ( subset @ SV114 @ SV352 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1187]) ).

thf(1453,plain,
    ! [SV115: $i,SV353: $i] :
      ( ( ( ~ ( subset @ SV353 @ SV115 ) )
        = $true )
      | ( ( ( binintersect @ SV115 @ SV353 )
          = SV353 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1188]) ).

thf(1454,plain,
    ! [SV355: $i,SV117: $i,SV523: $i] :
      ( ( ~ ( in @ SV523 @ ( binintersect @ SV117 @ SV355 ) )
        | ( in @ SV523 @ SV355 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1190]) ).

thf(1455,plain,
    ! [SV356: $i,SV118: $i] :
      ( ( ( ( binintersect @ SV118 @ SV356 )
         != SV356 )
        = $true )
      | ( ( subset @ SV356 @ SV118 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1191]) ).

thf(1456,plain,
    ! [SV357: $i,SV119: $i] :
      ( ( ( ~ ( subset @ SV119 @ SV357 ) )
        = $true )
      | ( ( ( binintersect @ SV119 @ SV357 )
          = SV119 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1192]) ).

thf(1457,plain,
    ! [SV359: $i,SV121: $i,SV524: $i] :
      ( ( ~ ( in @ SV524 @ ( binintersect @ SV121 @ SV359 ) )
        | ( in @ SV524 @ SV121 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1194]) ).

thf(1458,plain,
    ! [SV360: $i,SV122: $i,SV525: $i] :
      ( ( ~ ( subset @ SV525 @ SV122 )
        | ~ ( subset @ SV525 @ SV360 )
        | ( subset @ SV525 @ ( binintersect @ SV122 @ SV360 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1195]) ).

thf(1459,plain,
    ! [SV361: $i,SV123: $i,SV526: $i] :
      ( ( ~ ( in @ SV526 @ SV123 )
        | ~ ( in @ SV526 @ SV361 )
        | ( in @ SV526 @ ( binintersect @ SV123 @ SV361 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1196]) ).

thf(1460,plain,
    ! [SV364: $i,SV126: $i,SV527: $i] :
      ( ( ~ ( in @ SV527 @ ( binunion @ SV126 @ SV364 ) )
        | ( in @ SV527 @ SV126 )
        | ( in @ SV527 @ SV364 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1199]) ).

thf(1461,plain,
    ! [SV127: $i,SV365: $i,SV528: $i] :
      ( ( ~ ( in @ SV528 @ SV365 )
        | ( in @ SV528 @ ( binunion @ SV127 @ SV365 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1200]) ).

thf(1462,plain,
    ! [SV367: $i,SV129: $i,SV529: $i] :
      ( ( ~ ( in @ SV529 @ SV129 )
        | ( in @ SV529 @ ( binunion @ SV129 @ SV367 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1202]) ).

thf(1463,plain,
    ! [SV370: $i,SV132: $i] :
      ( ( ( ~ ( subset @ SV132 @ SV370 ) )
        = $true )
      | ( ( subset @ ( powerset @ SV132 ) @ ( powerset @ SV370 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1205]) ).

thf(1464,plain,
    ! [SV134: $i,SV371: $i] :
      ( ( ( ~ ( in @ SV371 @ ( powerset @ SV134 ) ) )
        = $true )
      | ( ( subset @ SV371 @ SV134 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1206]) ).

thf(1465,plain,
    ! [SV135: $i,SV372: $i] :
      ( ( ( ~ ( subset @ SV372 @ SV135 ) )
        = $true )
      | ( ( in @ SV372 @ ( powerset @ SV135 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1207]) ).

thf(1466,plain,
    ! [SV136: $i] :
      ( ( ( subset @ SV136 @ emptyset )
        = $false )
      | ( ( SV136 = emptyset )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1208]) ).

thf(1467,plain,
    ! [SV373: $i,SV137: $i] :
      ( ( ( ~ ( subset @ SV137 @ SV373 ) )
        = $true )
      | ( ( ~ ( subset @ SV373 @ SV137 )
          | ( SV137 = SV373 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1209]) ).

thf(1468,plain,
    ! [SV374: $i,SV138: $i] :
      ( ( ( ~ ( subset @ SV138 @ SV374 ) )
        = $true )
      | ( ( in @ SV138 @ ( powerset @ SV374 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1210]) ).

thf(1469,plain,
    ! [SV375: $i,SV530: $i,SV139: $i] :
      ( ( ~ ( subset @ SV139 @ SV530 )
        | ( subset @ SV139 @ ( setadjoin @ SV375 @ SV530 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1211]) ).

thf(1470,plain,
    ! [SV377: $i,SV141: $i] :
      ( ( ( ~ ( subset @ SV141 @ SV377 ) )
        = $true )
      | ( ( ! [SY2606: $i] :
              ( ~ ( subset @ SV377 @ SY2606 )
              | ( subset @ SV141 @ SY2606 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1213]) ).

thf(1471,plain,
    ! [SV378: $i,SV143: $i,SV531: $i] :
      ( ( ~ ( in @ SV531 @ SV143 )
        | ( in @ SV531 @ SV378 )
        | ( SV143 != SV378 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1214]) ).

thf(1472,plain,
    ! [SV379: $i,SV144: $i] :
      ( ( ( subset @ SV144 @ SV379 )
        = $true )
      | ( ( SV144 != SV379 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1215]) ).

thf(1473,plain,
    ! [SV380: $i,SV145: $i,SV532: $i] :
      ( ( ~ ( in @ SV532 @ SV145 )
        | ( in @ SV532 @ SV380 )
        | ~ ( subset @ SV145 @ SV380 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1216]) ).

thf(1474,plain,
    ! [SV381: $i,SV146: $i] :
      ( ( ( ~ ( subset @ SV146 @ SV381 ) )
        = $true )
      | ( ( ! [SY2609: $i] :
              ( ( in @ SY2609 @ SV381 )
              | ~ ( in @ SY2609 @ SV146 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1217]) ).

thf(1475,plain,
    ! [SV382: $i,SV147: $i] :
      ( ( ( ~ ( subset @ SV147 @ SV382 ) )
        = $true )
      | ( ( ! [SY2610: $i] :
              ( ~ ( in @ SY2610 @ SV147 )
              | ( in @ SY2610 @ SV382 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1218]) ).

thf(1476,plain,
    ! [SV383: $i,SV149: $i] :
      ( ( ( SV149 != SV383 )
        = $true )
      | ( ( subset @ SV149 @ SV383 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1219]) ).

thf(1477,plain,
    ! [SV384: $i,SV150: $i] :
      ( ( ( SV150 != SV384 )
        = $true )
      | ( ( subset @ SV384 @ SV150 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1220]) ).

thf(1478,plain,
    ! [SV385: $i,SV151: $i] :
      ( ( ( SV151 != SV385 )
        = $true )
      | ( ( ( setunion @ SV151 )
          = ( setunion @ SV385 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1221]) ).

thf(1479,plain,
    ! [SV386: $i,SV152: $i] :
      ( ( ( SV152 != SV386 )
        = $true )
      | ( ( ( powerset @ SV152 )
          = ( powerset @ SV386 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1222]) ).

thf(1480,plain,
    ! [SV387: $i,SV153: $i] :
      ( ( ( SV153 != SV387 )
        = $true )
      | ( ( ! [SY2611: $i,SY2612: $i] :
              ( ( SY2611 != SY2612 )
              | ( ( setadjoin @ SV153 @ SY2611 )
                = ( setadjoin @ SV387 @ SY2612 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1223]) ).

thf(1481,plain,
    ! [SV388: $i,SV154: $i] :
      ( ( ( SV154 != SV388 )
        = $true )
      | ( ( ! [SY2613: $i,SY2614: $i] :
              ( ( SY2613 != SY2614 )
              | ~ ( in @ SY2613 @ SV154 )
              | ( in @ SY2614 @ SV388 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1224]) ).

thf(1482,plain,
    ! [SV155: $o] :
      ( ( SV155 = $false )
      | ( ( set2prop @ ( prop2set @ SV155 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1225]) ).

thf(1483,plain,
    ( ( $true = $false )
    | ( ( set2prop @ ( prop2set @ $true ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1226]) ).

thf(1484,plain,
    ( ( $false = $false )
    | ( ( set2prop @ ( prop2set @ $false ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1227]) ).

thf(1485,plain,
    ! [SV156: $o] :
      ( ( SV156 = $false )
      | ( ( in @ emptyset @ ( prop2set @ SV156 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1228]) ).

thf(1486,plain,
    ( ( $true = $false )
    | ( ( in @ emptyset @ ( prop2set @ $true ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1229]) ).

thf(1487,plain,
    ( ( $false = $false )
    | ( ( in @ emptyset @ ( prop2set @ $false ) )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1230]) ).

thf(1488,plain,
    ! [SV157: $i > $o,SV389: $i] :
      ( ( ( ~ ( in @ SV389 @ emptyset ) )
        = $true )
      | ( ( SV157 @ SV389 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1231]) ).

thf(1489,plain,
    ! [SV158: $i,SV390: $i > $o] :
      ( ( ( ! [SY2615: $i] :
              ( ~ ( SV390 @ SY2615 )
              | ~ ( in @ SY2615 @ SV158 ) ) )
        = $true )
      | ( ( ( dsetconstr @ SV158
            @ ^ [SY2616: $i] : ( SV390 @ SY2616 ) )
         != emptyset )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1232]) ).

thf(1490,plain,
    ! [SV393: $i,SV161: $i,SV533: $i] :
      ( ( ~ ( in @ SV533 @ ( setadjoin @ SV161 @ ( setadjoin @ SV393 @ emptyset ) ) )
        | ( SV533 = SV161 )
        | ( SV533 = SV393 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1235]) ).

thf(1491,plain,
    ! [SV394: $i,SV162: $i] :
      ( ( ( ~ ( in @ SV162 @ ( setadjoin @ SV394 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV394 @ ( setadjoin @ SV162 @ emptyset ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1236]) ).

thf(1492,plain,
    ! [SV395: $i,SV163: $i] :
      ( ( ( SV163 != SV395 )
        = $true )
      | ( ( in @ SV163 @ ( setadjoin @ SV395 @ emptyset ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1237]) ).

thf(1493,plain,
    ! [SV396: $i,SV164: $i] :
      ( ( ( SV164 = SV396 )
        = $true )
      | ( ( ~ ( in @ SV396 @ ( setadjoin @ SV164 @ emptyset ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1238]) ).

thf(1494,plain,
    ! [SV397: $i,SV165: $i] :
      ( ( ( ~ ( in @ SV165 @ ( setadjoin @ SV397 @ emptyset ) ) )
        = $true )
      | ( ( SV165 = SV397 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1239]) ).

thf(1495,plain,
    ! [SV167: $i,SV398: $i] :
      ( ( ( ~ ( in @ SV398 @ SV167 ) )
        = $true )
      | ( ( in @ SV398 @ ( powerset @ ( setunion @ SV167 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1241]) ).

thf(1496,plain,
    ! [SV168: $i,SV534: $i,SV399: $i] :
      ( ( ~ ( in @ SV399 @ SV534 )
        | ~ ( in @ SV534 @ SV168 )
        | ( in @ SV399 @ ( setunion @ SV168 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1242]) ).

thf(1497,plain,
    ! [SV169: $i,SV400: $i] :
      ( ( ( ~ ( in @ SV400 @ ( powerset @ SV169 ) ) )
        = $true )
      | ( ( ! [SY2619: $i] :
              ( ~ ( in @ SY2619 @ SV400 )
              | ( in @ SY2619 @ SV169 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1243]) ).

thf(1498,plain,
    ! [SV401: $i,SV173: $i,SV535: $i] :
      ( ( ~ ( in @ SV535 @ ( setadjoin @ SV173 @ SV401 ) )
        | ( SV535 = SV173 )
        | ( in @ SV535 @ SV401 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1244]) ).

thf(1499,plain,
    ! [SV174: $i,SV402: $i,SV536: $i] :
      ( ( ~ ( in @ SV536 @ SV402 )
        | ( in @ SV536 @ ( setadjoin @ SV174 @ SV402 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1245]) ).

thf(1500,plain,
    ! [SV176: $i,SV537: $i] :
      ( ( ( ~ ( in @ SV537 @ SV176 ) )
        = $true )
      | ( ( SV176 != emptyset )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1247]) ).

thf(1501,plain,
    ! [SV404: $i > $o,SV177: $i,SV538: $i] :
      ( ( ~ ( in @ SV538 @ SV177 )
        | ~ ( SV404 @ SV538 )
        | ( ( dsetconstr @ SV177
            @ ^ [SY2623: $i] : ( SV404 @ SY2623 ) )
         != emptyset ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1248]) ).

thf(1502,plain,
    ! [SV405: $i] :
      ( ( ( in @ SV405 @ emptyset )
        = $false )
      | ( ( ! [Xphi: $o] : Xphi )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1254]) ).

thf(1503,plain,
    ! [SV183: $o,SV539: $i] :
      ( ( ( ~ ( in @ SV539 @ ( prop2set @ SV183 ) ) )
        = $true )
      | ( SV183 = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1255]) ).

thf(1504,plain,
    ! [SV540: $i] :
      ( ( ( ~ ( in @ SV540 @ ( prop2set @ $true ) ) )
        = $true )
      | ( $true = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1256]) ).

thf(1505,plain,
    ! [SV541: $i] :
      ( ( ( ~ ( in @ SV541 @ ( prop2set @ $false ) ) )
        = $true )
      | ( $false = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1257]) ).

thf(1506,plain,
    ! [SV406: $i > $o,SV184: $i,SV542: $i] :
      ( ( ~ ( in @ SV542
            @ ( dsetconstr @ SV184
              @ ^ [SY2625: $i] : ( SV406 @ SY2625 ) ) )
        | ( SV406 @ SV542 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1258]) ).

thf(1507,plain,
    ! [SV407: $i > $o,SV185: $i,SV543: $i] :
      ( ( ~ ( in @ SV543
            @ ( dsetconstr @ SV185
              @ ^ [SY2627: $i] : ( SV407 @ SY2627 ) ) )
        | ( in @ SV543 @ SV185 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1259]) ).

thf(1508,plain,
    ! [SV408: $i > $o,SV186: $i,SV544: $i] :
      ( ( ~ ( in @ SV544 @ SV186 )
        | ~ ( SV408 @ SV544 )
        | ( in @ SV544
          @ ( dsetconstr @ SV186
            @ ^ [SY2629: $i] : ( SV408 @ SY2629 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1260]) ).

thf(1509,plain,
    ! [SV187: $i] :
      ( ( ( in @ SV187 @ omega )
        = $false )
      | ( ( in @ ( setadjoin @ SV187 @ SV187 ) @ omega )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1261]) ).

thf(1510,plain,
    ! [SV189: $i,SV409: $i] :
      ( ( ( ~ ( in @ SV409 @ ( powerset @ SV189 ) ) )
        = $true )
      | ( ( ! [SY2630: $i] :
              ( ~ ( in @ SY2630 @ ( powerset @ SV189 ) )
              | ~ ( ~ ( in @ ( sK97_Xx @ SY2630 @ SV409 @ SV189 ) @ SV189 )
                  | ~ ~ ( ~ ( in @ ( sK97_Xx @ SY2630 @ SV409 @ SV189 ) @ SV409 )
                        | ~ ~ ( in @ ( sK97_Xx @ SY2630 @ SV409 @ SV189 ) @ SY2630 ) ) )
              | ( subset @ SV409 @ SY2630 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1263]) ).

thf(1511,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( ~ ( in @ ( sK7_Xx @ SX1 @ SX0 ) @ SX1 )
              | ~ ~ ( in @ ( sK7_Xx @ SX1 @ SX0 ) @ SX0 ) )
          | ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1264]) ).

thf(1512,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
          | ! [SX2: $i] :
              ( ~ ( in @ SX2 @ SX1 )
              | ( in @ SX2 @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1265]) ).

thf(1513,plain,
    ! [SV545: $i,SV190: $i > $o] :
      ( ( ( ~ ( ~ ( SV190 @ ( sK24_SY86 @ SV545 @ SV190 ) )
              | ~ ( ( SV545
                   != ( sK24_SY86 @ SV545 @ SV190 ) ) ) )
          | ~ ( SV190 @ SV545 ) )
        = $true )
      | ( ( SV190 @ ( sK23_Xx @ SV190 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1266]) ).

thf(1514,plain,
    ! [SV410: $o,SV191: $i,SV546: $i] :
      ( ( ~ ( in @ SV546 @ SV191 )
        | ! [SY2804: $i] :
            ( ~ ( in @ SY2804 @ SV191 )
            | ~ SV410
            | ( in @ SV546
              @ ( dsetconstr @ SV191
                @ ^ [SY2805: $i] :
                    ( ~ ( ~ SV410
                        | ( SY2805 != SV546 ) )
                    | ~ ( ~ ~ SV410
                        | ( SY2805 != SY2804 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1267]) ).

thf(1515,plain,
    ! [SV191: $i,SV547: $i] :
      ( ( ~ ( in @ SV547 @ SV191 )
        | ! [SY2806: $i] :
            ( ~ ( in @ SY2806 @ SV191 )
            | ~ $true
            | ( in @ SV547
              @ ( dsetconstr @ SV191
                @ ^ [SY2807: $i] :
                    ( ~ ( ~ $true
                        | ( SY2807 != SV547 ) )
                    | ~ ( ~ ~ $true
                        | ( SY2807 != SY2806 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1268]) ).

thf(1516,plain,
    ! [SV191: $i,SV548: $i] :
      ( ( ~ ( in @ SV548 @ SV191 )
        | ! [SY2808: $i] :
            ( ~ ( in @ SY2808 @ SV191 )
            | ~ $false
            | ( in @ SV548
              @ ( dsetconstr @ SV191
                @ ^ [SY2809: $i] :
                    ( ~ ( ~ $false
                        | ( SY2809 != SV548 ) )
                    | ~ ( ~ ~ $false
                        | ( SY2809 != SY2808 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1269]) ).

thf(1517,plain,
    ! [SV192: $i,SV411: $i,SV549: $i > $i] :
      ( ( ~ ( ~ ( in @ ( sK92_Xx @ SV549 @ SV411 @ SV192 ) @ SV192 )
            | ~ ~ ( in @ ( SV549 @ ( sK92_Xx @ SV549 @ SV411 @ SV192 ) ) @ SV411 ) )
        | ! [SY2810: $i] :
            ( ~ ( in @ SY2810 @ SV192 )
            | ( ( ap @ SV192 @ SV411
                @ ( lam @ SV192 @ SV411
                  @ ^ [SY2811: $i] : ( SV549 @ SY2811 ) )
                @ SY2810 )
              = ( SV549 @ SY2810 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1270]) ).

thf(1518,plain,
    ! [SV412: $i,SV193: $i,SV550: $i] :
      ( ( ~ ( in @ SV550 @ ( cartprod @ SV193 @ SV412 ) )
        | ~ ( ~ ~ ( ( SV550
                   != ( kpair @ ( sK67_Xx @ SV550 @ SV412 @ SV193 ) @ ( sK68_SY1876 @ SV550 @ SV412 @ SV193 ) ) )
                  | ~ ( in @ ( sK68_SY1876 @ SV550 @ SV412 @ SV193 ) @ SV412 ) )
            | ~ ( in @ ( sK67_Xx @ SV550 @ SV412 @ SV193 ) @ SV193 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1271]) ).

thf(1519,plain,
    ! [SV551: $i,SV194: $i > $o] :
      ( ( ( ~ ( ~ ( SV194 @ ( sK57_SY248 @ SV551 @ SV194 ) )
              | ~ ( ( SV551
                   != ( sK57_SY248 @ SV551 @ SV194 ) ) ) )
          | ~ ( SV194 @ SV551 ) )
        = $true )
      | ( ( ! [SY2258: $i] :
              ( ~ ( SV194 @ SY2258 )
              | ! [SY2259: $i] :
                  ( ~ ( SV194 @ SY2259 )
                  | ( SY2258 = SY2259 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1272]) ).

thf(1520,plain,
    ! [SV195: $i > $i > $o,SV413: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV413 )
              | ~ ! [SY2638: $i] :
                    ( ~ ( ~ ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SY2638 @ SV413 @ SV195 ) )
                        | ~ ( ( SY2638
                             != ( sK13_SY1837 @ SY2638 @ SV413 @ SV195 ) ) ) )
                    | ~ ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SY2638 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2639: $i] :
                    ( ! [SY2640: $i] :
                        ( ~ ( SV195 @ SY2640 @ SY2639 )
                        | ~ ( in @ SY2640 @ SV413 ) )
                    | ( in @ SY2639 @ ( sK10_B @ SV413 @ SV195 ) ) )
              | ~ ! [SY2641: $i] :
                    ( ~ ( in @ SY2641 @ ( sK10_B @ SV413 @ SV195 ) )
                    | ~ ( ~ ( SV195 @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SY2641 )
                        | ~ ( in @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SV413 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1273]) ).

thf(1521,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( ~ ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        | ~ ( ~ ~ ( ~ ( ( SV552 = SV196 )
                      | ( in @ SV552 @ SV414 )
                      | ! [SX3: $o] : SX3 )
                  | ~ ( ( SV552 = SV196 )
                      | ! [SX3: $o] :
                          ( ~ SX3
                          | SX3 ) ) )
            | ~ ~ ( ~ ! [SY2814: $o] :
                        ( ~ SY2814
                        | ( in @ SV552 @ SV414 )
                        | SY2814 )
                  | ~ ! [SX3: $o] :
                        ( ~ SX3
                        | ~ SX3
                        | SX3 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1274]) ).

thf(1522,plain,
    ! [SV197: $i,SV415: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK66_Xx @ SV415 @ SV197 ) @ SV197 )
              | ~ ( in @ ( sK66_Xx @ SV415 @ SV197 ) @ SV415 ) ) )
        = $true )
      | ( ( ( binintersect @ SV197 @ SV415 )
          = emptyset )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1275]) ).

thf(1523,plain,
    ! [SV198: $i] :
      ( ( ~ ! [SY2272: $i > $o,SY2273: $i] :
              ( ~ ( in @ SY2273 @ SV198 )
              | ~ ( SY2272 @ SY2273 )
              | ( in @ SY2273
                @ ( dsetconstr @ SV198
                  @ ^ [SX3: $i] : ( SY2272 @ SX3 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1276]) ).

thf(1524,plain,
    ! [SV198: $i] :
      ( ( ~ ! [SY2275: $i > $o,SY2276: $i] :
              ( ~ ( in @ SY2276 @ SV198 )
              | ~ ( in @ SY2276
                  @ ( dsetconstr @ SV198
                    @ ^ [SX3: $i] : ( SY2275 @ SX3 ) ) )
              | ( SY2275 @ SY2276 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1276]) ).

thf(1525,plain,
    ! [SV199: $i,SV416: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK30_Xx @ SV416 @ SV199 ) @ SV416 )
              | ~ ~ ( in @ ( sK30_Xx @ SV416 @ SV199 ) @ SV199 ) ) )
        = $true )
      | ( ( in @ SV416 @ ( powerset @ SV199 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1277]) ).

thf(1526,plain,
    ! [SV417: $i > $o,SV200: $i] :
      ( ( ( ! [SY2647: $i] :
              ( ~ ( in @ SY2647 @ SV200 )
              | ( SV417 @ SY2647 ) ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK40_Xx @ SV417 @ SV200 ) @ SV200 )
              | ~ ~ ( SV417 @ ( sK40_Xx @ SV417 @ SV200 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1278]) ).

thf(1527,plain,
    ! [SV201: $i,SV418: $i,SV553: $i > $i] :
      ( ( ~ ( ~ ( in @ ( sK78_Xx @ SV553 @ SV418 @ SV201 ) @ SV201 )
            | ~ ~ ( in @ ( SV553 @ ( sK78_Xx @ SV553 @ SV418 @ SV201 ) ) @ SV418 ) )
        | ( in
          @ ( lam @ SV201 @ SV418
            @ ^ [SY2816: $i] : ( SV553 @ SY2816 ) )
          @ ( funcSet @ SV201 @ SV418 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1279]) ).

thf(1528,plain,
    ! [SV419: $o,SV202: $i,SV554: $i] :
      ( ( ~ ( in @ SV554 @ SV202 )
        | ! [SY2817: $i] :
            ( ~ ( in @ SY2817 @ SV202 )
            | SV419
            | ( ( dsetconstr @ SV202
                @ ^ [SY2818: $i] :
                    ( ~ ( ~ SV419
                        | ( SY2818 != SV554 ) )
                    | ~ ( ~ ~ SV419
                        | ( SY2818 != SY2817 ) ) ) )
              = ( setadjoin @ SY2817 @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1280]) ).

thf(1529,plain,
    ! [SV202: $i,SV555: $i] :
      ( ( ~ ( in @ SV555 @ SV202 )
        | ! [SY2819: $i] :
            ( ~ ( in @ SY2819 @ SV202 )
            | $true
            | ( ( dsetconstr @ SV202
                @ ^ [SY2820: $i] :
                    ( ~ ( ~ $true
                        | ( SY2820 != SV555 ) )
                    | ~ ( ~ ~ $true
                        | ( SY2820 != SY2819 ) ) ) )
              = ( setadjoin @ SY2819 @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1281]) ).

thf(1530,plain,
    ! [SV202: $i,SV556: $i] :
      ( ( ~ ( in @ SV556 @ SV202 )
        | ! [SY2821: $i] :
            ( ~ ( in @ SY2821 @ SV202 )
            | $false
            | ( ( dsetconstr @ SV202
                @ ^ [SY2822: $i] :
                    ( ~ ( ~ $false
                        | ( SY2822 != SV556 ) )
                    | ~ ( ~ ~ $false
                        | ( SY2822 != SY2821 ) ) ) )
              = ( setadjoin @ SY2821 @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1282]) ).

thf(1531,plain,
    ( ( ! [SX0: $i > $o,SX1: $i > $o] :
          ( ~ ( ( ( sK55_Xx @ SX1 @ SX0 )
               != ( sK56_SY1873 @ SX1 @ SX0 ) )
              | ~ ~ ( ~ ( ~ ( SX0 @ ( sK55_Xx @ SX1 @ SX0 ) )
                        | ~ ( SX1 @ ( sK56_SY1873 @ SX1 @ SX0 ) ) )
                    | ~ ( ( SX0 @ ( sK55_Xx @ SX1 @ SX0 ) )
                        | ( SX1 @ ( sK56_SY1873 @ SX1 @ SX0 ) ) ) ) )
          | ! [SX2: $i] :
              ( ~ ( ~ ( SX0 @ ( sK54_SY233 @ SX2 @ SX1 @ SX0 ) )
                  | ~ ( ( SX2
                       != ( sK54_SY233 @ SX2 @ SX1 @ SX0 ) ) ) )
              | ~ ( SX0 @ SX2 ) )
          | ~ ( ~ ! [SX2: $i] :
                    ( ~ ( SX1 @ SX2 )
                    | ( ( sK53_SY235 @ SX1 @ SX0 )
                      = SX2 ) )
              | ~ ( SX1 @ ( sK53_SY235 @ SX1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1283]) ).

thf(1532,plain,
    ( ( ! [SX0: $i > $o,SX1: $i > $o] :
          ( ~ ( ( ( sK51_Xx @ SX1 @ SX0 )
               != ( sK52_SY1871 @ SX1 @ SX0 ) )
              | ~ ~ ( ~ ( ~ ( SX0 @ ( sK51_Xx @ SX1 @ SX0 ) )
                        | ~ ( SX1 @ ( sK52_SY1871 @ SX1 @ SX0 ) ) )
                    | ~ ( ( SX0 @ ( sK51_Xx @ SX1 @ SX0 ) )
                        | ( SX1 @ ( sK52_SY1871 @ SX1 @ SX0 ) ) ) ) )
          | ! [SX2: $i] :
              ( ~ ( ~ ( SX1 @ ( sK50_SY236 @ SX2 @ SX1 @ SX0 ) )
                  | ~ ( ( SX2
                       != ( sK50_SY236 @ SX2 @ SX1 @ SX0 ) ) ) )
              | ~ ( SX1 @ SX2 ) )
          | ~ ( ~ ! [SX2: $i] :
                    ( ~ ( SX0 @ SX2 )
                    | ( ( sK49_SY232 @ SX1 @ SX0 )
                      = SX2 ) )
              | ~ ( SX0 @ ( sK49_SY232 @ SX1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1284]) ).

thf(1533,plain,
    ! [SV203: $i,SV420: $i > $o] :
      ( ( ( ~ ( ~ ( SV420 @ ( sK39_Xx @ SV420 @ SV203 ) )
              | ~ ( in @ ( sK39_Xx @ SV420 @ SV203 ) @ SV203 ) ) )
        = $true )
      | ( ( ! [SY2653: $i] :
              ( ~ ( in @ SY2653 @ SV203 )
              | ~ ( SV420 @ SY2653 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1285]) ).

thf(1534,plain,
    ! [SV557: $i,SV204: $i > $o] :
      ( ( ( ~ ( ~ ( SV204 @ ( sK20_SY57 @ SV557 @ SV204 ) )
              | ~ ( ( SV557
                   != ( sK20_SY57 @ SV557 @ SV204 ) ) ) )
          | ~ ( SV204 @ SV557 ) )
        = $true )
      | ( ( SV204
          @ ( descr
            @ ^ [SY2291: $i] : ( SV204 @ SY2291 ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1286]) ).

thf(1535,plain,
    ! [SV558: $i,SV205: $i > $o] :
      ( ( ( ~ ( ~ ( SV205 @ ( sK42_Xy @ SV558 @ SV205 ) )
              | ~ ( ( SV558
                   != ( sK42_Xy @ SV558 @ SV205 ) ) ) )
          | ~ ( SV205 @ SV558 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2293: $i] :
                    ( ~ ( SV205 @ SY2293 )
                    | ( ( sK41_SY198 @ SV205 )
                      = SY2293 ) )
              | ~ ( SV205 @ ( sK41_SY198 @ SV205 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1287]) ).

thf(1536,plain,
    ! [SV206: $i,SV421: $i,SV559: $i > $i] :
      ( ( ~ ( ~ ( in @ ( sK94_Xx @ SV559 @ SV421 @ SV206 ) @ SV206 )
            | ~ ~ ( in @ ( SV559 @ ( sK94_Xx @ SV559 @ SV421 @ SV206 ) ) @ SV421 ) )
        | ! [SY2823: $i] :
            ( ~ ( in @ SY2823 @ SV206 )
            | ( ( ap @ SV206 @ SV421
                @ ( lam @ SV206 @ SV421
                  @ ^ [SY2824: $i] : ( SV559 @ SY2824 ) )
                @ SY2823 )
              = ( SV559 @ SY2823 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1288]) ).

thf(1537,plain,
    ( ( in @ sK2_SY1822 @ ( powerset @ sK1_A ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1289]) ).

thf(1538,plain,
    ( ( ~ ( ~ ( in @ sK3_SY1826 @ ( powerset @ sK1_A ) )
          | ~ ~ ( ~ ( in @ sK4_SY1829 @ ( powerset @ sK1_A ) )
                | ~ ~ ( ~ ( in @ sK5_SY1831 @ sK1_A )
                      | ~ ~ ( ~ ( in @ sK5_SY1831 @ ( binintersect @ sK2_SY1822 @ sK3_SY1826 ) )
                            | ~ ~ ( in @ sK5_SY1831 @ ( binunion @ sK3_SY1826 @ sK4_SY1829 ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1290]) ).

thf(1539,plain,
    ! [SV422: $i,SV207: $i,SV560: $i] :
      ( ( ~ ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        | ! [SY2825: $i > $o] :
            ( ~ ( ~ ( in @ ( sK81_Xx @ SY2825 @ SV560 @ SV422 @ SV207 ) @ SV207 )
                | ~ ~ ( ~ ( in @ ( sK82_SY1880 @ SY2825 @ SV560 @ SV422 @ SV207 ) @ SV422 )
                      | ~ ~ ( ~ ( in @ ( kpair @ ( sK81_Xx @ SY2825 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SY2825 @ SV560 @ SV422 @ SV207 ) ) @ SV560 )
                            | ~ ~ ( SY2825 @ ( kpair @ ( sK81_Xx @ SY2825 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SY2825 @ SV560 @ SV422 @ SV207 ) ) ) ) ) )
            | ! [SY2826: $i] :
                ( ~ ( in @ SY2826 @ SV560 )
                | ( SY2825 @ SY2826 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1291]) ).

thf(1540,plain,
    ! [SV423: $i,SV208: $i,SV561: $i] :
      ( ( ~ ( subset @ SV561 @ ( cartprod @ SV208 @ SV423 ) )
        | ! [SY2827: $i] :
            ( ~ ( subset @ SY2827 @ ( cartprod @ SV208 @ SV423 ) )
            | ~ ( ~ ( in @ ( sK84_Xx @ SY2827 @ SV561 @ SV423 @ SV208 ) @ SV208 )
                | ~ ~ ( ~ ( in @ ( sK85_SY1881 @ SY2827 @ SV561 @ SV423 @ SV208 ) @ SV423 )
                      | ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SY2827 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SY2827 @ SV561 @ SV423 @ SV208 ) ) @ SV561 )
                            | ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SY2827 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SY2827 @ SV561 @ SV423 @ SV208 ) ) @ SY2827 ) ) ) )
            | ( subset @ SV561 @ SY2827 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1292]) ).

thf(1541,plain,
    ! [SV209: $i,SV424: $i > $o] :
      ( ( ( ~ ( ~ ( in @ ( sK70_Xx @ SV424 @ SV209 ) @ SV209 )
              | ~ ~ ( ~ ( in @ ( sK71_SY1877 @ SV424 @ SV209 ) @ SV209 )
                    | ~ ~ ( ~ ( SV424 @ ( sK70_Xx @ SV424 @ SV209 ) )
                          | ~ ~ ( ~ ( SV424 @ ( sK71_SY1877 @ SV424 @ SV209 ) )
                                | ~ ( ( ( sK70_Xx @ SV424 @ SV209 )
                                     != ( sK71_SY1877 @ SV424 @ SV209 ) ) ) ) ) ) ) )
        = $true )
      | ( ( ! [SY2662: $i] :
              ( ~ ( SV424 @ SY2662 )
              | ~ ( in @ SY2662 @ SV209 ) )
          | ( singleton
            @ ( dsetconstr @ SV209
              @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1293]) ).

thf(1542,plain,
    ! [SV425: $i,SV210: $i] :
      ( ( ( SV210 != SV425 )
        = $true )
      | ( ( ~ ( ~ ! [SY2664: $i,SY2665: $i] :
                    ( ( SY2664 != SY2665 )
                    | ~ ( in @ SY2664 @ SV210 )
                    | ( in @ SY2665 @ SV425 ) )
              | ~ ! [SY2666: $i,SY2667: $i] :
                    ( ( SY2666 != SY2667 )
                    | ~ ( in @ SY2667 @ SV425 )
                    | ( in @ SY2666 @ SV210 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1294]) ).

thf(1543,plain,
    ! [SV562: $i,SV211: $i > $o] :
      ( ( ( ~ ( ~ ( SV211 @ ( sK48_SY224 @ SV562 @ SV211 ) )
              | ~ ( ( SV562
                   != ( sK48_SY224 @ SV562 @ SV211 ) ) ) )
          | ~ ( SV211 @ SV562 ) )
        = $true )
      | ( ( ! [SY2314: $i] :
              ( ~ ( SV211 @ SY2314 )
              | ! [SY2315: $i] :
                  ( ~ ( SV211 @ SY2315 )
                  | ( SY2314 = SY2315 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1295]) ).

thf(1544,plain,
    ! [SV212: $i,SV426: $i,SV563: $i > $i] :
      ( ( ~ ( ~ ( in @ ( sK77_Xx @ SV563 @ SV426 @ SV212 ) @ SV212 )
            | ~ ~ ( in @ ( SV563 @ ( sK77_Xx @ SV563 @ SV426 @ SV212 ) ) @ SV426 ) )
        | ( func @ SV212 @ SV426
          @ ( lam @ SV212 @ SV426
            @ ^ [SY2828: $i] : ( SV563 @ SY2828 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1296]) ).

thf(1545,plain,
    ! [SV213: $i > $o,SV427: $i > $o] :
      ( ( ( ~ ( ( ( sK60_Xx @ SV427 @ SV213 )
               != ( sK61_SY1874 @ SV427 @ SV213 ) )
              | ~ ~ ( ~ ( ~ ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
                        | ~ ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) ) )
                    | ~ ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
                        | ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) ) ) ) ) )
        = $true )
      | ( ( ! [SY2670: $i] :
              ( ~ ( ~ ( SV213 @ ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2670
                       != ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV213 @ SY2670 ) )
          | ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1297]) ).

thf(1546,plain,
    ! [SV214: $i,SV428: $i] :
      ( ( ( ~ ( in @ SV428 @ ( powerset @ SV214 ) ) )
        = $true )
      | ( ( ! [SY2674: $i] :
              ( ~ ( in @ SY2674 @ ( powerset @ SV214 ) )
              | ~ ( ~ ( in @ ( sK98_Xx @ SY2674 @ SV428 @ SV214 ) @ SV214 )
                  | ~ ~ ( ~ ( in @ ( sK98_Xx @ SY2674 @ SV428 @ SV214 ) @ SV428 )
                        | ~ ~ ( in @ ( sK98_Xx @ SY2674 @ SV428 @ SV214 ) @ SY2674 ) ) )
              | ( in @ SV428 @ ( powerset @ SY2674 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1298]) ).

thf(1547,plain,
    ! [SV215: $i,SV429: $i] :
      ( ( ( ~ ( in @ SV429 @ ( setunion @ SV215 ) ) )
        = $true )
      | ( ( ! [SY2675: $o] :
              ( ~ ( ~ ( in @ SV429 @ ( sK31_B @ SY2675 @ SV429 @ SV215 ) )
                  | ~ ~ ( ~ ( in @ ( sK31_B @ SY2675 @ SV429 @ SV215 ) @ SV215 )
                        | ~ ~ SY2675 ) )
              | SY2675 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1299]) ).

thf(1548,plain,
    ! [SV216: $i,SV430: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK26_Xx @ SV430 @ SV216 ) @ SV216 )
              | ~ ~ ( in @ ( sK26_Xx @ SV430 @ SV216 ) @ SV430 ) ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV430 )
              | ~ ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV216 ) )
          | ( SV216 = SV430 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1300]) ).

thf(1549,plain,
    ! [SV217: $i,SV431: $i] :
      ( ( ( ~ ( in @ SV431 @ ( setunion @ SV217 ) ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK69_X @ SV431 @ SV217 ) @ SV217 )
              | ~ ( in @ SV431 @ ( sK69_X @ SV431 @ SV217 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1301]) ).

thf(1550,plain,
    ! [SV564: $i,SV432: $i,SV218: $i] :
      ( ( ~ ( func @ SV218 @ SV432 @ SV564 )
        | ! [SY2829: $i] :
            ( ~ ( func @ SV218 @ SV432 @ SY2829 )
            | ~ ( ~ ( in @ ( sK83_Xx @ SY2829 @ SV564 @ SV432 @ SV218 ) @ SV218 )
                | ~ ( ( ( ap @ SV218 @ SV432 @ SV564 @ ( sK83_Xx @ SY2829 @ SV564 @ SV432 @ SV218 ) )
                     != ( ap @ SV218 @ SV432 @ SY2829 @ ( sK83_Xx @ SY2829 @ SV564 @ SV432 @ SV218 ) ) ) ) )
            | ! [SY2830: $i] :
                ( ~ ( in @ SY2830 @ SV218 )
                | ! [SY2831: $i] :
                    ( ~ ( in @ SY2831 @ SV432 )
                    | ~ ( in @ ( kpair @ SY2830 @ SY2831 ) @ SY2829 )
                    | ( in @ ( kpair @ SY2830 @ SY2831 ) @ SV564 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1302]) ).

thf(1551,plain,
    ! [SV219: $i,SV433: $i] :
      ( ( ( ~ ( in @ SV433 @ ( powerset @ SV219 ) ) )
        = $true )
      | ( ( ! [SY2680: $i] :
              ( ~ ( in @ SY2680 @ ( powerset @ SV219 ) )
              | ~ ( ~ ( in @ ( sK96_Xx @ SY2680 @ SV433 @ SV219 ) @ SV219 )
                  | ~ ~ ( ~ ( in @ ( sK96_Xx @ SY2680 @ SV433 @ SV219 ) @ SV433 )
                        | ~ ~ ( in @ ( sK96_Xx @ SY2680 @ SV433 @ SV219 ) @ SY2680 ) ) )
              | ~ ( ~ ( in @ ( sK95_Xx @ SY2680 @ SV433 @ SV219 ) @ SV219 )
                  | ~ ~ ( ~ ( in @ ( sK95_Xx @ SY2680 @ SV433 @ SV219 ) @ SY2680 )
                        | ~ ~ ( in @ ( sK95_Xx @ SY2680 @ SV433 @ SV219 ) @ SV433 ) ) )
              | ( SV433 = SY2680 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1303]) ).

thf(1552,plain,
    ! [SV434: $i > $o,SV220: $i,SV565: $i] :
      ( ( ~ ( in @ SV565 @ SV220 )
        | ~ ( SV434 @ SV565 )
        | ~ ( ~ ( in @ ( sK73_Xy @ SV565 @ SV434 @ SV220 ) @ SV220 )
            | ~ ~ ( ~ ( SV434 @ ( sK73_Xy @ SV565 @ SV434 @ SV220 ) )
                  | ~ ( ( ( sK73_Xy @ SV565 @ SV434 @ SV220 )
                       != SV565 ) ) ) )
        | ( singleton
          @ ( dsetconstr @ SV220
            @ ^ [SY2682: $i] : ( SV434 @ SY2682 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1304]) ).

thf(1553,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ~ ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        | ~ ( ~ ~ ( ~ ( ( in @ SV566 @ SV221 )
                      | ~ ( in @ SV566 @ SV221 )
                      | ! [SX3: $o] : SX3 )
                  | ~ ~ ( ~ ( ( in @ SV566 @ SV221 )
                            | ( in @ SV566 @ SV435 )
                            | ! [SX3: $o] : SX3 )
                        | ~ ( ( in @ SV566 @ SV221 )
                            | ! [SX3: $o] :
                                ( ~ SX3
                                | SX3 ) ) ) )
            | ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SV566 @ SV435 )
                            | ~ ( in @ SV566 @ SV221 )
                            | ! [SX3: $o] : SX3 )
                        | ~ ~ ( ~ ( ~ ( in @ SV566 @ SV435 )
                                  | ( in @ SV566 @ SV435 )
                                  | ! [SX3: $o] : SX3 )
                              | ~ ( ~ ( in @ SV566 @ SV435 )
                                  | ! [SX3: $o] :
                                      ( ~ SX3
                                      | SX3 ) ) ) )
                  | ~ ~ ( ~ ! [SY2839: $o] :
                              ( ~ SY2839
                              | ~ ( in @ SV566 @ SV221 )
                              | SY2839 )
                        | ~ ~ ( ~ ! [SY2840: $o] :
                                    ( ~ SY2840
                                    | ( in @ SV566 @ SV435 )
                                    | SY2840 )
                              | ~ ! [SX3: $o] :
                                    ( ~ SX3
                                    | ~ SX3
                                    | SX3 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1305]) ).

thf(1554,plain,
    ! [SV222: $i,SV436: $i,SV567: $i > $i] :
      ( ( ~ ( ~ ( in @ ( sK76_Xx @ SV567 @ SV436 @ SV222 ) @ SV222 )
            | ~ ~ ( in @ ( SV567 @ ( sK76_Xx @ SV567 @ SV436 @ SV222 ) ) @ SV436 ) )
        | ( func @ SV222 @ SV436
          @ ( dpsetconstr @ SV222 @ SV436
            @ ^ [SY2842: $i,SY2843: $i] :
                ( ( SV567 @ SY2842 )
                = SY2843 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1306]) ).

thf(1555,plain,
    ! [SV223: $i] :
      ( ( ~ ! [SY2355: $i,SY2356: $i] :
              ( ~ ( in @ SY2356 @ ( setadjoin @ SV223 @ SY2355 ) )
              | ( SY2356 = SV223 )
              | ( in @ SY2356 @ SY2355 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1307]) ).

thf(1556,plain,
    ! [SV223: $i] :
      ( ( ~ ~ ( ~ ! [SY2357: $i,SY2358: $i] :
                    ( ( SY2358 != SV223 )
                    | ( in @ SY2358 @ ( setadjoin @ SV223 @ SY2357 ) ) )
              | ~ ! [SY2359: $i,SY2360: $i] :
                    ( ~ ( in @ SY2360 @ SY2359 )
                    | ( in @ SY2360 @ ( setadjoin @ SV223 @ SY2359 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1307]) ).

thf(1557,plain,
    ! [SV224: $i,SV437: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK65_Xx @ SV437 @ SV224 ) @ SV224 )
              | ~ ~ ( in @ ( sK65_Xx @ SV437 @ SV224 ) @ SV437 ) ) )
        = $true )
      | ( ( subset @ SV224 @ SV437 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1308]) ).

thf(1558,plain,
    ! [SV225: $i,SV438: $i] :
      ( ( ( ~ ( ~ ( ~ ( in @ ( sK6_Xx @ SV438 @ SV225 ) @ SV225 )
                  | ~ ( in @ ( sK6_Xx @ SV438 @ SV225 ) @ SV438 ) )
              | ~ ( ( in @ ( sK6_Xx @ SV438 @ SV225 ) @ SV225 )
                  | ( in @ ( sK6_Xx @ SV438 @ SV225 ) @ SV438 ) ) ) )
        = $true )
      | ( ( SV225 = SV438 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1309]) ).

thf(1559,plain,
    ! [SV439: $i,SV226: $i] :
      ( ( ~ ~ ( ~ ! [SY2696: $i] :
                    ( ~ ( in @ SY2696 @ ( binunion @ SV226 @ SV439 ) )
                    | ( in @ SY2696 @ SV226 )
                    | ( in @ SY2696 @ SV439 )
                    | ! [SX3: $o] : SX3 )
              | ~ ! [SY2698: $i] :
                    ( ~ ( in @ SY2698 @ ( binunion @ SV226 @ SV439 ) )
                    | ( in @ SY2698 @ SV226 )
                    | ! [SX3: $o] :
                        ( ~ SX3
                        | SX3 ) ) )
        | ~ ~ ( ~ ! [SY2700: $i] :
                    ( ~ ( in @ SY2700 @ ( binunion @ SV226 @ SV439 ) )
                    | ! [SY2701: $o] :
                        ( ~ SY2701
                        | ( in @ SY2700 @ SV439 )
                        | SY2701 ) )
              | ~ ( ! [SY2702: $i] :
                      ~ ( in @ SY2702 @ ( binunion @ SV226 @ SV439 ) )
                  | ! [SX2: $o] :
                      ( ~ SX2
                      | ~ SX2
                      | SX2 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1310]) ).

thf(1560,plain,
    ! [SV440: $i > $o,SV227: $i] :
      ( ( ( ! [SY2704: $i] :
              ( ~ ( in @ SY2704 @ SV227 )
              | ( SV440 @ SY2704 ) ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK38_Xx @ SV440 @ SV227 ) @ SV227 )
              | ~ ~ ( SV440 @ ( sK38_Xx @ SV440 @ SV227 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1311]) ).

thf(1561,plain,
    ! [SV228: $i > $o,SV568: $i] :
      ( ( ( ~ ( ~ ( ( ( sK47_Xy @ SV568 @ SV228 )
                   != SV568 )
                  | ~ ( SV228 @ ( sK47_Xy @ SV568 @ SV228 ) ) )
              | ~ ( ( ( sK47_Xy @ SV568 @ SV228 )
                    = SV568 )
                  | ( SV228 @ ( sK47_Xy @ SV568 @ SV228 ) ) ) ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2375: $i] :
                    ( ~ ( SV228 @ SY2375 )
                    | ( ( sK46_SY211 @ SV228 )
                      = SY2375 ) )
              | ~ ( SV228 @ ( sK46_SY211 @ SV228 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1312]) ).

thf(1562,plain,
    ! [SV229: $i,SV441: $i > $o] :
      ( ( ( ~ ( ~ ( in @ ( sK74_Xx @ SV441 @ SV229 ) @ SV229 )
              | ~ ~ ( ~ ( in @ ( sK75_SY1878 @ SV441 @ SV229 ) @ SV229 )
                    | ~ ~ ( ~ ( SV441 @ ( sK74_Xx @ SV441 @ SV229 ) )
                          | ~ ~ ( ~ ( SV441 @ ( sK75_SY1878 @ SV441 @ SV229 ) )
                                | ~ ( ( ( sK74_Xx @ SV441 @ SV229 )
                                     != ( sK75_SY1878 @ SV441 @ SV229 ) ) ) ) ) ) ) )
        = $true )
      | ( ( ! [SY2705: $i] :
              ( ~ ( SV441 @ SY2705 )
              | ~ ( in @ SY2705 @ SV229 ) )
          | ( singleton
            @ ( dsetconstr @ SV229
              @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1313]) ).

thf(1563,plain,
    ! [SV442: $i,SV230: $i,SV569: $i] :
      ( ( ~ ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        | ! [SY2844: $i] :
            ( ~ ( subset @ SY2844 @ ( cartprod @ SV230 @ SV442 ) )
            | ~ ( ~ ( in @ ( sK88_Xx @ SY2844 @ SV569 @ SV442 @ SV230 ) @ SV230 )
                | ~ ~ ( ~ ( in @ ( sK89_SY1883 @ SY2844 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                      | ~ ~ ( ~ ( in @ ( kpair @ ( sK88_Xx @ SY2844 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SY2844 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
                            | ~ ~ ( in @ ( kpair @ ( sK88_Xx @ SY2844 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SY2844 @ SV569 @ SV442 @ SV230 ) ) @ SY2844 ) ) ) )
            | ~ ( ~ ( in @ ( sK86_Xx @ SY2844 @ SV569 @ SV442 @ SV230 ) @ SV230 )
                | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SY2844 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                      | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SY2844 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SY2844 @ SV569 @ SV442 @ SV230 ) ) @ SY2844 )
                            | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SY2844 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SY2844 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
            | ( SV569 = SY2844 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1314]) ).

thf(1564,plain,
    ! [SV231: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK9_Xx @ SV231 ) @ omega )
                    | ~ ( in @ ( sK9_Xx @ SV231 ) @ SV231 ) )
              | ~ ~ ( in @ ( setadjoin @ ( sK9_Xx @ SV231 ) @ ( sK9_Xx @ SV231 ) ) @ SV231 ) ) )
        = $true )
      | ( ( ~ ( in @ emptyset @ SV231 ) )
        = $true )
      | ( ( ! [SY2382: $i] :
              ( ~ ( in @ SY2382 @ omega )
              | ( in @ SY2382 @ SV231 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1315]) ).

thf(1565,plain,
    ! [SV443: $o,SV232: $i,SV570: $i] :
      ( ( ~ ( in @ SV570 @ SV232 )
        | ! [SY2845: $i] :
            ( ~ ( in @ SY2845 @ SV232 )
            | SV443
            | ( in @ SY2845
              @ ( dsetconstr @ SV232
                @ ^ [SY2846: $i] :
                    ( ~ ( ~ SV443
                        | ( SY2846 != SV570 ) )
                    | ~ ( ~ ~ SV443
                        | ( SY2846 != SY2845 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1316]) ).

thf(1566,plain,
    ! [SV232: $i,SV571: $i] :
      ( ( ~ ( in @ SV571 @ SV232 )
        | ! [SY2847: $i] :
            ( ~ ( in @ SY2847 @ SV232 )
            | $true
            | ( in @ SY2847
              @ ( dsetconstr @ SV232
                @ ^ [SY2848: $i] :
                    ( ~ ( ~ $true
                        | ( SY2848 != SV571 ) )
                    | ~ ( ~ ~ $true
                        | ( SY2848 != SY2847 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1317]) ).

thf(1567,plain,
    ! [SV232: $i,SV572: $i] :
      ( ( ~ ( in @ SV572 @ SV232 )
        | ! [SY2849: $i] :
            ( ~ ( in @ SY2849 @ SV232 )
            | $false
            | ( in @ SY2849
              @ ( dsetconstr @ SV232
                @ ^ [SY2850: $i] :
                    ( ~ ( ~ $false
                        | ( SY2850 != SV572 ) )
                    | ~ ( ~ ~ $false
                        | ( SY2850 != SY2849 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1318]) ).

thf(1568,plain,
    ! [SV233: $i] :
      ( ( ~ ! [SY2387: $i] :
              ( ~ ( ~ ( in @ ( sK19_Xx @ SY2387 @ SV233 ) @ SY2387 )
                  | ~ ~ ( in @ ( sK19_Xx @ SY2387 @ SV233 ) @ SV233 ) )
              | ! [SX2: $i] :
                  ~ ( in @ SX2 @ SY2387 )
              | ~ ( ~ ! [SY2389: $i] :
                        ( ~ ( in @ SY2389 @ ( sK15_B @ SV233 ) )
                        | ! [SY2390: $i] :
                            ( ~ ( in @ SY2390 @ SY2389 )
                            | ( in @ SY2390 @ ( sK17_SY1842 @ SY2387 @ SV233 ) ) )
                        | ( in @ ( sK18_SY1856 @ SY2387 @ SV233 ) @ SY2389 ) )
                  | ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1842 @ SY2387 @ SV233 ) @ ( sK15_B @ SV233 ) )
                              | ~ ( in @ ( sK18_SY1856 @ SY2387 @ SV233 ) @ SY2387 ) )
                        | ~ ! [SY2391: $i] :
                              ( ~ ( in @ SY2391 @ ( sK17_SY1842 @ SY2387 @ SV233 ) )
                              | ~ ( in @ SY2391 @ SY2387 ) ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1319]) ).

thf(1569,plain,
    ! [SV233: $i] :
      ( ( ~ ~ ( ~ ! [SY2392: $i,SY2393: $i] :
                    ( ~ ( in @ SY2392 @ ( sK15_B @ SV233 ) )
                    | ~ ( in @ SY2393 @ ( sK15_B @ SV233 ) )
                    | ! [SX3: $i] :
                        ( ~ ( in @ SX3 @ SY2392 )
                        | ( in @ SX3 @ SY2393 ) )
                    | ! [SX3: $i] :
                        ( ~ ( in @ SX3 @ SY2393 )
                        | ( in @ SX3 @ SY2392 ) ) )
              | ~ ~ ( ~ ! [SY2396: $i] :
                          ( ~ ( in @ SY2396 @ ( sK15_B @ SV233 ) )
                          | ! [SY2397: $i] :
                              ( ~ ( in @ SY2397 @ SY2396 )
                              | ( in @ SY2397 @ SV233 ) ) )
                    | ~ ! [SY2398: $i,SY2399: $i] :
                          ( ~ ( in @ SY2398 @ SV233 )
                          | ~ ( in @ SY2399 @ SV233 )
                          | ~ ( ~ ( in @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) @ ( sK15_B @ SV233 ) )
                              | ~ ~ ( ~ ( ~ ( in @ SY2398 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) )
                                        | ~ ( in @ SY2399 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) ) )
                                    | ~ ( ( in @ SY2398 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) )
                                        | ( in @ SY2399 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) ) ) ) )
                          | ( SY2398 = SY2399 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1319]) ).

thf(1570,plain,
    ! [SV234: $i,SV444: $i > $o] :
      ( ( ( ~ ( ~ ( SV444 @ ( sK37_Xx @ SV444 @ SV234 ) )
              | ~ ( in @ ( sK37_Xx @ SV444 @ SV234 ) @ SV234 ) ) )
        = $true )
      | ( ( ! [SY2712: $i] :
              ( ~ ( in @ SY2712 @ SV234 )
              | ~ ( SV444 @ SY2712 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1320]) ).

thf(1571,plain,
    ! [SV573: $i,SV235: $i > $o] :
      ( ( ( ~ ( ~ ( SV235 @ ( sK33_SY142 @ SV573 @ SV235 ) )
              | ~ ( ( SV573
                   != ( sK33_SY142 @ SV573 @ SV235 ) ) ) )
          | ~ ( SV235 @ SV573 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2403: $i] :
                    ( ( SY2403
                     != ( sK32_Xx @ SV235 ) )
                    | ( SV235 @ SY2403 ) )
              | ~ ! [SY2404: $i] :
                    ( ~ ( SV235 @ SY2404 )
                    | ( SY2404
                      = ( sK32_Xx @ SV235 ) ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1321]) ).

thf(1572,plain,
    ! [SV445: $i,SV236: $i,SV574: $i] :
      ( ( ~ ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        | ! [SY2851: $i > $o] :
            ( ~ ( ~ ( in @ ( sK79_Xx @ SY2851 @ SV574 @ SV445 @ SV236 ) @ SV236 )
                | ~ ~ ( ~ ( in @ ( sK80_SY1879 @ SY2851 @ SV574 @ SV445 @ SV236 ) @ SV445 )
                      | ~ ~ ( ~ ( in @ ( kpair @ ( sK79_Xx @ SY2851 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SY2851 @ SV574 @ SV445 @ SV236 ) ) @ SV574 )
                            | ~ ~ ( SY2851 @ ( kpair @ ( sK79_Xx @ SY2851 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SY2851 @ SV574 @ SV445 @ SV236 ) ) ) ) ) )
            | ! [SY2852: $i] :
                ( ~ ( in @ SY2852 @ SV574 )
                | ( SY2851 @ SY2852 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1322]) ).

thf(1573,plain,
    ! [SV446: $i > $o,SV237: $i] :
      ( ( ( ! [SY2716: $i] :
              ( ~ ( in @ SY2716 @ SV237 )
              | ( SV446 @ SY2716 ) ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK35_Xx @ SV446 @ SV237 ) @ SV237 )
              | ~ ~ ( SV446 @ ( sK35_Xx @ SV446 @ SV237 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1323]) ).

thf(1574,plain,
    ! [SV447: $o,SV238: $i,SV575: $i] :
      ( ( ~ ( in @ SV575 @ SV238 )
        | ! [SY2853: $i] :
            ( ~ ( in @ SY2853 @ SV238 )
            | ~ SV447
            | ( ( dsetconstr @ SV238
                @ ^ [SY2854: $i] :
                    ( ~ ( ~ SV447
                        | ( SY2854 != SV575 ) )
                    | ~ ( ~ ~ SV447
                        | ( SY2854 != SY2853 ) ) ) )
              = ( setadjoin @ SV575 @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1324]) ).

thf(1575,plain,
    ! [SV238: $i,SV576: $i] :
      ( ( ~ ( in @ SV576 @ SV238 )
        | ! [SY2855: $i] :
            ( ~ ( in @ SY2855 @ SV238 )
            | ~ $true
            | ( ( dsetconstr @ SV238
                @ ^ [SY2856: $i] :
                    ( ~ ( ~ $true
                        | ( SY2856 != SV576 ) )
                    | ~ ( ~ ~ $true
                        | ( SY2856 != SY2855 ) ) ) )
              = ( setadjoin @ SV576 @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1325]) ).

thf(1576,plain,
    ! [SV238: $i,SV577: $i] :
      ( ( ~ ( in @ SV577 @ SV238 )
        | ! [SY2857: $i] :
            ( ~ ( in @ SY2857 @ SV238 )
            | ~ $false
            | ( ( dsetconstr @ SV238
                @ ^ [SY2858: $i] :
                    ( ~ ( ~ $false
                        | ( SY2858 != SV577 ) )
                    | ~ ( ~ ~ $false
                        | ( SY2858 != SY2857 ) ) ) )
              = ( setadjoin @ SV577 @ emptyset ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1326]) ).

thf(1577,plain,
    ! [SV239: $i,SV578: $i] :
      ( ( ( ~ ( in @ SV578 @ SV239 ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK14_B @ SV239 ) @ SV239 )
              | ~ ! [SY2416: $i] :
                    ( ~ ( in @ SY2416 @ ( sK14_B @ SV239 ) )
                    | ~ ( in @ SY2416 @ SV239 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1327]) ).

thf(1578,plain,
    ! [SV448: $o,SV240: $i,SV579: $i] :
      ( ( ~ ( in @ SV579 @ SV240 )
        | ! [SY2859: $i] :
            ( ~ ( in @ SY2859 @ SV240 )
            | ( singleton
              @ ( dsetconstr @ SV240
                @ ^ [SY2860: $i] :
                    ( ~ ( ~ SV448
                        | ( SY2860 != SV579 ) )
                    | ~ ( ~ ~ SV448
                        | ( SY2860 != SY2859 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1328]) ).

thf(1579,plain,
    ! [SV240: $i,SV580: $i] :
      ( ( ~ ( in @ SV580 @ SV240 )
        | ! [SY2861: $i] :
            ( ~ ( in @ SY2861 @ SV240 )
            | ( singleton
              @ ( dsetconstr @ SV240
                @ ^ [SY2862: $i] :
                    ( ~ ( ~ $true
                        | ( SY2862 != SV580 ) )
                    | ~ ( ~ ~ $true
                        | ( SY2862 != SY2861 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1329]) ).

thf(1580,plain,
    ! [SV240: $i,SV581: $i] :
      ( ( ~ ( in @ SV581 @ SV240 )
        | ! [SY2863: $i] :
            ( ~ ( in @ SY2863 @ SV240 )
            | ( singleton
              @ ( dsetconstr @ SV240
                @ ^ [SY2864: $i] :
                    ( ~ ( ~ $false
                        | ( SY2864 != SV581 ) )
                    | ~ ( ~ ~ $false
                        | ( SY2864 != SY2863 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1330]) ).

thf(1581,plain,
    ! [SV582: $i,SV241: $i > $o] :
      ( ( ( ~ ( SV241 @ SV582 ) )
        = $true )
      | ( ( ~ ( ~ ( SV241 @ ( sK44_Xx @ SV241 ) )
              | ~ ~ ( ~ ( SV241 @ ( sK45_SY1868 @ SV241 ) )
                    | ~ ( ( ( sK44_Xx @ SV241 )
                         != ( sK45_SY1868 @ SV241 ) ) ) ) )
          | ~ ( ~ ! [SY2422: $i] :
                    ( ~ ( SV241 @ SY2422 )
                    | ( ( sK43_SY205 @ SV241 )
                      = SY2422 ) )
              | ~ ( SV241 @ ( sK43_SY205 @ SV241 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1331]) ).

thf(1582,plain,
    ! [SV242: $i,SV449: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK64_Xx @ SV449 @ SV242 ) @ SV242 )
              | ~ ~ ( in @ ( sK64_Xx @ SV449 @ SV242 ) @ SV449 ) ) )
        = $true )
      | ( ( subset @ SV242 @ SV449 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1332]) ).

thf(1583,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ! [SX2: $i] :
              ( ~ ( in @ SX1 @ SX2 )
              | ~ ( in @ SX2 @ SX0 ) )
          | ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1333]) ).

thf(1584,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
          | ~ ( ~ ( in @ SX1 @ ( sK8_B @ SX1 @ SX0 ) )
              | ~ ( in @ ( sK8_B @ SX1 @ SX0 ) @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1334]) ).

thf(1585,plain,
    ! [SV583: $i,SV450: $i,SV243: $i] :
      ( ( ~ ( func @ SV243 @ SV450 @ SV583 )
        | ! [SY2865: $i] :
            ( ~ ( func @ SV243 @ SV450 @ SY2865 )
            | ~ ( ~ ( in @ ( sK90_Xx @ SY2865 @ SV583 @ SV450 @ SV243 ) @ SV243 )
                | ~ ( ( ( ap @ SV243 @ SV450 @ SV583 @ ( sK90_Xx @ SY2865 @ SV583 @ SV450 @ SV243 ) )
                     != ( ap @ SV243 @ SV450 @ SY2865 @ ( sK90_Xx @ SY2865 @ SV583 @ SV450 @ SV243 ) ) ) ) )
            | ( SV583 = SY2865 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1335]) ).

thf(1586,plain,
    ! [SV244: $i,SV584: $i] :
      ( ( ( ! [SY2866: $i > $i] :
              ~ ( ~ ( in @ ( sK93_Xx @ SY2866 @ SV584 @ SV244 ) @ SV244 )
                | ~ ~ ( in @ ( SY2866 @ ( sK93_Xx @ SY2866 @ SV584 @ SV244 ) ) @ SV584 ) ) )
        = $true )
      | ( $true = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1336]) ).

thf(1587,plain,
    ! [SV451: $i,SV245: $i,SV585: $i] :
      ( ( ~ ( in @ SV585 @ ( funcSet @ SV245 @ SV451 ) )
        | ! [SY2867: $i] :
            ( ~ ( in @ SY2867 @ ( funcSet @ SV245 @ SV451 ) )
            | ~ ( ~ ( in @ ( sK91_Xx @ SY2867 @ SV585 @ SV451 @ SV245 ) @ SV245 )
                | ~ ( ( ( ap @ SV245 @ SV451 @ SV585 @ ( sK91_Xx @ SY2867 @ SV585 @ SV451 @ SV245 ) )
                     != ( ap @ SV245 @ SV451 @ SY2867 @ ( sK91_Xx @ SY2867 @ SV585 @ SV451 @ SV245 ) ) ) ) )
            | ( SV585 = SY2867 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1337]) ).

thf(1588,plain,
    ! [SV246: $i,SV452: $i > $o] :
      ( ( ( ~ ( ~ ( in @ ( sK36_Xx @ SV452 @ SV246 ) @ SV246 )
              | ~ ( SV452 @ ( sK36_Xx @ SV452 @ SV246 ) ) ) )
        = $true )
      | ( ( ! [SY2727: $i] :
              ( ~ ( SV452 @ SY2727 )
              | ~ ( in @ SY2727 @ SV246 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1338]) ).

thf(1589,plain,
    ! [SV586: $i,SV247: $i > $o] :
      ( ( ( ~ ( ~ ( SV247 @ ( sK22_SY74 @ SV586 @ SV247 ) )
              | ~ ( ( SV586
                   != ( sK22_SY74 @ SV586 @ SV247 ) ) ) )
          | ~ ( SV247 @ SV586 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2435: $i] :
                    ( ~ ( SV247 @ SY2435 )
                    | ( ( sK21_Xx @ SV247 )
                      = SY2435 ) )
              | ~ ( SV247 @ ( sK21_Xx @ SV247 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1339]) ).

thf(1590,plain,
    ! [SV453: $i,SV248: $i] :
      ( ( ( SV248 != SV453 )
        = $true )
      | ( ( ! [SY2728: $i > $o,SY2729: $i > $o] :
              ( ~ ( ~ ( in @ ( sK62_Xx @ SY2729 @ SY2728 @ SV453 @ SV248 ) @ SV248 )
                  | ~ ~ ( ~ ( in @ ( sK63_SY1875 @ SY2729 @ SY2728 @ SV453 @ SV248 ) @ SV453 )
                        | ~ ~ ( ( ( sK62_Xx @ SY2729 @ SY2728 @ SV453 @ SV248 )
                               != ( sK63_SY1875 @ SY2729 @ SY2728 @ SV453 @ SV248 ) )
                              | ~ ~ ( ~ ( ~ ( SY2728 @ ( sK62_Xx @ SY2729 @ SY2728 @ SV453 @ SV248 ) )
                                        | ~ ( SY2729 @ ( sK63_SY1875 @ SY2729 @ SY2728 @ SV453 @ SV248 ) ) )
                                    | ~ ( ( SY2728 @ ( sK62_Xx @ SY2729 @ SY2728 @ SV453 @ SV248 ) )
                                        | ( SY2729 @ ( sK63_SY1875 @ SY2729 @ SY2728 @ SV453 @ SV248 ) ) ) ) ) ) )
              | ( ( dsetconstr @ SV248
                  @ ^ [SX4: $i] : ( SY2728 @ SX4 ) )
                = ( dsetconstr @ SV453
                  @ ^ [SX4: $i] : ( SY2729 @ SX4 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1340]) ).

thf(1591,plain,
    ! [SV454: $i > $o,SV249: $i] :
      ( ( ( ~ ( singleton
              @ ( dsetconstr @ SV249
                @ ^ [SY2732: $i] : ( SV454 @ SY2732 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( SV454 @ ( sK72_Xx @ SV454 @ SV249 ) )
              | ~ ( in @ ( sK72_Xx @ SV454 @ SV249 ) @ SV249 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1341]) ).

thf(1592,plain,
    ! [SV1: $i,SV250: $i] :
      ( ( ( in @ SV250 @ ( powerset @ SV1 ) )
        = $false )
      | ( ( ! [SY2443: $i] :
              ( ~ ( in @ SY2443 @ ( powerset @ SV1 ) )
              | ! [SY2444: $i] :
                  ( ~ ( in @ SY2444 @ ( powerset @ SV1 ) )
                  | ! [SY2445: $i] :
                      ( ~ ( in @ SY2445 @ SV1 )
                      | ~ ( in @ SY2445 @ ( binintersect @ SV250 @ SY2443 ) )
                      | ( in @ SY2445 @ ( binunion @ SV250 @ SY2444 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1342]) ).

thf(1593,plain,
    ! [SV2: $i,SV251: $i] :
      ( ( ( in @ SV251 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( ! [SY2446: $i] :
              ( ~ ( in @ SY2446 @ ( powerset @ SV2 ) )
              | ! [SY2447: $i] :
                  ( ~ ( in @ SY2447 @ SV2 )
                  | ( in @ SY2447 @ ( binunion @ SV251 @ SY2446 ) )
                  | ~ ( in @ SY2447 @ SY2446 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1343]) ).

thf(1594,plain,
    ! [SV3: $i,SV252: $i] :
      ( ( ( in @ SV252 @ ( powerset @ SV3 ) )
        = $false )
      | ( ( ! [SY2448: $i] :
              ( ~ ( in @ SY2448 @ ( powerset @ SV3 ) )
              | ! [SY2449: $i] :
                  ( ~ ( in @ SY2449 @ SV3 )
                  | ( in @ SY2449 @ ( binunion @ SV252 @ SY2448 ) )
                  | ~ ( in @ SY2449 @ SV252 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1344]) ).

thf(1595,plain,
    ! [SV4: $i,SV253: $i] :
      ( ( ( in @ SV253 @ ( powerset @ SV4 ) )
        = $false )
      | ( ( ! [SY2450: $i] :
              ( ~ ( in @ SY2450 @ ( powerset @ SV4 ) )
              | ~ ( subset @ SV253 @ ( setminus @ SV4 @ SY2450 ) )
              | ( subset @ SY2450 @ ( setminus @ SV4 @ SV253 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1345]) ).

thf(1596,plain,
    ! [SV5: $i,SV254: $i] :
      ( ( ( in @ SV254 @ ( powerset @ SV5 ) )
        = $false )
      | ( ( ! [SY2451: $i] :
              ( ~ ( in @ SY2451 @ ( powerset @ SV5 ) )
              | ~ ( subset @ SV254 @ ( setminus @ SV5 @ SY2451 ) )
              | ! [SY2452: $i] :
                  ( ~ ( in @ SY2452 @ SV5 )
                  | ~ ( in @ SY2452 @ SY2451 )
                  | ( in @ SY2452 @ ( setminus @ SV5 @ SV254 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1346]) ).

thf(1597,plain,
    ! [SV6: $i,SV255: $i] :
      ( ( ( in @ SV255 @ ( powerset @ SV6 ) )
        = $false )
      | ( ( ! [SY2453: $i] :
              ( ~ ( in @ SY2453 @ ( powerset @ SV6 ) )
              | ( in @ ( setminus @ SV6 @ SV255 ) @ ( powerset @ ( setminus @ SV6 @ ( binintersect @ SV255 @ SY2453 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1347]) ).

thf(1598,plain,
    ! [SV7: $i,SV256: $i] :
      ( ( ( in @ SV256 @ ( powerset @ SV7 ) )
        = $false )
      | ( ( ! [SY2454: $i] :
              ( ~ ( in @ SY2454 @ ( powerset @ SV7 ) )
              | ( subset @ ( setminus @ SV7 @ SV256 ) @ ( setminus @ SV7 @ ( binintersect @ SV256 @ SY2454 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1348]) ).

thf(1599,plain,
    ! [SV8: $i,SV257: $i] :
      ( ( ( in @ SV257 @ ( powerset @ SV8 ) )
        = $false )
      | ( ( ! [SY2455: $i] :
              ( ~ ( in @ SY2455 @ ( powerset @ SV8 ) )
              | ! [SY2456: $i] :
                  ( ~ ( in @ SY2456 @ SV8 )
                  | ~ ( in @ SY2456 @ ( setminus @ SV8 @ SV257 ) )
                  | ( in @ SY2456 @ ( setminus @ SV8 @ ( binintersect @ SV257 @ SY2455 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1349]) ).

thf(1600,plain,
    ! [SV9: $i,SV258: $i] :
      ( ( ( in @ SV258 @ ( powerset @ SV9 ) )
        = $false )
      | ( ( ! [SY2457: $i] :
              ( ~ ( in @ SY2457 @ ( powerset @ SV9 ) )
              | ! [SY2458: $i] :
                  ( ~ ( in @ SY2458 @ SV9 )
                  | ~ ( in @ SY2458 @ ( setminus @ SV9 @ SV258 ) )
                  | ~ ( in @ SY2458 @ ( binintersect @ SV258 @ SY2457 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1350]) ).

thf(1601,plain,
    ! [SV10: $i,SV259: $i] :
      ( ( ( in @ SV259 @ ( powerset @ SV10 ) )
        = $false )
      | ( ( SV259
          = ( setminus @ SV10 @ ( setminus @ SV10 @ SV259 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1351]) ).

thf(1602,plain,
    ! [SV11: $i,SV260: $i] :
      ( ( ( in @ SV260 @ ( powerset @ SV11 ) )
        = $false )
      | ( ( subset @ ( setminus @ SV11 @ ( setminus @ SV11 @ SV260 ) ) @ SV260 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1352]) ).

thf(1603,plain,
    ! [SV12: $i,SV261: $i] :
      ( ( ( in @ SV261 @ ( powerset @ SV12 ) )
        = $false )
      | ( ( subset @ SV261 @ ( setminus @ SV12 @ ( setminus @ SV12 @ SV261 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1353]) ).

thf(1604,plain,
    ! [SV13: $i,SV262: $i] :
      ( ( ( in @ SV262 @ ( powerset @ SV13 ) )
        = $false )
      | ( ( ! [SY2459: $i] :
              ( ~ ( in @ SY2459 @ SV13 )
              | ~ ( in @ SY2459 @ ( setminus @ SV13 @ ( setminus @ SV13 @ SV262 ) ) )
              | ( in @ SY2459 @ SV262 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1354]) ).

thf(1605,plain,
    ! [SV14: $i,SV263: $i] :
      ( ( ( in @ SV263 @ ( powerset @ SV14 ) )
        = $false )
      | ( ( ! [SY2460: $i] :
              ( ~ ( in @ SY2460 @ SV14 )
              | ~ ( in @ SY2460 @ SV263 )
              | ( in @ SY2460 @ ( setminus @ SV14 @ ( setminus @ SV14 @ SV263 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1355]) ).

thf(1606,plain,
    ! [SV15: $i,SV264: $i] :
      ( ( ( in @ SV264 @ ( powerset @ SV15 ) )
        = $false )
      | ( ( ! [SY2461: $i] :
              ( ~ ( in @ SY2461 @ ( powerset @ SV15 ) )
              | ~ ( subset @ ( setminus @ SV15 @ SY2461 ) @ ( setminus @ SV15 @ SV264 ) )
              | ( subset @ SV264 @ SY2461 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1356]) ).

thf(1607,plain,
    ! [SV16: $i,SV265: $i] :
      ( ( ( in @ SV265 @ ( powerset @ SV16 ) )
        = $false )
      | ( ( ! [SY2462: $i] :
              ( ~ ( in @ SY2462 @ ( powerset @ SV16 ) )
              | ~ ( subset @ SV265 @ SY2462 )
              | ( subset @ ( setminus @ SV16 @ SY2462 ) @ ( setminus @ SV16 @ SV265 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1357]) ).

thf(1608,plain,
    ! [SV17: $i,SV266: $i] :
      ( ( ( in @ SV266 @ ( powerset @ SV17 ) )
        = $false )
      | ( ( ! [SY2463: $i] :
              ( ~ ( in @ SY2463 @ ( powerset @ SV17 ) )
              | ! [SY2464: $i] :
                  ( ~ ( in @ SY2464 @ SV17 )
                  | ~ ( subset @ SV266 @ SY2463 )
                  | ( in @ SY2464 @ SY2463 )
                  | ~ ( in @ SY2464 @ SV266 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1358]) ).

thf(1609,plain,
    ! [SV18: $i,SV267: $i] :
      ( ( ( in @ SV267 @ ( powerset @ SV18 ) )
        = $false )
      | ( ( ! [SY2465: $i] :
              ( ~ ( in @ SY2465 @ ( powerset @ SV18 ) )
              | ! [SY2466: $i] :
                  ( ~ ( in @ SY2466 @ SV18 )
                  | ~ ( subset @ SV267 @ ( setminus @ SV18 @ SY2465 ) )
                  | ~ ( in @ SY2466 @ SY2465 )
                  | ~ ( in @ SY2466 @ SV267 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1359]) ).

thf(1610,plain,
    ! [SV19: $i,SV268: $i] :
      ( ( ( in @ SV268 @ ( powerset @ SV19 ) )
        = $false )
      | ( ( ! [SY2467: $i] :
              ( ~ ( in @ SY2467 @ ( powerset @ SV19 ) )
              | ! [SY2468: $i] :
                  ( ~ ( in @ SY2468 @ SV19 )
                  | ( in @ SY2468 @ SY2467 )
                  | ~ ( in @ SY2468 @ ( binintersect @ SV268 @ SY2467 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1360]) ).

thf(1611,plain,
    ! [SV20: $i,SV269: $i] :
      ( ( ( in @ SV269 @ ( powerset @ SV20 ) )
        = $false )
      | ( ( ! [SY2469: $i] :
              ( ~ ( in @ SY2469 @ ( powerset @ SV20 ) )
              | ! [SY2470: $i] :
                  ( ~ ( in @ SY2470 @ SV20 )
                  | ( in @ SY2470 @ SV269 )
                  | ~ ( in @ SY2470 @ ( binintersect @ SV269 @ SY2469 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1361]) ).

thf(1612,plain,
    ! [SV21: $i,SV270: $i] :
      ( ( ( in @ SV270 @ ( powerset @ SV21 ) )
        = $false )
      | ( ( ! [SY2471: $i] :
              ( ~ ( in @ SY2471 @ SV21 )
              | ( in @ SY2471 @ ( setminus @ SV21 @ SV270 ) )
              | ( in @ SY2471 @ SV270 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1362]) ).

thf(1613,plain,
    ! [SV22: $i,SV271: $i] :
      ( ( ( in @ SV271 @ ( powerset @ SV22 ) )
        = $false )
      | ( ( ! [SY2472: $i] :
              ( ~ ( in @ SY2472 @ SV22 )
              | ~ ( in @ SY2472 @ SV271 )
              | ~ ( in @ SY2472 @ ( setminus @ SV22 @ SV271 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1363]) ).

thf(1614,plain,
    ! [SV23: $i,SV272: $i] :
      ( ( ( in @ SV272 @ ( powerset @ SV23 ) )
        = $false )
      | ( ( ! [SY2473: $i] :
              ( ~ ( in @ SY2473 @ ( powerset @ SV23 ) )
              | ! [SY2474: $i] :
                  ( ~ ( in @ SY2474 @ SV23 )
                  | ~ ( in @ SV272 @ ( powerset @ SY2473 ) )
                  | ~ ( in @ SY2474 @ SV272 )
                  | ( in @ SY2474 @ SY2473 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1364]) ).

thf(1615,plain,
    ! [SV24: $i,SV273: $i] :
      ( ( ( in @ SV273 @ ( powerset @ SV24 ) )
        = $false )
      | ( ( in @ ( setminus @ SV24 @ SV273 ) @ ( powerset @ SV24 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1365]) ).

thf(1616,plain,
    ! [SV25: $i,SV274: $i] :
      ( ( ( in @ SV274 @ ( powerset @ SV25 ) )
        = $false )
      | ( ( ! [SY2475: $i] :
              ( ~ ( in @ SY2475 @ ( powerset @ SV25 ) )
              | ( in @ ( setminus @ SV274 @ SY2475 ) @ ( powerset @ SV25 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1366]) ).

thf(1617,plain,
    ! [SV26: $i,SV275: $i] :
      ( ( ( in @ SV275 @ ( powerset @ SV26 ) )
        = $false )
      | ( ( in @ ( powerset @ SV275 ) @ ( powerset @ ( powerset @ SV26 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1367]) ).

thf(1618,plain,
    ! [SV27: $i,SV276: $i] :
      ( ( ( in @ SV276 @ ( powerset @ SV27 ) )
        = $false )
      | ( ( ! [SY2476: $i] :
              ( ~ ( in @ SY2476 @ ( powerset @ SV27 ) )
              | ( in @ ( binunion @ SV276 @ SY2476 ) @ ( powerset @ SV27 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1368]) ).

thf(1619,plain,
    ! [SV28: $i,SV277: $i] :
      ( ( ( in @ SV277 @ ( powerset @ SV28 ) )
        = $false )
      | ( ( ! [SY2477: $i] :
              ( ~ ( in @ SY2477 @ ( powerset @ SV28 ) )
              | ( in @ ( binintersect @ SV277 @ SY2477 ) @ ( powerset @ SV28 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1369]) ).

thf(1620,plain,
    ! [SV278: $o,SV29: $i,SV455: $i] :
      ( ( ( ~ ( in @ SV455 @ SV29 ) )
        = $true )
      | ( ( ! [SY2733: $i] :
              ( ~ ( in @ SY2733 @ SV29 )
              | ( in @ ( if @ SV29 @ SV278 @ SV455 @ SY2733 ) @ ( setadjoin @ SV455 @ ( setadjoin @ SY2733 @ emptyset ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1370]) ).

thf(1621,plain,
    ! [SV29: $i,SV456: $i] :
      ( ( ( ~ ( in @ SV456 @ SV29 ) )
        = $true )
      | ( ( ! [SY2734: $i] :
              ( ~ ( in @ SY2734 @ SV29 )
              | ( in @ ( if @ SV29 @ $true @ SV456 @ SY2734 ) @ ( setadjoin @ SV456 @ ( setadjoin @ SY2734 @ emptyset ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1371]) ).

thf(1622,plain,
    ! [SV29: $i,SV457: $i] :
      ( ( ( ~ ( in @ SV457 @ SV29 ) )
        = $true )
      | ( ( ! [SY2735: $i] :
              ( ~ ( in @ SY2735 @ SV29 )
              | ( in @ ( if @ SV29 @ $false @ SV457 @ SY2735 ) @ ( setadjoin @ SV457 @ ( setadjoin @ SY2735 @ emptyset ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1372]) ).

thf(1623,plain,
    ! [SV279: $o,SV30: $i,SV458: $i] :
      ( ( ( ~ ( in @ SV458 @ SV30 ) )
        = $true )
      | ( ( ! [SY2736: $i] :
              ( ~ ( in @ SY2736 @ SV30 )
              | SV279
              | ( ( if @ SV30 @ SV279 @ SV458 @ SY2736 )
                = SY2736 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1373]) ).

thf(1624,plain,
    ! [SV30: $i,SV459: $i] :
      ( ( ( ~ ( in @ SV459 @ SV30 ) )
        = $true )
      | ( ( ! [SY2737: $i] :
              ( ~ ( in @ SY2737 @ SV30 )
              | $true
              | ( ( if @ SV30 @ $true @ SV459 @ SY2737 )
                = SY2737 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1374]) ).

thf(1625,plain,
    ! [SV30: $i,SV460: $i] :
      ( ( ( ~ ( in @ SV460 @ SV30 ) )
        = $true )
      | ( ( ! [SY2738: $i] :
              ( ~ ( in @ SY2738 @ SV30 )
              | $false
              | ( ( if @ SV30 @ $false @ SV460 @ SY2738 )
                = SY2738 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1375]) ).

thf(1626,plain,
    ! [SV280: $o,SV31: $i,SV461: $i] :
      ( ( ( ~ ( in @ SV461 @ SV31 ) )
        = $true )
      | ( ( ! [SY2739: $i] :
              ( ~ ( in @ SY2739 @ SV31 )
              | ~ SV280
              | ( ( if @ SV31 @ SV280 @ SV461 @ SY2739 )
                = SV461 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1376]) ).

thf(1627,plain,
    ! [SV31: $i,SV462: $i] :
      ( ( ( ~ ( in @ SV462 @ SV31 ) )
        = $true )
      | ( ( ! [SY2740: $i] :
              ( ~ ( in @ SY2740 @ SV31 )
              | ~ $true
              | ( ( if @ SV31 @ $true @ SV462 @ SY2740 )
                = SV462 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1377]) ).

thf(1628,plain,
    ! [SV31: $i,SV463: $i] :
      ( ( ( ~ ( in @ SV463 @ SV31 ) )
        = $true )
      | ( ( ! [SY2741: $i] :
              ( ~ ( in @ SY2741 @ SV31 )
              | ~ $false
              | ( ( if @ SV31 @ $false @ SV463 @ SY2741 )
                = SV463 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1378]) ).

thf(1629,plain,
    ! [SV32: $i,SV587: $i] :
      ( ( ( ~ ( in @ SV587 @ SV32 )
          | ( ( setunion @ SV32 )
            = SV587 ) )
        = $true )
      | ( ( singleton @ SV32 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1379]) ).

thf(1630,plain,
    ! [SV281: $o,SV33: $i,SV464: $i] :
      ( ( ( ~ ( in @ SV464 @ SV33 ) )
        = $true )
      | ( ( ! [SY2742: $i] :
              ( ~ ( in @ SY2742 @ SV33 )
              | ( in @ ( if @ SV33 @ SV281 @ SV464 @ SY2742 ) @ SV33 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1380]) ).

thf(1631,plain,
    ! [SV33: $i,SV465: $i] :
      ( ( ( ~ ( in @ SV465 @ SV33 ) )
        = $true )
      | ( ( ! [SY2743: $i] :
              ( ~ ( in @ SY2743 @ SV33 )
              | ( in @ ( if @ SV33 @ $true @ SV465 @ SY2743 ) @ SV33 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1381]) ).

thf(1632,plain,
    ! [SV33: $i,SV466: $i] :
      ( ( ( ~ ( in @ SV466 @ SV33 ) )
        = $true )
      | ( ( ! [SY2744: $i] :
              ( ~ ( in @ SY2744 @ SV33 )
              | ( in @ ( if @ SV33 @ $false @ SV466 @ SY2744 ) @ SV33 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1382]) ).

thf(1633,plain,
    ! [SV282: $i,SV34: $i,SV467: $i] :
      ( ( ( ~ ( in @ SV467 @ ( funcSet @ SV34 @ SV282 ) ) )
        = $true )
      | ( ( ( lam @ SV34 @ SV282
            @ ^ [SY2745: $i] : ( ap @ SV34 @ SV282 @ SV467 @ SY2745 ) )
          = SV467 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1383]) ).

thf(1634,plain,
    ! [SV468: $i,SV283: $i,SV35: $i] :
      ( ( ( ~ ( func @ SV35 @ SV283 @ SV468 ) )
        = $true )
      | ( ( ( lam @ SV35 @ SV283
            @ ^ [SY2746: $i] : ( ap @ SV35 @ SV283 @ SV468 @ SY2746 ) )
          = SV468 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1384]) ).

thf(1635,plain,
    ! [SV588: $i,SV469: $i,SV36: $i] :
      ( ( ( ~ ( func @ SV36 @ SV469 @ SV588 ) )
        = $true )
      | ( ( ! [SY1968: $i] :
              ~ ( in @ SY1968 @ SV36 )
          | $true )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1385]) ).

thf(1636,plain,
    ! [SV470: $i,SV37: $i,SV589: $i] :
      ( ( ( ~ ( in @ SV589 @ ( funcSet @ SV37 @ SV470 ) ) )
        = $true )
      | ( ( ! [SY1971: $i] :
              ~ ( in @ SY1971 @ SV37 )
          | $true )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1386]) ).

thf(1637,plain,
    ! [SV284: $i,SV38: $i,SV471: $i] :
      ( ( ( ~ ( in @ SV471 @ ( funcSet @ SV38 @ SV284 ) ) )
        = $true )
      | ( ( ! [SY2749: $i] :
              ( ~ ( in @ SY2749 @ SV38 )
              | ! [SY2750: $i] :
                  ( ~ ( in @ SY2750 @ SV284 )
                  | ~ ( in @ ( kpair @ SY2749 @ SY2750 ) @ SV471 )
                  | ( ( ap @ SV38 @ SV284 @ SV471 @ SY2749 )
                    = SY2750 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1387]) ).

thf(1638,plain,
    ! [SV472: $i,SV285: $i,SV39: $i] :
      ( ( ( ~ ( func @ SV39 @ SV285 @ SV472 ) )
        = $true )
      | ( ( ! [SY2751: $i] :
              ( ~ ( in @ SY2751 @ SV39 )
              | ! [SY2752: $i] :
                  ( ~ ( in @ SY2752 @ SV285 )
                  | ~ ( in @ ( kpair @ SY2751 @ SY2752 ) @ SV472 )
                  | ( ( ap @ SV39 @ SV285 @ SV472 @ SY2751 )
                    = SY2752 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1388]) ).

thf(1639,plain,
    ! [SV286: $i,SV40: $i,SV473: $i] :
      ( ( ( ~ ( in @ SV473 @ ( funcSet @ SV40 @ SV286 ) ) )
        = $true )
      | ( ( ! [SY2753: $i] :
              ( ~ ( in @ SY2753 @ SV40 )
              | ( in @ ( kpair @ SY2753 @ ( ap @ SV40 @ SV286 @ SV473 @ SY2753 ) ) @ SV473 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1389]) ).

thf(1640,plain,
    ! [SV474: $i,SV287: $i,SV41: $i] :
      ( ( ( ~ ( func @ SV41 @ SV287 @ SV474 ) )
        = $true )
      | ( ( ! [SY2754: $i] :
              ( ~ ( in @ SY2754 @ SV41 )
              | ( in @ ( kpair @ SY2754 @ ( ap @ SV41 @ SV287 @ SV474 @ SY2754 ) ) @ SV474 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1390]) ).

thf(1641,plain,
    ! [SV288: $i > $o,SV42: $i] :
      ( ( ( singleton
          @ ( dsetconstr @ SV42
            @ ^ [SY2500: $i] : ( SV288 @ SY2500 ) ) )
        = $false )
      | ( ( ! [SY2501: $i] :
              ( ~ ( in @ SY2501 @ SV42 )
              | ! [SY2502: $i] :
                  ( ~ ( in @ SY2502 @ SV42 )
                  | ~ ( SV288 @ SY2501 )
                  | ~ ( SV288 @ SY2502 )
                  | ( SY2501 = SY2502 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1391]) ).

thf(1642,plain,
    ! [SV475: $i,SV289: $i,SV43: $i] :
      ( ( ( ~ ( func @ SV43 @ SV289 @ SV475 ) )
        = $true )
      | ( ( in @ SV475 @ ( funcSet @ SV43 @ SV289 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1392]) ).

thf(1643,plain,
    ! [SV290: $i,SV44: $i,SV476: $i] :
      ( ( ( ~ ( in @ SV476 @ ( funcSet @ SV44 @ SV290 ) ) )
        = $true )
      | ( ( ! [SY2755: $i] :
              ( ~ ( in @ SY2755 @ SV44 )
              | ( in @ ( ap @ SV44 @ SV290 @ SV476 @ SY2755 ) @ SV290 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1393]) ).

thf(1644,plain,
    ! [SV291: $i,SV45: $i,SV477: $i] :
      ( ( ( ~ ( in @ SV477 @ ( funcSet @ SV45 @ SV291 ) ) )
        = $true )
      | ( ( func @ SV45 @ SV291 @ SV477 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1394]) ).

thf(1645,plain,
    ! [SV478: $i,SV292: $i,SV46: $i] :
      ( ( ( ~ ( func @ SV46 @ SV292 @ SV478 ) )
        = $true )
      | ( ( ! [SY2756: $i] :
              ( ~ ( in @ SY2756 @ SV46 )
              | ( in @ ( ap @ SV46 @ SV292 @ SV478 @ SY2756 ) @ SV292 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1395]) ).

thf(1646,plain,
    ! [SV479: $i,SV293: $i,SV47: $i] :
      ( ( ( ~ ( func @ SV47 @ SV293 @ SV479 ) )
        = $true )
      | ( ( ! [SY2757: $i] :
              ( ~ ( in @ SY2757 @ SV47 )
              | ( in
                @ ( setunion
                  @ ( dsetconstr @ SV293
                    @ ^ [SY2758: $i] : ( in @ ( kpair @ SY2757 @ SY2758 ) @ SV479 ) ) )
                @ SV293 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1396]) ).

thf(1647,plain,
    ! [SV480: $i,SV294: $i,SV48: $i] :
      ( ( ( ~ ( func @ SV48 @ SV294 @ SV480 ) )
        = $true )
      | ( ( ! [SY2759: $i] :
              ( ~ ( in @ SY2759 @ SV48 )
              | ( singleton
                @ ( dsetconstr @ SV294
                  @ ^ [SY2760: $i] : ( in @ ( kpair @ SY2759 @ SY2760 ) @ SV480 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1397]) ).

thf(1648,plain,
    ! [SV481: $i > $i > $o,SV295: $i,SV49: $i,SV590: $i] :
      ( ( ! [SY2868: $i] :
            ( ~ ( in @ ( kpair @ SV590 @ SY2868 )
                @ ( dpsetconstr @ SV49 @ SV295
                  @ ^ [SY2763: $i,SY2764: $i] : ( SV481 @ SY2763 @ SY2764 ) ) )
            | ( SV481 @ SV590 @ SY2868 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1398]) ).

thf(1649,plain,
    ! [SV482: $i > $i > $o,SV296: $i,SV50: $i,SV591: $i] :
      ( ( ! [SY2871: $i] :
            ( ~ ( in @ ( kpair @ SV591 @ SY2871 )
                @ ( dpsetconstr @ SV50 @ SV296
                  @ ^ [SY2767: $i,SY2768: $i] : ( SV482 @ SY2767 @ SY2768 ) ) )
            | ( in @ SY2871 @ SV296 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1399]) ).

thf(1650,plain,
    ! [SV483: $i > $i > $o,SV297: $i,SV51: $i,SV592: $i] :
      ( ( ! [SY2874: $i] :
            ~ ( in @ ( kpair @ SV592 @ SY2874 )
              @ ( dpsetconstr @ SV51 @ SV297
                @ ^ [SY2771: $i,SY2772: $i] : ( SV483 @ SY2771 @ SY2772 ) ) )
        | ( in @ SV592 @ SV51 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1400]) ).

thf(1651,plain,
    ! [SV484: $i > $i > $o,SV298: $i,SV52: $i,SV593: $i] :
      ( ( ~ ( in @ SV593 @ SV52 )
        | ! [SY2877: $i] :
            ( ~ ( in @ SY2877 @ SV298 )
            | ~ ( in @ ( kpair @ SV593 @ SY2877 )
                @ ( dpsetconstr @ SV52 @ SV298
                  @ ^ [SY2775: $i,SY2776: $i] : ( SV484 @ SY2775 @ SY2776 ) ) )
            | ( SV484 @ SV593 @ SY2877 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1401]) ).

thf(1652,plain,
    ! [SV487: $i > $i > $o,SV301: $i,SV55: $i,SV594: $i] :
      ( ( ~ ( in @ SV594 @ SV55 )
        | ! [SY2880: $i] :
            ( ~ ( in @ SY2880 @ SV301 )
            | ~ ( SV487 @ SV594 @ SY2880 )
            | ( in @ ( kpair @ SV594 @ SY2880 )
              @ ( dpsetconstr @ SV55 @ SV301
                @ ^ [SY2783: $i,SY2784: $i] : ( SV487 @ SY2783 @ SY2784 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1404]) ).

thf(1653,plain,
    ! [SV302: $i,SV56: $i,SV488: $i] :
      ( ( ( ~ ( in @ SV488 @ ( cartprod @ SV56 @ SV302 ) ) )
        = $true )
      | ( ( ( kpair @ ( kfst @ SV488 ) @ ( ksnd @ SV488 ) )
          = SV488 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1405]) ).

thf(1654,plain,
    ! [SV303: $i,SV57: $i,SV489: $i] :
      ( ( ( ~ ( in @ SV489 @ SV57 ) )
        = $true )
      | ( ( ! [SY2785: $i] :
              ( ~ ( in @ SY2785 @ SV303 )
              | ( ( ksnd @ ( kpair @ SV489 @ SY2785 ) )
                = SY2785 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1406]) ).

thf(1655,plain,
    ! [SV304: $i,SV58: $i,SV490: $i] :
      ( ( ( ~ ( in @ SV490 @ SV58 ) )
        = $true )
      | ( ( ! [SY2786: $i] :
              ( ~ ( in @ SY2786 @ SV304 )
              | ( ( kfst @ ( kpair @ SV490 @ SY2786 ) )
                = SV490 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1407]) ).

thf(1656,plain,
    ! [SV59: $i,SV491: $i] :
      ( ( ( in @ SV491 @ SV59 )
        = $false )
      | ( ( ! [B: $i,Xy: $i] :
              ~ ( in @ Xy @ B )
          | $true )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1408]) ).

thf(1657,plain,
    ! [SV305: $i,SV60: $i,SV595: $i,SV492: $i] :
      ( ( ~ ( in @ ( kpair @ SV492 @ SV595 ) @ ( cartprod @ SV60 @ SV305 ) )
        | ( in @ SV595 @ SV305 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1409]) ).

thf(1658,plain,
    ! [SV306: $i,SV61: $i,SV493: $i] :
      ( ( ( ! [SY2788: $i] :
              ~ ( in @ ( kpair @ SV493 @ SY2788 ) @ ( cartprod @ SV61 @ SV306 ) ) )
        = $true )
      | ( ( in @ SV493 @ SV61 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1410]) ).

thf(1659,plain,
    ! [SV307: $i,SV62: $i,SV494: $i] :
      ( ( ( ~ ( in @ SV494 @ ( cartprod @ SV62 @ SV307 ) ) )
        = $true )
      | ( ( in @ ( ksnd @ SV494 ) @ SV307 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1411]) ).

thf(1660,plain,
    ! [SV596: $i,SV495: $i,SV309: $i,SV66: $i] :
      ( ( ( ( kpair @ SV66 @ SV309 )
         != ( kpair @ SV495 @ SV596 ) )
        | ( SV309 = SV596 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1414]) ).

thf(1661,plain,
    ! [SV597: $i,SV496: $i,SV310: $i,SV67: $i] :
      ( ( ( ( setadjoin @ ( setadjoin @ SV67 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV67 @ ( setadjoin @ SV310 @ emptyset ) ) @ emptyset ) )
         != ( setadjoin @ ( setadjoin @ SV496 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV496 @ ( setadjoin @ SV597 @ emptyset ) ) @ emptyset ) ) )
        | ( SV310 = SV597 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1415]) ).

thf(1662,plain,
    ! [SV598: $i,SV311: $i,SV68: $i] :
      ( ( ( ( setadjoin @ SV68 @ ( setadjoin @ SV311 @ emptyset ) )
         != ( setadjoin @ SV598 @ emptyset ) )
        = $true )
      | ( ( SV68 = SV311 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1416]) ).

thf(1663,plain,
    ! [SV599: $i,SV497: $i,SV312: $i,SV69: $i] :
      ( ( ( ( setadjoin @ ( setadjoin @ SV69 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV69 @ ( setadjoin @ SV312 @ emptyset ) ) @ emptyset ) )
         != ( setadjoin @ ( setadjoin @ SV497 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV497 @ ( setadjoin @ SV599 @ emptyset ) ) @ emptyset ) ) )
        | ( SV497 != SV599 )
        | ( SV312 = SV599 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1417]) ).

thf(1664,plain,
    ! [SV313: $i,SV70: $i] :
      ( ( ( SV70 = SV313 )
        = $false )
      | ( ( ( setadjoin @ ( setadjoin @ SV70 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV70 @ ( setadjoin @ SV313 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ SV70 @ emptyset ) @ emptyset ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1418]) ).

thf(1665,plain,
    ! [SV314: $i,SV71: $i] :
      ( ( ( SV71 = SV314 )
        = $false )
      | ( ( ( setadjoin @ SV71 @ ( setadjoin @ SV314 @ emptyset ) )
          = ( setadjoin @ SV71 @ emptyset ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1419]) ).

thf(1666,plain,
    ! [SV498: $i,SV315: $i,SV72: $i] :
      ( ( ( ! [SY2792: $i] :
              ( ( kpair @ SV72 @ SV315 )
             != ( kpair @ SV498 @ SY2792 ) ) )
        = $true )
      | ( ( SV72 = SV498 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1420]) ).

thf(1667,plain,
    ! [SV499: $i,SV316: $i,SV73: $i] :
      ( ( ( ! [SY2793: $i] :
              ( ( setadjoin @ ( setadjoin @ SV73 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV73 @ ( setadjoin @ SV316 @ emptyset ) ) @ emptyset ) )
             != ( setadjoin @ ( setadjoin @ SV499 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV499 @ ( setadjoin @ SY2793 @ emptyset ) ) @ emptyset ) ) ) )
        = $true )
      | ( ( SV73 = SV499 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1421]) ).

thf(1668,plain,
    ! [SV317: $i,SV74: $i,SV500: $i] :
      ( ( ( ~ ( in @ SV500 @ ( cartprod @ SV74 @ SV317 ) ) )
        = $true )
      | ( ( in @ ( kfst @ SV500 ) @ SV74 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1422]) ).

thf(1669,plain,
    ! [SV319: $i,SV78: $i,SV501: $i] :
      ( ( ( ~ ( in @ ( setadjoin @ SV501 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV78 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV78 @ ( setadjoin @ SV319 @ emptyset ) ) @ emptyset ) ) ) )
        = $true )
      | ( ( SV78 = SV501 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1425]) ).

thf(1670,plain,
    ! [SV320: $i,SV79: $i] :
      ( ( ( ( setadjoin @ SV79 @ emptyset )
          = ( setadjoin @ SV320 @ emptyset ) )
        = $false )
      | ( ( SV79 = SV320 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1426]) ).

thf(1671,plain,
    ! [SV321: $i,SV83: $i,SV502: $i] :
      ( ( ( ~ ( in @ SV502 @ ( cartprod @ SV83 @ SV321 ) ) )
        = $true )
      | ( ( iskpair @ SV502 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1427]) ).

thf(1672,plain,
    ! [SV322: $i,SV84: $i,SV503: $i] :
      ( ( ( ~ ( in @ SV503 @ SV84 ) )
        = $true )
      | ( ( ! [SY2794: $i] :
              ( ~ ( in @ SY2794 @ SV322 )
              | ( in @ ( kpair @ SV503 @ SY2794 ) @ ( cartprod @ SV84 @ SV322 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1428]) ).

thf(1673,plain,
    ! [SV323: $i,SV85: $i,SV504: $i] :
      ( ( ( ~ ( in @ SV504 @ SV85 ) )
        = $true )
      | ( ( ! [SY2795: $i] :
              ( ~ ( in @ SY2795 @ SV323 )
              | ( in @ ( kpair @ SV504 @ SY2795 ) @ ( powerset @ ( powerset @ ( binunion @ SV85 @ SV323 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1429]) ).

thf(1674,plain,
    ! [SV324: $i,SV86: $i,SV505: $i] :
      ( ( ( ~ ( in @ SV505 @ SV86 ) )
        = $true )
      | ( ( ! [SY2796: $i] :
              ( ~ ( in @ SY2796 @ SV324 )
              | ( in @ ( setadjoin @ ( setadjoin @ SV505 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV505 @ ( setadjoin @ SY2796 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV86 @ SV324 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1430]) ).

thf(1675,plain,
    ! [SV325: $i,SV87: $i,SV506: $i] :
      ( ( ( ~ ( in @ SV506 @ SV87 ) )
        = $true )
      | ( ( ! [SY2797: $i] :
              ( ~ ( in @ SY2797 @ SV325 )
              | ( subset @ ( setadjoin @ ( setadjoin @ SV506 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV506 @ ( setadjoin @ SY2797 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV87 @ SV325 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1431]) ).

thf(1676,plain,
    ! [SV326: $i,SV88: $i,SV507: $i] :
      ( ( ( ~ ( in @ SV507 @ SV88 ) )
        = $true )
      | ( ( ! [SY2798: $i] :
              ( ~ ( in @ SY2798 @ SV326 )
              | ( in @ ( setadjoin @ SV507 @ ( setadjoin @ SY2798 @ emptyset ) ) @ ( powerset @ ( binunion @ SV88 @ SV326 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1432]) ).

thf(1677,plain,
    ! [SV327: $i,SV89: $i,SV508: $i] :
      ( ( ( ~ ( in @ SV508 @ SV89 ) )
        = $true )
      | ( ( ! [SY2799: $i] :
              ( ~ ( in @ SY2799 @ SV327 )
              | ( subset @ ( setadjoin @ SV508 @ ( setadjoin @ SY2799 @ emptyset ) ) @ ( binunion @ SV89 @ SV327 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1433]) ).

thf(1678,plain,
    ! [SV328: $i,SV90: $i,SV509: $i] :
      ( ( ( ~ ( in @ SV509 @ ( setadjoin @ SV90 @ ( setadjoin @ SV328 @ emptyset ) ) ) )
        = $true )
      | ( ( ( SV509 = SV90 )
          | ( SV509 = SV328 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1434]) ).

thf(1679,plain,
    ! [SV329: $i,SV91: $i,SV510: $i] :
      ( ( ( ~ ( in @ SV510 @ SV91 ) )
        = $true )
      | ( ( in @ ( setadjoin @ SV510 @ emptyset ) @ ( powerset @ ( binunion @ SV91 @ SV329 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1435]) ).

thf(1680,plain,
    ! [SV92: $i,SV330: $i] :
      ( ( ( in @ SV330 @ SV92 )
        = $false )
      | ( ( in @ ( setadjoin @ SV330 @ emptyset ) @ ( powerset @ SV92 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1436]) ).

thf(1681,plain,
    ! [SV93: $i,SV331: $i] :
      ( ( ( in @ SV331 @ SV93 )
        = $false )
      | ( ( subset @ ( setadjoin @ SV331 @ emptyset ) @ SV93 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1437]) ).

thf(1682,plain,
    ! [SV337: $i,SV99: $i,SV511: $i] :
      ( ( ( in @ SV511 @ SV99 )
        = $true )
      | ( ( ( in @ SV511 @ SV337 )
          | ~ ( in @ SV511 @ ( symdiff @ SV99 @ SV337 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1438]) ).

thf(1683,plain,
    ! [SV338: $i,SV100: $i,SV512: $i] :
      ( ( ( ~ ( in @ SV512 @ SV100 ) )
        = $true )
      | ( ( ~ ( in @ SV512 @ SV338 )
          | ~ ( in @ SV512 @ ( symdiff @ SV100 @ SV338 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1439]) ).

thf(1684,plain,
    ! [SV339: $i,SV101: $i,SV513: $i] :
      ( ( ( in @ SV513 @ SV101 )
        = $true )
      | ( ( ~ ( in @ SV513 @ SV339 )
          | ( in @ SV513 @ ( symdiff @ SV101 @ SV339 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1440]) ).

thf(1685,plain,
    ! [SV340: $i,SV102: $i,SV514: $i] :
      ( ( ( ~ ( in @ SV514 @ SV102 ) )
        = $true )
      | ( ( ( in @ SV514 @ SV340 )
          | ( in @ SV514 @ ( symdiff @ SV102 @ SV340 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1441]) ).

thf(1686,plain,
    ! [SV341: $i,SV103: $i] :
      ( ( ( ( setminus @ SV103 @ SV341 )
          = emptyset )
        = $false )
      | ( ( subset @ SV103 @ SV341 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1442]) ).

thf(1687,plain,
    ! [SV105: $i,SV343: $i,SV515: $i] :
      ( ( ( ~ ( in @ SV515 @ SV343 ) )
        = $true )
      | ( ( ~ ( in @ SV515 @ ( setminus @ SV105 @ SV343 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1443]) ).

thf(1688,plain,
    ! [SV344: $i,SV106: $i,SV516: $i] :
      ( ( ( in @ SV516 @ SV106 )
        = $true )
      | ( ( ~ ( in @ SV516 @ ( setminus @ SV106 @ SV344 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1444]) ).

thf(1689,plain,
    ! [SV345: $i,SV107: $i,SV517: $i] :
      ( ( ( in @ SV517 @ ( setminus @ SV107 @ SV345 ) )
        = $true )
      | ( ( ( in @ SV517 @ SV345 )
          | ~ ( in @ SV517 @ SV107 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1445]) ).

thf(1690,plain,
    ! [SV346: $i,SV108: $i,SV518: $i] :
      ( ( ( in @ SV518 @ ( setminus @ SV108 @ SV346 ) )
        = $true )
      | ( ( ~ ( in @ SV518 @ SV108 )
          | ( in @ SV518 @ SV346 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1446]) ).

thf(1691,plain,
    ! [SV347: $i,SV109: $i] :
      ( ( ( subset @ SV109 @ SV347 )
        = $false )
      | ( ( ( setminus @ SV109 @ SV347 )
          = emptyset )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1447]) ).

thf(1692,plain,
    ! [SV348: $i,SV110: $i,SV519: $i] :
      ( ( ( ~ ( in @ SV519 @ ( setminus @ SV110 @ SV348 ) ) )
        = $true )
      | ( ( ~ ( in @ SV519 @ SV348 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1448]) ).

thf(1693,plain,
    ! [SV349: $i,SV111: $i,SV520: $i] :
      ( ( ( ~ ( in @ SV520 @ ( setminus @ SV111 @ SV349 ) ) )
        = $true )
      | ( ( in @ SV520 @ SV111 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1449]) ).

thf(1694,plain,
    ! [SV350: $i,SV112: $i,SV521: $i] :
      ( ( ( ~ ( in @ SV521 @ SV112 ) )
        = $true )
      | ( ( ( in @ SV521 @ SV350 )
          | ( in @ SV521 @ ( setminus @ SV112 @ SV350 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1450]) ).

thf(1695,plain,
    ! [SV352: $i,SV114: $i] :
      ( ( ( ( binintersect @ SV114 @ SV352 )
          = SV114 )
        = $false )
      | ( ( subset @ SV114 @ SV352 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1452]) ).

thf(1696,plain,
    ! [SV115: $i,SV353: $i] :
      ( ( ( subset @ SV353 @ SV115 )
        = $false )
      | ( ( ( binintersect @ SV115 @ SV353 )
          = SV353 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1453]) ).

thf(1697,plain,
    ! [SV355: $i,SV117: $i,SV523: $i] :
      ( ( ( ~ ( in @ SV523 @ ( binintersect @ SV117 @ SV355 ) ) )
        = $true )
      | ( ( in @ SV523 @ SV355 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1454]) ).

thf(1698,plain,
    ! [SV356: $i,SV118: $i] :
      ( ( ( ( binintersect @ SV118 @ SV356 )
          = SV356 )
        = $false )
      | ( ( subset @ SV356 @ SV118 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1455]) ).

thf(1699,plain,
    ! [SV357: $i,SV119: $i] :
      ( ( ( subset @ SV119 @ SV357 )
        = $false )
      | ( ( ( binintersect @ SV119 @ SV357 )
          = SV119 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1456]) ).

thf(1700,plain,
    ! [SV359: $i,SV121: $i,SV524: $i] :
      ( ( ( ~ ( in @ SV524 @ ( binintersect @ SV121 @ SV359 ) ) )
        = $true )
      | ( ( in @ SV524 @ SV121 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1457]) ).

thf(1701,plain,
    ! [SV360: $i,SV122: $i,SV525: $i] :
      ( ( ( ~ ( subset @ SV525 @ SV122 ) )
        = $true )
      | ( ( ~ ( subset @ SV525 @ SV360 )
          | ( subset @ SV525 @ ( binintersect @ SV122 @ SV360 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1458]) ).

thf(1702,plain,
    ! [SV361: $i,SV123: $i,SV526: $i] :
      ( ( ( ~ ( in @ SV526 @ SV123 ) )
        = $true )
      | ( ( ~ ( in @ SV526 @ SV361 )
          | ( in @ SV526 @ ( binintersect @ SV123 @ SV361 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1459]) ).

thf(1703,plain,
    ! [SV364: $i,SV126: $i,SV527: $i] :
      ( ( ( ~ ( in @ SV527 @ ( binunion @ SV126 @ SV364 ) ) )
        = $true )
      | ( ( ( in @ SV527 @ SV126 )
          | ( in @ SV527 @ SV364 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1460]) ).

thf(1704,plain,
    ! [SV127: $i,SV365: $i,SV528: $i] :
      ( ( ( ~ ( in @ SV528 @ SV365 ) )
        = $true )
      | ( ( in @ SV528 @ ( binunion @ SV127 @ SV365 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1461]) ).

thf(1705,plain,
    ! [SV367: $i,SV129: $i,SV529: $i] :
      ( ( ( ~ ( in @ SV529 @ SV129 ) )
        = $true )
      | ( ( in @ SV529 @ ( binunion @ SV129 @ SV367 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1462]) ).

thf(1706,plain,
    ! [SV370: $i,SV132: $i] :
      ( ( ( subset @ SV132 @ SV370 )
        = $false )
      | ( ( subset @ ( powerset @ SV132 ) @ ( powerset @ SV370 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1463]) ).

thf(1707,plain,
    ! [SV134: $i,SV371: $i] :
      ( ( ( in @ SV371 @ ( powerset @ SV134 ) )
        = $false )
      | ( ( subset @ SV371 @ SV134 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1464]) ).

thf(1708,plain,
    ! [SV135: $i,SV372: $i] :
      ( ( ( subset @ SV372 @ SV135 )
        = $false )
      | ( ( in @ SV372 @ ( powerset @ SV135 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1465]) ).

thf(1709,plain,
    ! [SV373: $i,SV137: $i] :
      ( ( ( subset @ SV137 @ SV373 )
        = $false )
      | ( ( ~ ( subset @ SV373 @ SV137 )
          | ( SV137 = SV373 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1467]) ).

thf(1710,plain,
    ! [SV374: $i,SV138: $i] :
      ( ( ( subset @ SV138 @ SV374 )
        = $false )
      | ( ( in @ SV138 @ ( powerset @ SV374 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1468]) ).

thf(1711,plain,
    ! [SV375: $i,SV530: $i,SV139: $i] :
      ( ( ( ~ ( subset @ SV139 @ SV530 ) )
        = $true )
      | ( ( subset @ SV139 @ ( setadjoin @ SV375 @ SV530 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1469]) ).

thf(1712,plain,
    ! [SV377: $i,SV141: $i] :
      ( ( ( subset @ SV141 @ SV377 )
        = $false )
      | ( ( ! [SY2606: $i] :
              ( ~ ( subset @ SV377 @ SY2606 )
              | ( subset @ SV141 @ SY2606 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1470]) ).

thf(1713,plain,
    ! [SV378: $i,SV143: $i,SV531: $i] :
      ( ( ( ~ ( in @ SV531 @ SV143 ) )
        = $true )
      | ( ( ( in @ SV531 @ SV378 )
          | ( SV143 != SV378 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1471]) ).

thf(1714,plain,
    ! [SV379: $i,SV144: $i] :
      ( ( ( SV144 = SV379 )
        = $false )
      | ( ( subset @ SV144 @ SV379 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1472]) ).

thf(1715,plain,
    ! [SV380: $i,SV145: $i,SV532: $i] :
      ( ( ( ~ ( in @ SV532 @ SV145 ) )
        = $true )
      | ( ( ( in @ SV532 @ SV380 )
          | ~ ( subset @ SV145 @ SV380 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1473]) ).

thf(1716,plain,
    ! [SV381: $i,SV146: $i] :
      ( ( ( subset @ SV146 @ SV381 )
        = $false )
      | ( ( ! [SY2609: $i] :
              ( ( in @ SY2609 @ SV381 )
              | ~ ( in @ SY2609 @ SV146 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1474]) ).

thf(1717,plain,
    ! [SV382: $i,SV147: $i] :
      ( ( ( subset @ SV147 @ SV382 )
        = $false )
      | ( ( ! [SY2610: $i] :
              ( ~ ( in @ SY2610 @ SV147 )
              | ( in @ SY2610 @ SV382 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1475]) ).

thf(1718,plain,
    ! [SV383: $i,SV149: $i] :
      ( ( ( SV149 = SV383 )
        = $false )
      | ( ( subset @ SV149 @ SV383 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1476]) ).

thf(1719,plain,
    ! [SV384: $i,SV150: $i] :
      ( ( ( SV150 = SV384 )
        = $false )
      | ( ( subset @ SV384 @ SV150 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1477]) ).

thf(1720,plain,
    ! [SV385: $i,SV151: $i] :
      ( ( ( SV151 = SV385 )
        = $false )
      | ( ( ( setunion @ SV151 )
          = ( setunion @ SV385 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1478]) ).

thf(1721,plain,
    ! [SV386: $i,SV152: $i] :
      ( ( ( SV152 = SV386 )
        = $false )
      | ( ( ( powerset @ SV152 )
          = ( powerset @ SV386 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1479]) ).

thf(1722,plain,
    ! [SV387: $i,SV153: $i] :
      ( ( ( SV153 = SV387 )
        = $false )
      | ( ( ! [SY2611: $i,SY2612: $i] :
              ( ( SY2611 != SY2612 )
              | ( ( setadjoin @ SV153 @ SY2611 )
                = ( setadjoin @ SV387 @ SY2612 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1480]) ).

thf(1723,plain,
    ! [SV388: $i,SV154: $i] :
      ( ( ( SV154 = SV388 )
        = $false )
      | ( ( ! [SY2613: $i,SY2614: $i] :
              ( ( SY2613 != SY2614 )
              | ~ ( in @ SY2613 @ SV154 )
              | ( in @ SY2614 @ SV388 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1481]) ).

thf(1724,plain,
    ! [SV157: $i > $o,SV389: $i] :
      ( ( ( in @ SV389 @ emptyset )
        = $false )
      | ( ( SV157 @ SV389 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1488]) ).

thf(1725,plain,
    ! [SV158: $i,SV600: $i,SV390: $i > $o] :
      ( ( ( ~ ( SV390 @ SV600 )
          | ~ ( in @ SV600 @ SV158 ) )
        = $true )
      | ( ( ( dsetconstr @ SV158
            @ ^ [SY2616: $i] : ( SV390 @ SY2616 ) )
         != emptyset )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1489]) ).

thf(1726,plain,
    ! [SV393: $i,SV161: $i,SV533: $i] :
      ( ( ( ~ ( in @ SV533 @ ( setadjoin @ SV161 @ ( setadjoin @ SV393 @ emptyset ) ) ) )
        = $true )
      | ( ( ( SV533 = SV161 )
          | ( SV533 = SV393 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1490]) ).

thf(1727,plain,
    ! [SV394: $i,SV162: $i] :
      ( ( ( in @ SV162 @ ( setadjoin @ SV394 @ emptyset ) )
        = $false )
      | ( ( in @ SV394 @ ( setadjoin @ SV162 @ emptyset ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1491]) ).

thf(1728,plain,
    ! [SV395: $i,SV163: $i] :
      ( ( ( SV163 = SV395 )
        = $false )
      | ( ( in @ SV163 @ ( setadjoin @ SV395 @ emptyset ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1492]) ).

thf(1729,plain,
    ! [SV164: $i,SV396: $i] :
      ( ( ( in @ SV396 @ ( setadjoin @ SV164 @ emptyset ) )
        = $false )
      | ( ( SV164 = SV396 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1493]) ).

thf(1730,plain,
    ! [SV397: $i,SV165: $i] :
      ( ( ( in @ SV165 @ ( setadjoin @ SV397 @ emptyset ) )
        = $false )
      | ( ( SV165 = SV397 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1494]) ).

thf(1731,plain,
    ! [SV167: $i,SV398: $i] :
      ( ( ( in @ SV398 @ SV167 )
        = $false )
      | ( ( in @ SV398 @ ( powerset @ ( setunion @ SV167 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1495]) ).

thf(1732,plain,
    ! [SV168: $i,SV534: $i,SV399: $i] :
      ( ( ( ~ ( in @ SV399 @ SV534 ) )
        = $true )
      | ( ( ~ ( in @ SV534 @ SV168 )
          | ( in @ SV399 @ ( setunion @ SV168 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1496]) ).

thf(1733,plain,
    ! [SV169: $i,SV400: $i] :
      ( ( ( in @ SV400 @ ( powerset @ SV169 ) )
        = $false )
      | ( ( ! [SY2619: $i] :
              ( ~ ( in @ SY2619 @ SV400 )
              | ( in @ SY2619 @ SV169 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1497]) ).

thf(1734,plain,
    ! [SV401: $i,SV173: $i,SV535: $i] :
      ( ( ( ~ ( in @ SV535 @ ( setadjoin @ SV173 @ SV401 ) ) )
        = $true )
      | ( ( ( SV535 = SV173 )
          | ( in @ SV535 @ SV401 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1498]) ).

thf(1735,plain,
    ! [SV174: $i,SV402: $i,SV536: $i] :
      ( ( ( ~ ( in @ SV536 @ SV402 ) )
        = $true )
      | ( ( in @ SV536 @ ( setadjoin @ SV174 @ SV402 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1499]) ).

thf(1736,plain,
    ! [SV176: $i,SV537: $i] :
      ( ( ( in @ SV537 @ SV176 )
        = $false )
      | ( ( SV176 != emptyset )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1500]) ).

thf(1737,plain,
    ! [SV404: $i > $o,SV177: $i,SV538: $i] :
      ( ( ( ~ ( in @ SV538 @ SV177 ) )
        = $true )
      | ( ( ~ ( SV404 @ SV538 )
          | ( ( dsetconstr @ SV177
              @ ^ [SY2623: $i] : ( SV404 @ SY2623 ) )
           != emptyset ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1501]) ).

thf(1738,plain,
    ! [SV405: $i,SV601: $o] :
      ( ( SV601 = $true )
      | ( ( in @ SV405 @ emptyset )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[1502]) ).

thf(1739,plain,
    ! [SV405: $i] :
      ( ( $true = $true )
      | ( ( in @ SV405 @ emptyset )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[1502]) ).

thf(1740,plain,
    ! [SV405: $i] :
      ( ( $false = $true )
      | ( ( in @ SV405 @ emptyset )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[1502]) ).

thf(1741,plain,
    ! [SV183: $o,SV539: $i] :
      ( ( ( in @ SV539 @ ( prop2set @ SV183 ) )
        = $false )
      | ( SV183 = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1503]) ).

thf(1742,plain,
    ! [SV540: $i] :
      ( ( ( in @ SV540 @ ( prop2set @ $true ) )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1504]) ).

thf(1743,plain,
    ! [SV541: $i] :
      ( ( ( in @ SV541 @ ( prop2set @ $false ) )
        = $false )
      | ( $false = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1505]) ).

thf(1744,plain,
    ! [SV406: $i > $o,SV184: $i,SV542: $i] :
      ( ( ( ~ ( in @ SV542
              @ ( dsetconstr @ SV184
                @ ^ [SY2625: $i] : ( SV406 @ SY2625 ) ) ) )
        = $true )
      | ( ( SV406 @ SV542 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1506]) ).

thf(1745,plain,
    ! [SV407: $i > $o,SV185: $i,SV543: $i] :
      ( ( ( ~ ( in @ SV543
              @ ( dsetconstr @ SV185
                @ ^ [SY2627: $i] : ( SV407 @ SY2627 ) ) ) )
        = $true )
      | ( ( in @ SV543 @ SV185 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1507]) ).

thf(1746,plain,
    ! [SV408: $i > $o,SV186: $i,SV544: $i] :
      ( ( ( ~ ( in @ SV544 @ SV186 ) )
        = $true )
      | ( ( ~ ( SV408 @ SV544 )
          | ( in @ SV544
            @ ( dsetconstr @ SV186
              @ ^ [SY2629: $i] : ( SV408 @ SY2629 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1508]) ).

thf(1747,plain,
    ! [SV189: $i,SV409: $i] :
      ( ( ( in @ SV409 @ ( powerset @ SV189 ) )
        = $false )
      | ( ( ! [SY2630: $i] :
              ( ~ ( in @ SY2630 @ ( powerset @ SV189 ) )
              | ~ ( ~ ( in @ ( sK97_Xx @ SY2630 @ SV409 @ SV189 ) @ SV189 )
                  | ~ ~ ( ~ ( in @ ( sK97_Xx @ SY2630 @ SV409 @ SV189 ) @ SV409 )
                        | ~ ~ ( in @ ( sK97_Xx @ SY2630 @ SV409 @ SV189 ) @ SY2630 ) ) )
              | ( subset @ SV409 @ SY2630 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1510]) ).

thf(1748,plain,
    ! [SV602: $i] :
      ( ( ! [SY2883: $i] :
            ( ~ ( ~ ( in @ ( sK7_Xx @ SY2883 @ SV602 ) @ SY2883 )
                | ~ ~ ( in @ ( sK7_Xx @ SY2883 @ SV602 ) @ SV602 ) )
            | ( in @ SY2883 @ ( powerset @ SV602 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1511]) ).

thf(1749,plain,
    ! [SV603: $i] :
      ( ( ! [SY2884: $i] :
            ( ~ ( in @ SY2884 @ ( powerset @ SV603 ) )
            | ! [SY2885: $i] :
                ( ~ ( in @ SY2885 @ SY2884 )
                | ( in @ SY2885 @ SV603 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1512]) ).

thf(1750,plain,
    ! [SV545: $i,SV190: $i > $o] :
      ( ( ( ~ ( ~ ( SV190 @ ( sK24_SY86 @ SV545 @ SV190 ) )
              | ~ ( ( SV545
                   != ( sK24_SY86 @ SV545 @ SV190 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV190 @ SV545 ) )
        = $true )
      | ( ( SV190 @ ( sK23_Xx @ SV190 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1513]) ).

thf(1751,plain,
    ! [SV410: $o,SV191: $i,SV546: $i] :
      ( ( ( ~ ( in @ SV546 @ SV191 ) )
        = $true )
      | ( ( ! [SY2804: $i] :
              ( ~ ( in @ SY2804 @ SV191 )
              | ~ SV410
              | ( in @ SV546
                @ ( dsetconstr @ SV191
                  @ ^ [SY2805: $i] :
                      ( ~ ( ~ SV410
                          | ( SY2805 != SV546 ) )
                      | ~ ( ~ ~ SV410
                          | ( SY2805 != SY2804 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1514]) ).

thf(1752,plain,
    ! [SV191: $i,SV547: $i] :
      ( ( ( ~ ( in @ SV547 @ SV191 ) )
        = $true )
      | ( ( ! [SY2806: $i] :
              ( ~ ( in @ SY2806 @ SV191 )
              | ~ $true
              | ( in @ SV547
                @ ( dsetconstr @ SV191
                  @ ^ [SY2807: $i] :
                      ( ~ ( ~ $true
                          | ( SY2807 != SV547 ) )
                      | ~ ( ~ ~ $true
                          | ( SY2807 != SY2806 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1515]) ).

thf(1753,plain,
    ! [SV191: $i,SV548: $i] :
      ( ( ( ~ ( in @ SV548 @ SV191 ) )
        = $true )
      | ( ( ! [SY2808: $i] :
              ( ~ ( in @ SY2808 @ SV191 )
              | ~ $false
              | ( in @ SV548
                @ ( dsetconstr @ SV191
                  @ ^ [SY2809: $i] :
                      ( ~ ( ~ $false
                          | ( SY2809 != SV548 ) )
                      | ~ ( ~ ~ $false
                          | ( SY2809 != SY2808 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1516]) ).

thf(1754,plain,
    ! [SV192: $i,SV411: $i,SV549: $i > $i] :
      ( ( ( ~ ( ~ ( in @ ( sK92_Xx @ SV549 @ SV411 @ SV192 ) @ SV192 )
              | ~ ~ ( in @ ( SV549 @ ( sK92_Xx @ SV549 @ SV411 @ SV192 ) ) @ SV411 ) ) )
        = $true )
      | ( ( ! [SY2810: $i] :
              ( ~ ( in @ SY2810 @ SV192 )
              | ( ( ap @ SV192 @ SV411
                  @ ( lam @ SV192 @ SV411
                    @ ^ [SY2811: $i] : ( SV549 @ SY2811 ) )
                  @ SY2810 )
                = ( SV549 @ SY2810 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1517]) ).

thf(1755,plain,
    ! [SV412: $i,SV193: $i,SV550: $i] :
      ( ( ( ~ ( in @ SV550 @ ( cartprod @ SV193 @ SV412 ) ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ( SV550
                     != ( kpair @ ( sK67_Xx @ SV550 @ SV412 @ SV193 ) @ ( sK68_SY1876 @ SV550 @ SV412 @ SV193 ) ) )
                    | ~ ( in @ ( sK68_SY1876 @ SV550 @ SV412 @ SV193 ) @ SV412 ) )
              | ~ ( in @ ( sK67_Xx @ SV550 @ SV412 @ SV193 ) @ SV193 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1518]) ).

thf(1756,plain,
    ! [SV551: $i,SV194: $i > $o] :
      ( ( ( ~ ( ~ ( SV194 @ ( sK57_SY248 @ SV551 @ SV194 ) )
              | ~ ( ( SV551
                   != ( sK57_SY248 @ SV551 @ SV194 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV194 @ SV551 ) )
        = $true )
      | ( ( ! [SY2258: $i] :
              ( ~ ( SV194 @ SY2258 )
              | ! [SY2259: $i] :
                  ( ~ ( SV194 @ SY2259 )
                  | ( SY2258 = SY2259 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1519]) ).

thf(1757,plain,
    ! [SV195: $i > $i > $o,SV413: $i] :
      ( ( ( ~ ( in @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV413 )
          | ~ ! [SY2638: $i] :
                ( ~ ( ~ ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SY2638 @ SV413 @ SV195 ) )
                    | ~ ( ( SY2638
                         != ( sK13_SY1837 @ SY2638 @ SV413 @ SV195 ) ) ) )
                | ~ ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SY2638 ) ) )
        = $false )
      | ( ( ~ ( ~ ! [SY2639: $i] :
                    ( ! [SY2640: $i] :
                        ( ~ ( SV195 @ SY2640 @ SY2639 )
                        | ~ ( in @ SY2640 @ SV413 ) )
                    | ( in @ SY2639 @ ( sK10_B @ SV413 @ SV195 ) ) )
              | ~ ! [SY2641: $i] :
                    ( ~ ( in @ SY2641 @ ( sK10_B @ SV413 @ SV195 ) )
                    | ~ ( ~ ( SV195 @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SY2641 )
                        | ~ ( in @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SV413 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1520]) ).

thf(1758,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( ( ~ ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( ( SV552 = SV196 )
                        | ( in @ SV552 @ SV414 )
                        | ! [SX3: $o] : SX3 )
                    | ~ ( ( SV552 = SV196 )
                        | ! [SX3: $o] :
                            ( ~ SX3
                            | SX3 ) ) )
              | ~ ~ ( ~ ! [SY2814: $o] :
                          ( ~ SY2814
                          | ( in @ SV552 @ SV414 )
                          | SY2814 )
                    | ~ ! [SX3: $o] :
                          ( ~ SX3
                          | ~ SX3
                          | SX3 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1521]) ).

thf(1759,plain,
    ! [SV197: $i,SV415: $i] :
      ( ( ( ~ ( in @ ( sK66_Xx @ SV415 @ SV197 ) @ SV197 )
          | ~ ( in @ ( sK66_Xx @ SV415 @ SV197 ) @ SV415 ) )
        = $false )
      | ( ( ( binintersect @ SV197 @ SV415 )
          = emptyset )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1522]) ).

thf(1760,plain,
    ! [SV198: $i] :
      ( ( ! [SY2272: $i > $o,SY2273: $i] :
            ( ~ ( in @ SY2273 @ SV198 )
            | ~ ( SY2272 @ SY2273 )
            | ( in @ SY2273
              @ ( dsetconstr @ SV198
                @ ^ [SX3: $i] : ( SY2272 @ SX3 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1523]) ).

thf(1761,plain,
    ! [SV198: $i] :
      ( ( ! [SY2275: $i > $o,SY2276: $i] :
            ( ~ ( in @ SY2276 @ SV198 )
            | ~ ( in @ SY2276
                @ ( dsetconstr @ SV198
                  @ ^ [SX3: $i] : ( SY2275 @ SX3 ) ) )
            | ( SY2275 @ SY2276 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1524]) ).

thf(1762,plain,
    ! [SV199: $i,SV416: $i] :
      ( ( ( ~ ( in @ ( sK30_Xx @ SV416 @ SV199 ) @ SV416 )
          | ~ ~ ( in @ ( sK30_Xx @ SV416 @ SV199 ) @ SV199 ) )
        = $false )
      | ( ( in @ SV416 @ ( powerset @ SV199 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1525]) ).

thf(1763,plain,
    ! [SV417: $i > $o,SV200: $i,SV604: $i] :
      ( ( ( ~ ( in @ SV604 @ SV200 )
          | ( SV417 @ SV604 ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK40_Xx @ SV417 @ SV200 ) @ SV200 )
              | ~ ~ ( SV417 @ ( sK40_Xx @ SV417 @ SV200 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1526]) ).

thf(1764,plain,
    ! [SV201: $i,SV418: $i,SV553: $i > $i] :
      ( ( ( ~ ( ~ ( in @ ( sK78_Xx @ SV553 @ SV418 @ SV201 ) @ SV201 )
              | ~ ~ ( in @ ( SV553 @ ( sK78_Xx @ SV553 @ SV418 @ SV201 ) ) @ SV418 ) ) )
        = $true )
      | ( ( in
          @ ( lam @ SV201 @ SV418
            @ ^ [SY2816: $i] : ( SV553 @ SY2816 ) )
          @ ( funcSet @ SV201 @ SV418 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1527]) ).

thf(1765,plain,
    ! [SV419: $o,SV202: $i,SV554: $i] :
      ( ( ( ~ ( in @ SV554 @ SV202 ) )
        = $true )
      | ( ( ! [SY2817: $i] :
              ( ~ ( in @ SY2817 @ SV202 )
              | SV419
              | ( ( dsetconstr @ SV202
                  @ ^ [SY2818: $i] :
                      ( ~ ( ~ SV419
                          | ( SY2818 != SV554 ) )
                      | ~ ( ~ ~ SV419
                          | ( SY2818 != SY2817 ) ) ) )
                = ( setadjoin @ SY2817 @ emptyset ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1528]) ).

thf(1766,plain,
    ! [SV202: $i,SV555: $i] :
      ( ( ( ~ ( in @ SV555 @ SV202 ) )
        = $true )
      | ( ( ! [SY2819: $i] :
              ( ~ ( in @ SY2819 @ SV202 )
              | $true
              | ( ( dsetconstr @ SV202
                  @ ^ [SY2820: $i] :
                      ( ~ ( ~ $true
                          | ( SY2820 != SV555 ) )
                      | ~ ( ~ ~ $true
                          | ( SY2820 != SY2819 ) ) ) )
                = ( setadjoin @ SY2819 @ emptyset ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1529]) ).

thf(1767,plain,
    ! [SV202: $i,SV556: $i] :
      ( ( ( ~ ( in @ SV556 @ SV202 ) )
        = $true )
      | ( ( ! [SY2821: $i] :
              ( ~ ( in @ SY2821 @ SV202 )
              | $false
              | ( ( dsetconstr @ SV202
                  @ ^ [SY2822: $i] :
                      ( ~ ( ~ $false
                          | ( SY2822 != SV556 ) )
                      | ~ ( ~ ~ $false
                          | ( SY2822 != SY2821 ) ) ) )
                = ( setadjoin @ SY2821 @ emptyset ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1530]) ).

thf(1768,plain,
    ! [SV605: $i > $o] :
      ( ( ! [SY2886: $i > $o] :
            ( ~ ( ( ( sK55_Xx @ SY2886 @ SV605 )
                 != ( sK56_SY1873 @ SY2886 @ SV605 ) )
                | ~ ~ ( ~ ( ~ ( SV605 @ ( sK55_Xx @ SY2886 @ SV605 ) )
                          | ~ ( SY2886 @ ( sK56_SY1873 @ SY2886 @ SV605 ) ) )
                      | ~ ( ( SV605 @ ( sK55_Xx @ SY2886 @ SV605 ) )
                          | ( SY2886 @ ( sK56_SY1873 @ SY2886 @ SV605 ) ) ) ) )
            | ! [SY2887: $i] :
                ( ~ ( ~ ( SV605 @ ( sK54_SY233 @ SY2887 @ SY2886 @ SV605 ) )
                    | ~ ( ( SY2887
                         != ( sK54_SY233 @ SY2887 @ SY2886 @ SV605 ) ) ) )
                | ~ ( SV605 @ SY2887 ) )
            | ~ ( ~ ! [SY2888: $i] :
                      ( ~ ( SY2886 @ SY2888 )
                      | ( ( sK53_SY235 @ SY2886 @ SV605 )
                        = SY2888 ) )
                | ~ ( SY2886 @ ( sK53_SY235 @ SY2886 @ SV605 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1531]) ).

thf(1769,plain,
    ! [SV606: $i > $o] :
      ( ( ! [SY2889: $i > $o] :
            ( ~ ( ( ( sK51_Xx @ SY2889 @ SV606 )
                 != ( sK52_SY1871 @ SY2889 @ SV606 ) )
                | ~ ~ ( ~ ( ~ ( SV606 @ ( sK51_Xx @ SY2889 @ SV606 ) )
                          | ~ ( SY2889 @ ( sK52_SY1871 @ SY2889 @ SV606 ) ) )
                      | ~ ( ( SV606 @ ( sK51_Xx @ SY2889 @ SV606 ) )
                          | ( SY2889 @ ( sK52_SY1871 @ SY2889 @ SV606 ) ) ) ) )
            | ! [SY2890: $i] :
                ( ~ ( ~ ( SY2889 @ ( sK50_SY236 @ SY2890 @ SY2889 @ SV606 ) )
                    | ~ ( ( SY2890
                         != ( sK50_SY236 @ SY2890 @ SY2889 @ SV606 ) ) ) )
                | ~ ( SY2889 @ SY2890 ) )
            | ~ ( ~ ! [SY2891: $i] :
                      ( ~ ( SV606 @ SY2891 )
                      | ( ( sK49_SY232 @ SY2889 @ SV606 )
                        = SY2891 ) )
                | ~ ( SV606 @ ( sK49_SY232 @ SY2889 @ SV606 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1532]) ).

thf(1770,plain,
    ! [SV203: $i,SV420: $i > $o] :
      ( ( ( ~ ( SV420 @ ( sK39_Xx @ SV420 @ SV203 ) )
          | ~ ( in @ ( sK39_Xx @ SV420 @ SV203 ) @ SV203 ) )
        = $false )
      | ( ( ! [SY2653: $i] :
              ( ~ ( in @ SY2653 @ SV203 )
              | ~ ( SV420 @ SY2653 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1533]) ).

thf(1771,plain,
    ! [SV557: $i,SV204: $i > $o] :
      ( ( ( ~ ( ~ ( SV204 @ ( sK20_SY57 @ SV557 @ SV204 ) )
              | ~ ( ( SV557
                   != ( sK20_SY57 @ SV557 @ SV204 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV204 @ SV557 ) )
        = $true )
      | ( ( SV204
          @ ( descr
            @ ^ [SY2291: $i] : ( SV204 @ SY2291 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1534]) ).

thf(1772,plain,
    ! [SV558: $i,SV205: $i > $o] :
      ( ( ( ~ ( ~ ( SV205 @ ( sK42_Xy @ SV558 @ SV205 ) )
              | ~ ( ( SV558
                   != ( sK42_Xy @ SV558 @ SV205 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV205 @ SV558 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2293: $i] :
                    ( ~ ( SV205 @ SY2293 )
                    | ( ( sK41_SY198 @ SV205 )
                      = SY2293 ) )
              | ~ ( SV205 @ ( sK41_SY198 @ SV205 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1535]) ).

thf(1773,plain,
    ! [SV206: $i,SV421: $i,SV559: $i > $i] :
      ( ( ( ~ ( ~ ( in @ ( sK94_Xx @ SV559 @ SV421 @ SV206 ) @ SV206 )
              | ~ ~ ( in @ ( SV559 @ ( sK94_Xx @ SV559 @ SV421 @ SV206 ) ) @ SV421 ) ) )
        = $true )
      | ( ( ! [SY2823: $i] :
              ( ~ ( in @ SY2823 @ SV206 )
              | ( ( ap @ SV206 @ SV421
                  @ ( lam @ SV206 @ SV421
                    @ ^ [SY2824: $i] : ( SV559 @ SY2824 ) )
                  @ SY2823 )
                = ( SV559 @ SY2823 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1536]) ).

thf(1774,plain,
    ( ( ~ ( in @ sK3_SY1826 @ ( powerset @ sK1_A ) )
      | ~ ~ ( ~ ( in @ sK4_SY1829 @ ( powerset @ sK1_A ) )
            | ~ ~ ( ~ ( in @ sK5_SY1831 @ sK1_A )
                  | ~ ~ ( ~ ( in @ sK5_SY1831 @ ( binintersect @ sK2_SY1822 @ sK3_SY1826 ) )
                        | ~ ~ ( in @ sK5_SY1831 @ ( binunion @ sK3_SY1826 @ sK4_SY1829 ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1538]) ).

thf(1775,plain,
    ! [SV422: $i,SV207: $i,SV560: $i] :
      ( ( ( ~ ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) ) )
        = $true )
      | ( ( ! [SY2825: $i > $o] :
              ( ~ ( ~ ( in @ ( sK81_Xx @ SY2825 @ SV560 @ SV422 @ SV207 ) @ SV207 )
                  | ~ ~ ( ~ ( in @ ( sK82_SY1880 @ SY2825 @ SV560 @ SV422 @ SV207 ) @ SV422 )
                        | ~ ~ ( ~ ( in @ ( kpair @ ( sK81_Xx @ SY2825 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SY2825 @ SV560 @ SV422 @ SV207 ) ) @ SV560 )
                              | ~ ~ ( SY2825 @ ( kpair @ ( sK81_Xx @ SY2825 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SY2825 @ SV560 @ SV422 @ SV207 ) ) ) ) ) )
              | ! [SY2826: $i] :
                  ( ~ ( in @ SY2826 @ SV560 )
                  | ( SY2825 @ SY2826 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1539]) ).

thf(1776,plain,
    ! [SV423: $i,SV208: $i,SV561: $i] :
      ( ( ( ~ ( subset @ SV561 @ ( cartprod @ SV208 @ SV423 ) ) )
        = $true )
      | ( ( ! [SY2827: $i] :
              ( ~ ( subset @ SY2827 @ ( cartprod @ SV208 @ SV423 ) )
              | ~ ( ~ ( in @ ( sK84_Xx @ SY2827 @ SV561 @ SV423 @ SV208 ) @ SV208 )
                  | ~ ~ ( ~ ( in @ ( sK85_SY1881 @ SY2827 @ SV561 @ SV423 @ SV208 ) @ SV423 )
                        | ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SY2827 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SY2827 @ SV561 @ SV423 @ SV208 ) ) @ SV561 )
                              | ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SY2827 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SY2827 @ SV561 @ SV423 @ SV208 ) ) @ SY2827 ) ) ) )
              | ( subset @ SV561 @ SY2827 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1540]) ).

thf(1777,plain,
    ! [SV209: $i,SV424: $i > $o] :
      ( ( ( ~ ( in @ ( sK70_Xx @ SV424 @ SV209 ) @ SV209 )
          | ~ ~ ( ~ ( in @ ( sK71_SY1877 @ SV424 @ SV209 ) @ SV209 )
                | ~ ~ ( ~ ( SV424 @ ( sK70_Xx @ SV424 @ SV209 ) )
                      | ~ ~ ( ~ ( SV424 @ ( sK71_SY1877 @ SV424 @ SV209 ) )
                            | ~ ( ( ( sK70_Xx @ SV424 @ SV209 )
                                 != ( sK71_SY1877 @ SV424 @ SV209 ) ) ) ) ) ) )
        = $false )
      | ( ( ! [SY2662: $i] :
              ( ~ ( SV424 @ SY2662 )
              | ~ ( in @ SY2662 @ SV209 ) )
          | ( singleton
            @ ( dsetconstr @ SV209
              @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1541]) ).

thf(1778,plain,
    ! [SV425: $i,SV210: $i] :
      ( ( ( SV210 = SV425 )
        = $false )
      | ( ( ~ ( ~ ! [SY2664: $i,SY2665: $i] :
                    ( ( SY2664 != SY2665 )
                    | ~ ( in @ SY2664 @ SV210 )
                    | ( in @ SY2665 @ SV425 ) )
              | ~ ! [SY2666: $i,SY2667: $i] :
                    ( ( SY2666 != SY2667 )
                    | ~ ( in @ SY2667 @ SV425 )
                    | ( in @ SY2666 @ SV210 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1542]) ).

thf(1779,plain,
    ! [SV562: $i,SV211: $i > $o] :
      ( ( ( ~ ( ~ ( SV211 @ ( sK48_SY224 @ SV562 @ SV211 ) )
              | ~ ( ( SV562
                   != ( sK48_SY224 @ SV562 @ SV211 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV211 @ SV562 ) )
        = $true )
      | ( ( ! [SY2314: $i] :
              ( ~ ( SV211 @ SY2314 )
              | ! [SY2315: $i] :
                  ( ~ ( SV211 @ SY2315 )
                  | ( SY2314 = SY2315 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1543]) ).

thf(1780,plain,
    ! [SV212: $i,SV426: $i,SV563: $i > $i] :
      ( ( ( ~ ( ~ ( in @ ( sK77_Xx @ SV563 @ SV426 @ SV212 ) @ SV212 )
              | ~ ~ ( in @ ( SV563 @ ( sK77_Xx @ SV563 @ SV426 @ SV212 ) ) @ SV426 ) ) )
        = $true )
      | ( ( func @ SV212 @ SV426
          @ ( lam @ SV212 @ SV426
            @ ^ [SY2828: $i] : ( SV563 @ SY2828 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1544]) ).

thf(1781,plain,
    ! [SV213: $i > $o,SV427: $i > $o] :
      ( ( ( ( ( sK60_Xx @ SV427 @ SV213 )
           != ( sK61_SY1874 @ SV427 @ SV213 ) )
          | ~ ~ ( ~ ( ~ ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
                    | ~ ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) ) )
                | ~ ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
                    | ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) ) ) ) )
        = $false )
      | ( ( ! [SY2670: $i] :
              ( ~ ( ~ ( SV213 @ ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2670
                       != ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV213 @ SY2670 ) )
          | ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1545]) ).

thf(1782,plain,
    ! [SV214: $i,SV428: $i] :
      ( ( ( in @ SV428 @ ( powerset @ SV214 ) )
        = $false )
      | ( ( ! [SY2674: $i] :
              ( ~ ( in @ SY2674 @ ( powerset @ SV214 ) )
              | ~ ( ~ ( in @ ( sK98_Xx @ SY2674 @ SV428 @ SV214 ) @ SV214 )
                  | ~ ~ ( ~ ( in @ ( sK98_Xx @ SY2674 @ SV428 @ SV214 ) @ SV428 )
                        | ~ ~ ( in @ ( sK98_Xx @ SY2674 @ SV428 @ SV214 ) @ SY2674 ) ) )
              | ( in @ SV428 @ ( powerset @ SY2674 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1546]) ).

thf(1783,plain,
    ! [SV215: $i,SV429: $i] :
      ( ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false )
      | ( ( ! [SY2675: $o] :
              ( ~ ( ~ ( in @ SV429 @ ( sK31_B @ SY2675 @ SV429 @ SV215 ) )
                  | ~ ~ ( ~ ( in @ ( sK31_B @ SY2675 @ SV429 @ SV215 ) @ SV215 )
                        | ~ ~ SY2675 ) )
              | SY2675 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1547]) ).

thf(1784,plain,
    ! [SV216: $i,SV430: $i] :
      ( ( ( ~ ( in @ ( sK26_Xx @ SV430 @ SV216 ) @ SV216 )
          | ~ ~ ( in @ ( sK26_Xx @ SV430 @ SV216 ) @ SV430 ) )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV430 )
              | ~ ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV216 ) )
          | ( SV216 = SV430 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1548]) ).

thf(1785,plain,
    ! [SV217: $i,SV431: $i] :
      ( ( ( in @ SV431 @ ( setunion @ SV217 ) )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK69_X @ SV431 @ SV217 ) @ SV217 )
              | ~ ( in @ SV431 @ ( sK69_X @ SV431 @ SV217 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1549]) ).

thf(1786,plain,
    ! [SV564: $i,SV432: $i,SV218: $i] :
      ( ( ( ~ ( func @ SV218 @ SV432 @ SV564 ) )
        = $true )
      | ( ( ! [SY2829: $i] :
              ( ~ ( func @ SV218 @ SV432 @ SY2829 )
              | ~ ( ~ ( in @ ( sK83_Xx @ SY2829 @ SV564 @ SV432 @ SV218 ) @ SV218 )
                  | ~ ( ( ( ap @ SV218 @ SV432 @ SV564 @ ( sK83_Xx @ SY2829 @ SV564 @ SV432 @ SV218 ) )
                       != ( ap @ SV218 @ SV432 @ SY2829 @ ( sK83_Xx @ SY2829 @ SV564 @ SV432 @ SV218 ) ) ) ) )
              | ! [SY2830: $i] :
                  ( ~ ( in @ SY2830 @ SV218 )
                  | ! [SY2831: $i] :
                      ( ~ ( in @ SY2831 @ SV432 )
                      | ~ ( in @ ( kpair @ SY2830 @ SY2831 ) @ SY2829 )
                      | ( in @ ( kpair @ SY2830 @ SY2831 ) @ SV564 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1550]) ).

thf(1787,plain,
    ! [SV219: $i,SV433: $i] :
      ( ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( ! [SY2680: $i] :
              ( ~ ( in @ SY2680 @ ( powerset @ SV219 ) )
              | ~ ( ~ ( in @ ( sK96_Xx @ SY2680 @ SV433 @ SV219 ) @ SV219 )
                  | ~ ~ ( ~ ( in @ ( sK96_Xx @ SY2680 @ SV433 @ SV219 ) @ SV433 )
                        | ~ ~ ( in @ ( sK96_Xx @ SY2680 @ SV433 @ SV219 ) @ SY2680 ) ) )
              | ~ ( ~ ( in @ ( sK95_Xx @ SY2680 @ SV433 @ SV219 ) @ SV219 )
                  | ~ ~ ( ~ ( in @ ( sK95_Xx @ SY2680 @ SV433 @ SV219 ) @ SY2680 )
                        | ~ ~ ( in @ ( sK95_Xx @ SY2680 @ SV433 @ SV219 ) @ SV433 ) ) )
              | ( SV433 = SY2680 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1551]) ).

thf(1788,plain,
    ! [SV434: $i > $o,SV220: $i,SV565: $i] :
      ( ( ( ~ ( in @ SV565 @ SV220 ) )
        = $true )
      | ( ( ~ ( SV434 @ SV565 )
          | ~ ( ~ ( in @ ( sK73_Xy @ SV565 @ SV434 @ SV220 ) @ SV220 )
              | ~ ~ ( ~ ( SV434 @ ( sK73_Xy @ SV565 @ SV434 @ SV220 ) )
                    | ~ ( ( ( sK73_Xy @ SV565 @ SV434 @ SV220 )
                         != SV565 ) ) ) )
          | ( singleton
            @ ( dsetconstr @ SV220
              @ ^ [SY2682: $i] : ( SV434 @ SY2682 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1552]) ).

thf(1789,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( ( in @ SV566 @ SV221 )
                        | ~ ( in @ SV566 @ SV221 )
                        | ! [SX3: $o] : SX3 )
                    | ~ ~ ( ~ ( ( in @ SV566 @ SV221 )
                              | ( in @ SV566 @ SV435 )
                              | ! [SX3: $o] : SX3 )
                          | ~ ( ( in @ SV566 @ SV221 )
                              | ! [SX3: $o] :
                                  ( ~ SX3
                                  | SX3 ) ) ) )
              | ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SV566 @ SV435 )
                              | ~ ( in @ SV566 @ SV221 )
                              | ! [SX3: $o] : SX3 )
                          | ~ ~ ( ~ ( ~ ( in @ SV566 @ SV435 )
                                    | ( in @ SV566 @ SV435 )
                                    | ! [SX3: $o] : SX3 )
                                | ~ ( ~ ( in @ SV566 @ SV435 )
                                    | ! [SX3: $o] :
                                        ( ~ SX3
                                        | SX3 ) ) ) )
                    | ~ ~ ( ~ ! [SY2839: $o] :
                                ( ~ SY2839
                                | ~ ( in @ SV566 @ SV221 )
                                | SY2839 )
                          | ~ ~ ( ~ ! [SY2840: $o] :
                                      ( ~ SY2840
                                      | ( in @ SV566 @ SV435 )
                                      | SY2840 )
                                | ~ ! [SX3: $o] :
                                      ( ~ SX3
                                      | ~ SX3
                                      | SX3 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1553]) ).

thf(1790,plain,
    ! [SV222: $i,SV436: $i,SV567: $i > $i] :
      ( ( ( ~ ( ~ ( in @ ( sK76_Xx @ SV567 @ SV436 @ SV222 ) @ SV222 )
              | ~ ~ ( in @ ( SV567 @ ( sK76_Xx @ SV567 @ SV436 @ SV222 ) ) @ SV436 ) ) )
        = $true )
      | ( ( func @ SV222 @ SV436
          @ ( dpsetconstr @ SV222 @ SV436
            @ ^ [SY2842: $i,SY2843: $i] :
                ( ( SV567 @ SY2842 )
                = SY2843 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1554]) ).

thf(1791,plain,
    ! [SV223: $i] :
      ( ( ! [SY2355: $i,SY2356: $i] :
            ( ~ ( in @ SY2356 @ ( setadjoin @ SV223 @ SY2355 ) )
            | ( SY2356 = SV223 )
            | ( in @ SY2356 @ SY2355 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1555]) ).

thf(1792,plain,
    ! [SV223: $i] :
      ( ( ~ ( ~ ! [SY2357: $i,SY2358: $i] :
                  ( ( SY2358 != SV223 )
                  | ( in @ SY2358 @ ( setadjoin @ SV223 @ SY2357 ) ) )
            | ~ ! [SY2359: $i,SY2360: $i] :
                  ( ~ ( in @ SY2360 @ SY2359 )
                  | ( in @ SY2360 @ ( setadjoin @ SV223 @ SY2359 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1556]) ).

thf(1793,plain,
    ! [SV224: $i,SV437: $i] :
      ( ( ( ~ ( in @ ( sK65_Xx @ SV437 @ SV224 ) @ SV224 )
          | ~ ~ ( in @ ( sK65_Xx @ SV437 @ SV224 ) @ SV437 ) )
        = $false )
      | ( ( subset @ SV224 @ SV437 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1557]) ).

thf(1794,plain,
    ! [SV225: $i,SV438: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK6_Xx @ SV438 @ SV225 ) @ SV225 )
              | ~ ( in @ ( sK6_Xx @ SV438 @ SV225 ) @ SV438 ) )
          | ~ ( ( in @ ( sK6_Xx @ SV438 @ SV225 ) @ SV225 )
              | ( in @ ( sK6_Xx @ SV438 @ SV225 ) @ SV438 ) ) )
        = $false )
      | ( ( SV225 = SV438 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1558]) ).

thf(1795,plain,
    ! [SV439: $i,SV226: $i] :
      ( ( ~ ~ ( ~ ! [SY2696: $i] :
                    ( ~ ( in @ SY2696 @ ( binunion @ SV226 @ SV439 ) )
                    | ( in @ SY2696 @ SV226 )
                    | ( in @ SY2696 @ SV439 )
                    | ! [SX3: $o] : SX3 )
              | ~ ! [SY2698: $i] :
                    ( ~ ( in @ SY2698 @ ( binunion @ SV226 @ SV439 ) )
                    | ( in @ SY2698 @ SV226 )
                    | ! [SX3: $o] :
                        ( ~ SX3
                        | SX3 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1559]) ).

thf(1796,plain,
    ! [SV439: $i,SV226: $i] :
      ( ( ~ ~ ( ~ ! [SY2700: $i] :
                    ( ~ ( in @ SY2700 @ ( binunion @ SV226 @ SV439 ) )
                    | ! [SY2701: $o] :
                        ( ~ SY2701
                        | ( in @ SY2700 @ SV439 )
                        | SY2701 ) )
              | ~ ( ! [SY2702: $i] :
                      ~ ( in @ SY2702 @ ( binunion @ SV226 @ SV439 ) )
                  | ! [SX2: $o] :
                      ( ~ SX2
                      | ~ SX2
                      | SX2 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1559]) ).

thf(1797,plain,
    ! [SV440: $i > $o,SV227: $i,SV607: $i] :
      ( ( ( ~ ( in @ SV607 @ SV227 )
          | ( SV440 @ SV607 ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK38_Xx @ SV440 @ SV227 ) @ SV227 )
              | ~ ~ ( SV440 @ ( sK38_Xx @ SV440 @ SV227 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1560]) ).

thf(1798,plain,
    ! [SV228: $i > $o,SV568: $i] :
      ( ( ( ~ ( ( ( sK47_Xy @ SV568 @ SV228 )
               != SV568 )
              | ~ ( SV228 @ ( sK47_Xy @ SV568 @ SV228 ) ) )
          | ~ ( ( ( sK47_Xy @ SV568 @ SV228 )
                = SV568 )
              | ( SV228 @ ( sK47_Xy @ SV568 @ SV228 ) ) ) )
        = $false )
      | ( ( ~ ( ~ ! [SY2375: $i] :
                    ( ~ ( SV228 @ SY2375 )
                    | ( ( sK46_SY211 @ SV228 )
                      = SY2375 ) )
              | ~ ( SV228 @ ( sK46_SY211 @ SV228 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1561]) ).

thf(1799,plain,
    ! [SV229: $i,SV441: $i > $o] :
      ( ( ( ~ ( in @ ( sK74_Xx @ SV441 @ SV229 ) @ SV229 )
          | ~ ~ ( ~ ( in @ ( sK75_SY1878 @ SV441 @ SV229 ) @ SV229 )
                | ~ ~ ( ~ ( SV441 @ ( sK74_Xx @ SV441 @ SV229 ) )
                      | ~ ~ ( ~ ( SV441 @ ( sK75_SY1878 @ SV441 @ SV229 ) )
                            | ~ ( ( ( sK74_Xx @ SV441 @ SV229 )
                                 != ( sK75_SY1878 @ SV441 @ SV229 ) ) ) ) ) ) )
        = $false )
      | ( ( ! [SY2705: $i] :
              ( ~ ( SV441 @ SY2705 )
              | ~ ( in @ SY2705 @ SV229 ) )
          | ( singleton
            @ ( dsetconstr @ SV229
              @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1562]) ).

thf(1800,plain,
    ! [SV442: $i,SV230: $i,SV569: $i] :
      ( ( ( ~ ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) ) )
        = $true )
      | ( ( ! [SY2844: $i] :
              ( ~ ( subset @ SY2844 @ ( cartprod @ SV230 @ SV442 ) )
              | ~ ( ~ ( in @ ( sK88_Xx @ SY2844 @ SV569 @ SV442 @ SV230 ) @ SV230 )
                  | ~ ~ ( ~ ( in @ ( sK89_SY1883 @ SY2844 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                        | ~ ~ ( ~ ( in @ ( kpair @ ( sK88_Xx @ SY2844 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SY2844 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
                              | ~ ~ ( in @ ( kpair @ ( sK88_Xx @ SY2844 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SY2844 @ SV569 @ SV442 @ SV230 ) ) @ SY2844 ) ) ) )
              | ~ ( ~ ( in @ ( sK86_Xx @ SY2844 @ SV569 @ SV442 @ SV230 ) @ SV230 )
                  | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SY2844 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                        | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SY2844 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SY2844 @ SV569 @ SV442 @ SV230 ) ) @ SY2844 )
                              | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SY2844 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SY2844 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
              | ( SV569 = SY2844 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1563]) ).

thf(1801,plain,
    ! [SV231: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK9_Xx @ SV231 ) @ omega )
                | ~ ( in @ ( sK9_Xx @ SV231 ) @ SV231 ) )
          | ~ ~ ( in @ ( setadjoin @ ( sK9_Xx @ SV231 ) @ ( sK9_Xx @ SV231 ) ) @ SV231 ) )
        = $false )
      | ( ( ~ ( in @ emptyset @ SV231 ) )
        = $true )
      | ( ( ! [SY2382: $i] :
              ( ~ ( in @ SY2382 @ omega )
              | ( in @ SY2382 @ SV231 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1564]) ).

thf(1802,plain,
    ! [SV443: $o,SV232: $i,SV570: $i] :
      ( ( ( ~ ( in @ SV570 @ SV232 ) )
        = $true )
      | ( ( ! [SY2845: $i] :
              ( ~ ( in @ SY2845 @ SV232 )
              | SV443
              | ( in @ SY2845
                @ ( dsetconstr @ SV232
                  @ ^ [SY2846: $i] :
                      ( ~ ( ~ SV443
                          | ( SY2846 != SV570 ) )
                      | ~ ( ~ ~ SV443
                          | ( SY2846 != SY2845 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1565]) ).

thf(1803,plain,
    ! [SV232: $i,SV571: $i] :
      ( ( ( ~ ( in @ SV571 @ SV232 ) )
        = $true )
      | ( ( ! [SY2847: $i] :
              ( ~ ( in @ SY2847 @ SV232 )
              | $true
              | ( in @ SY2847
                @ ( dsetconstr @ SV232
                  @ ^ [SY2848: $i] :
                      ( ~ ( ~ $true
                          | ( SY2848 != SV571 ) )
                      | ~ ( ~ ~ $true
                          | ( SY2848 != SY2847 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1566]) ).

thf(1804,plain,
    ! [SV232: $i,SV572: $i] :
      ( ( ( ~ ( in @ SV572 @ SV232 ) )
        = $true )
      | ( ( ! [SY2849: $i] :
              ( ~ ( in @ SY2849 @ SV232 )
              | $false
              | ( in @ SY2849
                @ ( dsetconstr @ SV232
                  @ ^ [SY2850: $i] :
                      ( ~ ( ~ $false
                          | ( SY2850 != SV572 ) )
                      | ~ ( ~ ~ $false
                          | ( SY2850 != SY2849 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1567]) ).

thf(1805,plain,
    ! [SV233: $i] :
      ( ( ! [SY2387: $i] :
            ( ~ ( ~ ( in @ ( sK19_Xx @ SY2387 @ SV233 ) @ SY2387 )
                | ~ ~ ( in @ ( sK19_Xx @ SY2387 @ SV233 ) @ SV233 ) )
            | ! [SX2: $i] :
                ~ ( in @ SX2 @ SY2387 )
            | ~ ( ~ ! [SY2389: $i] :
                      ( ~ ( in @ SY2389 @ ( sK15_B @ SV233 ) )
                      | ! [SY2390: $i] :
                          ( ~ ( in @ SY2390 @ SY2389 )
                          | ( in @ SY2390 @ ( sK17_SY1842 @ SY2387 @ SV233 ) ) )
                      | ( in @ ( sK18_SY1856 @ SY2387 @ SV233 ) @ SY2389 ) )
                | ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1842 @ SY2387 @ SV233 ) @ ( sK15_B @ SV233 ) )
                            | ~ ( in @ ( sK18_SY1856 @ SY2387 @ SV233 ) @ SY2387 ) )
                      | ~ ! [SY2391: $i] :
                            ( ~ ( in @ SY2391 @ ( sK17_SY1842 @ SY2387 @ SV233 ) )
                            | ~ ( in @ SY2391 @ SY2387 ) ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1568]) ).

thf(1806,plain,
    ! [SV233: $i] :
      ( ( ~ ( ~ ! [SY2392: $i,SY2393: $i] :
                  ( ~ ( in @ SY2392 @ ( sK15_B @ SV233 ) )
                  | ~ ( in @ SY2393 @ ( sK15_B @ SV233 ) )
                  | ! [SX3: $i] :
                      ( ~ ( in @ SX3 @ SY2392 )
                      | ( in @ SX3 @ SY2393 ) )
                  | ! [SX3: $i] :
                      ( ~ ( in @ SX3 @ SY2393 )
                      | ( in @ SX3 @ SY2392 ) ) )
            | ~ ~ ( ~ ! [SY2396: $i] :
                        ( ~ ( in @ SY2396 @ ( sK15_B @ SV233 ) )
                        | ! [SY2397: $i] :
                            ( ~ ( in @ SY2397 @ SY2396 )
                            | ( in @ SY2397 @ SV233 ) ) )
                  | ~ ! [SY2398: $i,SY2399: $i] :
                        ( ~ ( in @ SY2398 @ SV233 )
                        | ~ ( in @ SY2399 @ SV233 )
                        | ~ ( ~ ( in @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) @ ( sK15_B @ SV233 ) )
                            | ~ ~ ( ~ ( ~ ( in @ SY2398 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) )
                                      | ~ ( in @ SY2399 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) ) )
                                  | ~ ( ( in @ SY2398 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) )
                                      | ( in @ SY2399 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) ) ) ) )
                        | ( SY2398 = SY2399 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1569]) ).

thf(1807,plain,
    ! [SV234: $i,SV444: $i > $o] :
      ( ( ( ~ ( SV444 @ ( sK37_Xx @ SV444 @ SV234 ) )
          | ~ ( in @ ( sK37_Xx @ SV444 @ SV234 ) @ SV234 ) )
        = $false )
      | ( ( ! [SY2712: $i] :
              ( ~ ( in @ SY2712 @ SV234 )
              | ~ ( SV444 @ SY2712 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1570]) ).

thf(1808,plain,
    ! [SV573: $i,SV235: $i > $o] :
      ( ( ( ~ ( ~ ( SV235 @ ( sK33_SY142 @ SV573 @ SV235 ) )
              | ~ ( ( SV573
                   != ( sK33_SY142 @ SV573 @ SV235 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV235 @ SV573 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2403: $i] :
                    ( ( SY2403
                     != ( sK32_Xx @ SV235 ) )
                    | ( SV235 @ SY2403 ) )
              | ~ ! [SY2404: $i] :
                    ( ~ ( SV235 @ SY2404 )
                    | ( SY2404
                      = ( sK32_Xx @ SV235 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1571]) ).

thf(1809,plain,
    ! [SV445: $i,SV236: $i,SV574: $i] :
      ( ( ( ~ ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) ) )
        = $true )
      | ( ( ! [SY2851: $i > $o] :
              ( ~ ( ~ ( in @ ( sK79_Xx @ SY2851 @ SV574 @ SV445 @ SV236 ) @ SV236 )
                  | ~ ~ ( ~ ( in @ ( sK80_SY1879 @ SY2851 @ SV574 @ SV445 @ SV236 ) @ SV445 )
                        | ~ ~ ( ~ ( in @ ( kpair @ ( sK79_Xx @ SY2851 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SY2851 @ SV574 @ SV445 @ SV236 ) ) @ SV574 )
                              | ~ ~ ( SY2851 @ ( kpair @ ( sK79_Xx @ SY2851 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SY2851 @ SV574 @ SV445 @ SV236 ) ) ) ) ) )
              | ! [SY2852: $i] :
                  ( ~ ( in @ SY2852 @ SV574 )
                  | ( SY2851 @ SY2852 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1572]) ).

thf(1810,plain,
    ! [SV446: $i > $o,SV237: $i,SV608: $i] :
      ( ( ( ~ ( in @ SV608 @ SV237 )
          | ( SV446 @ SV608 ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK35_Xx @ SV446 @ SV237 ) @ SV237 )
              | ~ ~ ( SV446 @ ( sK35_Xx @ SV446 @ SV237 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1573]) ).

thf(1811,plain,
    ! [SV447: $o,SV238: $i,SV575: $i] :
      ( ( ( ~ ( in @ SV575 @ SV238 ) )
        = $true )
      | ( ( ! [SY2853: $i] :
              ( ~ ( in @ SY2853 @ SV238 )
              | ~ SV447
              | ( ( dsetconstr @ SV238
                  @ ^ [SY2854: $i] :
                      ( ~ ( ~ SV447
                          | ( SY2854 != SV575 ) )
                      | ~ ( ~ ~ SV447
                          | ( SY2854 != SY2853 ) ) ) )
                = ( setadjoin @ SV575 @ emptyset ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1574]) ).

thf(1812,plain,
    ! [SV238: $i,SV576: $i] :
      ( ( ( ~ ( in @ SV576 @ SV238 ) )
        = $true )
      | ( ( ! [SY2855: $i] :
              ( ~ ( in @ SY2855 @ SV238 )
              | ~ $true
              | ( ( dsetconstr @ SV238
                  @ ^ [SY2856: $i] :
                      ( ~ ( ~ $true
                          | ( SY2856 != SV576 ) )
                      | ~ ( ~ ~ $true
                          | ( SY2856 != SY2855 ) ) ) )
                = ( setadjoin @ SV576 @ emptyset ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1575]) ).

thf(1813,plain,
    ! [SV238: $i,SV577: $i] :
      ( ( ( ~ ( in @ SV577 @ SV238 ) )
        = $true )
      | ( ( ! [SY2857: $i] :
              ( ~ ( in @ SY2857 @ SV238 )
              | ~ $false
              | ( ( dsetconstr @ SV238
                  @ ^ [SY2858: $i] :
                      ( ~ ( ~ $false
                          | ( SY2858 != SV577 ) )
                      | ~ ( ~ ~ $false
                          | ( SY2858 != SY2857 ) ) ) )
                = ( setadjoin @ SV577 @ emptyset ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1576]) ).

thf(1814,plain,
    ! [SV239: $i,SV578: $i] :
      ( ( ( in @ SV578 @ SV239 )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK14_B @ SV239 ) @ SV239 )
              | ~ ! [SY2416: $i] :
                    ( ~ ( in @ SY2416 @ ( sK14_B @ SV239 ) )
                    | ~ ( in @ SY2416 @ SV239 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1577]) ).

thf(1815,plain,
    ! [SV448: $o,SV240: $i,SV579: $i] :
      ( ( ( ~ ( in @ SV579 @ SV240 ) )
        = $true )
      | ( ( ! [SY2859: $i] :
              ( ~ ( in @ SY2859 @ SV240 )
              | ( singleton
                @ ( dsetconstr @ SV240
                  @ ^ [SY2860: $i] :
                      ( ~ ( ~ SV448
                          | ( SY2860 != SV579 ) )
                      | ~ ( ~ ~ SV448
                          | ( SY2860 != SY2859 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1578]) ).

thf(1816,plain,
    ! [SV240: $i,SV580: $i] :
      ( ( ( ~ ( in @ SV580 @ SV240 ) )
        = $true )
      | ( ( ! [SY2861: $i] :
              ( ~ ( in @ SY2861 @ SV240 )
              | ( singleton
                @ ( dsetconstr @ SV240
                  @ ^ [SY2862: $i] :
                      ( ~ ( ~ $true
                          | ( SY2862 != SV580 ) )
                      | ~ ( ~ ~ $true
                          | ( SY2862 != SY2861 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1579]) ).

thf(1817,plain,
    ! [SV240: $i,SV581: $i] :
      ( ( ( ~ ( in @ SV581 @ SV240 ) )
        = $true )
      | ( ( ! [SY2863: $i] :
              ( ~ ( in @ SY2863 @ SV240 )
              | ( singleton
                @ ( dsetconstr @ SV240
                  @ ^ [SY2864: $i] :
                      ( ~ ( ~ $false
                          | ( SY2864 != SV581 ) )
                      | ~ ( ~ ~ $false
                          | ( SY2864 != SY2863 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1580]) ).

thf(1818,plain,
    ! [SV582: $i,SV241: $i > $o] :
      ( ( ( SV241 @ SV582 )
        = $false )
      | ( ( ~ ( ~ ( SV241 @ ( sK44_Xx @ SV241 ) )
              | ~ ~ ( ~ ( SV241 @ ( sK45_SY1868 @ SV241 ) )
                    | ~ ( ( ( sK44_Xx @ SV241 )
                         != ( sK45_SY1868 @ SV241 ) ) ) ) )
          | ~ ( ~ ! [SY2422: $i] :
                    ( ~ ( SV241 @ SY2422 )
                    | ( ( sK43_SY205 @ SV241 )
                      = SY2422 ) )
              | ~ ( SV241 @ ( sK43_SY205 @ SV241 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1581]) ).

thf(1819,plain,
    ! [SV242: $i,SV449: $i] :
      ( ( ( ~ ( in @ ( sK64_Xx @ SV449 @ SV242 ) @ SV242 )
          | ~ ~ ( in @ ( sK64_Xx @ SV449 @ SV242 ) @ SV449 ) )
        = $false )
      | ( ( subset @ SV242 @ SV449 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1582]) ).

thf(1820,plain,
    ! [SV609: $i] :
      ( ( ! [SY2892: $i] :
            ( ! [SY2893: $i] :
                ( ~ ( in @ SY2892 @ SY2893 )
                | ~ ( in @ SY2893 @ SV609 ) )
            | ( in @ SY2892 @ ( setunion @ SV609 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1583]) ).

thf(1821,plain,
    ! [SV610: $i] :
      ( ( ! [SY2894: $i] :
            ( ~ ( in @ SY2894 @ ( setunion @ SV610 ) )
            | ~ ( ~ ( in @ SY2894 @ ( sK8_B @ SY2894 @ SV610 ) )
                | ~ ( in @ ( sK8_B @ SY2894 @ SV610 ) @ SV610 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1584]) ).

thf(1822,plain,
    ! [SV583: $i,SV450: $i,SV243: $i] :
      ( ( ( ~ ( func @ SV243 @ SV450 @ SV583 ) )
        = $true )
      | ( ( ! [SY2865: $i] :
              ( ~ ( func @ SV243 @ SV450 @ SY2865 )
              | ~ ( ~ ( in @ ( sK90_Xx @ SY2865 @ SV583 @ SV450 @ SV243 ) @ SV243 )
                  | ~ ( ( ( ap @ SV243 @ SV450 @ SV583 @ ( sK90_Xx @ SY2865 @ SV583 @ SV450 @ SV243 ) )
                       != ( ap @ SV243 @ SV450 @ SY2865 @ ( sK90_Xx @ SY2865 @ SV583 @ SV450 @ SV243 ) ) ) ) )
              | ( SV583 = SY2865 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1585]) ).

thf(1823,plain,
    ! [SV244: $i,SV584: $i,SV611: $i > $i] :
      ( ( ( ~ ( ~ ( in @ ( sK93_Xx @ SV611 @ SV584 @ SV244 ) @ SV244 )
              | ~ ~ ( in @ ( SV611 @ ( sK93_Xx @ SV611 @ SV584 @ SV244 ) ) @ SV584 ) ) )
        = $true )
      | ( $true = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1586]) ).

thf(1824,plain,
    ! [SV451: $i,SV245: $i,SV585: $i] :
      ( ( ( ~ ( in @ SV585 @ ( funcSet @ SV245 @ SV451 ) ) )
        = $true )
      | ( ( ! [SY2867: $i] :
              ( ~ ( in @ SY2867 @ ( funcSet @ SV245 @ SV451 ) )
              | ~ ( ~ ( in @ ( sK91_Xx @ SY2867 @ SV585 @ SV451 @ SV245 ) @ SV245 )
                  | ~ ( ( ( ap @ SV245 @ SV451 @ SV585 @ ( sK91_Xx @ SY2867 @ SV585 @ SV451 @ SV245 ) )
                       != ( ap @ SV245 @ SV451 @ SY2867 @ ( sK91_Xx @ SY2867 @ SV585 @ SV451 @ SV245 ) ) ) ) )
              | ( SV585 = SY2867 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1587]) ).

thf(1825,plain,
    ! [SV246: $i,SV452: $i > $o] :
      ( ( ( ~ ( in @ ( sK36_Xx @ SV452 @ SV246 ) @ SV246 )
          | ~ ( SV452 @ ( sK36_Xx @ SV452 @ SV246 ) ) )
        = $false )
      | ( ( ! [SY2727: $i] :
              ( ~ ( SV452 @ SY2727 )
              | ~ ( in @ SY2727 @ SV246 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1588]) ).

thf(1826,plain,
    ! [SV586: $i,SV247: $i > $o] :
      ( ( ( ~ ( ~ ( SV247 @ ( sK22_SY74 @ SV586 @ SV247 ) )
              | ~ ( ( SV586
                   != ( sK22_SY74 @ SV586 @ SV247 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV247 @ SV586 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2435: $i] :
                    ( ~ ( SV247 @ SY2435 )
                    | ( ( sK21_Xx @ SV247 )
                      = SY2435 ) )
              | ~ ( SV247 @ ( sK21_Xx @ SV247 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1589]) ).

thf(1827,plain,
    ! [SV453: $i,SV248: $i] :
      ( ( ( SV248 = SV453 )
        = $false )
      | ( ( ! [SY2728: $i > $o,SY2729: $i > $o] :
              ( ~ ( ~ ( in @ ( sK62_Xx @ SY2729 @ SY2728 @ SV453 @ SV248 ) @ SV248 )
                  | ~ ~ ( ~ ( in @ ( sK63_SY1875 @ SY2729 @ SY2728 @ SV453 @ SV248 ) @ SV453 )
                        | ~ ~ ( ( ( sK62_Xx @ SY2729 @ SY2728 @ SV453 @ SV248 )
                               != ( sK63_SY1875 @ SY2729 @ SY2728 @ SV453 @ SV248 ) )
                              | ~ ~ ( ~ ( ~ ( SY2728 @ ( sK62_Xx @ SY2729 @ SY2728 @ SV453 @ SV248 ) )
                                        | ~ ( SY2729 @ ( sK63_SY1875 @ SY2729 @ SY2728 @ SV453 @ SV248 ) ) )
                                    | ~ ( ( SY2728 @ ( sK62_Xx @ SY2729 @ SY2728 @ SV453 @ SV248 ) )
                                        | ( SY2729 @ ( sK63_SY1875 @ SY2729 @ SY2728 @ SV453 @ SV248 ) ) ) ) ) ) )
              | ( ( dsetconstr @ SV248
                  @ ^ [SX4: $i] : ( SY2728 @ SX4 ) )
                = ( dsetconstr @ SV453
                  @ ^ [SX4: $i] : ( SY2729 @ SX4 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1590]) ).

thf(1828,plain,
    ! [SV454: $i > $o,SV249: $i] :
      ( ( ( singleton
          @ ( dsetconstr @ SV249
            @ ^ [SY2732: $i] : ( SV454 @ SY2732 ) ) )
        = $false )
      | ( ( ~ ( ~ ( SV454 @ ( sK72_Xx @ SV454 @ SV249 ) )
              | ~ ( in @ ( sK72_Xx @ SV454 @ SV249 ) @ SV249 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1591]) ).

thf(1829,plain,
    ! [SV250: $i,SV1: $i,SV612: $i] :
      ( ( ( ~ ( in @ SV612 @ ( powerset @ SV1 ) )
          | ! [SY2895: $i] :
              ( ~ ( in @ SY2895 @ ( powerset @ SV1 ) )
              | ! [SY2896: $i] :
                  ( ~ ( in @ SY2896 @ SV1 )
                  | ~ ( in @ SY2896 @ ( binintersect @ SV250 @ SV612 ) )
                  | ( in @ SY2896 @ ( binunion @ SV250 @ SY2895 ) ) ) ) )
        = $true )
      | ( ( in @ SV250 @ ( powerset @ SV1 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1592]) ).

thf(1830,plain,
    ! [SV251: $i,SV2: $i,SV613: $i] :
      ( ( ( ~ ( in @ SV613 @ ( powerset @ SV2 ) )
          | ! [SY2897: $i] :
              ( ~ ( in @ SY2897 @ SV2 )
              | ( in @ SY2897 @ ( binunion @ SV251 @ SV613 ) )
              | ~ ( in @ SY2897 @ SV613 ) ) )
        = $true )
      | ( ( in @ SV251 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1593]) ).

thf(1831,plain,
    ! [SV252: $i,SV3: $i,SV614: $i] :
      ( ( ( ~ ( in @ SV614 @ ( powerset @ SV3 ) )
          | ! [SY2898: $i] :
              ( ~ ( in @ SY2898 @ SV3 )
              | ( in @ SY2898 @ ( binunion @ SV252 @ SV614 ) )
              | ~ ( in @ SY2898 @ SV252 ) ) )
        = $true )
      | ( ( in @ SV252 @ ( powerset @ SV3 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1594]) ).

thf(1832,plain,
    ! [SV253: $i,SV4: $i,SV615: $i] :
      ( ( ( ~ ( in @ SV615 @ ( powerset @ SV4 ) )
          | ~ ( subset @ SV253 @ ( setminus @ SV4 @ SV615 ) )
          | ( subset @ SV615 @ ( setminus @ SV4 @ SV253 ) ) )
        = $true )
      | ( ( in @ SV253 @ ( powerset @ SV4 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1595]) ).

thf(1833,plain,
    ! [SV254: $i,SV5: $i,SV616: $i] :
      ( ( ( ~ ( in @ SV616 @ ( powerset @ SV5 ) )
          | ~ ( subset @ SV254 @ ( setminus @ SV5 @ SV616 ) )
          | ! [SY2899: $i] :
              ( ~ ( in @ SY2899 @ SV5 )
              | ~ ( in @ SY2899 @ SV616 )
              | ( in @ SY2899 @ ( setminus @ SV5 @ SV254 ) ) ) )
        = $true )
      | ( ( in @ SV254 @ ( powerset @ SV5 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1596]) ).

thf(1834,plain,
    ! [SV255: $i,SV6: $i,SV617: $i] :
      ( ( ( ~ ( in @ SV617 @ ( powerset @ SV6 ) )
          | ( in @ ( setminus @ SV6 @ SV255 ) @ ( powerset @ ( setminus @ SV6 @ ( binintersect @ SV255 @ SV617 ) ) ) ) )
        = $true )
      | ( ( in @ SV255 @ ( powerset @ SV6 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1597]) ).

thf(1835,plain,
    ! [SV256: $i,SV7: $i,SV618: $i] :
      ( ( ( ~ ( in @ SV618 @ ( powerset @ SV7 ) )
          | ( subset @ ( setminus @ SV7 @ SV256 ) @ ( setminus @ SV7 @ ( binintersect @ SV256 @ SV618 ) ) ) )
        = $true )
      | ( ( in @ SV256 @ ( powerset @ SV7 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1598]) ).

thf(1836,plain,
    ! [SV257: $i,SV8: $i,SV619: $i] :
      ( ( ( ~ ( in @ SV619 @ ( powerset @ SV8 ) )
          | ! [SY2900: $i] :
              ( ~ ( in @ SY2900 @ SV8 )
              | ~ ( in @ SY2900 @ ( setminus @ SV8 @ SV257 ) )
              | ( in @ SY2900 @ ( setminus @ SV8 @ ( binintersect @ SV257 @ SV619 ) ) ) ) )
        = $true )
      | ( ( in @ SV257 @ ( powerset @ SV8 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1599]) ).

thf(1837,plain,
    ! [SV258: $i,SV9: $i,SV620: $i] :
      ( ( ( ~ ( in @ SV620 @ ( powerset @ SV9 ) )
          | ! [SY2901: $i] :
              ( ~ ( in @ SY2901 @ SV9 )
              | ~ ( in @ SY2901 @ ( setminus @ SV9 @ SV258 ) )
              | ~ ( in @ SY2901 @ ( binintersect @ SV258 @ SV620 ) ) ) )
        = $true )
      | ( ( in @ SV258 @ ( powerset @ SV9 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1600]) ).

thf(1838,plain,
    ! [SV262: $i,SV13: $i,SV621: $i] :
      ( ( ( ~ ( in @ SV621 @ SV13 )
          | ~ ( in @ SV621 @ ( setminus @ SV13 @ ( setminus @ SV13 @ SV262 ) ) )
          | ( in @ SV621 @ SV262 ) )
        = $true )
      | ( ( in @ SV262 @ ( powerset @ SV13 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1604]) ).

thf(1839,plain,
    ! [SV263: $i,SV14: $i,SV622: $i] :
      ( ( ( ~ ( in @ SV622 @ SV14 )
          | ~ ( in @ SV622 @ SV263 )
          | ( in @ SV622 @ ( setminus @ SV14 @ ( setminus @ SV14 @ SV263 ) ) ) )
        = $true )
      | ( ( in @ SV263 @ ( powerset @ SV14 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1605]) ).

thf(1840,plain,
    ! [SV264: $i,SV15: $i,SV623: $i] :
      ( ( ( ~ ( in @ SV623 @ ( powerset @ SV15 ) )
          | ~ ( subset @ ( setminus @ SV15 @ SV623 ) @ ( setminus @ SV15 @ SV264 ) )
          | ( subset @ SV264 @ SV623 ) )
        = $true )
      | ( ( in @ SV264 @ ( powerset @ SV15 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1606]) ).

thf(1841,plain,
    ! [SV265: $i,SV16: $i,SV624: $i] :
      ( ( ( ~ ( in @ SV624 @ ( powerset @ SV16 ) )
          | ~ ( subset @ SV265 @ SV624 )
          | ( subset @ ( setminus @ SV16 @ SV624 ) @ ( setminus @ SV16 @ SV265 ) ) )
        = $true )
      | ( ( in @ SV265 @ ( powerset @ SV16 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1607]) ).

thf(1842,plain,
    ! [SV266: $i,SV17: $i,SV625: $i] :
      ( ( ( ~ ( in @ SV625 @ ( powerset @ SV17 ) )
          | ! [SY2902: $i] :
              ( ~ ( in @ SY2902 @ SV17 )
              | ~ ( subset @ SV266 @ SV625 )
              | ( in @ SY2902 @ SV625 )
              | ~ ( in @ SY2902 @ SV266 ) ) )
        = $true )
      | ( ( in @ SV266 @ ( powerset @ SV17 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1608]) ).

thf(1843,plain,
    ! [SV267: $i,SV18: $i,SV626: $i] :
      ( ( ( ~ ( in @ SV626 @ ( powerset @ SV18 ) )
          | ! [SY2903: $i] :
              ( ~ ( in @ SY2903 @ SV18 )
              | ~ ( subset @ SV267 @ ( setminus @ SV18 @ SV626 ) )
              | ~ ( in @ SY2903 @ SV626 )
              | ~ ( in @ SY2903 @ SV267 ) ) )
        = $true )
      | ( ( in @ SV267 @ ( powerset @ SV18 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1609]) ).

thf(1844,plain,
    ! [SV268: $i,SV19: $i,SV627: $i] :
      ( ( ( ~ ( in @ SV627 @ ( powerset @ SV19 ) )
          | ! [SY2904: $i] :
              ( ~ ( in @ SY2904 @ SV19 )
              | ( in @ SY2904 @ SV627 )
              | ~ ( in @ SY2904 @ ( binintersect @ SV268 @ SV627 ) ) ) )
        = $true )
      | ( ( in @ SV268 @ ( powerset @ SV19 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1610]) ).

thf(1845,plain,
    ! [SV269: $i,SV20: $i,SV628: $i] :
      ( ( ( ~ ( in @ SV628 @ ( powerset @ SV20 ) )
          | ! [SY2905: $i] :
              ( ~ ( in @ SY2905 @ SV20 )
              | ( in @ SY2905 @ SV269 )
              | ~ ( in @ SY2905 @ ( binintersect @ SV269 @ SV628 ) ) ) )
        = $true )
      | ( ( in @ SV269 @ ( powerset @ SV20 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1611]) ).

thf(1846,plain,
    ! [SV270: $i,SV21: $i,SV629: $i] :
      ( ( ( ~ ( in @ SV629 @ SV21 )
          | ( in @ SV629 @ ( setminus @ SV21 @ SV270 ) )
          | ( in @ SV629 @ SV270 ) )
        = $true )
      | ( ( in @ SV270 @ ( powerset @ SV21 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1612]) ).

thf(1847,plain,
    ! [SV271: $i,SV22: $i,SV630: $i] :
      ( ( ( ~ ( in @ SV630 @ SV22 )
          | ~ ( in @ SV630 @ SV271 )
          | ~ ( in @ SV630 @ ( setminus @ SV22 @ SV271 ) ) )
        = $true )
      | ( ( in @ SV271 @ ( powerset @ SV22 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1613]) ).

thf(1848,plain,
    ! [SV272: $i,SV23: $i,SV631: $i] :
      ( ( ( ~ ( in @ SV631 @ ( powerset @ SV23 ) )
          | ! [SY2906: $i] :
              ( ~ ( in @ SY2906 @ SV23 )
              | ~ ( in @ SV272 @ ( powerset @ SV631 ) )
              | ~ ( in @ SY2906 @ SV272 )
              | ( in @ SY2906 @ SV631 ) ) )
        = $true )
      | ( ( in @ SV272 @ ( powerset @ SV23 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1614]) ).

thf(1849,plain,
    ! [SV274: $i,SV25: $i,SV632: $i] :
      ( ( ( ~ ( in @ SV632 @ ( powerset @ SV25 ) )
          | ( in @ ( setminus @ SV274 @ SV632 ) @ ( powerset @ SV25 ) ) )
        = $true )
      | ( ( in @ SV274 @ ( powerset @ SV25 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1616]) ).

thf(1850,plain,
    ! [SV276: $i,SV27: $i,SV633: $i] :
      ( ( ( ~ ( in @ SV633 @ ( powerset @ SV27 ) )
          | ( in @ ( binunion @ SV276 @ SV633 ) @ ( powerset @ SV27 ) ) )
        = $true )
      | ( ( in @ SV276 @ ( powerset @ SV27 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1618]) ).

thf(1851,plain,
    ! [SV277: $i,SV28: $i,SV634: $i] :
      ( ( ( ~ ( in @ SV634 @ ( powerset @ SV28 ) )
          | ( in @ ( binintersect @ SV277 @ SV634 ) @ ( powerset @ SV28 ) ) )
        = $true )
      | ( ( in @ SV277 @ ( powerset @ SV28 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1619]) ).

thf(1852,plain,
    ! [SV278: $o,SV29: $i,SV455: $i] :
      ( ( ( in @ SV455 @ SV29 )
        = $false )
      | ( ( ! [SY2733: $i] :
              ( ~ ( in @ SY2733 @ SV29 )
              | ( in @ ( if @ SV29 @ SV278 @ SV455 @ SY2733 ) @ ( setadjoin @ SV455 @ ( setadjoin @ SY2733 @ emptyset ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1620]) ).

thf(1853,plain,
    ! [SV29: $i,SV456: $i] :
      ( ( ( in @ SV456 @ SV29 )
        = $false )
      | ( ( ! [SY2734: $i] :
              ( ~ ( in @ SY2734 @ SV29 )
              | ( in @ ( if @ SV29 @ $true @ SV456 @ SY2734 ) @ ( setadjoin @ SV456 @ ( setadjoin @ SY2734 @ emptyset ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1621]) ).

thf(1854,plain,
    ! [SV29: $i,SV457: $i] :
      ( ( ( in @ SV457 @ SV29 )
        = $false )
      | ( ( ! [SY2735: $i] :
              ( ~ ( in @ SY2735 @ SV29 )
              | ( in @ ( if @ SV29 @ $false @ SV457 @ SY2735 ) @ ( setadjoin @ SV457 @ ( setadjoin @ SY2735 @ emptyset ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1622]) ).

thf(1855,plain,
    ! [SV279: $o,SV30: $i,SV458: $i] :
      ( ( ( in @ SV458 @ SV30 )
        = $false )
      | ( ( ! [SY2736: $i] :
              ( ~ ( in @ SY2736 @ SV30 )
              | SV279
              | ( ( if @ SV30 @ SV279 @ SV458 @ SY2736 )
                = SY2736 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1623]) ).

thf(1856,plain,
    ! [SV30: $i,SV459: $i] :
      ( ( ( in @ SV459 @ SV30 )
        = $false )
      | ( ( ! [SY2737: $i] :
              ( ~ ( in @ SY2737 @ SV30 )
              | $true
              | ( ( if @ SV30 @ $true @ SV459 @ SY2737 )
                = SY2737 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1624]) ).

thf(1857,plain,
    ! [SV30: $i,SV460: $i] :
      ( ( ( in @ SV460 @ SV30 )
        = $false )
      | ( ( ! [SY2738: $i] :
              ( ~ ( in @ SY2738 @ SV30 )
              | $false
              | ( ( if @ SV30 @ $false @ SV460 @ SY2738 )
                = SY2738 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1625]) ).

thf(1858,plain,
    ! [SV280: $o,SV31: $i,SV461: $i] :
      ( ( ( in @ SV461 @ SV31 )
        = $false )
      | ( ( ! [SY2739: $i] :
              ( ~ ( in @ SY2739 @ SV31 )
              | ~ SV280
              | ( ( if @ SV31 @ SV280 @ SV461 @ SY2739 )
                = SV461 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1626]) ).

thf(1859,plain,
    ! [SV31: $i,SV462: $i] :
      ( ( ( in @ SV462 @ SV31 )
        = $false )
      | ( ( ! [SY2740: $i] :
              ( ~ ( in @ SY2740 @ SV31 )
              | ~ $true
              | ( ( if @ SV31 @ $true @ SV462 @ SY2740 )
                = SV462 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1627]) ).

thf(1860,plain,
    ! [SV31: $i,SV463: $i] :
      ( ( ( in @ SV463 @ SV31 )
        = $false )
      | ( ( ! [SY2741: $i] :
              ( ~ ( in @ SY2741 @ SV31 )
              | ~ $false
              | ( ( if @ SV31 @ $false @ SV463 @ SY2741 )
                = SV463 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1628]) ).

thf(1861,plain,
    ! [SV32: $i,SV587: $i] :
      ( ( ( ~ ( in @ SV587 @ SV32 ) )
        = $true )
      | ( ( ( setunion @ SV32 )
          = SV587 )
        = $true )
      | ( ( singleton @ SV32 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1629]) ).

thf(1862,plain,
    ! [SV281: $o,SV33: $i,SV464: $i] :
      ( ( ( in @ SV464 @ SV33 )
        = $false )
      | ( ( ! [SY2742: $i] :
              ( ~ ( in @ SY2742 @ SV33 )
              | ( in @ ( if @ SV33 @ SV281 @ SV464 @ SY2742 ) @ SV33 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1630]) ).

thf(1863,plain,
    ! [SV33: $i,SV465: $i] :
      ( ( ( in @ SV465 @ SV33 )
        = $false )
      | ( ( ! [SY2743: $i] :
              ( ~ ( in @ SY2743 @ SV33 )
              | ( in @ ( if @ SV33 @ $true @ SV465 @ SY2743 ) @ SV33 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1631]) ).

thf(1864,plain,
    ! [SV33: $i,SV466: $i] :
      ( ( ( in @ SV466 @ SV33 )
        = $false )
      | ( ( ! [SY2744: $i] :
              ( ~ ( in @ SY2744 @ SV33 )
              | ( in @ ( if @ SV33 @ $false @ SV466 @ SY2744 ) @ SV33 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1632]) ).

thf(1865,plain,
    ! [SV282: $i,SV34: $i,SV467: $i] :
      ( ( ( in @ SV467 @ ( funcSet @ SV34 @ SV282 ) )
        = $false )
      | ( ( ( lam @ SV34 @ SV282
            @ ^ [SY2745: $i] : ( ap @ SV34 @ SV282 @ SV467 @ SY2745 ) )
          = SV467 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1633]) ).

thf(1866,plain,
    ! [SV468: $i,SV283: $i,SV35: $i] :
      ( ( ( func @ SV35 @ SV283 @ SV468 )
        = $false )
      | ( ( ( lam @ SV35 @ SV283
            @ ^ [SY2746: $i] : ( ap @ SV35 @ SV283 @ SV468 @ SY2746 ) )
          = SV468 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1634]) ).

thf(1867,plain,
    ! [SV588: $i,SV469: $i,SV36: $i] :
      ( ( ( func @ SV36 @ SV469 @ SV588 )
        = $false )
      | ( ( ! [SY1968: $i] :
              ~ ( in @ SY1968 @ SV36 )
          | $true )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1635]) ).

thf(1868,plain,
    ! [SV470: $i,SV37: $i,SV589: $i] :
      ( ( ( in @ SV589 @ ( funcSet @ SV37 @ SV470 ) )
        = $false )
      | ( ( ! [SY1971: $i] :
              ~ ( in @ SY1971 @ SV37 )
          | $true )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1636]) ).

thf(1869,plain,
    ! [SV284: $i,SV38: $i,SV471: $i] :
      ( ( ( in @ SV471 @ ( funcSet @ SV38 @ SV284 ) )
        = $false )
      | ( ( ! [SY2749: $i] :
              ( ~ ( in @ SY2749 @ SV38 )
              | ! [SY2750: $i] :
                  ( ~ ( in @ SY2750 @ SV284 )
                  | ~ ( in @ ( kpair @ SY2749 @ SY2750 ) @ SV471 )
                  | ( ( ap @ SV38 @ SV284 @ SV471 @ SY2749 )
                    = SY2750 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1637]) ).

thf(1870,plain,
    ! [SV472: $i,SV285: $i,SV39: $i] :
      ( ( ( func @ SV39 @ SV285 @ SV472 )
        = $false )
      | ( ( ! [SY2751: $i] :
              ( ~ ( in @ SY2751 @ SV39 )
              | ! [SY2752: $i] :
                  ( ~ ( in @ SY2752 @ SV285 )
                  | ~ ( in @ ( kpair @ SY2751 @ SY2752 ) @ SV472 )
                  | ( ( ap @ SV39 @ SV285 @ SV472 @ SY2751 )
                    = SY2752 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1638]) ).

thf(1871,plain,
    ! [SV286: $i,SV40: $i,SV473: $i] :
      ( ( ( in @ SV473 @ ( funcSet @ SV40 @ SV286 ) )
        = $false )
      | ( ( ! [SY2753: $i] :
              ( ~ ( in @ SY2753 @ SV40 )
              | ( in @ ( kpair @ SY2753 @ ( ap @ SV40 @ SV286 @ SV473 @ SY2753 ) ) @ SV473 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1639]) ).

thf(1872,plain,
    ! [SV474: $i,SV287: $i,SV41: $i] :
      ( ( ( func @ SV41 @ SV287 @ SV474 )
        = $false )
      | ( ( ! [SY2754: $i] :
              ( ~ ( in @ SY2754 @ SV41 )
              | ( in @ ( kpair @ SY2754 @ ( ap @ SV41 @ SV287 @ SV474 @ SY2754 ) ) @ SV474 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1640]) ).

thf(1873,plain,
    ! [SV288: $i > $o,SV42: $i,SV635: $i] :
      ( ( ( ~ ( in @ SV635 @ SV42 )
          | ! [SY2907: $i] :
              ( ~ ( in @ SY2907 @ SV42 )
              | ~ ( SV288 @ SV635 )
              | ~ ( SV288 @ SY2907 )
              | ( SV635 = SY2907 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV42
            @ ^ [SY2500: $i] : ( SV288 @ SY2500 ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1641]) ).

thf(1874,plain,
    ! [SV475: $i,SV289: $i,SV43: $i] :
      ( ( ( func @ SV43 @ SV289 @ SV475 )
        = $false )
      | ( ( in @ SV475 @ ( funcSet @ SV43 @ SV289 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1642]) ).

thf(1875,plain,
    ! [SV290: $i,SV44: $i,SV476: $i] :
      ( ( ( in @ SV476 @ ( funcSet @ SV44 @ SV290 ) )
        = $false )
      | ( ( ! [SY2755: $i] :
              ( ~ ( in @ SY2755 @ SV44 )
              | ( in @ ( ap @ SV44 @ SV290 @ SV476 @ SY2755 ) @ SV290 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1643]) ).

thf(1876,plain,
    ! [SV291: $i,SV45: $i,SV477: $i] :
      ( ( ( in @ SV477 @ ( funcSet @ SV45 @ SV291 ) )
        = $false )
      | ( ( func @ SV45 @ SV291 @ SV477 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1644]) ).

thf(1877,plain,
    ! [SV478: $i,SV292: $i,SV46: $i] :
      ( ( ( func @ SV46 @ SV292 @ SV478 )
        = $false )
      | ( ( ! [SY2756: $i] :
              ( ~ ( in @ SY2756 @ SV46 )
              | ( in @ ( ap @ SV46 @ SV292 @ SV478 @ SY2756 ) @ SV292 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1645]) ).

thf(1878,plain,
    ! [SV479: $i,SV293: $i,SV47: $i] :
      ( ( ( func @ SV47 @ SV293 @ SV479 )
        = $false )
      | ( ( ! [SY2757: $i] :
              ( ~ ( in @ SY2757 @ SV47 )
              | ( in
                @ ( setunion
                  @ ( dsetconstr @ SV293
                    @ ^ [SY2758: $i] : ( in @ ( kpair @ SY2757 @ SY2758 ) @ SV479 ) ) )
                @ SV293 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1646]) ).

thf(1879,plain,
    ! [SV480: $i,SV294: $i,SV48: $i] :
      ( ( ( func @ SV48 @ SV294 @ SV480 )
        = $false )
      | ( ( ! [SY2759: $i] :
              ( ~ ( in @ SY2759 @ SV48 )
              | ( singleton
                @ ( dsetconstr @ SV294
                  @ ^ [SY2760: $i] : ( in @ ( kpair @ SY2759 @ SY2760 ) @ SV480 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1647]) ).

thf(1880,plain,
    ! [SV481: $i > $i > $o,SV295: $i,SV49: $i,SV636: $i,SV590: $i] :
      ( ( ~ ( in @ ( kpair @ SV590 @ SV636 )
            @ ( dpsetconstr @ SV49 @ SV295
              @ ^ [SY2763: $i,SY2764: $i] : ( SV481 @ SY2763 @ SY2764 ) ) )
        | ( SV481 @ SV590 @ SV636 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1648]) ).

thf(1881,plain,
    ! [SV482: $i > $i > $o,SV296: $i,SV50: $i,SV637: $i,SV591: $i] :
      ( ( ~ ( in @ ( kpair @ SV591 @ SV637 )
            @ ( dpsetconstr @ SV50 @ SV296
              @ ^ [SY2767: $i,SY2768: $i] : ( SV482 @ SY2767 @ SY2768 ) ) )
        | ( in @ SV637 @ SV296 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1649]) ).

thf(1882,plain,
    ! [SV483: $i > $i > $o,SV297: $i,SV51: $i,SV592: $i] :
      ( ( ( ! [SY2874: $i] :
              ~ ( in @ ( kpair @ SV592 @ SY2874 )
                @ ( dpsetconstr @ SV51 @ SV297
                  @ ^ [SY2771: $i,SY2772: $i] : ( SV483 @ SY2771 @ SY2772 ) ) ) )
        = $true )
      | ( ( in @ SV592 @ SV51 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1650]) ).

thf(1883,plain,
    ! [SV484: $i > $i > $o,SV298: $i,SV52: $i,SV593: $i] :
      ( ( ( ~ ( in @ SV593 @ SV52 ) )
        = $true )
      | ( ( ! [SY2877: $i] :
              ( ~ ( in @ SY2877 @ SV298 )
              | ~ ( in @ ( kpair @ SV593 @ SY2877 )
                  @ ( dpsetconstr @ SV52 @ SV298
                    @ ^ [SY2775: $i,SY2776: $i] : ( SV484 @ SY2775 @ SY2776 ) ) )
              | ( SV484 @ SV593 @ SY2877 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1651]) ).

thf(1884,plain,
    ! [SV487: $i > $i > $o,SV301: $i,SV55: $i,SV594: $i] :
      ( ( ( ~ ( in @ SV594 @ SV55 ) )
        = $true )
      | ( ( ! [SY2880: $i] :
              ( ~ ( in @ SY2880 @ SV301 )
              | ~ ( SV487 @ SV594 @ SY2880 )
              | ( in @ ( kpair @ SV594 @ SY2880 )
                @ ( dpsetconstr @ SV55 @ SV301
                  @ ^ [SY2783: $i,SY2784: $i] : ( SV487 @ SY2783 @ SY2784 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1652]) ).

thf(1885,plain,
    ! [SV302: $i,SV56: $i,SV488: $i] :
      ( ( ( in @ SV488 @ ( cartprod @ SV56 @ SV302 ) )
        = $false )
      | ( ( ( kpair @ ( kfst @ SV488 ) @ ( ksnd @ SV488 ) )
          = SV488 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1653]) ).

thf(1886,plain,
    ! [SV303: $i,SV57: $i,SV489: $i] :
      ( ( ( in @ SV489 @ SV57 )
        = $false )
      | ( ( ! [SY2785: $i] :
              ( ~ ( in @ SY2785 @ SV303 )
              | ( ( ksnd @ ( kpair @ SV489 @ SY2785 ) )
                = SY2785 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1654]) ).

thf(1887,plain,
    ! [SV304: $i,SV58: $i,SV490: $i] :
      ( ( ( in @ SV490 @ SV58 )
        = $false )
      | ( ( ! [SY2786: $i] :
              ( ~ ( in @ SY2786 @ SV304 )
              | ( ( kfst @ ( kpair @ SV490 @ SY2786 ) )
                = SV490 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1655]) ).

thf(1888,plain,
    ! [SV59: $i,SV491: $i] :
      ( ( ( ! [B: $i,Xy: $i] :
              ~ ( in @ Xy @ B ) )
        = $true )
      | ( $true = $true )
      | ( ( in @ SV491 @ SV59 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1656]) ).

thf(1889,plain,
    ! [SV305: $i,SV60: $i,SV595: $i,SV492: $i] :
      ( ( ( ~ ( in @ ( kpair @ SV492 @ SV595 ) @ ( cartprod @ SV60 @ SV305 ) ) )
        = $true )
      | ( ( in @ SV595 @ SV305 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1657]) ).

thf(1890,plain,
    ! [SV306: $i,SV61: $i,SV638: $i,SV493: $i] :
      ( ( ( ~ ( in @ ( kpair @ SV493 @ SV638 ) @ ( cartprod @ SV61 @ SV306 ) ) )
        = $true )
      | ( ( in @ SV493 @ SV61 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1658]) ).

thf(1891,plain,
    ! [SV307: $i,SV62: $i,SV494: $i] :
      ( ( ( in @ SV494 @ ( cartprod @ SV62 @ SV307 ) )
        = $false )
      | ( ( in @ ( ksnd @ SV494 ) @ SV307 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1659]) ).

thf(1892,plain,
    ! [SV596: $i,SV495: $i,SV309: $i,SV66: $i] :
      ( ( ( ( kpair @ SV66 @ SV309 )
         != ( kpair @ SV495 @ SV596 ) )
        = $true )
      | ( ( SV309 = SV596 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1660]) ).

thf(1893,plain,
    ! [SV597: $i,SV496: $i,SV310: $i,SV67: $i] :
      ( ( ( ( setadjoin @ ( setadjoin @ SV67 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV67 @ ( setadjoin @ SV310 @ emptyset ) ) @ emptyset ) )
         != ( setadjoin @ ( setadjoin @ SV496 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV496 @ ( setadjoin @ SV597 @ emptyset ) ) @ emptyset ) ) )
        = $true )
      | ( ( SV310 = SV597 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1661]) ).

thf(1894,plain,
    ! [SV598: $i,SV311: $i,SV68: $i] :
      ( ( ( ( setadjoin @ SV68 @ ( setadjoin @ SV311 @ emptyset ) )
          = ( setadjoin @ SV598 @ emptyset ) )
        = $false )
      | ( ( SV68 = SV311 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1662]) ).

thf(1895,plain,
    ! [SV599: $i,SV497: $i,SV312: $i,SV69: $i] :
      ( ( ( ( setadjoin @ ( setadjoin @ SV69 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV69 @ ( setadjoin @ SV312 @ emptyset ) ) @ emptyset ) )
         != ( setadjoin @ ( setadjoin @ SV497 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV497 @ ( setadjoin @ SV599 @ emptyset ) ) @ emptyset ) ) )
        = $true )
      | ( ( ( SV497 != SV599 )
          | ( SV312 = SV599 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1663]) ).

thf(1896,plain,
    ! [SV639: $i,SV498: $i,SV315: $i,SV72: $i] :
      ( ( ( ( kpair @ SV72 @ SV315 )
         != ( kpair @ SV498 @ SV639 ) )
        = $true )
      | ( ( SV72 = SV498 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1666]) ).

thf(1897,plain,
    ! [SV640: $i,SV499: $i,SV316: $i,SV73: $i] :
      ( ( ( ( setadjoin @ ( setadjoin @ SV73 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV73 @ ( setadjoin @ SV316 @ emptyset ) ) @ emptyset ) )
         != ( setadjoin @ ( setadjoin @ SV499 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV499 @ ( setadjoin @ SV640 @ emptyset ) ) @ emptyset ) ) )
        = $true )
      | ( ( SV73 = SV499 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1667]) ).

thf(1898,plain,
    ! [SV317: $i,SV74: $i,SV500: $i] :
      ( ( ( in @ SV500 @ ( cartprod @ SV74 @ SV317 ) )
        = $false )
      | ( ( in @ ( kfst @ SV500 ) @ SV74 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1668]) ).

thf(1899,plain,
    ! [SV319: $i,SV78: $i,SV501: $i] :
      ( ( ( in @ ( setadjoin @ SV501 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV78 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV78 @ ( setadjoin @ SV319 @ emptyset ) ) @ emptyset ) ) )
        = $false )
      | ( ( SV78 = SV501 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1669]) ).

thf(1900,plain,
    ! [SV321: $i,SV83: $i,SV502: $i] :
      ( ( ( in @ SV502 @ ( cartprod @ SV83 @ SV321 ) )
        = $false )
      | ( ( iskpair @ SV502 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1671]) ).

thf(1901,plain,
    ! [SV322: $i,SV84: $i,SV503: $i] :
      ( ( ( in @ SV503 @ SV84 )
        = $false )
      | ( ( ! [SY2794: $i] :
              ( ~ ( in @ SY2794 @ SV322 )
              | ( in @ ( kpair @ SV503 @ SY2794 ) @ ( cartprod @ SV84 @ SV322 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1672]) ).

thf(1902,plain,
    ! [SV323: $i,SV85: $i,SV504: $i] :
      ( ( ( in @ SV504 @ SV85 )
        = $false )
      | ( ( ! [SY2795: $i] :
              ( ~ ( in @ SY2795 @ SV323 )
              | ( in @ ( kpair @ SV504 @ SY2795 ) @ ( powerset @ ( powerset @ ( binunion @ SV85 @ SV323 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1673]) ).

thf(1903,plain,
    ! [SV324: $i,SV86: $i,SV505: $i] :
      ( ( ( in @ SV505 @ SV86 )
        = $false )
      | ( ( ! [SY2796: $i] :
              ( ~ ( in @ SY2796 @ SV324 )
              | ( in @ ( setadjoin @ ( setadjoin @ SV505 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV505 @ ( setadjoin @ SY2796 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV86 @ SV324 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1674]) ).

thf(1904,plain,
    ! [SV325: $i,SV87: $i,SV506: $i] :
      ( ( ( in @ SV506 @ SV87 )
        = $false )
      | ( ( ! [SY2797: $i] :
              ( ~ ( in @ SY2797 @ SV325 )
              | ( subset @ ( setadjoin @ ( setadjoin @ SV506 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV506 @ ( setadjoin @ SY2797 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV87 @ SV325 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1675]) ).

thf(1905,plain,
    ! [SV326: $i,SV88: $i,SV507: $i] :
      ( ( ( in @ SV507 @ SV88 )
        = $false )
      | ( ( ! [SY2798: $i] :
              ( ~ ( in @ SY2798 @ SV326 )
              | ( in @ ( setadjoin @ SV507 @ ( setadjoin @ SY2798 @ emptyset ) ) @ ( powerset @ ( binunion @ SV88 @ SV326 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1676]) ).

thf(1906,plain,
    ! [SV327: $i,SV89: $i,SV508: $i] :
      ( ( ( in @ SV508 @ SV89 )
        = $false )
      | ( ( ! [SY2799: $i] :
              ( ~ ( in @ SY2799 @ SV327 )
              | ( subset @ ( setadjoin @ SV508 @ ( setadjoin @ SY2799 @ emptyset ) ) @ ( binunion @ SV89 @ SV327 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1677]) ).

thf(1907,plain,
    ! [SV328: $i,SV90: $i,SV509: $i] :
      ( ( ( in @ SV509 @ ( setadjoin @ SV90 @ ( setadjoin @ SV328 @ emptyset ) ) )
        = $false )
      | ( ( ( SV509 = SV90 )
          | ( SV509 = SV328 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1678]) ).

thf(1908,plain,
    ! [SV329: $i,SV91: $i,SV510: $i] :
      ( ( ( in @ SV510 @ SV91 )
        = $false )
      | ( ( in @ ( setadjoin @ SV510 @ emptyset ) @ ( powerset @ ( binunion @ SV91 @ SV329 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1679]) ).

thf(1909,plain,
    ! [SV99: $i,SV337: $i,SV511: $i] :
      ( ( ( in @ SV511 @ SV337 )
        = $true )
      | ( ( ~ ( in @ SV511 @ ( symdiff @ SV99 @ SV337 ) ) )
        = $true )
      | ( ( in @ SV511 @ SV99 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1682]) ).

thf(1910,plain,
    ! [SV338: $i,SV100: $i,SV512: $i] :
      ( ( ( in @ SV512 @ SV100 )
        = $false )
      | ( ( ~ ( in @ SV512 @ SV338 )
          | ~ ( in @ SV512 @ ( symdiff @ SV100 @ SV338 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1683]) ).

thf(1911,plain,
    ! [SV101: $i,SV339: $i,SV513: $i] :
      ( ( ( ~ ( in @ SV513 @ SV339 ) )
        = $true )
      | ( ( in @ SV513 @ ( symdiff @ SV101 @ SV339 ) )
        = $true )
      | ( ( in @ SV513 @ SV101 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1684]) ).

thf(1912,plain,
    ! [SV340: $i,SV102: $i,SV514: $i] :
      ( ( ( in @ SV514 @ SV102 )
        = $false )
      | ( ( ( in @ SV514 @ SV340 )
          | ( in @ SV514 @ ( symdiff @ SV102 @ SV340 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1685]) ).

thf(1913,plain,
    ! [SV105: $i,SV343: $i,SV515: $i] :
      ( ( ( in @ SV515 @ SV343 )
        = $false )
      | ( ( ~ ( in @ SV515 @ ( setminus @ SV105 @ SV343 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1687]) ).

thf(1914,plain,
    ! [SV344: $i,SV106: $i,SV516: $i] :
      ( ( ( in @ SV516 @ ( setminus @ SV106 @ SV344 ) )
        = $false )
      | ( ( in @ SV516 @ SV106 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1688]) ).

thf(1915,plain,
    ! [SV107: $i,SV345: $i,SV517: $i] :
      ( ( ( in @ SV517 @ SV345 )
        = $true )
      | ( ( ~ ( in @ SV517 @ SV107 ) )
        = $true )
      | ( ( in @ SV517 @ ( setminus @ SV107 @ SV345 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1689]) ).

thf(1916,plain,
    ! [SV346: $i,SV108: $i,SV518: $i] :
      ( ( ( ~ ( in @ SV518 @ SV108 ) )
        = $true )
      | ( ( in @ SV518 @ SV346 )
        = $true )
      | ( ( in @ SV518 @ ( setminus @ SV108 @ SV346 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1690]) ).

thf(1917,plain,
    ! [SV348: $i,SV110: $i,SV519: $i] :
      ( ( ( in @ SV519 @ ( setminus @ SV110 @ SV348 ) )
        = $false )
      | ( ( ~ ( in @ SV519 @ SV348 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1692]) ).

thf(1918,plain,
    ! [SV349: $i,SV111: $i,SV520: $i] :
      ( ( ( in @ SV520 @ ( setminus @ SV111 @ SV349 ) )
        = $false )
      | ( ( in @ SV520 @ SV111 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1693]) ).

thf(1919,plain,
    ! [SV350: $i,SV112: $i,SV521: $i] :
      ( ( ( in @ SV521 @ SV112 )
        = $false )
      | ( ( ( in @ SV521 @ SV350 )
          | ( in @ SV521 @ ( setminus @ SV112 @ SV350 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1694]) ).

thf(1920,plain,
    ! [SV355: $i,SV117: $i,SV523: $i] :
      ( ( ( in @ SV523 @ ( binintersect @ SV117 @ SV355 ) )
        = $false )
      | ( ( in @ SV523 @ SV355 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1697]) ).

thf(1921,plain,
    ! [SV359: $i,SV121: $i,SV524: $i] :
      ( ( ( in @ SV524 @ ( binintersect @ SV121 @ SV359 ) )
        = $false )
      | ( ( in @ SV524 @ SV121 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1700]) ).

thf(1922,plain,
    ! [SV360: $i,SV122: $i,SV525: $i] :
      ( ( ( subset @ SV525 @ SV122 )
        = $false )
      | ( ( ~ ( subset @ SV525 @ SV360 )
          | ( subset @ SV525 @ ( binintersect @ SV122 @ SV360 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1701]) ).

thf(1923,plain,
    ! [SV361: $i,SV123: $i,SV526: $i] :
      ( ( ( in @ SV526 @ SV123 )
        = $false )
      | ( ( ~ ( in @ SV526 @ SV361 )
          | ( in @ SV526 @ ( binintersect @ SV123 @ SV361 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1702]) ).

thf(1924,plain,
    ! [SV364: $i,SV126: $i,SV527: $i] :
      ( ( ( in @ SV527 @ ( binunion @ SV126 @ SV364 ) )
        = $false )
      | ( ( ( in @ SV527 @ SV126 )
          | ( in @ SV527 @ SV364 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1703]) ).

thf(1925,plain,
    ! [SV127: $i,SV365: $i,SV528: $i] :
      ( ( ( in @ SV528 @ SV365 )
        = $false )
      | ( ( in @ SV528 @ ( binunion @ SV127 @ SV365 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1704]) ).

thf(1926,plain,
    ! [SV367: $i,SV129: $i,SV529: $i] :
      ( ( ( in @ SV529 @ SV129 )
        = $false )
      | ( ( in @ SV529 @ ( binunion @ SV129 @ SV367 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1705]) ).

thf(1927,plain,
    ! [SV137: $i,SV373: $i] :
      ( ( ( ~ ( subset @ SV373 @ SV137 ) )
        = $true )
      | ( ( SV137 = SV373 )
        = $true )
      | ( ( subset @ SV137 @ SV373 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1709]) ).

thf(1928,plain,
    ! [SV375: $i,SV530: $i,SV139: $i] :
      ( ( ( subset @ SV139 @ SV530 )
        = $false )
      | ( ( subset @ SV139 @ ( setadjoin @ SV375 @ SV530 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1711]) ).

thf(1929,plain,
    ! [SV141: $i,SV641: $i,SV377: $i] :
      ( ( ( ~ ( subset @ SV377 @ SV641 )
          | ( subset @ SV141 @ SV641 ) )
        = $true )
      | ( ( subset @ SV141 @ SV377 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1712]) ).

thf(1930,plain,
    ! [SV378: $i,SV143: $i,SV531: $i] :
      ( ( ( in @ SV531 @ SV143 )
        = $false )
      | ( ( ( in @ SV531 @ SV378 )
          | ( SV143 != SV378 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1713]) ).

thf(1931,plain,
    ! [SV380: $i,SV145: $i,SV532: $i] :
      ( ( ( in @ SV532 @ SV145 )
        = $false )
      | ( ( ( in @ SV532 @ SV380 )
          | ~ ( subset @ SV145 @ SV380 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1715]) ).

thf(1932,plain,
    ! [SV146: $i,SV381: $i,SV642: $i] :
      ( ( ( ( in @ SV642 @ SV381 )
          | ~ ( in @ SV642 @ SV146 ) )
        = $true )
      | ( ( subset @ SV146 @ SV381 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1716]) ).

thf(1933,plain,
    ! [SV382: $i,SV147: $i,SV643: $i] :
      ( ( ( ~ ( in @ SV643 @ SV147 )
          | ( in @ SV643 @ SV382 ) )
        = $true )
      | ( ( subset @ SV147 @ SV382 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1717]) ).

thf(1934,plain,
    ! [SV387: $i,SV153: $i,SV644: $i] :
      ( ( ( ! [SY2912: $i] :
              ( ( SV644 != SY2912 )
              | ( ( setadjoin @ SV153 @ SV644 )
                = ( setadjoin @ SV387 @ SY2912 ) ) ) )
        = $true )
      | ( ( SV153 = SV387 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1722]) ).

thf(1935,plain,
    ! [SV388: $i,SV154: $i,SV645: $i] :
      ( ( ( ! [SY2913: $i] :
              ( ( SV645 != SY2913 )
              | ~ ( in @ SV645 @ SV154 )
              | ( in @ SY2913 @ SV388 ) ) )
        = $true )
      | ( ( SV154 = SV388 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1723]) ).

thf(1936,plain,
    ! [SV158: $i,SV600: $i,SV390: $i > $o] :
      ( ( ( ~ ( SV390 @ SV600 ) )
        = $true )
      | ( ( ~ ( in @ SV600 @ SV158 ) )
        = $true )
      | ( ( ( dsetconstr @ SV158
            @ ^ [SY2616: $i] : ( SV390 @ SY2616 ) )
         != emptyset )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1725]) ).

thf(1937,plain,
    ! [SV393: $i,SV161: $i,SV533: $i] :
      ( ( ( in @ SV533 @ ( setadjoin @ SV161 @ ( setadjoin @ SV393 @ emptyset ) ) )
        = $false )
      | ( ( ( SV533 = SV161 )
          | ( SV533 = SV393 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1726]) ).

thf(1938,plain,
    ! [SV168: $i,SV534: $i,SV399: $i] :
      ( ( ( in @ SV399 @ SV534 )
        = $false )
      | ( ( ~ ( in @ SV534 @ SV168 )
          | ( in @ SV399 @ ( setunion @ SV168 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1732]) ).

thf(1939,plain,
    ! [SV169: $i,SV400: $i,SV646: $i] :
      ( ( ( ~ ( in @ SV646 @ SV400 )
          | ( in @ SV646 @ SV169 ) )
        = $true )
      | ( ( in @ SV400 @ ( powerset @ SV169 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1733]) ).

thf(1940,plain,
    ! [SV401: $i,SV173: $i,SV535: $i] :
      ( ( ( in @ SV535 @ ( setadjoin @ SV173 @ SV401 ) )
        = $false )
      | ( ( ( SV535 = SV173 )
          | ( in @ SV535 @ SV401 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1734]) ).

thf(1941,plain,
    ! [SV174: $i,SV402: $i,SV536: $i] :
      ( ( ( in @ SV536 @ SV402 )
        = $false )
      | ( ( in @ SV536 @ ( setadjoin @ SV174 @ SV402 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1735]) ).

thf(1942,plain,
    ! [SV537: $i,SV176: $i] :
      ( ( ( SV176 = emptyset )
        = $false )
      | ( ( in @ SV537 @ SV176 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1736]) ).

thf(1943,plain,
    ! [SV404: $i > $o,SV177: $i,SV538: $i] :
      ( ( ( in @ SV538 @ SV177 )
        = $false )
      | ( ( ~ ( SV404 @ SV538 )
          | ( ( dsetconstr @ SV177
              @ ^ [SY2623: $i] : ( SV404 @ SY2623 ) )
           != emptyset ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1737]) ).

thf(1944,plain,
    ! [SV406: $i > $o,SV184: $i,SV542: $i] :
      ( ( ( in @ SV542
          @ ( dsetconstr @ SV184
            @ ^ [SY2625: $i] : ( SV406 @ SY2625 ) ) )
        = $false )
      | ( ( SV406 @ SV542 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1744]) ).

thf(1945,plain,
    ! [SV407: $i > $o,SV185: $i,SV543: $i] :
      ( ( ( in @ SV543
          @ ( dsetconstr @ SV185
            @ ^ [SY2627: $i] : ( SV407 @ SY2627 ) ) )
        = $false )
      | ( ( in @ SV543 @ SV185 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1745]) ).

thf(1946,plain,
    ! [SV408: $i > $o,SV186: $i,SV544: $i] :
      ( ( ( in @ SV544 @ SV186 )
        = $false )
      | ( ( ~ ( SV408 @ SV544 )
          | ( in @ SV544
            @ ( dsetconstr @ SV186
              @ ^ [SY2629: $i] : ( SV408 @ SY2629 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1746]) ).

thf(1947,plain,
    ! [SV409: $i,SV189: $i,SV647: $i] :
      ( ( ( ~ ( in @ SV647 @ ( powerset @ SV189 ) )
          | ~ ( ~ ( in @ ( sK97_Xx @ SV647 @ SV409 @ SV189 ) @ SV189 )
              | ~ ~ ( ~ ( in @ ( sK97_Xx @ SV647 @ SV409 @ SV189 ) @ SV409 )
                    | ~ ~ ( in @ ( sK97_Xx @ SV647 @ SV409 @ SV189 ) @ SV647 ) ) )
          | ( subset @ SV409 @ SV647 ) )
        = $true )
      | ( ( in @ SV409 @ ( powerset @ SV189 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1747]) ).

thf(1948,plain,
    ! [SV602: $i,SV648: $i] :
      ( ( ~ ( ~ ( in @ ( sK7_Xx @ SV648 @ SV602 ) @ SV648 )
            | ~ ~ ( in @ ( sK7_Xx @ SV648 @ SV602 ) @ SV602 ) )
        | ( in @ SV648 @ ( powerset @ SV602 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1748]) ).

thf(1949,plain,
    ! [SV603: $i,SV649: $i] :
      ( ( ~ ( in @ SV649 @ ( powerset @ SV603 ) )
        | ! [SY2914: $i] :
            ( ~ ( in @ SY2914 @ SV649 )
            | ( in @ SY2914 @ SV603 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1749]) ).

thf(1950,plain,
    ! [SV545: $i,SV190: $i > $o] :
      ( ( ( ~ ( SV190 @ ( sK24_SY86 @ SV545 @ SV190 ) )
          | ~ ( ( SV545
               != ( sK24_SY86 @ SV545 @ SV190 ) ) ) )
        = $false )
      | ( ( ~ ( SV190 @ SV545 ) )
        = $true )
      | ( ( SV190 @ ( sK23_Xx @ SV190 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1750]) ).

thf(1951,plain,
    ! [SV410: $o,SV191: $i,SV546: $i] :
      ( ( ( in @ SV546 @ SV191 )
        = $false )
      | ( ( ! [SY2804: $i] :
              ( ~ ( in @ SY2804 @ SV191 )
              | ~ SV410
              | ( in @ SV546
                @ ( dsetconstr @ SV191
                  @ ^ [SY2805: $i] :
                      ( ~ ( ~ SV410
                          | ( SY2805 != SV546 ) )
                      | ~ ( ~ ~ SV410
                          | ( SY2805 != SY2804 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1751]) ).

thf(1952,plain,
    ! [SV191: $i,SV547: $i] :
      ( ( ( in @ SV547 @ SV191 )
        = $false )
      | ( ( ! [SY2806: $i] :
              ( ~ ( in @ SY2806 @ SV191 )
              | ~ $true
              | ( in @ SV547
                @ ( dsetconstr @ SV191
                  @ ^ [SY2807: $i] :
                      ( ~ ( ~ $true
                          | ( SY2807 != SV547 ) )
                      | ~ ( ~ ~ $true
                          | ( SY2807 != SY2806 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1752]) ).

thf(1953,plain,
    ! [SV191: $i,SV548: $i] :
      ( ( ( in @ SV548 @ SV191 )
        = $false )
      | ( ( ! [SY2808: $i] :
              ( ~ ( in @ SY2808 @ SV191 )
              | ~ $false
              | ( in @ SV548
                @ ( dsetconstr @ SV191
                  @ ^ [SY2809: $i] :
                      ( ~ ( ~ $false
                          | ( SY2809 != SV548 ) )
                      | ~ ( ~ ~ $false
                          | ( SY2809 != SY2808 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1753]) ).

thf(1954,plain,
    ! [SV192: $i,SV411: $i,SV549: $i > $i] :
      ( ( ( ~ ( in @ ( sK92_Xx @ SV549 @ SV411 @ SV192 ) @ SV192 )
          | ~ ~ ( in @ ( SV549 @ ( sK92_Xx @ SV549 @ SV411 @ SV192 ) ) @ SV411 ) )
        = $false )
      | ( ( ! [SY2810: $i] :
              ( ~ ( in @ SY2810 @ SV192 )
              | ( ( ap @ SV192 @ SV411
                  @ ( lam @ SV192 @ SV411
                    @ ^ [SY2811: $i] : ( SV549 @ SY2811 ) )
                  @ SY2810 )
                = ( SV549 @ SY2810 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1754]) ).

thf(1955,plain,
    ! [SV412: $i,SV193: $i,SV550: $i] :
      ( ( ( in @ SV550 @ ( cartprod @ SV193 @ SV412 ) )
        = $false )
      | ( ( ~ ( ~ ~ ( ( SV550
                     != ( kpair @ ( sK67_Xx @ SV550 @ SV412 @ SV193 ) @ ( sK68_SY1876 @ SV550 @ SV412 @ SV193 ) ) )
                    | ~ ( in @ ( sK68_SY1876 @ SV550 @ SV412 @ SV193 ) @ SV412 ) )
              | ~ ( in @ ( sK67_Xx @ SV550 @ SV412 @ SV193 ) @ SV193 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1755]) ).

thf(1956,plain,
    ! [SV551: $i,SV194: $i > $o] :
      ( ( ( ~ ( SV194 @ ( sK57_SY248 @ SV551 @ SV194 ) )
          | ~ ( ( SV551
               != ( sK57_SY248 @ SV551 @ SV194 ) ) ) )
        = $false )
      | ( ( ~ ( SV194 @ SV551 ) )
        = $true )
      | ( ( ! [SY2258: $i] :
              ( ~ ( SV194 @ SY2258 )
              | ! [SY2259: $i] :
                  ( ~ ( SV194 @ SY2259 )
                  | ( SY2258 = SY2259 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1756]) ).

thf(1957,plain,
    ! [SV195: $i > $i > $o,SV413: $i] :
      ( ( ( ~ ( in @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV413 ) )
        = $false )
      | ( ( ~ ( ~ ! [SY2639: $i] :
                    ( ! [SY2640: $i] :
                        ( ~ ( SV195 @ SY2640 @ SY2639 )
                        | ~ ( in @ SY2640 @ SV413 ) )
                    | ( in @ SY2639 @ ( sK10_B @ SV413 @ SV195 ) ) )
              | ~ ! [SY2641: $i] :
                    ( ~ ( in @ SY2641 @ ( sK10_B @ SV413 @ SV195 ) )
                    | ~ ( ~ ( SV195 @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SY2641 )
                        | ~ ( in @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SV413 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1757]) ).

thf(1958,plain,
    ! [SV413: $i,SV195: $i > $i > $o] :
      ( ( ( ~ ! [SY2638: $i] :
                ( ~ ( ~ ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SY2638 @ SV413 @ SV195 ) )
                    | ~ ( ( SY2638
                         != ( sK13_SY1837 @ SY2638 @ SV413 @ SV195 ) ) ) )
                | ~ ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SY2638 ) ) )
        = $false )
      | ( ( ~ ( ~ ! [SY2639: $i] :
                    ( ! [SY2640: $i] :
                        ( ~ ( SV195 @ SY2640 @ SY2639 )
                        | ~ ( in @ SY2640 @ SV413 ) )
                    | ( in @ SY2639 @ ( sK10_B @ SV413 @ SV195 ) ) )
              | ~ ! [SY2641: $i] :
                    ( ~ ( in @ SY2641 @ ( sK10_B @ SV413 @ SV195 ) )
                    | ~ ( ~ ( SV195 @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SY2641 )
                        | ~ ( in @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SV413 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1757]) ).

thf(1959,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false )
      | ( ( ~ ( ~ ~ ( ~ ( ( SV552 = SV196 )
                        | ( in @ SV552 @ SV414 )
                        | ! [SX3: $o] : SX3 )
                    | ~ ( ( SV552 = SV196 )
                        | ! [SX3: $o] :
                            ( ~ SX3
                            | SX3 ) ) )
              | ~ ~ ( ~ ! [SY2814: $o] :
                          ( ~ SY2814
                          | ( in @ SV552 @ SV414 )
                          | SY2814 )
                    | ~ ! [SX3: $o] :
                          ( ~ SX3
                          | ~ SX3
                          | SX3 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1758]) ).

thf(1960,plain,
    ! [SV197: $i,SV415: $i] :
      ( ( ( ~ ( in @ ( sK66_Xx @ SV415 @ SV197 ) @ SV197 ) )
        = $false )
      | ( ( ( binintersect @ SV197 @ SV415 )
          = emptyset )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1759]) ).

thf(1961,plain,
    ! [SV197: $i,SV415: $i] :
      ( ( ( ~ ( in @ ( sK66_Xx @ SV415 @ SV197 ) @ SV415 ) )
        = $false )
      | ( ( ( binintersect @ SV197 @ SV415 )
          = emptyset )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1759]) ).

thf(1962,plain,
    ! [SV650: $i > $o,SV198: $i] :
      ( ( ! [SY2915: $i] :
            ( ~ ( in @ SY2915 @ SV198 )
            | ~ ( SV650 @ SY2915 )
            | ( in @ SY2915
              @ ( dsetconstr @ SV198
                @ ^ [SY2916: $i] : ( SV650 @ SY2916 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1760]) ).

thf(1963,plain,
    ! [SV651: $i > $o,SV198: $i] :
      ( ( ! [SY2917: $i] :
            ( ~ ( in @ SY2917 @ SV198 )
            | ~ ( in @ SY2917
                @ ( dsetconstr @ SV198
                  @ ^ [SY2918: $i] : ( SV651 @ SY2918 ) ) )
            | ( SV651 @ SY2917 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1761]) ).

thf(1964,plain,
    ! [SV199: $i,SV416: $i] :
      ( ( ( ~ ( in @ ( sK30_Xx @ SV416 @ SV199 ) @ SV416 ) )
        = $false )
      | ( ( in @ SV416 @ ( powerset @ SV199 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1762]) ).

thf(1965,plain,
    ! [SV199: $i,SV416: $i] :
      ( ( ( ~ ~ ( in @ ( sK30_Xx @ SV416 @ SV199 ) @ SV199 ) )
        = $false )
      | ( ( in @ SV416 @ ( powerset @ SV199 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1762]) ).

thf(1966,plain,
    ! [SV417: $i > $o,SV200: $i,SV604: $i] :
      ( ( ( ~ ( in @ SV604 @ SV200 ) )
        = $true )
      | ( ( SV417 @ SV604 )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK40_Xx @ SV417 @ SV200 ) @ SV200 )
              | ~ ~ ( SV417 @ ( sK40_Xx @ SV417 @ SV200 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1763]) ).

thf(1967,plain,
    ! [SV201: $i,SV418: $i,SV553: $i > $i] :
      ( ( ( ~ ( in @ ( sK78_Xx @ SV553 @ SV418 @ SV201 ) @ SV201 )
          | ~ ~ ( in @ ( SV553 @ ( sK78_Xx @ SV553 @ SV418 @ SV201 ) ) @ SV418 ) )
        = $false )
      | ( ( in
          @ ( lam @ SV201 @ SV418
            @ ^ [SY2816: $i] : ( SV553 @ SY2816 ) )
          @ ( funcSet @ SV201 @ SV418 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1764]) ).

thf(1968,plain,
    ! [SV419: $o,SV202: $i,SV554: $i] :
      ( ( ( in @ SV554 @ SV202 )
        = $false )
      | ( ( ! [SY2817: $i] :
              ( ~ ( in @ SY2817 @ SV202 )
              | SV419
              | ( ( dsetconstr @ SV202
                  @ ^ [SY2818: $i] :
                      ( ~ ( ~ SV419
                          | ( SY2818 != SV554 ) )
                      | ~ ( ~ ~ SV419
                          | ( SY2818 != SY2817 ) ) ) )
                = ( setadjoin @ SY2817 @ emptyset ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1765]) ).

thf(1969,plain,
    ! [SV202: $i,SV555: $i] :
      ( ( ( in @ SV555 @ SV202 )
        = $false )
      | ( ( ! [SY2819: $i] :
              ( ~ ( in @ SY2819 @ SV202 )
              | $true
              | ( ( dsetconstr @ SV202
                  @ ^ [SY2820: $i] :
                      ( ~ ( ~ $true
                          | ( SY2820 != SV555 ) )
                      | ~ ( ~ ~ $true
                          | ( SY2820 != SY2819 ) ) ) )
                = ( setadjoin @ SY2819 @ emptyset ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1766]) ).

thf(1970,plain,
    ! [SV202: $i,SV556: $i] :
      ( ( ( in @ SV556 @ SV202 )
        = $false )
      | ( ( ! [SY2821: $i] :
              ( ~ ( in @ SY2821 @ SV202 )
              | $false
              | ( ( dsetconstr @ SV202
                  @ ^ [SY2822: $i] :
                      ( ~ ( ~ $false
                          | ( SY2822 != SV556 ) )
                      | ~ ( ~ ~ $false
                          | ( SY2822 != SY2821 ) ) ) )
                = ( setadjoin @ SY2821 @ emptyset ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1767]) ).

thf(1971,plain,
    ! [SV605: $i > $o,SV652: $i > $o] :
      ( ( ~ ( ( ( sK55_Xx @ SV652 @ SV605 )
             != ( sK56_SY1873 @ SV652 @ SV605 ) )
            | ~ ~ ( ~ ( ~ ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
                      | ~ ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) ) )
                  | ~ ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
                      | ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) ) ) ) )
        | ! [SY2919: $i] :
            ( ~ ( ~ ( SV605 @ ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) )
                | ~ ( ( SY2919
                     != ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) ) ) )
            | ~ ( SV605 @ SY2919 ) )
        | ~ ( ~ ! [SY2920: $i] :
                  ( ~ ( SV652 @ SY2920 )
                  | ( ( sK53_SY235 @ SV652 @ SV605 )
                    = SY2920 ) )
            | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1768]) ).

thf(1972,plain,
    ! [SV606: $i > $o,SV653: $i > $o] :
      ( ( ~ ( ( ( sK51_Xx @ SV653 @ SV606 )
             != ( sK52_SY1871 @ SV653 @ SV606 ) )
            | ~ ~ ( ~ ( ~ ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
                      | ~ ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) ) )
                  | ~ ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
                      | ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) ) ) ) )
        | ! [SY2921: $i] :
            ( ~ ( ~ ( SV653 @ ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) )
                | ~ ( ( SY2921
                     != ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) ) ) )
            | ~ ( SV653 @ SY2921 ) )
        | ~ ( ~ ! [SY2922: $i] :
                  ( ~ ( SV606 @ SY2922 )
                  | ( ( sK49_SY232 @ SV653 @ SV606 )
                    = SY2922 ) )
            | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1769]) ).

thf(1973,plain,
    ! [SV203: $i,SV420: $i > $o] :
      ( ( ( ~ ( SV420 @ ( sK39_Xx @ SV420 @ SV203 ) ) )
        = $false )
      | ( ( ! [SY2653: $i] :
              ( ~ ( in @ SY2653 @ SV203 )
              | ~ ( SV420 @ SY2653 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1770]) ).

thf(1974,plain,
    ! [SV203: $i,SV420: $i > $o] :
      ( ( ( ~ ( in @ ( sK39_Xx @ SV420 @ SV203 ) @ SV203 ) )
        = $false )
      | ( ( ! [SY2653: $i] :
              ( ~ ( in @ SY2653 @ SV203 )
              | ~ ( SV420 @ SY2653 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1770]) ).

thf(1975,plain,
    ! [SV557: $i,SV204: $i > $o] :
      ( ( ( ~ ( SV204 @ ( sK20_SY57 @ SV557 @ SV204 ) )
          | ~ ( ( SV557
               != ( sK20_SY57 @ SV557 @ SV204 ) ) ) )
        = $false )
      | ( ( ~ ( SV204 @ SV557 ) )
        = $true )
      | ( ( SV204
          @ ( descr
            @ ^ [SY2291: $i] : ( SV204 @ SY2291 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1771]) ).

thf(1976,plain,
    ! [SV558: $i,SV205: $i > $o] :
      ( ( ( ~ ( SV205 @ ( sK42_Xy @ SV558 @ SV205 ) )
          | ~ ( ( SV558
               != ( sK42_Xy @ SV558 @ SV205 ) ) ) )
        = $false )
      | ( ( ~ ( SV205 @ SV558 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2293: $i] :
                    ( ~ ( SV205 @ SY2293 )
                    | ( ( sK41_SY198 @ SV205 )
                      = SY2293 ) )
              | ~ ( SV205 @ ( sK41_SY198 @ SV205 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1772]) ).

thf(1977,plain,
    ! [SV206: $i,SV421: $i,SV559: $i > $i] :
      ( ( ( ~ ( in @ ( sK94_Xx @ SV559 @ SV421 @ SV206 ) @ SV206 )
          | ~ ~ ( in @ ( SV559 @ ( sK94_Xx @ SV559 @ SV421 @ SV206 ) ) @ SV421 ) )
        = $false )
      | ( ( ! [SY2823: $i] :
              ( ~ ( in @ SY2823 @ SV206 )
              | ( ( ap @ SV206 @ SV421
                  @ ( lam @ SV206 @ SV421
                    @ ^ [SY2824: $i] : ( SV559 @ SY2824 ) )
                  @ SY2823 )
                = ( SV559 @ SY2823 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1773]) ).

thf(1978,plain,
    ( ( ~ ( in @ sK3_SY1826 @ ( powerset @ sK1_A ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1774]) ).

thf(1979,plain,
    ( ( ~ ~ ( ~ ( in @ sK4_SY1829 @ ( powerset @ sK1_A ) )
            | ~ ~ ( ~ ( in @ sK5_SY1831 @ sK1_A )
                  | ~ ~ ( ~ ( in @ sK5_SY1831 @ ( binintersect @ sK2_SY1822 @ sK3_SY1826 ) )
                        | ~ ~ ( in @ sK5_SY1831 @ ( binunion @ sK3_SY1826 @ sK4_SY1829 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[1774]) ).

thf(1980,plain,
    ! [SV422: $i,SV207: $i,SV560: $i] :
      ( ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false )
      | ( ( ! [SY2825: $i > $o] :
              ( ~ ( ~ ( in @ ( sK81_Xx @ SY2825 @ SV560 @ SV422 @ SV207 ) @ SV207 )
                  | ~ ~ ( ~ ( in @ ( sK82_SY1880 @ SY2825 @ SV560 @ SV422 @ SV207 ) @ SV422 )
                        | ~ ~ ( ~ ( in @ ( kpair @ ( sK81_Xx @ SY2825 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SY2825 @ SV560 @ SV422 @ SV207 ) ) @ SV560 )
                              | ~ ~ ( SY2825 @ ( kpair @ ( sK81_Xx @ SY2825 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SY2825 @ SV560 @ SV422 @ SV207 ) ) ) ) ) )
              | ! [SY2826: $i] :
                  ( ~ ( in @ SY2826 @ SV560 )
                  | ( SY2825 @ SY2826 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1775]) ).

thf(1981,plain,
    ! [SV423: $i,SV208: $i,SV561: $i] :
      ( ( ( subset @ SV561 @ ( cartprod @ SV208 @ SV423 ) )
        = $false )
      | ( ( ! [SY2827: $i] :
              ( ~ ( subset @ SY2827 @ ( cartprod @ SV208 @ SV423 ) )
              | ~ ( ~ ( in @ ( sK84_Xx @ SY2827 @ SV561 @ SV423 @ SV208 ) @ SV208 )
                  | ~ ~ ( ~ ( in @ ( sK85_SY1881 @ SY2827 @ SV561 @ SV423 @ SV208 ) @ SV423 )
                        | ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SY2827 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SY2827 @ SV561 @ SV423 @ SV208 ) ) @ SV561 )
                              | ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SY2827 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SY2827 @ SV561 @ SV423 @ SV208 ) ) @ SY2827 ) ) ) )
              | ( subset @ SV561 @ SY2827 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1776]) ).

thf(1982,plain,
    ! [SV209: $i,SV424: $i > $o] :
      ( ( ( ~ ( in @ ( sK70_Xx @ SV424 @ SV209 ) @ SV209 ) )
        = $false )
      | ( ( ! [SY2662: $i] :
              ( ~ ( SV424 @ SY2662 )
              | ~ ( in @ SY2662 @ SV209 ) )
          | ( singleton
            @ ( dsetconstr @ SV209
              @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1777]) ).

thf(1983,plain,
    ! [SV209: $i,SV424: $i > $o] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK71_SY1877 @ SV424 @ SV209 ) @ SV209 )
                | ~ ~ ( ~ ( SV424 @ ( sK70_Xx @ SV424 @ SV209 ) )
                      | ~ ~ ( ~ ( SV424 @ ( sK71_SY1877 @ SV424 @ SV209 ) )
                            | ~ ( ( ( sK70_Xx @ SV424 @ SV209 )
                                 != ( sK71_SY1877 @ SV424 @ SV209 ) ) ) ) ) ) )
        = $false )
      | ( ( ! [SY2662: $i] :
              ( ~ ( SV424 @ SY2662 )
              | ~ ( in @ SY2662 @ SV209 ) )
          | ( singleton
            @ ( dsetconstr @ SV209
              @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1777]) ).

thf(1984,plain,
    ! [SV425: $i,SV210: $i] :
      ( ( ( ~ ! [SY2664: $i,SY2665: $i] :
                ( ( SY2664 != SY2665 )
                | ~ ( in @ SY2664 @ SV210 )
                | ( in @ SY2665 @ SV425 ) )
          | ~ ! [SY2666: $i,SY2667: $i] :
                ( ( SY2666 != SY2667 )
                | ~ ( in @ SY2667 @ SV425 )
                | ( in @ SY2666 @ SV210 ) ) )
        = $false )
      | ( ( SV210 = SV425 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1778]) ).

thf(1985,plain,
    ! [SV562: $i,SV211: $i > $o] :
      ( ( ( ~ ( SV211 @ ( sK48_SY224 @ SV562 @ SV211 ) )
          | ~ ( ( SV562
               != ( sK48_SY224 @ SV562 @ SV211 ) ) ) )
        = $false )
      | ( ( ~ ( SV211 @ SV562 ) )
        = $true )
      | ( ( ! [SY2314: $i] :
              ( ~ ( SV211 @ SY2314 )
              | ! [SY2315: $i] :
                  ( ~ ( SV211 @ SY2315 )
                  | ( SY2314 = SY2315 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1779]) ).

thf(1986,plain,
    ! [SV212: $i,SV426: $i,SV563: $i > $i] :
      ( ( ( ~ ( in @ ( sK77_Xx @ SV563 @ SV426 @ SV212 ) @ SV212 )
          | ~ ~ ( in @ ( SV563 @ ( sK77_Xx @ SV563 @ SV426 @ SV212 ) ) @ SV426 ) )
        = $false )
      | ( ( func @ SV212 @ SV426
          @ ( lam @ SV212 @ SV426
            @ ^ [SY2828: $i] : ( SV563 @ SY2828 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1780]) ).

thf(1987,plain,
    ! [SV213: $i > $o,SV427: $i > $o] :
      ( ( ( ( sK60_Xx @ SV427 @ SV213 )
         != ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false )
      | ( ( ! [SY2670: $i] :
              ( ~ ( ~ ( SV213 @ ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2670
                       != ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV213 @ SY2670 ) )
          | ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1781]) ).

thf(1988,plain,
    ! [SV427: $i > $o,SV213: $i > $o] :
      ( ( ( ~ ~ ( ~ ( ~ ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
                    | ~ ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) ) )
                | ~ ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
                    | ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) ) ) ) )
        = $false )
      | ( ( ! [SY2670: $i] :
              ( ~ ( ~ ( SV213 @ ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2670
                       != ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV213 @ SY2670 ) )
          | ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1781]) ).

thf(1989,plain,
    ! [SV428: $i,SV214: $i,SV654: $i] :
      ( ( ( ~ ( in @ SV654 @ ( powerset @ SV214 ) )
          | ~ ( ~ ( in @ ( sK98_Xx @ SV654 @ SV428 @ SV214 ) @ SV214 )
              | ~ ~ ( ~ ( in @ ( sK98_Xx @ SV654 @ SV428 @ SV214 ) @ SV428 )
                    | ~ ~ ( in @ ( sK98_Xx @ SV654 @ SV428 @ SV214 ) @ SV654 ) ) )
          | ( in @ SV428 @ ( powerset @ SV654 ) ) )
        = $true )
      | ( ( in @ SV428 @ ( powerset @ SV214 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1782]) ).

thf(1990,plain,
    ! [SV215: $i,SV655: $o,SV429: $i] :
      ( ( ( ~ ( ~ ( in @ SV429 @ ( sK31_B @ SV655 @ SV429 @ SV215 ) )
              | ~ ~ ( ~ ( in @ ( sK31_B @ SV655 @ SV429 @ SV215 ) @ SV215 )
                    | ~ ~ SV655 ) )
          | SV655 )
        = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[1783]) ).

thf(1991,plain,
    ! [SV215: $i,SV429: $i] :
      ( ( ( ~ ( ~ ( in @ SV429 @ ( sK31_B @ $true @ SV429 @ SV215 ) )
              | ~ ~ ( ~ ( in @ ( sK31_B @ $true @ SV429 @ SV215 ) @ SV215 )
                    | ~ ~ $true ) )
          | $true )
        = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[1783]) ).

thf(1992,plain,
    ! [SV215: $i,SV429: $i] :
      ( ( ( ~ ( ~ ( in @ SV429 @ ( sK31_B @ $false @ SV429 @ SV215 ) )
              | ~ ~ ( ~ ( in @ ( sK31_B @ $false @ SV429 @ SV215 ) @ SV215 )
                    | ~ ~ $false ) )
          | $false )
        = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[1783]) ).

thf(1993,plain,
    ! [SV216: $i,SV430: $i] :
      ( ( ( ~ ( in @ ( sK26_Xx @ SV430 @ SV216 ) @ SV216 ) )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV430 )
              | ~ ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV216 ) )
          | ( SV216 = SV430 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1784]) ).

thf(1994,plain,
    ! [SV216: $i,SV430: $i] :
      ( ( ( ~ ~ ( in @ ( sK26_Xx @ SV430 @ SV216 ) @ SV430 ) )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV430 )
              | ~ ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV216 ) )
          | ( SV216 = SV430 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1784]) ).

thf(1995,plain,
    ! [SV217: $i,SV431: $i] :
      ( ( ( ~ ( in @ ( sK69_X @ SV431 @ SV217 ) @ SV217 )
          | ~ ( in @ SV431 @ ( sK69_X @ SV431 @ SV217 ) ) )
        = $false )
      | ( ( in @ SV431 @ ( setunion @ SV217 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1785]) ).

thf(1996,plain,
    ! [SV564: $i,SV432: $i,SV218: $i] :
      ( ( ( func @ SV218 @ SV432 @ SV564 )
        = $false )
      | ( ( ! [SY2829: $i] :
              ( ~ ( func @ SV218 @ SV432 @ SY2829 )
              | ~ ( ~ ( in @ ( sK83_Xx @ SY2829 @ SV564 @ SV432 @ SV218 ) @ SV218 )
                  | ~ ( ( ( ap @ SV218 @ SV432 @ SV564 @ ( sK83_Xx @ SY2829 @ SV564 @ SV432 @ SV218 ) )
                       != ( ap @ SV218 @ SV432 @ SY2829 @ ( sK83_Xx @ SY2829 @ SV564 @ SV432 @ SV218 ) ) ) ) )
              | ! [SY2830: $i] :
                  ( ~ ( in @ SY2830 @ SV218 )
                  | ! [SY2831: $i] :
                      ( ~ ( in @ SY2831 @ SV432 )
                      | ~ ( in @ ( kpair @ SY2830 @ SY2831 ) @ SY2829 )
                      | ( in @ ( kpair @ SY2830 @ SY2831 ) @ SV564 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1786]) ).

thf(1997,plain,
    ! [SV433: $i,SV219: $i,SV656: $i] :
      ( ( ( ~ ( in @ SV656 @ ( powerset @ SV219 ) )
          | ~ ( ~ ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
              | ~ ~ ( ~ ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 )
                    | ~ ~ ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 ) ) )
          | ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
              | ~ ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
                    | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) ) )
          | ( SV433 = SV656 ) )
        = $true )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1787]) ).

thf(1998,plain,
    ! [SV434: $i > $o,SV220: $i,SV565: $i] :
      ( ( ( in @ SV565 @ SV220 )
        = $false )
      | ( ( ~ ( SV434 @ SV565 )
          | ~ ( ~ ( in @ ( sK73_Xy @ SV565 @ SV434 @ SV220 ) @ SV220 )
              | ~ ~ ( ~ ( SV434 @ ( sK73_Xy @ SV565 @ SV434 @ SV220 ) )
                    | ~ ( ( ( sK73_Xy @ SV565 @ SV434 @ SV220 )
                         != SV565 ) ) ) )
          | ( singleton
            @ ( dsetconstr @ SV220
              @ ^ [SY2682: $i] : ( SV434 @ SY2682 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1788]) ).

thf(1999,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false )
      | ( ( ~ ( ~ ~ ( ~ ( ( in @ SV566 @ SV221 )
                        | ~ ( in @ SV566 @ SV221 )
                        | ! [SX3: $o] : SX3 )
                    | ~ ~ ( ~ ( ( in @ SV566 @ SV221 )
                              | ( in @ SV566 @ SV435 )
                              | ! [SX3: $o] : SX3 )
                          | ~ ( ( in @ SV566 @ SV221 )
                              | ! [SX3: $o] :
                                  ( ~ SX3
                                  | SX3 ) ) ) )
              | ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SV566 @ SV435 )
                              | ~ ( in @ SV566 @ SV221 )
                              | ! [SX3: $o] : SX3 )
                          | ~ ~ ( ~ ( ~ ( in @ SV566 @ SV435 )
                                    | ( in @ SV566 @ SV435 )
                                    | ! [SX3: $o] : SX3 )
                                | ~ ( ~ ( in @ SV566 @ SV435 )
                                    | ! [SX3: $o] :
                                        ( ~ SX3
                                        | SX3 ) ) ) )
                    | ~ ~ ( ~ ! [SY2839: $o] :
                                ( ~ SY2839
                                | ~ ( in @ SV566 @ SV221 )
                                | SY2839 )
                          | ~ ~ ( ~ ! [SY2840: $o] :
                                      ( ~ SY2840
                                      | ( in @ SV566 @ SV435 )
                                      | SY2840 )
                                | ~ ! [SX3: $o] :
                                      ( ~ SX3
                                      | ~ SX3
                                      | SX3 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1789]) ).

thf(2000,plain,
    ! [SV222: $i,SV436: $i,SV567: $i > $i] :
      ( ( ( ~ ( in @ ( sK76_Xx @ SV567 @ SV436 @ SV222 ) @ SV222 )
          | ~ ~ ( in @ ( SV567 @ ( sK76_Xx @ SV567 @ SV436 @ SV222 ) ) @ SV436 ) )
        = $false )
      | ( ( func @ SV222 @ SV436
          @ ( dpsetconstr @ SV222 @ SV436
            @ ^ [SY2842: $i,SY2843: $i] :
                ( ( SV567 @ SY2842 )
                = SY2843 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1790]) ).

thf(2001,plain,
    ! [SV657: $i,SV223: $i] :
      ( ( ! [SY2923: $i] :
            ( ~ ( in @ SY2923 @ ( setadjoin @ SV223 @ SV657 ) )
            | ( SY2923 = SV223 )
            | ( in @ SY2923 @ SV657 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1791]) ).

thf(2002,plain,
    ! [SV223: $i] :
      ( ( ~ ! [SY2357: $i,SY2358: $i] :
              ( ( SY2358 != SV223 )
              | ( in @ SY2358 @ ( setadjoin @ SV223 @ SY2357 ) ) )
        | ~ ! [SY2359: $i,SY2360: $i] :
              ( ~ ( in @ SY2360 @ SY2359 )
              | ( in @ SY2360 @ ( setadjoin @ SV223 @ SY2359 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1792]) ).

thf(2003,plain,
    ! [SV224: $i,SV437: $i] :
      ( ( ( ~ ( in @ ( sK65_Xx @ SV437 @ SV224 ) @ SV224 ) )
        = $false )
      | ( ( subset @ SV224 @ SV437 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1793]) ).

thf(2004,plain,
    ! [SV224: $i,SV437: $i] :
      ( ( ( ~ ~ ( in @ ( sK65_Xx @ SV437 @ SV224 ) @ SV437 ) )
        = $false )
      | ( ( subset @ SV224 @ SV437 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1793]) ).

thf(2005,plain,
    ! [SV225: $i,SV438: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK6_Xx @ SV438 @ SV225 ) @ SV225 )
              | ~ ( in @ ( sK6_Xx @ SV438 @ SV225 ) @ SV438 ) ) )
        = $false )
      | ( ( SV225 = SV438 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1794]) ).

thf(2006,plain,
    ! [SV225: $i,SV438: $i] :
      ( ( ( ~ ( ( in @ ( sK6_Xx @ SV438 @ SV225 ) @ SV225 )
              | ( in @ ( sK6_Xx @ SV438 @ SV225 ) @ SV438 ) ) )
        = $false )
      | ( ( SV225 = SV438 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1794]) ).

thf(2007,plain,
    ! [SV439: $i,SV226: $i] :
      ( ( ~ ( ~ ! [SY2696: $i] :
                  ( ~ ( in @ SY2696 @ ( binunion @ SV226 @ SV439 ) )
                  | ( in @ SY2696 @ SV226 )
                  | ( in @ SY2696 @ SV439 )
                  | ! [SX3: $o] : SX3 )
            | ~ ! [SY2698: $i] :
                  ( ~ ( in @ SY2698 @ ( binunion @ SV226 @ SV439 ) )
                  | ( in @ SY2698 @ SV226 )
                  | ! [SX3: $o] :
                      ( ~ SX3
                      | SX3 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1795]) ).

thf(2008,plain,
    ! [SV439: $i,SV226: $i] :
      ( ( ~ ( ~ ! [SY2700: $i] :
                  ( ~ ( in @ SY2700 @ ( binunion @ SV226 @ SV439 ) )
                  | ! [SY2701: $o] :
                      ( ~ SY2701
                      | ( in @ SY2700 @ SV439 )
                      | SY2701 ) )
            | ~ ( ! [SY2702: $i] :
                    ~ ( in @ SY2702 @ ( binunion @ SV226 @ SV439 ) )
                | ! [SX2: $o] :
                    ( ~ SX2
                    | ~ SX2
                    | SX2 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1796]) ).

thf(2009,plain,
    ! [SV440: $i > $o,SV227: $i,SV607: $i] :
      ( ( ( ~ ( in @ SV607 @ SV227 ) )
        = $true )
      | ( ( SV440 @ SV607 )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK38_Xx @ SV440 @ SV227 ) @ SV227 )
              | ~ ~ ( SV440 @ ( sK38_Xx @ SV440 @ SV227 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1797]) ).

thf(2010,plain,
    ! [SV228: $i > $o,SV568: $i] :
      ( ( ( ~ ( ( ( sK47_Xy @ SV568 @ SV228 )
               != SV568 )
              | ~ ( SV228 @ ( sK47_Xy @ SV568 @ SV228 ) ) ) )
        = $false )
      | ( ( ~ ( ~ ! [SY2375: $i] :
                    ( ~ ( SV228 @ SY2375 )
                    | ( ( sK46_SY211 @ SV228 )
                      = SY2375 ) )
              | ~ ( SV228 @ ( sK46_SY211 @ SV228 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1798]) ).

thf(2011,plain,
    ! [SV228: $i > $o,SV568: $i] :
      ( ( ( ~ ( ( ( sK47_Xy @ SV568 @ SV228 )
                = SV568 )
              | ( SV228 @ ( sK47_Xy @ SV568 @ SV228 ) ) ) )
        = $false )
      | ( ( ~ ( ~ ! [SY2375: $i] :
                    ( ~ ( SV228 @ SY2375 )
                    | ( ( sK46_SY211 @ SV228 )
                      = SY2375 ) )
              | ~ ( SV228 @ ( sK46_SY211 @ SV228 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1798]) ).

thf(2012,plain,
    ! [SV229: $i,SV441: $i > $o] :
      ( ( ( ~ ( in @ ( sK74_Xx @ SV441 @ SV229 ) @ SV229 ) )
        = $false )
      | ( ( ! [SY2705: $i] :
              ( ~ ( SV441 @ SY2705 )
              | ~ ( in @ SY2705 @ SV229 ) )
          | ( singleton
            @ ( dsetconstr @ SV229
              @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1799]) ).

thf(2013,plain,
    ! [SV229: $i,SV441: $i > $o] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK75_SY1878 @ SV441 @ SV229 ) @ SV229 )
                | ~ ~ ( ~ ( SV441 @ ( sK74_Xx @ SV441 @ SV229 ) )
                      | ~ ~ ( ~ ( SV441 @ ( sK75_SY1878 @ SV441 @ SV229 ) )
                            | ~ ( ( ( sK74_Xx @ SV441 @ SV229 )
                                 != ( sK75_SY1878 @ SV441 @ SV229 ) ) ) ) ) ) )
        = $false )
      | ( ( ! [SY2705: $i] :
              ( ~ ( SV441 @ SY2705 )
              | ~ ( in @ SY2705 @ SV229 ) )
          | ( singleton
            @ ( dsetconstr @ SV229
              @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1799]) ).

thf(2014,plain,
    ! [SV442: $i,SV230: $i,SV569: $i] :
      ( ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( ! [SY2844: $i] :
              ( ~ ( subset @ SY2844 @ ( cartprod @ SV230 @ SV442 ) )
              | ~ ( ~ ( in @ ( sK88_Xx @ SY2844 @ SV569 @ SV442 @ SV230 ) @ SV230 )
                  | ~ ~ ( ~ ( in @ ( sK89_SY1883 @ SY2844 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                        | ~ ~ ( ~ ( in @ ( kpair @ ( sK88_Xx @ SY2844 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SY2844 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
                              | ~ ~ ( in @ ( kpair @ ( sK88_Xx @ SY2844 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SY2844 @ SV569 @ SV442 @ SV230 ) ) @ SY2844 ) ) ) )
              | ~ ( ~ ( in @ ( sK86_Xx @ SY2844 @ SV569 @ SV442 @ SV230 ) @ SV230 )
                  | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SY2844 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                        | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SY2844 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SY2844 @ SV569 @ SV442 @ SV230 ) ) @ SY2844 )
                              | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SY2844 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SY2844 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
              | ( SV569 = SY2844 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1800]) ).

thf(2015,plain,
    ! [SV231: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK9_Xx @ SV231 ) @ omega )
                | ~ ( in @ ( sK9_Xx @ SV231 ) @ SV231 ) ) )
        = $false )
      | ( ( ~ ( in @ emptyset @ SV231 ) )
        = $true )
      | ( ( ! [SY2382: $i] :
              ( ~ ( in @ SY2382 @ omega )
              | ( in @ SY2382 @ SV231 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1801]) ).

thf(2016,plain,
    ! [SV231: $i] :
      ( ( ( ~ ~ ( in @ ( setadjoin @ ( sK9_Xx @ SV231 ) @ ( sK9_Xx @ SV231 ) ) @ SV231 ) )
        = $false )
      | ( ( ~ ( in @ emptyset @ SV231 ) )
        = $true )
      | ( ( ! [SY2382: $i] :
              ( ~ ( in @ SY2382 @ omega )
              | ( in @ SY2382 @ SV231 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1801]) ).

thf(2017,plain,
    ! [SV443: $o,SV232: $i,SV570: $i] :
      ( ( ( in @ SV570 @ SV232 )
        = $false )
      | ( ( ! [SY2845: $i] :
              ( ~ ( in @ SY2845 @ SV232 )
              | SV443
              | ( in @ SY2845
                @ ( dsetconstr @ SV232
                  @ ^ [SY2846: $i] :
                      ( ~ ( ~ SV443
                          | ( SY2846 != SV570 ) )
                      | ~ ( ~ ~ SV443
                          | ( SY2846 != SY2845 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1802]) ).

thf(2018,plain,
    ! [SV232: $i,SV571: $i] :
      ( ( ( in @ SV571 @ SV232 )
        = $false )
      | ( ( ! [SY2847: $i] :
              ( ~ ( in @ SY2847 @ SV232 )
              | $true
              | ( in @ SY2847
                @ ( dsetconstr @ SV232
                  @ ^ [SY2848: $i] :
                      ( ~ ( ~ $true
                          | ( SY2848 != SV571 ) )
                      | ~ ( ~ ~ $true
                          | ( SY2848 != SY2847 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1803]) ).

thf(2019,plain,
    ! [SV232: $i,SV572: $i] :
      ( ( ( in @ SV572 @ SV232 )
        = $false )
      | ( ( ! [SY2849: $i] :
              ( ~ ( in @ SY2849 @ SV232 )
              | $false
              | ( in @ SY2849
                @ ( dsetconstr @ SV232
                  @ ^ [SY2850: $i] :
                      ( ~ ( ~ $false
                          | ( SY2850 != SV572 ) )
                      | ~ ( ~ ~ $false
                          | ( SY2850 != SY2849 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1804]) ).

thf(2020,plain,
    ! [SV233: $i,SV658: $i] :
      ( ( ~ ( ~ ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
            | ~ ~ ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 ) )
        | ! [SY2924: $i] :
            ~ ( in @ SY2924 @ SV658 )
        | ~ ( ~ ! [SY2925: $i] :
                  ( ~ ( in @ SY2925 @ ( sK15_B @ SV233 ) )
                  | ! [SY2926: $i] :
                      ( ~ ( in @ SY2926 @ SY2925 )
                      | ( in @ SY2926 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) )
                  | ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SY2925 ) )
            | ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) )
                        | ~ ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 ) )
                  | ~ ! [SY2927: $i] :
                        ( ~ ( in @ SY2927 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
                        | ~ ( in @ SY2927 @ SV658 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1805]) ).

thf(2021,plain,
    ! [SV233: $i] :
      ( ( ~ ! [SY2392: $i,SY2393: $i] :
              ( ~ ( in @ SY2392 @ ( sK15_B @ SV233 ) )
              | ~ ( in @ SY2393 @ ( sK15_B @ SV233 ) )
              | ! [SX3: $i] :
                  ( ~ ( in @ SX3 @ SY2392 )
                  | ( in @ SX3 @ SY2393 ) )
              | ! [SX3: $i] :
                  ( ~ ( in @ SX3 @ SY2393 )
                  | ( in @ SX3 @ SY2392 ) ) )
        | ~ ~ ( ~ ! [SY2396: $i] :
                    ( ~ ( in @ SY2396 @ ( sK15_B @ SV233 ) )
                    | ! [SY2397: $i] :
                        ( ~ ( in @ SY2397 @ SY2396 )
                        | ( in @ SY2397 @ SV233 ) ) )
              | ~ ! [SY2398: $i,SY2399: $i] :
                    ( ~ ( in @ SY2398 @ SV233 )
                    | ~ ( in @ SY2399 @ SV233 )
                    | ~ ( ~ ( in @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) @ ( sK15_B @ SV233 ) )
                        | ~ ~ ( ~ ( ~ ( in @ SY2398 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) )
                                  | ~ ( in @ SY2399 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) ) )
                              | ~ ( ( in @ SY2398 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) )
                                  | ( in @ SY2399 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) ) ) ) )
                    | ( SY2398 = SY2399 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1806]) ).

thf(2022,plain,
    ! [SV234: $i,SV444: $i > $o] :
      ( ( ( ~ ( SV444 @ ( sK37_Xx @ SV444 @ SV234 ) ) )
        = $false )
      | ( ( ! [SY2712: $i] :
              ( ~ ( in @ SY2712 @ SV234 )
              | ~ ( SV444 @ SY2712 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1807]) ).

thf(2023,plain,
    ! [SV234: $i,SV444: $i > $o] :
      ( ( ( ~ ( in @ ( sK37_Xx @ SV444 @ SV234 ) @ SV234 ) )
        = $false )
      | ( ( ! [SY2712: $i] :
              ( ~ ( in @ SY2712 @ SV234 )
              | ~ ( SV444 @ SY2712 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1807]) ).

thf(2024,plain,
    ! [SV573: $i,SV235: $i > $o] :
      ( ( ( ~ ( SV235 @ ( sK33_SY142 @ SV573 @ SV235 ) )
          | ~ ( ( SV573
               != ( sK33_SY142 @ SV573 @ SV235 ) ) ) )
        = $false )
      | ( ( ~ ( SV235 @ SV573 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2403: $i] :
                    ( ( SY2403
                     != ( sK32_Xx @ SV235 ) )
                    | ( SV235 @ SY2403 ) )
              | ~ ! [SY2404: $i] :
                    ( ~ ( SV235 @ SY2404 )
                    | ( SY2404
                      = ( sK32_Xx @ SV235 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1808]) ).

thf(2025,plain,
    ! [SV445: $i,SV236: $i,SV574: $i] :
      ( ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false )
      | ( ( ! [SY2851: $i > $o] :
              ( ~ ( ~ ( in @ ( sK79_Xx @ SY2851 @ SV574 @ SV445 @ SV236 ) @ SV236 )
                  | ~ ~ ( ~ ( in @ ( sK80_SY1879 @ SY2851 @ SV574 @ SV445 @ SV236 ) @ SV445 )
                        | ~ ~ ( ~ ( in @ ( kpair @ ( sK79_Xx @ SY2851 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SY2851 @ SV574 @ SV445 @ SV236 ) ) @ SV574 )
                              | ~ ~ ( SY2851 @ ( kpair @ ( sK79_Xx @ SY2851 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SY2851 @ SV574 @ SV445 @ SV236 ) ) ) ) ) )
              | ! [SY2852: $i] :
                  ( ~ ( in @ SY2852 @ SV574 )
                  | ( SY2851 @ SY2852 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1809]) ).

thf(2026,plain,
    ! [SV446: $i > $o,SV237: $i,SV608: $i] :
      ( ( ( ~ ( in @ SV608 @ SV237 ) )
        = $true )
      | ( ( SV446 @ SV608 )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK35_Xx @ SV446 @ SV237 ) @ SV237 )
              | ~ ~ ( SV446 @ ( sK35_Xx @ SV446 @ SV237 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1810]) ).

thf(2027,plain,
    ! [SV447: $o,SV238: $i,SV575: $i] :
      ( ( ( in @ SV575 @ SV238 )
        = $false )
      | ( ( ! [SY2853: $i] :
              ( ~ ( in @ SY2853 @ SV238 )
              | ~ SV447
              | ( ( dsetconstr @ SV238
                  @ ^ [SY2854: $i] :
                      ( ~ ( ~ SV447
                          | ( SY2854 != SV575 ) )
                      | ~ ( ~ ~ SV447
                          | ( SY2854 != SY2853 ) ) ) )
                = ( setadjoin @ SV575 @ emptyset ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1811]) ).

thf(2028,plain,
    ! [SV238: $i,SV576: $i] :
      ( ( ( in @ SV576 @ SV238 )
        = $false )
      | ( ( ! [SY2855: $i] :
              ( ~ ( in @ SY2855 @ SV238 )
              | ~ $true
              | ( ( dsetconstr @ SV238
                  @ ^ [SY2856: $i] :
                      ( ~ ( ~ $true
                          | ( SY2856 != SV576 ) )
                      | ~ ( ~ ~ $true
                          | ( SY2856 != SY2855 ) ) ) )
                = ( setadjoin @ SV576 @ emptyset ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1812]) ).

thf(2029,plain,
    ! [SV238: $i,SV577: $i] :
      ( ( ( in @ SV577 @ SV238 )
        = $false )
      | ( ( ! [SY2857: $i] :
              ( ~ ( in @ SY2857 @ SV238 )
              | ~ $false
              | ( ( dsetconstr @ SV238
                  @ ^ [SY2858: $i] :
                      ( ~ ( ~ $false
                          | ( SY2858 != SV577 ) )
                      | ~ ( ~ ~ $false
                          | ( SY2858 != SY2857 ) ) ) )
                = ( setadjoin @ SV577 @ emptyset ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1813]) ).

thf(2030,plain,
    ! [SV578: $i,SV239: $i] :
      ( ( ( ~ ( in @ ( sK14_B @ SV239 ) @ SV239 )
          | ~ ! [SY2416: $i] :
                ( ~ ( in @ SY2416 @ ( sK14_B @ SV239 ) )
                | ~ ( in @ SY2416 @ SV239 ) ) )
        = $false )
      | ( ( in @ SV578 @ SV239 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1814]) ).

thf(2031,plain,
    ! [SV448: $o,SV240: $i,SV579: $i] :
      ( ( ( in @ SV579 @ SV240 )
        = $false )
      | ( ( ! [SY2859: $i] :
              ( ~ ( in @ SY2859 @ SV240 )
              | ( singleton
                @ ( dsetconstr @ SV240
                  @ ^ [SY2860: $i] :
                      ( ~ ( ~ SV448
                          | ( SY2860 != SV579 ) )
                      | ~ ( ~ ~ SV448
                          | ( SY2860 != SY2859 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1815]) ).

thf(2032,plain,
    ! [SV240: $i,SV580: $i] :
      ( ( ( in @ SV580 @ SV240 )
        = $false )
      | ( ( ! [SY2861: $i] :
              ( ~ ( in @ SY2861 @ SV240 )
              | ( singleton
                @ ( dsetconstr @ SV240
                  @ ^ [SY2862: $i] :
                      ( ~ ( ~ $true
                          | ( SY2862 != SV580 ) )
                      | ~ ( ~ ~ $true
                          | ( SY2862 != SY2861 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1816]) ).

thf(2033,plain,
    ! [SV240: $i,SV581: $i] :
      ( ( ( in @ SV581 @ SV240 )
        = $false )
      | ( ( ! [SY2863: $i] :
              ( ~ ( in @ SY2863 @ SV240 )
              | ( singleton
                @ ( dsetconstr @ SV240
                  @ ^ [SY2864: $i] :
                      ( ~ ( ~ $false
                          | ( SY2864 != SV581 ) )
                      | ~ ( ~ ~ $false
                          | ( SY2864 != SY2863 ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1817]) ).

thf(2034,plain,
    ! [SV582: $i,SV241: $i > $o] :
      ( ( ( ~ ( ~ ( SV241 @ ( sK44_Xx @ SV241 ) )
              | ~ ~ ( ~ ( SV241 @ ( sK45_SY1868 @ SV241 ) )
                    | ~ ( ( ( sK44_Xx @ SV241 )
                         != ( sK45_SY1868 @ SV241 ) ) ) ) ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2422: $i] :
                    ( ~ ( SV241 @ SY2422 )
                    | ( ( sK43_SY205 @ SV241 )
                      = SY2422 ) )
              | ~ ( SV241 @ ( sK43_SY205 @ SV241 ) ) ) )
        = $true )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1818]) ).

thf(2035,plain,
    ! [SV242: $i,SV449: $i] :
      ( ( ( ~ ( in @ ( sK64_Xx @ SV449 @ SV242 ) @ SV242 ) )
        = $false )
      | ( ( subset @ SV242 @ SV449 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1819]) ).

thf(2036,plain,
    ! [SV242: $i,SV449: $i] :
      ( ( ( ~ ~ ( in @ ( sK64_Xx @ SV449 @ SV242 ) @ SV449 ) )
        = $false )
      | ( ( subset @ SV242 @ SV449 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1819]) ).

thf(2037,plain,
    ! [SV609: $i,SV659: $i] :
      ( ( ! [SY2928: $i] :
            ( ~ ( in @ SV659 @ SY2928 )
            | ~ ( in @ SY2928 @ SV609 ) )
        | ( in @ SV659 @ ( setunion @ SV609 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1820]) ).

thf(2038,plain,
    ! [SV610: $i,SV660: $i] :
      ( ( ~ ( in @ SV660 @ ( setunion @ SV610 ) )
        | ~ ( ~ ( in @ SV660 @ ( sK8_B @ SV660 @ SV610 ) )
            | ~ ( in @ ( sK8_B @ SV660 @ SV610 ) @ SV610 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1821]) ).

thf(2039,plain,
    ! [SV583: $i,SV450: $i,SV243: $i] :
      ( ( ( func @ SV243 @ SV450 @ SV583 )
        = $false )
      | ( ( ! [SY2865: $i] :
              ( ~ ( func @ SV243 @ SV450 @ SY2865 )
              | ~ ( ~ ( in @ ( sK90_Xx @ SY2865 @ SV583 @ SV450 @ SV243 ) @ SV243 )
                  | ~ ( ( ( ap @ SV243 @ SV450 @ SV583 @ ( sK90_Xx @ SY2865 @ SV583 @ SV450 @ SV243 ) )
                       != ( ap @ SV243 @ SV450 @ SY2865 @ ( sK90_Xx @ SY2865 @ SV583 @ SV450 @ SV243 ) ) ) ) )
              | ( SV583 = SY2865 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1822]) ).

thf(2040,plain,
    ! [SV244: $i,SV584: $i,SV611: $i > $i] :
      ( ( ( ~ ( in @ ( sK93_Xx @ SV611 @ SV584 @ SV244 ) @ SV244 )
          | ~ ~ ( in @ ( SV611 @ ( sK93_Xx @ SV611 @ SV584 @ SV244 ) ) @ SV584 ) )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1823]) ).

thf(2041,plain,
    ! [SV451: $i,SV245: $i,SV585: $i] :
      ( ( ( in @ SV585 @ ( funcSet @ SV245 @ SV451 ) )
        = $false )
      | ( ( ! [SY2867: $i] :
              ( ~ ( in @ SY2867 @ ( funcSet @ SV245 @ SV451 ) )
              | ~ ( ~ ( in @ ( sK91_Xx @ SY2867 @ SV585 @ SV451 @ SV245 ) @ SV245 )
                  | ~ ( ( ( ap @ SV245 @ SV451 @ SV585 @ ( sK91_Xx @ SY2867 @ SV585 @ SV451 @ SV245 ) )
                       != ( ap @ SV245 @ SV451 @ SY2867 @ ( sK91_Xx @ SY2867 @ SV585 @ SV451 @ SV245 ) ) ) ) )
              | ( SV585 = SY2867 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1824]) ).

thf(2042,plain,
    ! [SV246: $i,SV452: $i > $o] :
      ( ( ( ~ ( in @ ( sK36_Xx @ SV452 @ SV246 ) @ SV246 ) )
        = $false )
      | ( ( ! [SY2727: $i] :
              ( ~ ( SV452 @ SY2727 )
              | ~ ( in @ SY2727 @ SV246 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1825]) ).

thf(2043,plain,
    ! [SV246: $i,SV452: $i > $o] :
      ( ( ( ~ ( SV452 @ ( sK36_Xx @ SV452 @ SV246 ) ) )
        = $false )
      | ( ( ! [SY2727: $i] :
              ( ~ ( SV452 @ SY2727 )
              | ~ ( in @ SY2727 @ SV246 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1825]) ).

thf(2044,plain,
    ! [SV586: $i,SV247: $i > $o] :
      ( ( ( ~ ( SV247 @ ( sK22_SY74 @ SV586 @ SV247 ) )
          | ~ ( ( SV586
               != ( sK22_SY74 @ SV586 @ SV247 ) ) ) )
        = $false )
      | ( ( ~ ( SV247 @ SV586 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2435: $i] :
                    ( ~ ( SV247 @ SY2435 )
                    | ( ( sK21_Xx @ SV247 )
                      = SY2435 ) )
              | ~ ( SV247 @ ( sK21_Xx @ SV247 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1826]) ).

thf(2045,plain,
    ! [SV248: $i,SV453: $i,SV661: $i > $o] :
      ( ( ( ! [SY2929: $i > $o] :
              ( ~ ( ~ ( in @ ( sK62_Xx @ SY2929 @ SV661 @ SV453 @ SV248 ) @ SV248 )
                  | ~ ~ ( ~ ( in @ ( sK63_SY1875 @ SY2929 @ SV661 @ SV453 @ SV248 ) @ SV453 )
                        | ~ ~ ( ( ( sK62_Xx @ SY2929 @ SV661 @ SV453 @ SV248 )
                               != ( sK63_SY1875 @ SY2929 @ SV661 @ SV453 @ SV248 ) )
                              | ~ ~ ( ~ ( ~ ( SV661 @ ( sK62_Xx @ SY2929 @ SV661 @ SV453 @ SV248 ) )
                                        | ~ ( SY2929 @ ( sK63_SY1875 @ SY2929 @ SV661 @ SV453 @ SV248 ) ) )
                                    | ~ ( ( SV661 @ ( sK62_Xx @ SY2929 @ SV661 @ SV453 @ SV248 ) )
                                        | ( SY2929 @ ( sK63_SY1875 @ SY2929 @ SV661 @ SV453 @ SV248 ) ) ) ) ) ) )
              | ( ( dsetconstr @ SV248
                  @ ^ [SY2930: $i] : ( SV661 @ SY2930 ) )
                = ( dsetconstr @ SV453
                  @ ^ [SX4: $i] : ( SY2929 @ SX4 ) ) ) ) )
        = $true )
      | ( ( SV248 = SV453 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1827]) ).

thf(2046,plain,
    ! [SV249: $i,SV454: $i > $o] :
      ( ( ( ~ ( SV454 @ ( sK72_Xx @ SV454 @ SV249 ) )
          | ~ ( in @ ( sK72_Xx @ SV454 @ SV249 ) @ SV249 ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV249
            @ ^ [SY2732: $i] : ( SV454 @ SY2732 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1828]) ).

thf(2047,plain,
    ! [SV250: $i,SV1: $i,SV612: $i] :
      ( ( ( ~ ( in @ SV612 @ ( powerset @ SV1 ) ) )
        = $true )
      | ( ( ! [SY2895: $i] :
              ( ~ ( in @ SY2895 @ ( powerset @ SV1 ) )
              | ! [SY2896: $i] :
                  ( ~ ( in @ SY2896 @ SV1 )
                  | ~ ( in @ SY2896 @ ( binintersect @ SV250 @ SV612 ) )
                  | ( in @ SY2896 @ ( binunion @ SV250 @ SY2895 ) ) ) ) )
        = $true )
      | ( ( in @ SV250 @ ( powerset @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1829]) ).

thf(2048,plain,
    ! [SV251: $i,SV2: $i,SV613: $i] :
      ( ( ( ~ ( in @ SV613 @ ( powerset @ SV2 ) ) )
        = $true )
      | ( ( ! [SY2897: $i] :
              ( ~ ( in @ SY2897 @ SV2 )
              | ( in @ SY2897 @ ( binunion @ SV251 @ SV613 ) )
              | ~ ( in @ SY2897 @ SV613 ) ) )
        = $true )
      | ( ( in @ SV251 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1830]) ).

thf(2049,plain,
    ! [SV252: $i,SV3: $i,SV614: $i] :
      ( ( ( ~ ( in @ SV614 @ ( powerset @ SV3 ) ) )
        = $true )
      | ( ( ! [SY2898: $i] :
              ( ~ ( in @ SY2898 @ SV3 )
              | ( in @ SY2898 @ ( binunion @ SV252 @ SV614 ) )
              | ~ ( in @ SY2898 @ SV252 ) ) )
        = $true )
      | ( ( in @ SV252 @ ( powerset @ SV3 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1831]) ).

thf(2050,plain,
    ! [SV253: $i,SV4: $i,SV615: $i] :
      ( ( ( ~ ( in @ SV615 @ ( powerset @ SV4 ) ) )
        = $true )
      | ( ( ~ ( subset @ SV253 @ ( setminus @ SV4 @ SV615 ) )
          | ( subset @ SV615 @ ( setminus @ SV4 @ SV253 ) ) )
        = $true )
      | ( ( in @ SV253 @ ( powerset @ SV4 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1832]) ).

thf(2051,plain,
    ! [SV254: $i,SV5: $i,SV616: $i] :
      ( ( ( ~ ( in @ SV616 @ ( powerset @ SV5 ) ) )
        = $true )
      | ( ( ~ ( subset @ SV254 @ ( setminus @ SV5 @ SV616 ) )
          | ! [SY2899: $i] :
              ( ~ ( in @ SY2899 @ SV5 )
              | ~ ( in @ SY2899 @ SV616 )
              | ( in @ SY2899 @ ( setminus @ SV5 @ SV254 ) ) ) )
        = $true )
      | ( ( in @ SV254 @ ( powerset @ SV5 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1833]) ).

thf(2052,plain,
    ! [SV255: $i,SV6: $i,SV617: $i] :
      ( ( ( ~ ( in @ SV617 @ ( powerset @ SV6 ) ) )
        = $true )
      | ( ( in @ ( setminus @ SV6 @ SV255 ) @ ( powerset @ ( setminus @ SV6 @ ( binintersect @ SV255 @ SV617 ) ) ) )
        = $true )
      | ( ( in @ SV255 @ ( powerset @ SV6 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1834]) ).

thf(2053,plain,
    ! [SV256: $i,SV7: $i,SV618: $i] :
      ( ( ( ~ ( in @ SV618 @ ( powerset @ SV7 ) ) )
        = $true )
      | ( ( subset @ ( setminus @ SV7 @ SV256 ) @ ( setminus @ SV7 @ ( binintersect @ SV256 @ SV618 ) ) )
        = $true )
      | ( ( in @ SV256 @ ( powerset @ SV7 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1835]) ).

thf(2054,plain,
    ! [SV257: $i,SV8: $i,SV619: $i] :
      ( ( ( ~ ( in @ SV619 @ ( powerset @ SV8 ) ) )
        = $true )
      | ( ( ! [SY2900: $i] :
              ( ~ ( in @ SY2900 @ SV8 )
              | ~ ( in @ SY2900 @ ( setminus @ SV8 @ SV257 ) )
              | ( in @ SY2900 @ ( setminus @ SV8 @ ( binintersect @ SV257 @ SV619 ) ) ) ) )
        = $true )
      | ( ( in @ SV257 @ ( powerset @ SV8 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1836]) ).

thf(2055,plain,
    ! [SV258: $i,SV9: $i,SV620: $i] :
      ( ( ( ~ ( in @ SV620 @ ( powerset @ SV9 ) ) )
        = $true )
      | ( ( ! [SY2901: $i] :
              ( ~ ( in @ SY2901 @ SV9 )
              | ~ ( in @ SY2901 @ ( setminus @ SV9 @ SV258 ) )
              | ~ ( in @ SY2901 @ ( binintersect @ SV258 @ SV620 ) ) ) )
        = $true )
      | ( ( in @ SV258 @ ( powerset @ SV9 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1837]) ).

thf(2056,plain,
    ! [SV262: $i,SV13: $i,SV621: $i] :
      ( ( ( ~ ( in @ SV621 @ SV13 ) )
        = $true )
      | ( ( ~ ( in @ SV621 @ ( setminus @ SV13 @ ( setminus @ SV13 @ SV262 ) ) )
          | ( in @ SV621 @ SV262 ) )
        = $true )
      | ( ( in @ SV262 @ ( powerset @ SV13 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1838]) ).

thf(2057,plain,
    ! [SV263: $i,SV14: $i,SV622: $i] :
      ( ( ( ~ ( in @ SV622 @ SV14 ) )
        = $true )
      | ( ( ~ ( in @ SV622 @ SV263 )
          | ( in @ SV622 @ ( setminus @ SV14 @ ( setminus @ SV14 @ SV263 ) ) ) )
        = $true )
      | ( ( in @ SV263 @ ( powerset @ SV14 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1839]) ).

thf(2058,plain,
    ! [SV264: $i,SV15: $i,SV623: $i] :
      ( ( ( ~ ( in @ SV623 @ ( powerset @ SV15 ) ) )
        = $true )
      | ( ( ~ ( subset @ ( setminus @ SV15 @ SV623 ) @ ( setminus @ SV15 @ SV264 ) )
          | ( subset @ SV264 @ SV623 ) )
        = $true )
      | ( ( in @ SV264 @ ( powerset @ SV15 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1840]) ).

thf(2059,plain,
    ! [SV265: $i,SV16: $i,SV624: $i] :
      ( ( ( ~ ( in @ SV624 @ ( powerset @ SV16 ) ) )
        = $true )
      | ( ( ~ ( subset @ SV265 @ SV624 )
          | ( subset @ ( setminus @ SV16 @ SV624 ) @ ( setminus @ SV16 @ SV265 ) ) )
        = $true )
      | ( ( in @ SV265 @ ( powerset @ SV16 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1841]) ).

thf(2060,plain,
    ! [SV266: $i,SV17: $i,SV625: $i] :
      ( ( ( ~ ( in @ SV625 @ ( powerset @ SV17 ) ) )
        = $true )
      | ( ( ! [SY2902: $i] :
              ( ~ ( in @ SY2902 @ SV17 )
              | ~ ( subset @ SV266 @ SV625 )
              | ( in @ SY2902 @ SV625 )
              | ~ ( in @ SY2902 @ SV266 ) ) )
        = $true )
      | ( ( in @ SV266 @ ( powerset @ SV17 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1842]) ).

thf(2061,plain,
    ! [SV267: $i,SV18: $i,SV626: $i] :
      ( ( ( ~ ( in @ SV626 @ ( powerset @ SV18 ) ) )
        = $true )
      | ( ( ! [SY2903: $i] :
              ( ~ ( in @ SY2903 @ SV18 )
              | ~ ( subset @ SV267 @ ( setminus @ SV18 @ SV626 ) )
              | ~ ( in @ SY2903 @ SV626 )
              | ~ ( in @ SY2903 @ SV267 ) ) )
        = $true )
      | ( ( in @ SV267 @ ( powerset @ SV18 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1843]) ).

thf(2062,plain,
    ! [SV268: $i,SV19: $i,SV627: $i] :
      ( ( ( ~ ( in @ SV627 @ ( powerset @ SV19 ) ) )
        = $true )
      | ( ( ! [SY2904: $i] :
              ( ~ ( in @ SY2904 @ SV19 )
              | ( in @ SY2904 @ SV627 )
              | ~ ( in @ SY2904 @ ( binintersect @ SV268 @ SV627 ) ) ) )
        = $true )
      | ( ( in @ SV268 @ ( powerset @ SV19 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1844]) ).

thf(2063,plain,
    ! [SV269: $i,SV20: $i,SV628: $i] :
      ( ( ( ~ ( in @ SV628 @ ( powerset @ SV20 ) ) )
        = $true )
      | ( ( ! [SY2905: $i] :
              ( ~ ( in @ SY2905 @ SV20 )
              | ( in @ SY2905 @ SV269 )
              | ~ ( in @ SY2905 @ ( binintersect @ SV269 @ SV628 ) ) ) )
        = $true )
      | ( ( in @ SV269 @ ( powerset @ SV20 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1845]) ).

thf(2064,plain,
    ! [SV270: $i,SV21: $i,SV629: $i] :
      ( ( ( ~ ( in @ SV629 @ SV21 ) )
        = $true )
      | ( ( ( in @ SV629 @ ( setminus @ SV21 @ SV270 ) )
          | ( in @ SV629 @ SV270 ) )
        = $true )
      | ( ( in @ SV270 @ ( powerset @ SV21 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1846]) ).

thf(2065,plain,
    ! [SV271: $i,SV22: $i,SV630: $i] :
      ( ( ( ~ ( in @ SV630 @ SV22 ) )
        = $true )
      | ( ( ~ ( in @ SV630 @ SV271 )
          | ~ ( in @ SV630 @ ( setminus @ SV22 @ SV271 ) ) )
        = $true )
      | ( ( in @ SV271 @ ( powerset @ SV22 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1847]) ).

thf(2066,plain,
    ! [SV272: $i,SV23: $i,SV631: $i] :
      ( ( ( ~ ( in @ SV631 @ ( powerset @ SV23 ) ) )
        = $true )
      | ( ( ! [SY2906: $i] :
              ( ~ ( in @ SY2906 @ SV23 )
              | ~ ( in @ SV272 @ ( powerset @ SV631 ) )
              | ~ ( in @ SY2906 @ SV272 )
              | ( in @ SY2906 @ SV631 ) ) )
        = $true )
      | ( ( in @ SV272 @ ( powerset @ SV23 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1848]) ).

thf(2067,plain,
    ! [SV274: $i,SV25: $i,SV632: $i] :
      ( ( ( ~ ( in @ SV632 @ ( powerset @ SV25 ) ) )
        = $true )
      | ( ( in @ ( setminus @ SV274 @ SV632 ) @ ( powerset @ SV25 ) )
        = $true )
      | ( ( in @ SV274 @ ( powerset @ SV25 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1849]) ).

thf(2068,plain,
    ! [SV276: $i,SV27: $i,SV633: $i] :
      ( ( ( ~ ( in @ SV633 @ ( powerset @ SV27 ) ) )
        = $true )
      | ( ( in @ ( binunion @ SV276 @ SV633 ) @ ( powerset @ SV27 ) )
        = $true )
      | ( ( in @ SV276 @ ( powerset @ SV27 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1850]) ).

thf(2069,plain,
    ! [SV277: $i,SV28: $i,SV634: $i] :
      ( ( ( ~ ( in @ SV634 @ ( powerset @ SV28 ) ) )
        = $true )
      | ( ( in @ ( binintersect @ SV277 @ SV634 ) @ ( powerset @ SV28 ) )
        = $true )
      | ( ( in @ SV277 @ ( powerset @ SV28 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1851]) ).

thf(2070,plain,
    ! [SV455: $i,SV278: $o,SV29: $i,SV662: $i] :
      ( ( ( ~ ( in @ SV662 @ SV29 )
          | ( in @ ( if @ SV29 @ SV278 @ SV455 @ SV662 ) @ ( setadjoin @ SV455 @ ( setadjoin @ SV662 @ emptyset ) ) ) )
        = $true )
      | ( ( in @ SV455 @ SV29 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1852]) ).

thf(2071,plain,
    ! [SV456: $i,SV29: $i,SV663: $i] :
      ( ( ( ~ ( in @ SV663 @ SV29 )
          | ( in @ ( if @ SV29 @ $true @ SV456 @ SV663 ) @ ( setadjoin @ SV456 @ ( setadjoin @ SV663 @ emptyset ) ) ) )
        = $true )
      | ( ( in @ SV456 @ SV29 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1853]) ).

thf(2072,plain,
    ! [SV457: $i,SV29: $i,SV664: $i] :
      ( ( ( ~ ( in @ SV664 @ SV29 )
          | ( in @ ( if @ SV29 @ $false @ SV457 @ SV664 ) @ ( setadjoin @ SV457 @ ( setadjoin @ SV664 @ emptyset ) ) ) )
        = $true )
      | ( ( in @ SV457 @ SV29 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1854]) ).

thf(2073,plain,
    ! [SV458: $i,SV279: $o,SV30: $i,SV665: $i] :
      ( ( ( ~ ( in @ SV665 @ SV30 )
          | SV279
          | ( ( if @ SV30 @ SV279 @ SV458 @ SV665 )
            = SV665 ) )
        = $true )
      | ( ( in @ SV458 @ SV30 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1855]) ).

thf(2074,plain,
    ! [SV459: $i,SV30: $i,SV666: $i] :
      ( ( ( ~ ( in @ SV666 @ SV30 )
          | $true
          | ( ( if @ SV30 @ $true @ SV459 @ SV666 )
            = SV666 ) )
        = $true )
      | ( ( in @ SV459 @ SV30 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1856]) ).

thf(2075,plain,
    ! [SV460: $i,SV30: $i,SV667: $i] :
      ( ( ( ~ ( in @ SV667 @ SV30 )
          | $false
          | ( ( if @ SV30 @ $false @ SV460 @ SV667 )
            = SV667 ) )
        = $true )
      | ( ( in @ SV460 @ SV30 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1857]) ).

thf(2076,plain,
    ! [SV461: $i,SV280: $o,SV31: $i,SV668: $i] :
      ( ( ( ~ ( in @ SV668 @ SV31 )
          | ~ SV280
          | ( ( if @ SV31 @ SV280 @ SV461 @ SV668 )
            = SV461 ) )
        = $true )
      | ( ( in @ SV461 @ SV31 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1858]) ).

thf(2077,plain,
    ! [SV462: $i,SV31: $i,SV669: $i] :
      ( ( ( ~ ( in @ SV669 @ SV31 )
          | ~ $true
          | ( ( if @ SV31 @ $true @ SV462 @ SV669 )
            = SV462 ) )
        = $true )
      | ( ( in @ SV462 @ SV31 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1859]) ).

thf(2078,plain,
    ! [SV463: $i,SV31: $i,SV670: $i] :
      ( ( ( ~ ( in @ SV670 @ SV31 )
          | ~ $false
          | ( ( if @ SV31 @ $false @ SV463 @ SV670 )
            = SV463 ) )
        = $true )
      | ( ( in @ SV463 @ SV31 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1860]) ).

thf(2079,plain,
    ! [SV32: $i,SV587: $i] :
      ( ( ( in @ SV587 @ SV32 )
        = $false )
      | ( ( ( setunion @ SV32 )
          = SV587 )
        = $true )
      | ( ( singleton @ SV32 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1861]) ).

thf(2080,plain,
    ! [SV464: $i,SV281: $o,SV33: $i,SV671: $i] :
      ( ( ( ~ ( in @ SV671 @ SV33 )
          | ( in @ ( if @ SV33 @ SV281 @ SV464 @ SV671 ) @ SV33 ) )
        = $true )
      | ( ( in @ SV464 @ SV33 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1862]) ).

thf(2081,plain,
    ! [SV465: $i,SV33: $i,SV672: $i] :
      ( ( ( ~ ( in @ SV672 @ SV33 )
          | ( in @ ( if @ SV33 @ $true @ SV465 @ SV672 ) @ SV33 ) )
        = $true )
      | ( ( in @ SV465 @ SV33 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1863]) ).

thf(2082,plain,
    ! [SV466: $i,SV33: $i,SV673: $i] :
      ( ( ( ~ ( in @ SV673 @ SV33 )
          | ( in @ ( if @ SV33 @ $false @ SV466 @ SV673 ) @ SV33 ) )
        = $true )
      | ( ( in @ SV466 @ SV33 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1864]) ).

thf(2083,plain,
    ! [SV588: $i,SV469: $i,SV36: $i] :
      ( ( ( ! [SY1968: $i] :
              ~ ( in @ SY1968 @ SV36 ) )
        = $true )
      | ( $true = $true )
      | ( ( func @ SV36 @ SV469 @ SV588 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1867]) ).

thf(2084,plain,
    ! [SV470: $i,SV589: $i,SV37: $i] :
      ( ( ( ! [SY1971: $i] :
              ~ ( in @ SY1971 @ SV37 ) )
        = $true )
      | ( $true = $true )
      | ( ( in @ SV589 @ ( funcSet @ SV37 @ SV470 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1868]) ).

thf(2085,plain,
    ! [SV471: $i,SV284: $i,SV38: $i,SV674: $i] :
      ( ( ( ~ ( in @ SV674 @ SV38 )
          | ! [SY2932: $i] :
              ( ~ ( in @ SY2932 @ SV284 )
              | ~ ( in @ ( kpair @ SV674 @ SY2932 ) @ SV471 )
              | ( ( ap @ SV38 @ SV284 @ SV471 @ SV674 )
                = SY2932 ) ) )
        = $true )
      | ( ( in @ SV471 @ ( funcSet @ SV38 @ SV284 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1869]) ).

thf(2086,plain,
    ! [SV472: $i,SV285: $i,SV39: $i,SV675: $i] :
      ( ( ( ~ ( in @ SV675 @ SV39 )
          | ! [SY2933: $i] :
              ( ~ ( in @ SY2933 @ SV285 )
              | ~ ( in @ ( kpair @ SV675 @ SY2933 ) @ SV472 )
              | ( ( ap @ SV39 @ SV285 @ SV472 @ SV675 )
                = SY2933 ) ) )
        = $true )
      | ( ( func @ SV39 @ SV285 @ SV472 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1870]) ).

thf(2087,plain,
    ! [SV473: $i,SV286: $i,SV40: $i,SV676: $i] :
      ( ( ( ~ ( in @ SV676 @ SV40 )
          | ( in @ ( kpair @ SV676 @ ( ap @ SV40 @ SV286 @ SV473 @ SV676 ) ) @ SV473 ) )
        = $true )
      | ( ( in @ SV473 @ ( funcSet @ SV40 @ SV286 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1871]) ).

thf(2088,plain,
    ! [SV474: $i,SV287: $i,SV41: $i,SV677: $i] :
      ( ( ( ~ ( in @ SV677 @ SV41 )
          | ( in @ ( kpair @ SV677 @ ( ap @ SV41 @ SV287 @ SV474 @ SV677 ) ) @ SV474 ) )
        = $true )
      | ( ( func @ SV41 @ SV287 @ SV474 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1872]) ).

thf(2089,plain,
    ! [SV288: $i > $o,SV42: $i,SV635: $i] :
      ( ( ( ~ ( in @ SV635 @ SV42 ) )
        = $true )
      | ( ( ! [SY2907: $i] :
              ( ~ ( in @ SY2907 @ SV42 )
              | ~ ( SV288 @ SV635 )
              | ~ ( SV288 @ SY2907 )
              | ( SV635 = SY2907 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV42
            @ ^ [SY2500: $i] : ( SV288 @ SY2500 ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1873]) ).

thf(2090,plain,
    ! [SV476: $i,SV290: $i,SV44: $i,SV678: $i] :
      ( ( ( ~ ( in @ SV678 @ SV44 )
          | ( in @ ( ap @ SV44 @ SV290 @ SV476 @ SV678 ) @ SV290 ) )
        = $true )
      | ( ( in @ SV476 @ ( funcSet @ SV44 @ SV290 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1875]) ).

thf(2091,plain,
    ! [SV478: $i,SV292: $i,SV46: $i,SV679: $i] :
      ( ( ( ~ ( in @ SV679 @ SV46 )
          | ( in @ ( ap @ SV46 @ SV292 @ SV478 @ SV679 ) @ SV292 ) )
        = $true )
      | ( ( func @ SV46 @ SV292 @ SV478 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1877]) ).

thf(2092,plain,
    ! [SV479: $i,SV293: $i,SV47: $i,SV680: $i] :
      ( ( ( ~ ( in @ SV680 @ SV47 )
          | ( in
            @ ( setunion
              @ ( dsetconstr @ SV293
                @ ^ [SY2934: $i] : ( in @ ( kpair @ SV680 @ SY2934 ) @ SV479 ) ) )
            @ SV293 ) )
        = $true )
      | ( ( func @ SV47 @ SV293 @ SV479 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1878]) ).

thf(2093,plain,
    ! [SV480: $i,SV294: $i,SV48: $i,SV681: $i] :
      ( ( ( ~ ( in @ SV681 @ SV48 )
          | ( singleton
            @ ( dsetconstr @ SV294
              @ ^ [SY2935: $i] : ( in @ ( kpair @ SV681 @ SY2935 ) @ SV480 ) ) ) )
        = $true )
      | ( ( func @ SV48 @ SV294 @ SV480 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1879]) ).

thf(2094,plain,
    ! [SV481: $i > $i > $o,SV295: $i,SV49: $i,SV636: $i,SV590: $i] :
      ( ( ( ~ ( in @ ( kpair @ SV590 @ SV636 )
              @ ( dpsetconstr @ SV49 @ SV295
                @ ^ [SY2763: $i,SY2764: $i] : ( SV481 @ SY2763 @ SY2764 ) ) ) )
        = $true )
      | ( ( SV481 @ SV590 @ SV636 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1880]) ).

thf(2095,plain,
    ! [SV482: $i > $i > $o,SV296: $i,SV50: $i,SV637: $i,SV591: $i] :
      ( ( ( ~ ( in @ ( kpair @ SV591 @ SV637 )
              @ ( dpsetconstr @ SV50 @ SV296
                @ ^ [SY2767: $i,SY2768: $i] : ( SV482 @ SY2767 @ SY2768 ) ) ) )
        = $true )
      | ( ( in @ SV637 @ SV296 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1881]) ).

thf(2096,plain,
    ! [SV483: $i > $i > $o,SV297: $i,SV51: $i,SV682: $i,SV592: $i] :
      ( ( ( ~ ( in @ ( kpair @ SV592 @ SV682 )
              @ ( dpsetconstr @ SV51 @ SV297
                @ ^ [SY2771: $i,SY2772: $i] : ( SV483 @ SY2771 @ SY2772 ) ) ) )
        = $true )
      | ( ( in @ SV592 @ SV51 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[1882]) ).

thf(2097,plain,
    ! [SV484: $i > $i > $o,SV298: $i,SV52: $i,SV593: $i] :
      ( ( ( in @ SV593 @ SV52 )
        = $false )
      | ( ( ! [SY2877: $i] :
              ( ~ ( in @ SY2877 @ SV298 )
              | ~ ( in @ ( kpair @ SV593 @ SY2877 )
                  @ ( dpsetconstr @ SV52 @ SV298
                    @ ^ [SY2775: $i,SY2776: $i] : ( SV484 @ SY2775 @ SY2776 ) ) )
              | ( SV484 @ SV593 @ SY2877 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1883]) ).

thf(2098,plain,
    ! [SV487: $i > $i > $o,SV301: $i,SV55: $i,SV594: $i] :
      ( ( ( in @ SV594 @ SV55 )
        = $false )
      | ( ( ! [SY2880: $i] :
              ( ~ ( in @ SY2880 @ SV301 )
              | ~ ( SV487 @ SV594 @ SY2880 )
              | ( in @ ( kpair @ SV594 @ SY2880 )
                @ ( dpsetconstr @ SV55 @ SV301
                  @ ^ [SY2783: $i,SY2784: $i] : ( SV487 @ SY2783 @ SY2784 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1884]) ).

thf(2099,plain,
    ! [SV57: $i,SV489: $i,SV303: $i,SV683: $i] :
      ( ( ( ~ ( in @ SV683 @ SV303 )
          | ( ( ksnd @ ( kpair @ SV489 @ SV683 ) )
            = SV683 ) )
        = $true )
      | ( ( in @ SV489 @ SV57 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1886]) ).

thf(2100,plain,
    ! [SV58: $i,SV490: $i,SV304: $i,SV684: $i] :
      ( ( ( ~ ( in @ SV684 @ SV304 )
          | ( ( kfst @ ( kpair @ SV490 @ SV684 ) )
            = SV490 ) )
        = $true )
      | ( ( in @ SV490 @ SV58 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1887]) ).

thf(2101,plain,
    ! [SV59: $i,SV491: $i,SV685: $i] :
      ( ( ( ! [SY2938: $i] :
              ~ ( in @ SY2938 @ SV685 ) )
        = $true )
      | ( $true = $true )
      | ( ( in @ SV491 @ SV59 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1888]) ).

thf(2102,plain,
    ! [SV305: $i,SV60: $i,SV595: $i,SV492: $i] :
      ( ( ( in @ ( kpair @ SV492 @ SV595 ) @ ( cartprod @ SV60 @ SV305 ) )
        = $false )
      | ( ( in @ SV595 @ SV305 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1889]) ).

thf(2103,plain,
    ! [SV306: $i,SV61: $i,SV638: $i,SV493: $i] :
      ( ( ( in @ ( kpair @ SV493 @ SV638 ) @ ( cartprod @ SV61 @ SV306 ) )
        = $false )
      | ( ( in @ SV493 @ SV61 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1890]) ).

thf(2104,plain,
    ! [SV596: $i,SV495: $i,SV309: $i,SV66: $i] :
      ( ( ( ( kpair @ SV66 @ SV309 )
          = ( kpair @ SV495 @ SV596 ) )
        = $false )
      | ( ( SV309 = SV596 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1892]) ).

thf(2105,plain,
    ! [SV597: $i,SV496: $i,SV310: $i,SV67: $i] :
      ( ( ( ( setadjoin @ ( setadjoin @ SV67 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV67 @ ( setadjoin @ SV310 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ SV496 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV496 @ ( setadjoin @ SV597 @ emptyset ) ) @ emptyset ) ) )
        = $false )
      | ( ( SV310 = SV597 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1893]) ).

thf(2106,plain,
    ! [SV599: $i,SV497: $i,SV312: $i,SV69: $i] :
      ( ( ( ( setadjoin @ ( setadjoin @ SV69 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV69 @ ( setadjoin @ SV312 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ SV497 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV497 @ ( setadjoin @ SV599 @ emptyset ) ) @ emptyset ) ) )
        = $false )
      | ( ( ( SV497 != SV599 )
          | ( SV312 = SV599 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1895]) ).

thf(2107,plain,
    ! [SV639: $i,SV498: $i,SV315: $i,SV72: $i] :
      ( ( ( ( kpair @ SV72 @ SV315 )
          = ( kpair @ SV498 @ SV639 ) )
        = $false )
      | ( ( SV72 = SV498 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1896]) ).

thf(2108,plain,
    ! [SV640: $i,SV499: $i,SV316: $i,SV73: $i] :
      ( ( ( ( setadjoin @ ( setadjoin @ SV73 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV73 @ ( setadjoin @ SV316 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ SV499 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV499 @ ( setadjoin @ SV640 @ emptyset ) ) @ emptyset ) ) )
        = $false )
      | ( ( SV73 = SV499 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1897]) ).

thf(2109,plain,
    ! [SV84: $i,SV503: $i,SV322: $i,SV686: $i] :
      ( ( ( ~ ( in @ SV686 @ SV322 )
          | ( in @ ( kpair @ SV503 @ SV686 ) @ ( cartprod @ SV84 @ SV322 ) ) )
        = $true )
      | ( ( in @ SV503 @ SV84 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1901]) ).

thf(2110,plain,
    ! [SV85: $i,SV504: $i,SV323: $i,SV687: $i] :
      ( ( ( ~ ( in @ SV687 @ SV323 )
          | ( in @ ( kpair @ SV504 @ SV687 ) @ ( powerset @ ( powerset @ ( binunion @ SV85 @ SV323 ) ) ) ) )
        = $true )
      | ( ( in @ SV504 @ SV85 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1902]) ).

thf(2111,plain,
    ! [SV86: $i,SV505: $i,SV324: $i,SV688: $i] :
      ( ( ( ~ ( in @ SV688 @ SV324 )
          | ( in @ ( setadjoin @ ( setadjoin @ SV505 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV505 @ ( setadjoin @ SV688 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV86 @ SV324 ) ) ) ) )
        = $true )
      | ( ( in @ SV505 @ SV86 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1903]) ).

thf(2112,plain,
    ! [SV87: $i,SV506: $i,SV325: $i,SV689: $i] :
      ( ( ( ~ ( in @ SV689 @ SV325 )
          | ( subset @ ( setadjoin @ ( setadjoin @ SV506 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV506 @ ( setadjoin @ SV689 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV87 @ SV325 ) ) ) )
        = $true )
      | ( ( in @ SV506 @ SV87 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1904]) ).

thf(2113,plain,
    ! [SV88: $i,SV507: $i,SV326: $i,SV690: $i] :
      ( ( ( ~ ( in @ SV690 @ SV326 )
          | ( in @ ( setadjoin @ SV507 @ ( setadjoin @ SV690 @ emptyset ) ) @ ( powerset @ ( binunion @ SV88 @ SV326 ) ) ) )
        = $true )
      | ( ( in @ SV507 @ SV88 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1905]) ).

thf(2114,plain,
    ! [SV89: $i,SV508: $i,SV327: $i,SV691: $i] :
      ( ( ( ~ ( in @ SV691 @ SV327 )
          | ( subset @ ( setadjoin @ SV508 @ ( setadjoin @ SV691 @ emptyset ) ) @ ( binunion @ SV89 @ SV327 ) ) )
        = $true )
      | ( ( in @ SV508 @ SV89 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1906]) ).

thf(2115,plain,
    ! [SV328: $i,SV90: $i,SV509: $i] :
      ( ( ( SV509 = SV90 )
        = $true )
      | ( ( SV509 = SV328 )
        = $true )
      | ( ( in @ SV509 @ ( setadjoin @ SV90 @ ( setadjoin @ SV328 @ emptyset ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1907]) ).

thf(2116,plain,
    ! [SV337: $i,SV99: $i,SV511: $i] :
      ( ( ( in @ SV511 @ ( symdiff @ SV99 @ SV337 ) )
        = $false )
      | ( ( in @ SV511 @ SV337 )
        = $true )
      | ( ( in @ SV511 @ SV99 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1909]) ).

thf(2117,plain,
    ! [SV100: $i,SV338: $i,SV512: $i] :
      ( ( ( ~ ( in @ SV512 @ SV338 ) )
        = $true )
      | ( ( ~ ( in @ SV512 @ ( symdiff @ SV100 @ SV338 ) ) )
        = $true )
      | ( ( in @ SV512 @ SV100 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1910]) ).

thf(2118,plain,
    ! [SV101: $i,SV339: $i,SV513: $i] :
      ( ( ( in @ SV513 @ SV339 )
        = $false )
      | ( ( in @ SV513 @ ( symdiff @ SV101 @ SV339 ) )
        = $true )
      | ( ( in @ SV513 @ SV101 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1911]) ).

thf(2119,plain,
    ! [SV102: $i,SV340: $i,SV514: $i] :
      ( ( ( in @ SV514 @ SV340 )
        = $true )
      | ( ( in @ SV514 @ ( symdiff @ SV102 @ SV340 ) )
        = $true )
      | ( ( in @ SV514 @ SV102 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1912]) ).

thf(2120,plain,
    ! [SV343: $i,SV105: $i,SV515: $i] :
      ( ( ( in @ SV515 @ ( setminus @ SV105 @ SV343 ) )
        = $false )
      | ( ( in @ SV515 @ SV343 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1913]) ).

thf(2121,plain,
    ! [SV345: $i,SV107: $i,SV517: $i] :
      ( ( ( in @ SV517 @ SV107 )
        = $false )
      | ( ( in @ SV517 @ SV345 )
        = $true )
      | ( ( in @ SV517 @ ( setminus @ SV107 @ SV345 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1915]) ).

thf(2122,plain,
    ! [SV346: $i,SV108: $i,SV518: $i] :
      ( ( ( in @ SV518 @ SV108 )
        = $false )
      | ( ( in @ SV518 @ SV346 )
        = $true )
      | ( ( in @ SV518 @ ( setminus @ SV108 @ SV346 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1916]) ).

thf(2123,plain,
    ! [SV110: $i,SV348: $i,SV519: $i] :
      ( ( ( in @ SV519 @ SV348 )
        = $false )
      | ( ( in @ SV519 @ ( setminus @ SV110 @ SV348 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1917]) ).

thf(2124,plain,
    ! [SV112: $i,SV350: $i,SV521: $i] :
      ( ( ( in @ SV521 @ SV350 )
        = $true )
      | ( ( in @ SV521 @ ( setminus @ SV112 @ SV350 ) )
        = $true )
      | ( ( in @ SV521 @ SV112 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1919]) ).

thf(2125,plain,
    ! [SV122: $i,SV360: $i,SV525: $i] :
      ( ( ( ~ ( subset @ SV525 @ SV360 ) )
        = $true )
      | ( ( subset @ SV525 @ ( binintersect @ SV122 @ SV360 ) )
        = $true )
      | ( ( subset @ SV525 @ SV122 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1922]) ).

thf(2126,plain,
    ! [SV123: $i,SV361: $i,SV526: $i] :
      ( ( ( ~ ( in @ SV526 @ SV361 ) )
        = $true )
      | ( ( in @ SV526 @ ( binintersect @ SV123 @ SV361 ) )
        = $true )
      | ( ( in @ SV526 @ SV123 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1923]) ).

thf(2127,plain,
    ! [SV364: $i,SV126: $i,SV527: $i] :
      ( ( ( in @ SV527 @ SV126 )
        = $true )
      | ( ( in @ SV527 @ SV364 )
        = $true )
      | ( ( in @ SV527 @ ( binunion @ SV126 @ SV364 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1924]) ).

thf(2128,plain,
    ! [SV137: $i,SV373: $i] :
      ( ( ( subset @ SV373 @ SV137 )
        = $false )
      | ( ( SV137 = SV373 )
        = $true )
      | ( ( subset @ SV137 @ SV373 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1927]) ).

thf(2129,plain,
    ! [SV141: $i,SV641: $i,SV377: $i] :
      ( ( ( ~ ( subset @ SV377 @ SV641 ) )
        = $true )
      | ( ( subset @ SV141 @ SV641 )
        = $true )
      | ( ( subset @ SV141 @ SV377 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1929]) ).

thf(2130,plain,
    ! [SV143: $i,SV378: $i,SV531: $i] :
      ( ( ( in @ SV531 @ SV378 )
        = $true )
      | ( ( SV143 != SV378 )
        = $true )
      | ( ( in @ SV531 @ SV143 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1930]) ).

thf(2131,plain,
    ! [SV145: $i,SV380: $i,SV532: $i] :
      ( ( ( in @ SV532 @ SV380 )
        = $true )
      | ( ( ~ ( subset @ SV145 @ SV380 ) )
        = $true )
      | ( ( in @ SV532 @ SV145 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1931]) ).

thf(2132,plain,
    ! [SV146: $i,SV381: $i,SV642: $i] :
      ( ( ( in @ SV642 @ SV381 )
        = $true )
      | ( ( ~ ( in @ SV642 @ SV146 ) )
        = $true )
      | ( ( subset @ SV146 @ SV381 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1932]) ).

thf(2133,plain,
    ! [SV382: $i,SV147: $i,SV643: $i] :
      ( ( ( ~ ( in @ SV643 @ SV147 ) )
        = $true )
      | ( ( in @ SV643 @ SV382 )
        = $true )
      | ( ( subset @ SV147 @ SV382 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1933]) ).

thf(2134,plain,
    ! [SV387: $i,SV153: $i,SV692: $i,SV644: $i] :
      ( ( ( ( SV644 != SV692 )
          | ( ( setadjoin @ SV153 @ SV644 )
            = ( setadjoin @ SV387 @ SV692 ) ) )
        = $true )
      | ( ( SV153 = SV387 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1934]) ).

thf(2135,plain,
    ! [SV388: $i,SV154: $i,SV693: $i,SV645: $i] :
      ( ( ( ( SV645 != SV693 )
          | ~ ( in @ SV645 @ SV154 )
          | ( in @ SV693 @ SV388 ) )
        = $true )
      | ( ( SV154 = SV388 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1935]) ).

thf(2136,plain,
    ! [SV158: $i,SV600: $i,SV390: $i > $o] :
      ( ( ( SV390 @ SV600 )
        = $false )
      | ( ( ~ ( in @ SV600 @ SV158 ) )
        = $true )
      | ( ( ( dsetconstr @ SV158
            @ ^ [SY2616: $i] : ( SV390 @ SY2616 ) )
         != emptyset )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1936]) ).

thf(2137,plain,
    ! [SV393: $i,SV161: $i,SV533: $i] :
      ( ( ( SV533 = SV161 )
        = $true )
      | ( ( SV533 = SV393 )
        = $true )
      | ( ( in @ SV533 @ ( setadjoin @ SV161 @ ( setadjoin @ SV393 @ emptyset ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1937]) ).

thf(2138,plain,
    ! [SV399: $i,SV168: $i,SV534: $i] :
      ( ( ( ~ ( in @ SV534 @ SV168 ) )
        = $true )
      | ( ( in @ SV399 @ ( setunion @ SV168 ) )
        = $true )
      | ( ( in @ SV399 @ SV534 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1938]) ).

thf(2139,plain,
    ! [SV169: $i,SV400: $i,SV646: $i] :
      ( ( ( ~ ( in @ SV646 @ SV400 ) )
        = $true )
      | ( ( in @ SV646 @ SV169 )
        = $true )
      | ( ( in @ SV400 @ ( powerset @ SV169 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1939]) ).

thf(2140,plain,
    ! [SV401: $i,SV173: $i,SV535: $i] :
      ( ( ( SV535 = SV173 )
        = $true )
      | ( ( in @ SV535 @ SV401 )
        = $true )
      | ( ( in @ SV535 @ ( setadjoin @ SV173 @ SV401 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1940]) ).

thf(2141,plain,
    ! [SV177: $i,SV538: $i,SV404: $i > $o] :
      ( ( ( ~ ( SV404 @ SV538 ) )
        = $true )
      | ( ( ( dsetconstr @ SV177
            @ ^ [SY2623: $i] : ( SV404 @ SY2623 ) )
         != emptyset )
        = $true )
      | ( ( in @ SV538 @ SV177 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1943]) ).

thf(2142,plain,
    ! [SV186: $i,SV544: $i,SV408: $i > $o] :
      ( ( ( ~ ( SV408 @ SV544 ) )
        = $true )
      | ( ( in @ SV544
          @ ( dsetconstr @ SV186
            @ ^ [SY2629: $i] : ( SV408 @ SY2629 ) ) )
        = $true )
      | ( ( in @ SV544 @ SV186 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1946]) ).

thf(2143,plain,
    ! [SV409: $i,SV189: $i,SV647: $i] :
      ( ( ( ~ ( in @ SV647 @ ( powerset @ SV189 ) ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK97_Xx @ SV647 @ SV409 @ SV189 ) @ SV189 )
              | ~ ~ ( ~ ( in @ ( sK97_Xx @ SV647 @ SV409 @ SV189 ) @ SV409 )
                    | ~ ~ ( in @ ( sK97_Xx @ SV647 @ SV409 @ SV189 ) @ SV647 ) ) )
          | ( subset @ SV409 @ SV647 ) )
        = $true )
      | ( ( in @ SV409 @ ( powerset @ SV189 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1947]) ).

thf(2144,plain,
    ! [SV602: $i,SV648: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK7_Xx @ SV648 @ SV602 ) @ SV648 )
              | ~ ~ ( in @ ( sK7_Xx @ SV648 @ SV602 ) @ SV602 ) ) )
        = $true )
      | ( ( in @ SV648 @ ( powerset @ SV602 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1948]) ).

thf(2145,plain,
    ! [SV603: $i,SV649: $i] :
      ( ( ( ~ ( in @ SV649 @ ( powerset @ SV603 ) ) )
        = $true )
      | ( ( ! [SY2914: $i] :
              ( ~ ( in @ SY2914 @ SV649 )
              | ( in @ SY2914 @ SV603 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1949]) ).

thf(2146,plain,
    ! [SV545: $i,SV190: $i > $o] :
      ( ( ( ~ ( SV190 @ ( sK24_SY86 @ SV545 @ SV190 ) ) )
        = $false )
      | ( ( ~ ( SV190 @ SV545 ) )
        = $true )
      | ( ( SV190 @ ( sK23_Xx @ SV190 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1950]) ).

thf(2147,plain,
    ! [SV190: $i > $o,SV545: $i] :
      ( ( ( ~ ( ( SV545
               != ( sK24_SY86 @ SV545 @ SV190 ) ) ) )
        = $false )
      | ( ( ~ ( SV190 @ SV545 ) )
        = $true )
      | ( ( SV190 @ ( sK23_Xx @ SV190 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1950]) ).

thf(2148,plain,
    ! [SV546: $i,SV410: $o,SV191: $i,SV694: $i] :
      ( ( ( ~ ( in @ SV694 @ SV191 )
          | ~ SV410
          | ( in @ SV546
            @ ( dsetconstr @ SV191
              @ ^ [SY2939: $i] :
                  ( ~ ( ~ SV410
                      | ( SY2939 != SV546 ) )
                  | ~ ( ~ ~ SV410
                      | ( SY2939 != SV694 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV546 @ SV191 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1951]) ).

thf(2149,plain,
    ! [SV547: $i,SV191: $i,SV695: $i] :
      ( ( ( ~ ( in @ SV695 @ SV191 )
          | ~ $true
          | ( in @ SV547
            @ ( dsetconstr @ SV191
              @ ^ [SY2940: $i] :
                  ( ~ ( ~ $true
                      | ( SY2940 != SV547 ) )
                  | ~ ( ~ ~ $true
                      | ( SY2940 != SV695 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV547 @ SV191 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1952]) ).

thf(2150,plain,
    ! [SV548: $i,SV191: $i,SV696: $i] :
      ( ( ( ~ ( in @ SV696 @ SV191 )
          | ~ $false
          | ( in @ SV548
            @ ( dsetconstr @ SV191
              @ ^ [SY2941: $i] :
                  ( ~ ( ~ $false
                      | ( SY2941 != SV548 ) )
                  | ~ ( ~ ~ $false
                      | ( SY2941 != SV696 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV548 @ SV191 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1953]) ).

thf(2151,plain,
    ! [SV192: $i,SV411: $i,SV549: $i > $i] :
      ( ( ( ~ ( in @ ( sK92_Xx @ SV549 @ SV411 @ SV192 ) @ SV192 ) )
        = $false )
      | ( ( ! [SY2810: $i] :
              ( ~ ( in @ SY2810 @ SV192 )
              | ( ( ap @ SV192 @ SV411
                  @ ( lam @ SV192 @ SV411
                    @ ^ [SY2811: $i] : ( SV549 @ SY2811 ) )
                  @ SY2810 )
                = ( SV549 @ SY2810 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1954]) ).

thf(2152,plain,
    ! [SV192: $i,SV411: $i,SV549: $i > $i] :
      ( ( ( ~ ~ ( in @ ( SV549 @ ( sK92_Xx @ SV549 @ SV411 @ SV192 ) ) @ SV411 ) )
        = $false )
      | ( ( ! [SY2810: $i] :
              ( ~ ( in @ SY2810 @ SV192 )
              | ( ( ap @ SV192 @ SV411
                  @ ( lam @ SV192 @ SV411
                    @ ^ [SY2811: $i] : ( SV549 @ SY2811 ) )
                  @ SY2810 )
                = ( SV549 @ SY2810 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1954]) ).

thf(2153,plain,
    ! [SV193: $i,SV412: $i,SV550: $i] :
      ( ( ( ~ ~ ( ( SV550
                 != ( kpair @ ( sK67_Xx @ SV550 @ SV412 @ SV193 ) @ ( sK68_SY1876 @ SV550 @ SV412 @ SV193 ) ) )
                | ~ ( in @ ( sK68_SY1876 @ SV550 @ SV412 @ SV193 ) @ SV412 ) )
          | ~ ( in @ ( sK67_Xx @ SV550 @ SV412 @ SV193 ) @ SV193 ) )
        = $false )
      | ( ( in @ SV550 @ ( cartprod @ SV193 @ SV412 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1955]) ).

thf(2154,plain,
    ! [SV551: $i,SV194: $i > $o] :
      ( ( ( ~ ( SV194 @ ( sK57_SY248 @ SV551 @ SV194 ) ) )
        = $false )
      | ( ( ~ ( SV194 @ SV551 ) )
        = $true )
      | ( ( ! [SY2258: $i] :
              ( ~ ( SV194 @ SY2258 )
              | ! [SY2259: $i] :
                  ( ~ ( SV194 @ SY2259 )
                  | ( SY2258 = SY2259 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1956]) ).

thf(2155,plain,
    ! [SV194: $i > $o,SV551: $i] :
      ( ( ( ~ ( ( SV551
               != ( sK57_SY248 @ SV551 @ SV194 ) ) ) )
        = $false )
      | ( ( ~ ( SV194 @ SV551 ) )
        = $true )
      | ( ( ! [SY2258: $i] :
              ( ~ ( SV194 @ SY2258 )
              | ! [SY2259: $i] :
                  ( ~ ( SV194 @ SY2259 )
                  | ( SY2258 = SY2259 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1956]) ).

thf(2156,plain,
    ! [SV195: $i > $i > $o,SV413: $i] :
      ( ( ( in @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV413 )
        = $true )
      | ( ( ~ ( ~ ! [SY2639: $i] :
                    ( ! [SY2640: $i] :
                        ( ~ ( SV195 @ SY2640 @ SY2639 )
                        | ~ ( in @ SY2640 @ SV413 ) )
                    | ( in @ SY2639 @ ( sK10_B @ SV413 @ SV195 ) ) )
              | ~ ! [SY2641: $i] :
                    ( ~ ( in @ SY2641 @ ( sK10_B @ SV413 @ SV195 ) )
                    | ~ ( ~ ( SV195 @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SY2641 )
                        | ~ ( in @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SV413 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1957]) ).

thf(2157,plain,
    ! [SV413: $i,SV195: $i > $i > $o] :
      ( ( ( ! [SY2638: $i] :
              ( ~ ( ~ ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SY2638 @ SV413 @ SV195 ) )
                  | ~ ( ( SY2638
                       != ( sK13_SY1837 @ SY2638 @ SV413 @ SV195 ) ) ) )
              | ~ ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SY2638 ) ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2639: $i] :
                    ( ! [SY2640: $i] :
                        ( ~ ( SV195 @ SY2640 @ SY2639 )
                        | ~ ( in @ SY2640 @ SV413 ) )
                    | ( in @ SY2639 @ ( sK10_B @ SV413 @ SV195 ) ) )
              | ~ ! [SY2641: $i] :
                    ( ~ ( in @ SY2641 @ ( sK10_B @ SV413 @ SV195 ) )
                    | ~ ( ~ ( SV195 @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SY2641 )
                        | ~ ( in @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SV413 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1958]) ).

thf(2158,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( ( ~ ~ ( ~ ( ( SV552 = SV196 )
                    | ( in @ SV552 @ SV414 )
                    | ! [SX3: $o] : SX3 )
                | ~ ( ( SV552 = SV196 )
                    | ! [SX3: $o] :
                        ( ~ SX3
                        | SX3 ) ) )
          | ~ ~ ( ~ ! [SY2814: $o] :
                      ( ~ SY2814
                      | ( in @ SV552 @ SV414 )
                      | SY2814 )
                | ~ ! [SX3: $o] :
                      ( ~ SX3
                      | ~ SX3
                      | SX3 ) ) )
        = $false )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1959]) ).

thf(2159,plain,
    ! [SV197: $i,SV415: $i] :
      ( ( ( in @ ( sK66_Xx @ SV415 @ SV197 ) @ SV197 )
        = $true )
      | ( ( ( binintersect @ SV197 @ SV415 )
          = emptyset )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1960]) ).

thf(2160,plain,
    ! [SV197: $i,SV415: $i] :
      ( ( ( in @ ( sK66_Xx @ SV415 @ SV197 ) @ SV415 )
        = $true )
      | ( ( ( binintersect @ SV197 @ SV415 )
          = emptyset )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1961]) ).

thf(2161,plain,
    ! [SV650: $i > $o,SV198: $i,SV697: $i] :
      ( ( ~ ( in @ SV697 @ SV198 )
        | ~ ( SV650 @ SV697 )
        | ( in @ SV697
          @ ( dsetconstr @ SV198
            @ ^ [SY2916: $i] : ( SV650 @ SY2916 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1962]) ).

thf(2162,plain,
    ! [SV651: $i > $o,SV198: $i,SV698: $i] :
      ( ( ~ ( in @ SV698 @ SV198 )
        | ~ ( in @ SV698
            @ ( dsetconstr @ SV198
              @ ^ [SY2918: $i] : ( SV651 @ SY2918 ) ) )
        | ( SV651 @ SV698 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1963]) ).

thf(2163,plain,
    ! [SV199: $i,SV416: $i] :
      ( ( ( in @ ( sK30_Xx @ SV416 @ SV199 ) @ SV416 )
        = $true )
      | ( ( in @ SV416 @ ( powerset @ SV199 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1964]) ).

thf(2164,plain,
    ! [SV199: $i,SV416: $i] :
      ( ( ( ~ ( in @ ( sK30_Xx @ SV416 @ SV199 ) @ SV199 ) )
        = $true )
      | ( ( in @ SV416 @ ( powerset @ SV199 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1965]) ).

thf(2165,plain,
    ! [SV417: $i > $o,SV200: $i,SV604: $i] :
      ( ( ( in @ SV604 @ SV200 )
        = $false )
      | ( ( SV417 @ SV604 )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK40_Xx @ SV417 @ SV200 ) @ SV200 )
              | ~ ~ ( SV417 @ ( sK40_Xx @ SV417 @ SV200 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1966]) ).

thf(2166,plain,
    ! [SV201: $i,SV418: $i,SV553: $i > $i] :
      ( ( ( ~ ( in @ ( sK78_Xx @ SV553 @ SV418 @ SV201 ) @ SV201 ) )
        = $false )
      | ( ( in
          @ ( lam @ SV201 @ SV418
            @ ^ [SY2816: $i] : ( SV553 @ SY2816 ) )
          @ ( funcSet @ SV201 @ SV418 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1967]) ).

thf(2167,plain,
    ! [SV201: $i,SV418: $i,SV553: $i > $i] :
      ( ( ( ~ ~ ( in @ ( SV553 @ ( sK78_Xx @ SV553 @ SV418 @ SV201 ) ) @ SV418 ) )
        = $false )
      | ( ( in
          @ ( lam @ SV201 @ SV418
            @ ^ [SY2816: $i] : ( SV553 @ SY2816 ) )
          @ ( funcSet @ SV201 @ SV418 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1967]) ).

thf(2168,plain,
    ! [SV554: $i,SV419: $o,SV202: $i,SV699: $i] :
      ( ( ( ~ ( in @ SV699 @ SV202 )
          | SV419
          | ( ( dsetconstr @ SV202
              @ ^ [SY2944: $i] :
                  ( ~ ( ~ SV419
                      | ( SY2944 != SV554 ) )
                  | ~ ( ~ ~ SV419
                      | ( SY2944 != SV699 ) ) ) )
            = ( setadjoin @ SV699 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV554 @ SV202 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1968]) ).

thf(2169,plain,
    ! [SV555: $i,SV202: $i,SV700: $i] :
      ( ( ( ~ ( in @ SV700 @ SV202 )
          | $true
          | ( ( dsetconstr @ SV202
              @ ^ [SY2945: $i] :
                  ( ~ ( ~ $true
                      | ( SY2945 != SV555 ) )
                  | ~ ( ~ ~ $true
                      | ( SY2945 != SV700 ) ) ) )
            = ( setadjoin @ SV700 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV555 @ SV202 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1969]) ).

thf(2170,plain,
    ! [SV556: $i,SV202: $i,SV701: $i] :
      ( ( ( ~ ( in @ SV701 @ SV202 )
          | $false
          | ( ( dsetconstr @ SV202
              @ ^ [SY2946: $i] :
                  ( ~ ( ~ $false
                      | ( SY2946 != SV556 ) )
                  | ~ ( ~ ~ $false
                      | ( SY2946 != SV701 ) ) ) )
            = ( setadjoin @ SV701 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV556 @ SV202 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1970]) ).

thf(2171,plain,
    ! [SV605: $i > $o,SV652: $i > $o] :
      ( ( ( ~ ( ( ( sK55_Xx @ SV652 @ SV605 )
               != ( sK56_SY1873 @ SV652 @ SV605 ) )
              | ~ ~ ( ~ ( ~ ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
                        | ~ ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) ) )
                    | ~ ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
                        | ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) ) ) ) ) )
        = $true )
      | ( ( ! [SY2919: $i] :
              ( ~ ( ~ ( SV605 @ ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) )
                  | ~ ( ( SY2919
                       != ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) ) ) )
              | ~ ( SV605 @ SY2919 ) )
          | ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1971]) ).

thf(2172,plain,
    ! [SV606: $i > $o,SV653: $i > $o] :
      ( ( ( ~ ( ( ( sK51_Xx @ SV653 @ SV606 )
               != ( sK52_SY1871 @ SV653 @ SV606 ) )
              | ~ ~ ( ~ ( ~ ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
                        | ~ ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) ) )
                    | ~ ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
                        | ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) ) ) ) ) )
        = $true )
      | ( ( ! [SY2921: $i] :
              ( ~ ( ~ ( SV653 @ ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) )
                  | ~ ( ( SY2921
                       != ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) ) ) )
              | ~ ( SV653 @ SY2921 ) )
          | ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1972]) ).

thf(2173,plain,
    ! [SV203: $i,SV420: $i > $o] :
      ( ( ( SV420 @ ( sK39_Xx @ SV420 @ SV203 ) )
        = $true )
      | ( ( ! [SY2653: $i] :
              ( ~ ( in @ SY2653 @ SV203 )
              | ~ ( SV420 @ SY2653 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1973]) ).

thf(2174,plain,
    ! [SV203: $i,SV420: $i > $o] :
      ( ( ( in @ ( sK39_Xx @ SV420 @ SV203 ) @ SV203 )
        = $true )
      | ( ( ! [SY2653: $i] :
              ( ~ ( in @ SY2653 @ SV203 )
              | ~ ( SV420 @ SY2653 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1974]) ).

thf(2175,plain,
    ! [SV557: $i,SV204: $i > $o] :
      ( ( ( ~ ( SV204 @ ( sK20_SY57 @ SV557 @ SV204 ) ) )
        = $false )
      | ( ( ~ ( SV204 @ SV557 ) )
        = $true )
      | ( ( SV204
          @ ( descr
            @ ^ [SY2291: $i] : ( SV204 @ SY2291 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1975]) ).

thf(2176,plain,
    ! [SV204: $i > $o,SV557: $i] :
      ( ( ( ~ ( ( SV557
               != ( sK20_SY57 @ SV557 @ SV204 ) ) ) )
        = $false )
      | ( ( ~ ( SV204 @ SV557 ) )
        = $true )
      | ( ( SV204
          @ ( descr
            @ ^ [SY2291: $i] : ( SV204 @ SY2291 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1975]) ).

thf(2177,plain,
    ! [SV558: $i,SV205: $i > $o] :
      ( ( ( ~ ( SV205 @ ( sK42_Xy @ SV558 @ SV205 ) ) )
        = $false )
      | ( ( ~ ( SV205 @ SV558 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2293: $i] :
                    ( ~ ( SV205 @ SY2293 )
                    | ( ( sK41_SY198 @ SV205 )
                      = SY2293 ) )
              | ~ ( SV205 @ ( sK41_SY198 @ SV205 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1976]) ).

thf(2178,plain,
    ! [SV205: $i > $o,SV558: $i] :
      ( ( ( ~ ( ( SV558
               != ( sK42_Xy @ SV558 @ SV205 ) ) ) )
        = $false )
      | ( ( ~ ( SV205 @ SV558 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2293: $i] :
                    ( ~ ( SV205 @ SY2293 )
                    | ( ( sK41_SY198 @ SV205 )
                      = SY2293 ) )
              | ~ ( SV205 @ ( sK41_SY198 @ SV205 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1976]) ).

thf(2179,plain,
    ! [SV206: $i,SV421: $i,SV559: $i > $i] :
      ( ( ( ~ ( in @ ( sK94_Xx @ SV559 @ SV421 @ SV206 ) @ SV206 ) )
        = $false )
      | ( ( ! [SY2823: $i] :
              ( ~ ( in @ SY2823 @ SV206 )
              | ( ( ap @ SV206 @ SV421
                  @ ( lam @ SV206 @ SV421
                    @ ^ [SY2824: $i] : ( SV559 @ SY2824 ) )
                  @ SY2823 )
                = ( SV559 @ SY2823 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1977]) ).

thf(2180,plain,
    ! [SV206: $i,SV421: $i,SV559: $i > $i] :
      ( ( ( ~ ~ ( in @ ( SV559 @ ( sK94_Xx @ SV559 @ SV421 @ SV206 ) ) @ SV421 ) )
        = $false )
      | ( ( ! [SY2823: $i] :
              ( ~ ( in @ SY2823 @ SV206 )
              | ( ( ap @ SV206 @ SV421
                  @ ( lam @ SV206 @ SV421
                    @ ^ [SY2824: $i] : ( SV559 @ SY2824 ) )
                  @ SY2823 )
                = ( SV559 @ SY2823 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1977]) ).

thf(2181,plain,
    ( ( in @ sK3_SY1826 @ ( powerset @ sK1_A ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1978]) ).

thf(2182,plain,
    ( ( ~ ( ~ ( in @ sK4_SY1829 @ ( powerset @ sK1_A ) )
          | ~ ~ ( ~ ( in @ sK5_SY1831 @ sK1_A )
                | ~ ~ ( ~ ( in @ sK5_SY1831 @ ( binintersect @ sK2_SY1822 @ sK3_SY1826 ) )
                      | ~ ~ ( in @ sK5_SY1831 @ ( binunion @ sK3_SY1826 @ sK4_SY1829 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[1979]) ).

thf(2183,plain,
    ! [SV207: $i,SV422: $i,SV560: $i,SV702: $i > $o] :
      ( ( ( ~ ( ~ ( in @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ SV207 )
              | ~ ~ ( ~ ( in @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) @ SV422 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) ) @ SV560 )
                          | ~ ~ ( SV702 @ ( kpair @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) ) ) ) ) )
          | ! [SY2947: $i] :
              ( ~ ( in @ SY2947 @ SV560 )
              | ( SV702 @ SY2947 ) ) )
        = $true )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1980]) ).

thf(2184,plain,
    ! [SV561: $i,SV423: $i,SV208: $i,SV703: $i] :
      ( ( ( ~ ( subset @ SV703 @ ( cartprod @ SV208 @ SV423 ) )
          | ~ ( ~ ( in @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ SV208 )
              | ~ ~ ( ~ ( in @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) @ SV423 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) ) @ SV561 )
                          | ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) ) @ SV703 ) ) ) )
          | ( subset @ SV561 @ SV703 ) )
        = $true )
      | ( ( subset @ SV561 @ ( cartprod @ SV208 @ SV423 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1981]) ).

thf(2185,plain,
    ! [SV209: $i,SV424: $i > $o] :
      ( ( ( in @ ( sK70_Xx @ SV424 @ SV209 ) @ SV209 )
        = $true )
      | ( ( ! [SY2662: $i] :
              ( ~ ( SV424 @ SY2662 )
              | ~ ( in @ SY2662 @ SV209 ) )
          | ( singleton
            @ ( dsetconstr @ SV209
              @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1982]) ).

thf(2186,plain,
    ! [SV209: $i,SV424: $i > $o] :
      ( ( ( ~ ( ~ ( in @ ( sK71_SY1877 @ SV424 @ SV209 ) @ SV209 )
              | ~ ~ ( ~ ( SV424 @ ( sK70_Xx @ SV424 @ SV209 ) )
                    | ~ ~ ( ~ ( SV424 @ ( sK71_SY1877 @ SV424 @ SV209 ) )
                          | ~ ( ( ( sK70_Xx @ SV424 @ SV209 )
                               != ( sK71_SY1877 @ SV424 @ SV209 ) ) ) ) ) ) )
        = $true )
      | ( ( ! [SY2662: $i] :
              ( ~ ( SV424 @ SY2662 )
              | ~ ( in @ SY2662 @ SV209 ) )
          | ( singleton
            @ ( dsetconstr @ SV209
              @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1983]) ).

thf(2187,plain,
    ! [SV425: $i,SV210: $i] :
      ( ( ( ~ ! [SY2664: $i,SY2665: $i] :
                ( ( SY2664 != SY2665 )
                | ~ ( in @ SY2664 @ SV210 )
                | ( in @ SY2665 @ SV425 ) ) )
        = $false )
      | ( ( SV210 = SV425 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1984]) ).

thf(2188,plain,
    ! [SV210: $i,SV425: $i] :
      ( ( ( ~ ! [SY2666: $i,SY2667: $i] :
                ( ( SY2666 != SY2667 )
                | ~ ( in @ SY2667 @ SV425 )
                | ( in @ SY2666 @ SV210 ) ) )
        = $false )
      | ( ( SV210 = SV425 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1984]) ).

thf(2189,plain,
    ! [SV562: $i,SV211: $i > $o] :
      ( ( ( ~ ( SV211 @ ( sK48_SY224 @ SV562 @ SV211 ) ) )
        = $false )
      | ( ( ~ ( SV211 @ SV562 ) )
        = $true )
      | ( ( ! [SY2314: $i] :
              ( ~ ( SV211 @ SY2314 )
              | ! [SY2315: $i] :
                  ( ~ ( SV211 @ SY2315 )
                  | ( SY2314 = SY2315 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1985]) ).

thf(2190,plain,
    ! [SV211: $i > $o,SV562: $i] :
      ( ( ( ~ ( ( SV562
               != ( sK48_SY224 @ SV562 @ SV211 ) ) ) )
        = $false )
      | ( ( ~ ( SV211 @ SV562 ) )
        = $true )
      | ( ( ! [SY2314: $i] :
              ( ~ ( SV211 @ SY2314 )
              | ! [SY2315: $i] :
                  ( ~ ( SV211 @ SY2315 )
                  | ( SY2314 = SY2315 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1985]) ).

thf(2191,plain,
    ! [SV212: $i,SV426: $i,SV563: $i > $i] :
      ( ( ( ~ ( in @ ( sK77_Xx @ SV563 @ SV426 @ SV212 ) @ SV212 ) )
        = $false )
      | ( ( func @ SV212 @ SV426
          @ ( lam @ SV212 @ SV426
            @ ^ [SY2828: $i] : ( SV563 @ SY2828 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1986]) ).

thf(2192,plain,
    ! [SV212: $i,SV426: $i,SV563: $i > $i] :
      ( ( ( ~ ~ ( in @ ( SV563 @ ( sK77_Xx @ SV563 @ SV426 @ SV212 ) ) @ SV426 ) )
        = $false )
      | ( ( func @ SV212 @ SV426
          @ ( lam @ SV212 @ SV426
            @ ^ [SY2828: $i] : ( SV563 @ SY2828 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[1986]) ).

thf(2193,plain,
    ! [SV213: $i > $o,SV427: $i > $o] :
      ( ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( ! [SY2670: $i] :
              ( ~ ( ~ ( SV213 @ ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2670
                       != ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV213 @ SY2670 ) )
          | ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1987]) ).

thf(2194,plain,
    ! [SV427: $i > $o,SV213: $i > $o] :
      ( ( ( ~ ( ~ ( ~ ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
                  | ~ ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) ) )
              | ~ ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
                  | ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) ) ) ) )
        = $true )
      | ( ( ! [SY2670: $i] :
              ( ~ ( ~ ( SV213 @ ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2670
                       != ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV213 @ SY2670 ) )
          | ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1988]) ).

thf(2195,plain,
    ! [SV428: $i,SV214: $i,SV654: $i] :
      ( ( ( ~ ( in @ SV654 @ ( powerset @ SV214 ) ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK98_Xx @ SV654 @ SV428 @ SV214 ) @ SV214 )
              | ~ ~ ( ~ ( in @ ( sK98_Xx @ SV654 @ SV428 @ SV214 ) @ SV428 )
                    | ~ ~ ( in @ ( sK98_Xx @ SV654 @ SV428 @ SV214 ) @ SV654 ) ) )
          | ( in @ SV428 @ ( powerset @ SV654 ) ) )
        = $true )
      | ( ( in @ SV428 @ ( powerset @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1989]) ).

thf(2196,plain,
    ! [SV215: $i,SV655: $o,SV429: $i] :
      ( ( ( ~ ( ~ ( in @ SV429 @ ( sK31_B @ SV655 @ SV429 @ SV215 ) )
              | ~ ~ ( ~ ( in @ ( sK31_B @ SV655 @ SV429 @ SV215 ) @ SV215 )
                    | ~ ~ SV655 ) ) )
        = $true )
      | ( SV655 = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1990]) ).

thf(2197,plain,
    ! [SV215: $i,SV429: $i] :
      ( ( ( ~ ( ~ ( in @ SV429 @ ( sK31_B @ $true @ SV429 @ SV215 ) )
              | ~ ~ ( ~ ( in @ ( sK31_B @ $true @ SV429 @ SV215 ) @ SV215 )
                    | ~ ~ $true ) ) )
        = $true )
      | ( $true = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1991]) ).

thf(2198,plain,
    ! [SV215: $i,SV429: $i] :
      ( ( ( ~ ( ~ ( in @ SV429 @ ( sK31_B @ $false @ SV429 @ SV215 ) )
              | ~ ~ ( ~ ( in @ ( sK31_B @ $false @ SV429 @ SV215 ) @ SV215 )
                    | ~ ~ $false ) ) )
        = $true )
      | ( $false = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1992]) ).

thf(2199,plain,
    ! [SV216: $i,SV430: $i] :
      ( ( ( in @ ( sK26_Xx @ SV430 @ SV216 ) @ SV216 )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV430 )
              | ~ ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV216 ) )
          | ( SV216 = SV430 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1993]) ).

thf(2200,plain,
    ! [SV216: $i,SV430: $i] :
      ( ( ( ~ ( in @ ( sK26_Xx @ SV430 @ SV216 ) @ SV430 ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV430 )
              | ~ ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV216 ) )
          | ( SV216 = SV430 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[1994]) ).

thf(2201,plain,
    ! [SV217: $i,SV431: $i] :
      ( ( ( ~ ( in @ ( sK69_X @ SV431 @ SV217 ) @ SV217 ) )
        = $false )
      | ( ( in @ SV431 @ ( setunion @ SV217 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1995]) ).

thf(2202,plain,
    ! [SV217: $i,SV431: $i] :
      ( ( ( ~ ( in @ SV431 @ ( sK69_X @ SV431 @ SV217 ) ) )
        = $false )
      | ( ( in @ SV431 @ ( setunion @ SV217 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[1995]) ).

thf(2203,plain,
    ! [SV564: $i,SV704: $i,SV432: $i,SV218: $i] :
      ( ( ( ~ ( func @ SV218 @ SV432 @ SV704 )
          | ~ ( ~ ( in @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) @ SV218 )
              | ~ ( ( ( ap @ SV218 @ SV432 @ SV564 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) )
                   != ( ap @ SV218 @ SV432 @ SV704 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) ) ) ) )
          | ! [SY2948: $i] :
              ( ~ ( in @ SY2948 @ SV218 )
              | ! [SY2949: $i] :
                  ( ~ ( in @ SY2949 @ SV432 )
                  | ~ ( in @ ( kpair @ SY2948 @ SY2949 ) @ SV704 )
                  | ( in @ ( kpair @ SY2948 @ SY2949 ) @ SV564 ) ) ) )
        = $true )
      | ( ( func @ SV218 @ SV432 @ SV564 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[1996]) ).

thf(2204,plain,
    ! [SV433: $i,SV219: $i,SV656: $i] :
      ( ( ( ~ ( in @ SV656 @ ( powerset @ SV219 ) ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
              | ~ ~ ( ~ ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 )
                    | ~ ~ ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 ) ) )
          | ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
              | ~ ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
                    | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) ) )
          | ( SV433 = SV656 ) )
        = $true )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1997]) ).

thf(2205,plain,
    ! [SV220: $i,SV565: $i,SV434: $i > $o] :
      ( ( ( ~ ( SV434 @ SV565 ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK73_Xy @ SV565 @ SV434 @ SV220 ) @ SV220 )
              | ~ ~ ( ~ ( SV434 @ ( sK73_Xy @ SV565 @ SV434 @ SV220 ) )
                    | ~ ( ( ( sK73_Xy @ SV565 @ SV434 @ SV220 )
                         != SV565 ) ) ) )
          | ( singleton
            @ ( dsetconstr @ SV220
              @ ^ [SY2682: $i] : ( SV434 @ SY2682 ) ) ) )
        = $true )
      | ( ( in @ SV565 @ SV220 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1998]) ).

thf(2206,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ ~ ( ~ ( ( in @ SV566 @ SV221 )
                    | ~ ( in @ SV566 @ SV221 )
                    | ! [SX3: $o] : SX3 )
                | ~ ~ ( ~ ( ( in @ SV566 @ SV221 )
                          | ( in @ SV566 @ SV435 )
                          | ! [SX3: $o] : SX3 )
                      | ~ ( ( in @ SV566 @ SV221 )
                          | ! [SX3: $o] :
                              ( ~ SX3
                              | SX3 ) ) ) )
          | ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SV566 @ SV435 )
                          | ~ ( in @ SV566 @ SV221 )
                          | ! [SX3: $o] : SX3 )
                      | ~ ~ ( ~ ( ~ ( in @ SV566 @ SV435 )
                                | ( in @ SV566 @ SV435 )
                                | ! [SX3: $o] : SX3 )
                            | ~ ( ~ ( in @ SV566 @ SV435 )
                                | ! [SX3: $o] :
                                    ( ~ SX3
                                    | SX3 ) ) ) )
                | ~ ~ ( ~ ! [SY2839: $o] :
                            ( ~ SY2839
                            | ~ ( in @ SV566 @ SV221 )
                            | SY2839 )
                      | ~ ~ ( ~ ! [SY2840: $o] :
                                  ( ~ SY2840
                                  | ( in @ SV566 @ SV435 )
                                  | SY2840 )
                            | ~ ! [SX3: $o] :
                                  ( ~ SX3
                                  | ~ SX3
                                  | SX3 ) ) ) ) )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1999]) ).

thf(2207,plain,
    ! [SV222: $i,SV436: $i,SV567: $i > $i] :
      ( ( ( ~ ( in @ ( sK76_Xx @ SV567 @ SV436 @ SV222 ) @ SV222 ) )
        = $false )
      | ( ( func @ SV222 @ SV436
          @ ( dpsetconstr @ SV222 @ SV436
            @ ^ [SY2842: $i,SY2843: $i] :
                ( ( SV567 @ SY2842 )
                = SY2843 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2000]) ).

thf(2208,plain,
    ! [SV222: $i,SV436: $i,SV567: $i > $i] :
      ( ( ( ~ ~ ( in @ ( SV567 @ ( sK76_Xx @ SV567 @ SV436 @ SV222 ) ) @ SV436 ) )
        = $false )
      | ( ( func @ SV222 @ SV436
          @ ( dpsetconstr @ SV222 @ SV436
            @ ^ [SY2842: $i,SY2843: $i] :
                ( ( SV567 @ SY2842 )
                = SY2843 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2000]) ).

thf(2209,plain,
    ! [SV657: $i,SV223: $i,SV705: $i] :
      ( ( ~ ( in @ SV705 @ ( setadjoin @ SV223 @ SV657 ) )
        | ( SV705 = SV223 )
        | ( in @ SV705 @ SV657 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2001]) ).

thf(2210,plain,
    ! [SV223: $i] :
      ( ( ~ ! [SY2357: $i,SY2358: $i] :
              ( ( SY2358 != SV223 )
              | ( in @ SY2358 @ ( setadjoin @ SV223 @ SY2357 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2002]) ).

thf(2211,plain,
    ! [SV223: $i] :
      ( ( ~ ! [SY2359: $i,SY2360: $i] :
              ( ~ ( in @ SY2360 @ SY2359 )
              | ( in @ SY2360 @ ( setadjoin @ SV223 @ SY2359 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2002]) ).

thf(2212,plain,
    ! [SV224: $i,SV437: $i] :
      ( ( ( in @ ( sK65_Xx @ SV437 @ SV224 ) @ SV224 )
        = $true )
      | ( ( subset @ SV224 @ SV437 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2003]) ).

thf(2213,plain,
    ! [SV224: $i,SV437: $i] :
      ( ( ( ~ ( in @ ( sK65_Xx @ SV437 @ SV224 ) @ SV437 ) )
        = $true )
      | ( ( subset @ SV224 @ SV437 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2004]) ).

thf(2214,plain,
    ! [SV225: $i,SV438: $i] :
      ( ( ( ~ ( in @ ( sK6_Xx @ SV438 @ SV225 ) @ SV225 )
          | ~ ( in @ ( sK6_Xx @ SV438 @ SV225 ) @ SV438 ) )
        = $true )
      | ( ( SV225 = SV438 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2005]) ).

thf(2215,plain,
    ! [SV225: $i,SV438: $i] :
      ( ( ( ( in @ ( sK6_Xx @ SV438 @ SV225 ) @ SV225 )
          | ( in @ ( sK6_Xx @ SV438 @ SV225 ) @ SV438 ) )
        = $true )
      | ( ( SV225 = SV438 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2006]) ).

thf(2216,plain,
    ! [SV439: $i,SV226: $i] :
      ( ( ~ ! [SY2696: $i] :
              ( ~ ( in @ SY2696 @ ( binunion @ SV226 @ SV439 ) )
              | ( in @ SY2696 @ SV226 )
              | ( in @ SY2696 @ SV439 )
              | ! [SX3: $o] : SX3 )
        | ~ ! [SY2698: $i] :
              ( ~ ( in @ SY2698 @ ( binunion @ SV226 @ SV439 ) )
              | ( in @ SY2698 @ SV226 )
              | ! [SX3: $o] :
                  ( ~ SX3
                  | SX3 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[2007]) ).

thf(2217,plain,
    ! [SV439: $i,SV226: $i] :
      ( ( ~ ! [SY2700: $i] :
              ( ~ ( in @ SY2700 @ ( binunion @ SV226 @ SV439 ) )
              | ! [SY2701: $o] :
                  ( ~ SY2701
                  | ( in @ SY2700 @ SV439 )
                  | SY2701 ) )
        | ~ ( ! [SY2702: $i] :
                ~ ( in @ SY2702 @ ( binunion @ SV226 @ SV439 ) )
            | ! [SX2: $o] :
                ( ~ SX2
                | ~ SX2
                | SX2 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[2008]) ).

thf(2218,plain,
    ! [SV440: $i > $o,SV227: $i,SV607: $i] :
      ( ( ( in @ SV607 @ SV227 )
        = $false )
      | ( ( SV440 @ SV607 )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK38_Xx @ SV440 @ SV227 ) @ SV227 )
              | ~ ~ ( SV440 @ ( sK38_Xx @ SV440 @ SV227 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2009]) ).

thf(2219,plain,
    ! [SV228: $i > $o,SV568: $i] :
      ( ( ( ( ( sK47_Xy @ SV568 @ SV228 )
           != SV568 )
          | ~ ( SV228 @ ( sK47_Xy @ SV568 @ SV228 ) ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2375: $i] :
                    ( ~ ( SV228 @ SY2375 )
                    | ( ( sK46_SY211 @ SV228 )
                      = SY2375 ) )
              | ~ ( SV228 @ ( sK46_SY211 @ SV228 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2010]) ).

thf(2220,plain,
    ! [SV228: $i > $o,SV568: $i] :
      ( ( ( ( ( sK47_Xy @ SV568 @ SV228 )
            = SV568 )
          | ( SV228 @ ( sK47_Xy @ SV568 @ SV228 ) ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2375: $i] :
                    ( ~ ( SV228 @ SY2375 )
                    | ( ( sK46_SY211 @ SV228 )
                      = SY2375 ) )
              | ~ ( SV228 @ ( sK46_SY211 @ SV228 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2011]) ).

thf(2221,plain,
    ! [SV229: $i,SV441: $i > $o] :
      ( ( ( in @ ( sK74_Xx @ SV441 @ SV229 ) @ SV229 )
        = $true )
      | ( ( ! [SY2705: $i] :
              ( ~ ( SV441 @ SY2705 )
              | ~ ( in @ SY2705 @ SV229 ) )
          | ( singleton
            @ ( dsetconstr @ SV229
              @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2012]) ).

thf(2222,plain,
    ! [SV229: $i,SV441: $i > $o] :
      ( ( ( ~ ( ~ ( in @ ( sK75_SY1878 @ SV441 @ SV229 ) @ SV229 )
              | ~ ~ ( ~ ( SV441 @ ( sK74_Xx @ SV441 @ SV229 ) )
                    | ~ ~ ( ~ ( SV441 @ ( sK75_SY1878 @ SV441 @ SV229 ) )
                          | ~ ( ( ( sK74_Xx @ SV441 @ SV229 )
                               != ( sK75_SY1878 @ SV441 @ SV229 ) ) ) ) ) ) )
        = $true )
      | ( ( ! [SY2705: $i] :
              ( ~ ( SV441 @ SY2705 )
              | ~ ( in @ SY2705 @ SV229 ) )
          | ( singleton
            @ ( dsetconstr @ SV229
              @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2013]) ).

thf(2223,plain,
    ! [SV569: $i,SV442: $i,SV230: $i,SV706: $i] :
      ( ( ( ~ ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
          | ~ ( ~ ( in @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
              | ~ ~ ( ~ ( in @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
                          | ~ ~ ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 ) ) ) )
          | ~ ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
              | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                          | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
          | ( SV569 = SV706 ) )
        = $true )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2014]) ).

thf(2224,plain,
    ! [SV231: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK9_Xx @ SV231 ) @ omega )
              | ~ ( in @ ( sK9_Xx @ SV231 ) @ SV231 ) ) )
        = $true )
      | ( ( ~ ( in @ emptyset @ SV231 ) )
        = $true )
      | ( ( ! [SY2382: $i] :
              ( ~ ( in @ SY2382 @ omega )
              | ( in @ SY2382 @ SV231 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2015]) ).

thf(2225,plain,
    ! [SV231: $i] :
      ( ( ( ~ ( in @ ( setadjoin @ ( sK9_Xx @ SV231 ) @ ( sK9_Xx @ SV231 ) ) @ SV231 ) )
        = $true )
      | ( ( ~ ( in @ emptyset @ SV231 ) )
        = $true )
      | ( ( ! [SY2382: $i] :
              ( ~ ( in @ SY2382 @ omega )
              | ( in @ SY2382 @ SV231 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2016]) ).

thf(2226,plain,
    ! [SV570: $i,SV443: $o,SV232: $i,SV707: $i] :
      ( ( ( ~ ( in @ SV707 @ SV232 )
          | SV443
          | ( in @ SV707
            @ ( dsetconstr @ SV232
              @ ^ [SY2950: $i] :
                  ( ~ ( ~ SV443
                      | ( SY2950 != SV570 ) )
                  | ~ ( ~ ~ SV443
                      | ( SY2950 != SV707 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV570 @ SV232 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2017]) ).

thf(2227,plain,
    ! [SV571: $i,SV232: $i,SV708: $i] :
      ( ( ( ~ ( in @ SV708 @ SV232 )
          | $true
          | ( in @ SV708
            @ ( dsetconstr @ SV232
              @ ^ [SY2951: $i] :
                  ( ~ ( ~ $true
                      | ( SY2951 != SV571 ) )
                  | ~ ( ~ ~ $true
                      | ( SY2951 != SV708 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV571 @ SV232 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2018]) ).

thf(2228,plain,
    ! [SV572: $i,SV232: $i,SV709: $i] :
      ( ( ( ~ ( in @ SV709 @ SV232 )
          | $false
          | ( in @ SV709
            @ ( dsetconstr @ SV232
              @ ^ [SY2952: $i] :
                  ( ~ ( ~ $false
                      | ( SY2952 != SV572 ) )
                  | ~ ( ~ ~ $false
                      | ( SY2952 != SV709 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV572 @ SV232 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2019]) ).

thf(2229,plain,
    ! [SV233: $i,SV658: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
              | ~ ~ ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 ) )
          | ! [SY2924: $i] :
              ~ ( in @ SY2924 @ SV658 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2925: $i] :
                    ( ~ ( in @ SY2925 @ ( sK15_B @ SV233 ) )
                    | ! [SY2926: $i] :
                        ( ~ ( in @ SY2926 @ SY2925 )
                        | ( in @ SY2926 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) )
                    | ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SY2925 ) )
              | ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) )
                          | ~ ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 ) )
                    | ~ ! [SY2927: $i] :
                          ( ~ ( in @ SY2927 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
                          | ~ ( in @ SY2927 @ SV658 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2020]) ).

thf(2230,plain,
    ! [SV233: $i] :
      ( ( ~ ! [SY2392: $i,SY2393: $i] :
              ( ~ ( in @ SY2392 @ ( sK15_B @ SV233 ) )
              | ~ ( in @ SY2393 @ ( sK15_B @ SV233 ) )
              | ! [SX3: $i] :
                  ( ~ ( in @ SX3 @ SY2392 )
                  | ( in @ SX3 @ SY2393 ) )
              | ! [SX3: $i] :
                  ( ~ ( in @ SX3 @ SY2393 )
                  | ( in @ SX3 @ SY2392 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2021]) ).

thf(2231,plain,
    ! [SV233: $i] :
      ( ( ~ ~ ( ~ ! [SY2396: $i] :
                    ( ~ ( in @ SY2396 @ ( sK15_B @ SV233 ) )
                    | ! [SY2397: $i] :
                        ( ~ ( in @ SY2397 @ SY2396 )
                        | ( in @ SY2397 @ SV233 ) ) )
              | ~ ! [SY2398: $i,SY2399: $i] :
                    ( ~ ( in @ SY2398 @ SV233 )
                    | ~ ( in @ SY2399 @ SV233 )
                    | ~ ( ~ ( in @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) @ ( sK15_B @ SV233 ) )
                        | ~ ~ ( ~ ( ~ ( in @ SY2398 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) )
                                  | ~ ( in @ SY2399 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) ) )
                              | ~ ( ( in @ SY2398 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) )
                                  | ( in @ SY2399 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) ) ) ) )
                    | ( SY2398 = SY2399 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2021]) ).

thf(2232,plain,
    ! [SV234: $i,SV444: $i > $o] :
      ( ( ( SV444 @ ( sK37_Xx @ SV444 @ SV234 ) )
        = $true )
      | ( ( ! [SY2712: $i] :
              ( ~ ( in @ SY2712 @ SV234 )
              | ~ ( SV444 @ SY2712 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2022]) ).

thf(2233,plain,
    ! [SV234: $i,SV444: $i > $o] :
      ( ( ( in @ ( sK37_Xx @ SV444 @ SV234 ) @ SV234 )
        = $true )
      | ( ( ! [SY2712: $i] :
              ( ~ ( in @ SY2712 @ SV234 )
              | ~ ( SV444 @ SY2712 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2023]) ).

thf(2234,plain,
    ! [SV573: $i,SV235: $i > $o] :
      ( ( ( ~ ( SV235 @ ( sK33_SY142 @ SV573 @ SV235 ) ) )
        = $false )
      | ( ( ~ ( SV235 @ SV573 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2403: $i] :
                    ( ( SY2403
                     != ( sK32_Xx @ SV235 ) )
                    | ( SV235 @ SY2403 ) )
              | ~ ! [SY2404: $i] :
                    ( ~ ( SV235 @ SY2404 )
                    | ( SY2404
                      = ( sK32_Xx @ SV235 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2024]) ).

thf(2235,plain,
    ! [SV235: $i > $o,SV573: $i] :
      ( ( ( ~ ( ( SV573
               != ( sK33_SY142 @ SV573 @ SV235 ) ) ) )
        = $false )
      | ( ( ~ ( SV235 @ SV573 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2403: $i] :
                    ( ( SY2403
                     != ( sK32_Xx @ SV235 ) )
                    | ( SV235 @ SY2403 ) )
              | ~ ! [SY2404: $i] :
                    ( ~ ( SV235 @ SY2404 )
                    | ( SY2404
                      = ( sK32_Xx @ SV235 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2024]) ).

thf(2236,plain,
    ! [SV236: $i,SV445: $i,SV574: $i,SV710: $i > $o] :
      ( ( ( ~ ( ~ ( in @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ SV236 )
              | ~ ~ ( ~ ( in @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) @ SV445 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) ) @ SV574 )
                          | ~ ~ ( SV710 @ ( kpair @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) ) ) ) ) )
          | ! [SY2953: $i] :
              ( ~ ( in @ SY2953 @ SV574 )
              | ( SV710 @ SY2953 ) ) )
        = $true )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2025]) ).

thf(2237,plain,
    ! [SV446: $i > $o,SV237: $i,SV608: $i] :
      ( ( ( in @ SV608 @ SV237 )
        = $false )
      | ( ( SV446 @ SV608 )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK35_Xx @ SV446 @ SV237 ) @ SV237 )
              | ~ ~ ( SV446 @ ( sK35_Xx @ SV446 @ SV237 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2026]) ).

thf(2238,plain,
    ! [SV575: $i,SV447: $o,SV238: $i,SV711: $i] :
      ( ( ( ~ ( in @ SV711 @ SV238 )
          | ~ SV447
          | ( ( dsetconstr @ SV238
              @ ^ [SY2954: $i] :
                  ( ~ ( ~ SV447
                      | ( SY2954 != SV575 ) )
                  | ~ ( ~ ~ SV447
                      | ( SY2954 != SV711 ) ) ) )
            = ( setadjoin @ SV575 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV575 @ SV238 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2027]) ).

thf(2239,plain,
    ! [SV576: $i,SV238: $i,SV712: $i] :
      ( ( ( ~ ( in @ SV712 @ SV238 )
          | ~ $true
          | ( ( dsetconstr @ SV238
              @ ^ [SY2955: $i] :
                  ( ~ ( ~ $true
                      | ( SY2955 != SV576 ) )
                  | ~ ( ~ ~ $true
                      | ( SY2955 != SV712 ) ) ) )
            = ( setadjoin @ SV576 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV576 @ SV238 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2028]) ).

thf(2240,plain,
    ! [SV577: $i,SV238: $i,SV713: $i] :
      ( ( ( ~ ( in @ SV713 @ SV238 )
          | ~ $false
          | ( ( dsetconstr @ SV238
              @ ^ [SY2956: $i] :
                  ( ~ ( ~ $false
                      | ( SY2956 != SV577 ) )
                  | ~ ( ~ ~ $false
                      | ( SY2956 != SV713 ) ) ) )
            = ( setadjoin @ SV577 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV577 @ SV238 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2029]) ).

thf(2241,plain,
    ! [SV578: $i,SV239: $i] :
      ( ( ( ~ ( in @ ( sK14_B @ SV239 ) @ SV239 ) )
        = $false )
      | ( ( in @ SV578 @ SV239 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2030]) ).

thf(2242,plain,
    ! [SV578: $i,SV239: $i] :
      ( ( ( ~ ! [SY2416: $i] :
                ( ~ ( in @ SY2416 @ ( sK14_B @ SV239 ) )
                | ~ ( in @ SY2416 @ SV239 ) ) )
        = $false )
      | ( ( in @ SV578 @ SV239 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2030]) ).

thf(2243,plain,
    ! [SV579: $i,SV448: $o,SV240: $i,SV714: $i] :
      ( ( ( ~ ( in @ SV714 @ SV240 )
          | ( singleton
            @ ( dsetconstr @ SV240
              @ ^ [SY2957: $i] :
                  ( ~ ( ~ SV448
                      | ( SY2957 != SV579 ) )
                  | ~ ( ~ ~ SV448
                      | ( SY2957 != SV714 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV579 @ SV240 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2031]) ).

thf(2244,plain,
    ! [SV580: $i,SV240: $i,SV715: $i] :
      ( ( ( ~ ( in @ SV715 @ SV240 )
          | ( singleton
            @ ( dsetconstr @ SV240
              @ ^ [SY2958: $i] :
                  ( ~ ( ~ $true
                      | ( SY2958 != SV580 ) )
                  | ~ ( ~ ~ $true
                      | ( SY2958 != SV715 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV580 @ SV240 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2032]) ).

thf(2245,plain,
    ! [SV581: $i,SV240: $i,SV716: $i] :
      ( ( ( ~ ( in @ SV716 @ SV240 )
          | ( singleton
            @ ( dsetconstr @ SV240
              @ ^ [SY2959: $i] :
                  ( ~ ( ~ $false
                      | ( SY2959 != SV581 ) )
                  | ~ ( ~ ~ $false
                      | ( SY2959 != SV716 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV581 @ SV240 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2033]) ).

thf(2246,plain,
    ! [SV582: $i,SV241: $i > $o] :
      ( ( ( ~ ( SV241 @ ( sK44_Xx @ SV241 ) )
          | ~ ~ ( ~ ( SV241 @ ( sK45_SY1868 @ SV241 ) )
                | ~ ( ( ( sK44_Xx @ SV241 )
                     != ( sK45_SY1868 @ SV241 ) ) ) ) )
        = $false )
      | ( ( ~ ( ~ ! [SY2422: $i] :
                    ( ~ ( SV241 @ SY2422 )
                    | ( ( sK43_SY205 @ SV241 )
                      = SY2422 ) )
              | ~ ( SV241 @ ( sK43_SY205 @ SV241 ) ) ) )
        = $true )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2034]) ).

thf(2247,plain,
    ! [SV242: $i,SV449: $i] :
      ( ( ( in @ ( sK64_Xx @ SV449 @ SV242 ) @ SV242 )
        = $true )
      | ( ( subset @ SV242 @ SV449 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2035]) ).

thf(2248,plain,
    ! [SV242: $i,SV449: $i] :
      ( ( ( ~ ( in @ ( sK64_Xx @ SV449 @ SV242 ) @ SV449 ) )
        = $true )
      | ( ( subset @ SV242 @ SV449 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2036]) ).

thf(2249,plain,
    ! [SV609: $i,SV659: $i] :
      ( ( ( ! [SY2928: $i] :
              ( ~ ( in @ SV659 @ SY2928 )
              | ~ ( in @ SY2928 @ SV609 ) ) )
        = $true )
      | ( ( in @ SV659 @ ( setunion @ SV609 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2037]) ).

thf(2250,plain,
    ! [SV610: $i,SV660: $i] :
      ( ( ( ~ ( in @ SV660 @ ( setunion @ SV610 ) ) )
        = $true )
      | ( ( ~ ( ~ ( in @ SV660 @ ( sK8_B @ SV660 @ SV610 ) )
              | ~ ( in @ ( sK8_B @ SV660 @ SV610 ) @ SV610 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2038]) ).

thf(2251,plain,
    ! [SV583: $i,SV717: $i,SV450: $i,SV243: $i] :
      ( ( ( ~ ( func @ SV243 @ SV450 @ SV717 )
          | ~ ( ~ ( in @ ( sK90_Xx @ SV717 @ SV583 @ SV450 @ SV243 ) @ SV243 )
              | ~ ( ( ( ap @ SV243 @ SV450 @ SV583 @ ( sK90_Xx @ SV717 @ SV583 @ SV450 @ SV243 ) )
                   != ( ap @ SV243 @ SV450 @ SV717 @ ( sK90_Xx @ SV717 @ SV583 @ SV450 @ SV243 ) ) ) ) )
          | ( SV583 = SV717 ) )
        = $true )
      | ( ( func @ SV243 @ SV450 @ SV583 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2039]) ).

thf(2252,plain,
    ! [SV244: $i,SV584: $i,SV611: $i > $i] :
      ( ( ( ~ ( in @ ( sK93_Xx @ SV611 @ SV584 @ SV244 ) @ SV244 ) )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2040]) ).

thf(2253,plain,
    ! [SV244: $i,SV584: $i,SV611: $i > $i] :
      ( ( ( ~ ~ ( in @ ( SV611 @ ( sK93_Xx @ SV611 @ SV584 @ SV244 ) ) @ SV584 ) )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2040]) ).

thf(2254,plain,
    ! [SV585: $i,SV451: $i,SV245: $i,SV718: $i] :
      ( ( ( ~ ( in @ SV718 @ ( funcSet @ SV245 @ SV451 ) )
          | ~ ( ~ ( in @ ( sK91_Xx @ SV718 @ SV585 @ SV451 @ SV245 ) @ SV245 )
              | ~ ( ( ( ap @ SV245 @ SV451 @ SV585 @ ( sK91_Xx @ SV718 @ SV585 @ SV451 @ SV245 ) )
                   != ( ap @ SV245 @ SV451 @ SV718 @ ( sK91_Xx @ SV718 @ SV585 @ SV451 @ SV245 ) ) ) ) )
          | ( SV585 = SV718 ) )
        = $true )
      | ( ( in @ SV585 @ ( funcSet @ SV245 @ SV451 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2041]) ).

thf(2255,plain,
    ! [SV246: $i,SV452: $i > $o] :
      ( ( ( in @ ( sK36_Xx @ SV452 @ SV246 ) @ SV246 )
        = $true )
      | ( ( ! [SY2727: $i] :
              ( ~ ( SV452 @ SY2727 )
              | ~ ( in @ SY2727 @ SV246 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2042]) ).

thf(2256,plain,
    ! [SV246: $i,SV452: $i > $o] :
      ( ( ( SV452 @ ( sK36_Xx @ SV452 @ SV246 ) )
        = $true )
      | ( ( ! [SY2727: $i] :
              ( ~ ( SV452 @ SY2727 )
              | ~ ( in @ SY2727 @ SV246 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2043]) ).

thf(2257,plain,
    ! [SV586: $i,SV247: $i > $o] :
      ( ( ( ~ ( SV247 @ ( sK22_SY74 @ SV586 @ SV247 ) ) )
        = $false )
      | ( ( ~ ( SV247 @ SV586 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2435: $i] :
                    ( ~ ( SV247 @ SY2435 )
                    | ( ( sK21_Xx @ SV247 )
                      = SY2435 ) )
              | ~ ( SV247 @ ( sK21_Xx @ SV247 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2044]) ).

thf(2258,plain,
    ! [SV247: $i > $o,SV586: $i] :
      ( ( ( ~ ( ( SV586
               != ( sK22_SY74 @ SV586 @ SV247 ) ) ) )
        = $false )
      | ( ( ~ ( SV247 @ SV586 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2435: $i] :
                    ( ~ ( SV247 @ SY2435 )
                    | ( ( sK21_Xx @ SV247 )
                      = SY2435 ) )
              | ~ ( SV247 @ ( sK21_Xx @ SV247 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2044]) ).

thf(2259,plain,
    ! [SV248: $i,SV453: $i,SV661: $i > $o,SV719: $i > $o] :
      ( ( ( ~ ( ~ ( in @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) @ SV248 )
              | ~ ~ ( ~ ( in @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) @ SV453 )
                    | ~ ~ ( ( ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 )
                           != ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) )
                          | ~ ~ ( ~ ( ~ ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
                                    | ~ ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) )
                                | ~ ( ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
                                    | ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) ) ) ) ) )
          | ( ( dsetconstr @ SV248
              @ ^ [SY2930: $i] : ( SV661 @ SY2930 ) )
            = ( dsetconstr @ SV453
              @ ^ [SY2961: $i] : ( SV719 @ SY2961 ) ) ) )
        = $true )
      | ( ( SV248 = SV453 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2045]) ).

thf(2260,plain,
    ! [SV249: $i,SV454: $i > $o] :
      ( ( ( ~ ( SV454 @ ( sK72_Xx @ SV454 @ SV249 ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV249
            @ ^ [SY2732: $i] : ( SV454 @ SY2732 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2046]) ).

thf(2261,plain,
    ! [SV249: $i,SV454: $i > $o] :
      ( ( ( ~ ( in @ ( sK72_Xx @ SV454 @ SV249 ) @ SV249 ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV249
            @ ^ [SY2732: $i] : ( SV454 @ SY2732 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2046]) ).

thf(2262,plain,
    ! [SV250: $i,SV1: $i,SV612: $i] :
      ( ( ( in @ SV612 @ ( powerset @ SV1 ) )
        = $false )
      | ( ( ! [SY2895: $i] :
              ( ~ ( in @ SY2895 @ ( powerset @ SV1 ) )
              | ! [SY2896: $i] :
                  ( ~ ( in @ SY2896 @ SV1 )
                  | ~ ( in @ SY2896 @ ( binintersect @ SV250 @ SV612 ) )
                  | ( in @ SY2896 @ ( binunion @ SV250 @ SY2895 ) ) ) ) )
        = $true )
      | ( ( in @ SV250 @ ( powerset @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2047]) ).

thf(2263,plain,
    ! [SV251: $i,SV2: $i,SV613: $i] :
      ( ( ( in @ SV613 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( ! [SY2897: $i] :
              ( ~ ( in @ SY2897 @ SV2 )
              | ( in @ SY2897 @ ( binunion @ SV251 @ SV613 ) )
              | ~ ( in @ SY2897 @ SV613 ) ) )
        = $true )
      | ( ( in @ SV251 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2048]) ).

thf(2264,plain,
    ! [SV252: $i,SV3: $i,SV614: $i] :
      ( ( ( in @ SV614 @ ( powerset @ SV3 ) )
        = $false )
      | ( ( ! [SY2898: $i] :
              ( ~ ( in @ SY2898 @ SV3 )
              | ( in @ SY2898 @ ( binunion @ SV252 @ SV614 ) )
              | ~ ( in @ SY2898 @ SV252 ) ) )
        = $true )
      | ( ( in @ SV252 @ ( powerset @ SV3 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2049]) ).

thf(2265,plain,
    ! [SV253: $i,SV4: $i,SV615: $i] :
      ( ( ( in @ SV615 @ ( powerset @ SV4 ) )
        = $false )
      | ( ( ~ ( subset @ SV253 @ ( setminus @ SV4 @ SV615 ) )
          | ( subset @ SV615 @ ( setminus @ SV4 @ SV253 ) ) )
        = $true )
      | ( ( in @ SV253 @ ( powerset @ SV4 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2050]) ).

thf(2266,plain,
    ! [SV254: $i,SV5: $i,SV616: $i] :
      ( ( ( in @ SV616 @ ( powerset @ SV5 ) )
        = $false )
      | ( ( ~ ( subset @ SV254 @ ( setminus @ SV5 @ SV616 ) )
          | ! [SY2899: $i] :
              ( ~ ( in @ SY2899 @ SV5 )
              | ~ ( in @ SY2899 @ SV616 )
              | ( in @ SY2899 @ ( setminus @ SV5 @ SV254 ) ) ) )
        = $true )
      | ( ( in @ SV254 @ ( powerset @ SV5 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2051]) ).

thf(2267,plain,
    ! [SV255: $i,SV6: $i,SV617: $i] :
      ( ( ( in @ SV617 @ ( powerset @ SV6 ) )
        = $false )
      | ( ( in @ ( setminus @ SV6 @ SV255 ) @ ( powerset @ ( setminus @ SV6 @ ( binintersect @ SV255 @ SV617 ) ) ) )
        = $true )
      | ( ( in @ SV255 @ ( powerset @ SV6 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2052]) ).

thf(2268,plain,
    ! [SV256: $i,SV7: $i,SV618: $i] :
      ( ( ( in @ SV618 @ ( powerset @ SV7 ) )
        = $false )
      | ( ( subset @ ( setminus @ SV7 @ SV256 ) @ ( setminus @ SV7 @ ( binintersect @ SV256 @ SV618 ) ) )
        = $true )
      | ( ( in @ SV256 @ ( powerset @ SV7 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2053]) ).

thf(2269,plain,
    ! [SV257: $i,SV8: $i,SV619: $i] :
      ( ( ( in @ SV619 @ ( powerset @ SV8 ) )
        = $false )
      | ( ( ! [SY2900: $i] :
              ( ~ ( in @ SY2900 @ SV8 )
              | ~ ( in @ SY2900 @ ( setminus @ SV8 @ SV257 ) )
              | ( in @ SY2900 @ ( setminus @ SV8 @ ( binintersect @ SV257 @ SV619 ) ) ) ) )
        = $true )
      | ( ( in @ SV257 @ ( powerset @ SV8 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2054]) ).

thf(2270,plain,
    ! [SV258: $i,SV9: $i,SV620: $i] :
      ( ( ( in @ SV620 @ ( powerset @ SV9 ) )
        = $false )
      | ( ( ! [SY2901: $i] :
              ( ~ ( in @ SY2901 @ SV9 )
              | ~ ( in @ SY2901 @ ( setminus @ SV9 @ SV258 ) )
              | ~ ( in @ SY2901 @ ( binintersect @ SV258 @ SV620 ) ) ) )
        = $true )
      | ( ( in @ SV258 @ ( powerset @ SV9 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2055]) ).

thf(2271,plain,
    ! [SV262: $i,SV13: $i,SV621: $i] :
      ( ( ( in @ SV621 @ SV13 )
        = $false )
      | ( ( ~ ( in @ SV621 @ ( setminus @ SV13 @ ( setminus @ SV13 @ SV262 ) ) )
          | ( in @ SV621 @ SV262 ) )
        = $true )
      | ( ( in @ SV262 @ ( powerset @ SV13 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2056]) ).

thf(2272,plain,
    ! [SV263: $i,SV14: $i,SV622: $i] :
      ( ( ( in @ SV622 @ SV14 )
        = $false )
      | ( ( ~ ( in @ SV622 @ SV263 )
          | ( in @ SV622 @ ( setminus @ SV14 @ ( setminus @ SV14 @ SV263 ) ) ) )
        = $true )
      | ( ( in @ SV263 @ ( powerset @ SV14 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2057]) ).

thf(2273,plain,
    ! [SV264: $i,SV15: $i,SV623: $i] :
      ( ( ( in @ SV623 @ ( powerset @ SV15 ) )
        = $false )
      | ( ( ~ ( subset @ ( setminus @ SV15 @ SV623 ) @ ( setminus @ SV15 @ SV264 ) )
          | ( subset @ SV264 @ SV623 ) )
        = $true )
      | ( ( in @ SV264 @ ( powerset @ SV15 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2058]) ).

thf(2274,plain,
    ! [SV265: $i,SV16: $i,SV624: $i] :
      ( ( ( in @ SV624 @ ( powerset @ SV16 ) )
        = $false )
      | ( ( ~ ( subset @ SV265 @ SV624 )
          | ( subset @ ( setminus @ SV16 @ SV624 ) @ ( setminus @ SV16 @ SV265 ) ) )
        = $true )
      | ( ( in @ SV265 @ ( powerset @ SV16 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2059]) ).

thf(2275,plain,
    ! [SV266: $i,SV17: $i,SV625: $i] :
      ( ( ( in @ SV625 @ ( powerset @ SV17 ) )
        = $false )
      | ( ( ! [SY2902: $i] :
              ( ~ ( in @ SY2902 @ SV17 )
              | ~ ( subset @ SV266 @ SV625 )
              | ( in @ SY2902 @ SV625 )
              | ~ ( in @ SY2902 @ SV266 ) ) )
        = $true )
      | ( ( in @ SV266 @ ( powerset @ SV17 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2060]) ).

thf(2276,plain,
    ! [SV267: $i,SV18: $i,SV626: $i] :
      ( ( ( in @ SV626 @ ( powerset @ SV18 ) )
        = $false )
      | ( ( ! [SY2903: $i] :
              ( ~ ( in @ SY2903 @ SV18 )
              | ~ ( subset @ SV267 @ ( setminus @ SV18 @ SV626 ) )
              | ~ ( in @ SY2903 @ SV626 )
              | ~ ( in @ SY2903 @ SV267 ) ) )
        = $true )
      | ( ( in @ SV267 @ ( powerset @ SV18 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2061]) ).

thf(2277,plain,
    ! [SV268: $i,SV19: $i,SV627: $i] :
      ( ( ( in @ SV627 @ ( powerset @ SV19 ) )
        = $false )
      | ( ( ! [SY2904: $i] :
              ( ~ ( in @ SY2904 @ SV19 )
              | ( in @ SY2904 @ SV627 )
              | ~ ( in @ SY2904 @ ( binintersect @ SV268 @ SV627 ) ) ) )
        = $true )
      | ( ( in @ SV268 @ ( powerset @ SV19 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2062]) ).

thf(2278,plain,
    ! [SV269: $i,SV20: $i,SV628: $i] :
      ( ( ( in @ SV628 @ ( powerset @ SV20 ) )
        = $false )
      | ( ( ! [SY2905: $i] :
              ( ~ ( in @ SY2905 @ SV20 )
              | ( in @ SY2905 @ SV269 )
              | ~ ( in @ SY2905 @ ( binintersect @ SV269 @ SV628 ) ) ) )
        = $true )
      | ( ( in @ SV269 @ ( powerset @ SV20 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2063]) ).

thf(2279,plain,
    ! [SV270: $i,SV21: $i,SV629: $i] :
      ( ( ( in @ SV629 @ SV21 )
        = $false )
      | ( ( ( in @ SV629 @ ( setminus @ SV21 @ SV270 ) )
          | ( in @ SV629 @ SV270 ) )
        = $true )
      | ( ( in @ SV270 @ ( powerset @ SV21 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2064]) ).

thf(2280,plain,
    ! [SV271: $i,SV22: $i,SV630: $i] :
      ( ( ( in @ SV630 @ SV22 )
        = $false )
      | ( ( ~ ( in @ SV630 @ SV271 )
          | ~ ( in @ SV630 @ ( setminus @ SV22 @ SV271 ) ) )
        = $true )
      | ( ( in @ SV271 @ ( powerset @ SV22 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2065]) ).

thf(2281,plain,
    ! [SV272: $i,SV23: $i,SV631: $i] :
      ( ( ( in @ SV631 @ ( powerset @ SV23 ) )
        = $false )
      | ( ( ! [SY2906: $i] :
              ( ~ ( in @ SY2906 @ SV23 )
              | ~ ( in @ SV272 @ ( powerset @ SV631 ) )
              | ~ ( in @ SY2906 @ SV272 )
              | ( in @ SY2906 @ SV631 ) ) )
        = $true )
      | ( ( in @ SV272 @ ( powerset @ SV23 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2066]) ).

thf(2282,plain,
    ! [SV274: $i,SV25: $i,SV632: $i] :
      ( ( ( in @ SV632 @ ( powerset @ SV25 ) )
        = $false )
      | ( ( in @ ( setminus @ SV274 @ SV632 ) @ ( powerset @ SV25 ) )
        = $true )
      | ( ( in @ SV274 @ ( powerset @ SV25 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2067]) ).

thf(2283,plain,
    ! [SV276: $i,SV27: $i,SV633: $i] :
      ( ( ( in @ SV633 @ ( powerset @ SV27 ) )
        = $false )
      | ( ( in @ ( binunion @ SV276 @ SV633 ) @ ( powerset @ SV27 ) )
        = $true )
      | ( ( in @ SV276 @ ( powerset @ SV27 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2068]) ).

thf(2284,plain,
    ! [SV277: $i,SV28: $i,SV634: $i] :
      ( ( ( in @ SV634 @ ( powerset @ SV28 ) )
        = $false )
      | ( ( in @ ( binintersect @ SV277 @ SV634 ) @ ( powerset @ SV28 ) )
        = $true )
      | ( ( in @ SV277 @ ( powerset @ SV28 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2069]) ).

thf(2285,plain,
    ! [SV455: $i,SV278: $o,SV29: $i,SV662: $i] :
      ( ( ( ~ ( in @ SV662 @ SV29 ) )
        = $true )
      | ( ( in @ ( if @ SV29 @ SV278 @ SV455 @ SV662 ) @ ( setadjoin @ SV455 @ ( setadjoin @ SV662 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV455 @ SV29 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2070]) ).

thf(2286,plain,
    ! [SV456: $i,SV29: $i,SV663: $i] :
      ( ( ( ~ ( in @ SV663 @ SV29 ) )
        = $true )
      | ( ( in @ ( if @ SV29 @ $true @ SV456 @ SV663 ) @ ( setadjoin @ SV456 @ ( setadjoin @ SV663 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV456 @ SV29 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2071]) ).

thf(2287,plain,
    ! [SV457: $i,SV29: $i,SV664: $i] :
      ( ( ( ~ ( in @ SV664 @ SV29 ) )
        = $true )
      | ( ( in @ ( if @ SV29 @ $false @ SV457 @ SV664 ) @ ( setadjoin @ SV457 @ ( setadjoin @ SV664 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV457 @ SV29 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2072]) ).

thf(2288,plain,
    ! [SV458: $i,SV279: $o,SV30: $i,SV665: $i] :
      ( ( ( ~ ( in @ SV665 @ SV30 ) )
        = $true )
      | ( ( SV279
          | ( ( if @ SV30 @ SV279 @ SV458 @ SV665 )
            = SV665 ) )
        = $true )
      | ( ( in @ SV458 @ SV30 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2073]) ).

thf(2289,plain,
    ! [SV459: $i,SV30: $i,SV666: $i] :
      ( ( ( ~ ( in @ SV666 @ SV30 ) )
        = $true )
      | ( ( $true
          | ( ( if @ SV30 @ $true @ SV459 @ SV666 )
            = SV666 ) )
        = $true )
      | ( ( in @ SV459 @ SV30 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2074]) ).

thf(2290,plain,
    ! [SV460: $i,SV30: $i,SV667: $i] :
      ( ( ( ~ ( in @ SV667 @ SV30 ) )
        = $true )
      | ( ( $false
          | ( ( if @ SV30 @ $false @ SV460 @ SV667 )
            = SV667 ) )
        = $true )
      | ( ( in @ SV460 @ SV30 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2075]) ).

thf(2291,plain,
    ! [SV461: $i,SV280: $o,SV31: $i,SV668: $i] :
      ( ( ( ~ ( in @ SV668 @ SV31 ) )
        = $true )
      | ( ( ~ SV280
          | ( ( if @ SV31 @ SV280 @ SV461 @ SV668 )
            = SV461 ) )
        = $true )
      | ( ( in @ SV461 @ SV31 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2076]) ).

thf(2292,plain,
    ! [SV462: $i,SV31: $i,SV669: $i] :
      ( ( ( ~ ( in @ SV669 @ SV31 ) )
        = $true )
      | ( ( ~ $true
          | ( ( if @ SV31 @ $true @ SV462 @ SV669 )
            = SV462 ) )
        = $true )
      | ( ( in @ SV462 @ SV31 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2077]) ).

thf(2293,plain,
    ! [SV463: $i,SV31: $i,SV670: $i] :
      ( ( ( ~ ( in @ SV670 @ SV31 ) )
        = $true )
      | ( ( ~ $false
          | ( ( if @ SV31 @ $false @ SV463 @ SV670 )
            = SV463 ) )
        = $true )
      | ( ( in @ SV463 @ SV31 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2078]) ).

thf(2294,plain,
    ! [SV464: $i,SV281: $o,SV33: $i,SV671: $i] :
      ( ( ( ~ ( in @ SV671 @ SV33 ) )
        = $true )
      | ( ( in @ ( if @ SV33 @ SV281 @ SV464 @ SV671 ) @ SV33 )
        = $true )
      | ( ( in @ SV464 @ SV33 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2080]) ).

thf(2295,plain,
    ! [SV465: $i,SV33: $i,SV672: $i] :
      ( ( ( ~ ( in @ SV672 @ SV33 ) )
        = $true )
      | ( ( in @ ( if @ SV33 @ $true @ SV465 @ SV672 ) @ SV33 )
        = $true )
      | ( ( in @ SV465 @ SV33 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2081]) ).

thf(2296,plain,
    ! [SV466: $i,SV33: $i,SV673: $i] :
      ( ( ( ~ ( in @ SV673 @ SV33 ) )
        = $true )
      | ( ( in @ ( if @ SV33 @ $false @ SV466 @ SV673 ) @ SV33 )
        = $true )
      | ( ( in @ SV466 @ SV33 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2082]) ).

thf(2297,plain,
    ! [SV588: $i,SV469: $i,SV36: $i,SV720: $i] :
      ( ( ( ~ ( in @ SV720 @ SV36 ) )
        = $true )
      | ( $true = $true )
      | ( ( func @ SV36 @ SV469 @ SV588 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2083]) ).

thf(2298,plain,
    ! [SV470: $i,SV589: $i,SV37: $i,SV721: $i] :
      ( ( ( ~ ( in @ SV721 @ SV37 ) )
        = $true )
      | ( $true = $true )
      | ( ( in @ SV589 @ ( funcSet @ SV37 @ SV470 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2084]) ).

thf(2299,plain,
    ! [SV471: $i,SV284: $i,SV38: $i,SV674: $i] :
      ( ( ( ~ ( in @ SV674 @ SV38 ) )
        = $true )
      | ( ( ! [SY2932: $i] :
              ( ~ ( in @ SY2932 @ SV284 )
              | ~ ( in @ ( kpair @ SV674 @ SY2932 ) @ SV471 )
              | ( ( ap @ SV38 @ SV284 @ SV471 @ SV674 )
                = SY2932 ) ) )
        = $true )
      | ( ( in @ SV471 @ ( funcSet @ SV38 @ SV284 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2085]) ).

thf(2300,plain,
    ! [SV472: $i,SV285: $i,SV39: $i,SV675: $i] :
      ( ( ( ~ ( in @ SV675 @ SV39 ) )
        = $true )
      | ( ( ! [SY2933: $i] :
              ( ~ ( in @ SY2933 @ SV285 )
              | ~ ( in @ ( kpair @ SV675 @ SY2933 ) @ SV472 )
              | ( ( ap @ SV39 @ SV285 @ SV472 @ SV675 )
                = SY2933 ) ) )
        = $true )
      | ( ( func @ SV39 @ SV285 @ SV472 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2086]) ).

thf(2301,plain,
    ! [SV473: $i,SV286: $i,SV40: $i,SV676: $i] :
      ( ( ( ~ ( in @ SV676 @ SV40 ) )
        = $true )
      | ( ( in @ ( kpair @ SV676 @ ( ap @ SV40 @ SV286 @ SV473 @ SV676 ) ) @ SV473 )
        = $true )
      | ( ( in @ SV473 @ ( funcSet @ SV40 @ SV286 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2087]) ).

thf(2302,plain,
    ! [SV474: $i,SV287: $i,SV41: $i,SV677: $i] :
      ( ( ( ~ ( in @ SV677 @ SV41 ) )
        = $true )
      | ( ( in @ ( kpair @ SV677 @ ( ap @ SV41 @ SV287 @ SV474 @ SV677 ) ) @ SV474 )
        = $true )
      | ( ( func @ SV41 @ SV287 @ SV474 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2088]) ).

thf(2303,plain,
    ! [SV288: $i > $o,SV42: $i,SV635: $i] :
      ( ( ( in @ SV635 @ SV42 )
        = $false )
      | ( ( ! [SY2907: $i] :
              ( ~ ( in @ SY2907 @ SV42 )
              | ~ ( SV288 @ SV635 )
              | ~ ( SV288 @ SY2907 )
              | ( SV635 = SY2907 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV42
            @ ^ [SY2500: $i] : ( SV288 @ SY2500 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2089]) ).

thf(2304,plain,
    ! [SV476: $i,SV290: $i,SV44: $i,SV678: $i] :
      ( ( ( ~ ( in @ SV678 @ SV44 ) )
        = $true )
      | ( ( in @ ( ap @ SV44 @ SV290 @ SV476 @ SV678 ) @ SV290 )
        = $true )
      | ( ( in @ SV476 @ ( funcSet @ SV44 @ SV290 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2090]) ).

thf(2305,plain,
    ! [SV478: $i,SV292: $i,SV46: $i,SV679: $i] :
      ( ( ( ~ ( in @ SV679 @ SV46 ) )
        = $true )
      | ( ( in @ ( ap @ SV46 @ SV292 @ SV478 @ SV679 ) @ SV292 )
        = $true )
      | ( ( func @ SV46 @ SV292 @ SV478 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2091]) ).

thf(2306,plain,
    ! [SV479: $i,SV293: $i,SV47: $i,SV680: $i] :
      ( ( ( ~ ( in @ SV680 @ SV47 ) )
        = $true )
      | ( ( in
          @ ( setunion
            @ ( dsetconstr @ SV293
              @ ^ [SY2934: $i] : ( in @ ( kpair @ SV680 @ SY2934 ) @ SV479 ) ) )
          @ SV293 )
        = $true )
      | ( ( func @ SV47 @ SV293 @ SV479 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2092]) ).

thf(2307,plain,
    ! [SV480: $i,SV294: $i,SV48: $i,SV681: $i] :
      ( ( ( ~ ( in @ SV681 @ SV48 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV294
            @ ^ [SY2935: $i] : ( in @ ( kpair @ SV681 @ SY2935 ) @ SV480 ) ) )
        = $true )
      | ( ( func @ SV48 @ SV294 @ SV480 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2093]) ).

thf(2308,plain,
    ! [SV481: $i > $i > $o,SV295: $i,SV49: $i,SV636: $i,SV590: $i] :
      ( ( ( in @ ( kpair @ SV590 @ SV636 )
          @ ( dpsetconstr @ SV49 @ SV295
            @ ^ [SY2763: $i,SY2764: $i] : ( SV481 @ SY2763 @ SY2764 ) ) )
        = $false )
      | ( ( SV481 @ SV590 @ SV636 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2094]) ).

thf(2309,plain,
    ! [SV482: $i > $i > $o,SV296: $i,SV50: $i,SV637: $i,SV591: $i] :
      ( ( ( in @ ( kpair @ SV591 @ SV637 )
          @ ( dpsetconstr @ SV50 @ SV296
            @ ^ [SY2767: $i,SY2768: $i] : ( SV482 @ SY2767 @ SY2768 ) ) )
        = $false )
      | ( ( in @ SV637 @ SV296 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2095]) ).

thf(2310,plain,
    ! [SV483: $i > $i > $o,SV297: $i,SV51: $i,SV682: $i,SV592: $i] :
      ( ( ( in @ ( kpair @ SV592 @ SV682 )
          @ ( dpsetconstr @ SV51 @ SV297
            @ ^ [SY2771: $i,SY2772: $i] : ( SV483 @ SY2771 @ SY2772 ) ) )
        = $false )
      | ( ( in @ SV592 @ SV51 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2096]) ).

thf(2311,plain,
    ! [SV484: $i > $i > $o,SV52: $i,SV593: $i,SV298: $i,SV722: $i] :
      ( ( ( ~ ( in @ SV722 @ SV298 )
          | ~ ( in @ ( kpair @ SV593 @ SV722 )
              @ ( dpsetconstr @ SV52 @ SV298
                @ ^ [SY2775: $i,SY2776: $i] : ( SV484 @ SY2775 @ SY2776 ) ) )
          | ( SV484 @ SV593 @ SV722 ) )
        = $true )
      | ( ( in @ SV593 @ SV52 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2097]) ).

thf(2312,plain,
    ! [SV55: $i,SV594: $i,SV487: $i > $i > $o,SV301: $i,SV723: $i] :
      ( ( ( ~ ( in @ SV723 @ SV301 )
          | ~ ( SV487 @ SV594 @ SV723 )
          | ( in @ ( kpair @ SV594 @ SV723 )
            @ ( dpsetconstr @ SV55 @ SV301
              @ ^ [SY2783: $i,SY2784: $i] : ( SV487 @ SY2783 @ SY2784 ) ) ) )
        = $true )
      | ( ( in @ SV594 @ SV55 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2098]) ).

thf(2313,plain,
    ! [SV57: $i,SV489: $i,SV303: $i,SV683: $i] :
      ( ( ( ~ ( in @ SV683 @ SV303 ) )
        = $true )
      | ( ( ( ksnd @ ( kpair @ SV489 @ SV683 ) )
          = SV683 )
        = $true )
      | ( ( in @ SV489 @ SV57 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2099]) ).

thf(2314,plain,
    ! [SV58: $i,SV490: $i,SV304: $i,SV684: $i] :
      ( ( ( ~ ( in @ SV684 @ SV304 ) )
        = $true )
      | ( ( ( kfst @ ( kpair @ SV490 @ SV684 ) )
          = SV490 )
        = $true )
      | ( ( in @ SV490 @ SV58 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2100]) ).

thf(2315,plain,
    ! [SV59: $i,SV491: $i,SV685: $i,SV724: $i] :
      ( ( ( ~ ( in @ SV724 @ SV685 ) )
        = $true )
      | ( $true = $true )
      | ( ( in @ SV491 @ SV59 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2101]) ).

thf(2316,plain,
    ! [SV69: $i,SV312: $i,SV599: $i,SV497: $i] :
      ( ( ( SV497 != SV599 )
        = $true )
      | ( ( SV312 = SV599 )
        = $true )
      | ( ( ( setadjoin @ ( setadjoin @ SV69 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV69 @ ( setadjoin @ SV312 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ SV497 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV497 @ ( setadjoin @ SV599 @ emptyset ) ) @ emptyset ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2106]) ).

thf(2317,plain,
    ! [SV84: $i,SV503: $i,SV322: $i,SV686: $i] :
      ( ( ( ~ ( in @ SV686 @ SV322 ) )
        = $true )
      | ( ( in @ ( kpair @ SV503 @ SV686 ) @ ( cartprod @ SV84 @ SV322 ) )
        = $true )
      | ( ( in @ SV503 @ SV84 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2109]) ).

thf(2318,plain,
    ! [SV85: $i,SV504: $i,SV323: $i,SV687: $i] :
      ( ( ( ~ ( in @ SV687 @ SV323 ) )
        = $true )
      | ( ( in @ ( kpair @ SV504 @ SV687 ) @ ( powerset @ ( powerset @ ( binunion @ SV85 @ SV323 ) ) ) )
        = $true )
      | ( ( in @ SV504 @ SV85 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2110]) ).

thf(2319,plain,
    ! [SV86: $i,SV505: $i,SV324: $i,SV688: $i] :
      ( ( ( ~ ( in @ SV688 @ SV324 ) )
        = $true )
      | ( ( in @ ( setadjoin @ ( setadjoin @ SV505 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV505 @ ( setadjoin @ SV688 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV86 @ SV324 ) ) ) )
        = $true )
      | ( ( in @ SV505 @ SV86 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2111]) ).

thf(2320,plain,
    ! [SV87: $i,SV506: $i,SV325: $i,SV689: $i] :
      ( ( ( ~ ( in @ SV689 @ SV325 ) )
        = $true )
      | ( ( subset @ ( setadjoin @ ( setadjoin @ SV506 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV506 @ ( setadjoin @ SV689 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV87 @ SV325 ) ) )
        = $true )
      | ( ( in @ SV506 @ SV87 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2112]) ).

thf(2321,plain,
    ! [SV88: $i,SV507: $i,SV326: $i,SV690: $i] :
      ( ( ( ~ ( in @ SV690 @ SV326 ) )
        = $true )
      | ( ( in @ ( setadjoin @ SV507 @ ( setadjoin @ SV690 @ emptyset ) ) @ ( powerset @ ( binunion @ SV88 @ SV326 ) ) )
        = $true )
      | ( ( in @ SV507 @ SV88 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2113]) ).

thf(2322,plain,
    ! [SV89: $i,SV508: $i,SV327: $i,SV691: $i] :
      ( ( ( ~ ( in @ SV691 @ SV327 ) )
        = $true )
      | ( ( subset @ ( setadjoin @ SV508 @ ( setadjoin @ SV691 @ emptyset ) ) @ ( binunion @ SV89 @ SV327 ) )
        = $true )
      | ( ( in @ SV508 @ SV89 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2114]) ).

thf(2323,plain,
    ! [SV100: $i,SV338: $i,SV512: $i] :
      ( ( ( in @ SV512 @ SV338 )
        = $false )
      | ( ( ~ ( in @ SV512 @ ( symdiff @ SV100 @ SV338 ) ) )
        = $true )
      | ( ( in @ SV512 @ SV100 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2117]) ).

thf(2324,plain,
    ! [SV122: $i,SV360: $i,SV525: $i] :
      ( ( ( subset @ SV525 @ SV360 )
        = $false )
      | ( ( subset @ SV525 @ ( binintersect @ SV122 @ SV360 ) )
        = $true )
      | ( ( subset @ SV525 @ SV122 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2125]) ).

thf(2325,plain,
    ! [SV123: $i,SV361: $i,SV526: $i] :
      ( ( ( in @ SV526 @ SV361 )
        = $false )
      | ( ( in @ SV526 @ ( binintersect @ SV123 @ SV361 ) )
        = $true )
      | ( ( in @ SV526 @ SV123 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2126]) ).

thf(2326,plain,
    ! [SV141: $i,SV641: $i,SV377: $i] :
      ( ( ( subset @ SV377 @ SV641 )
        = $false )
      | ( ( subset @ SV141 @ SV641 )
        = $true )
      | ( ( subset @ SV141 @ SV377 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2129]) ).

thf(2327,plain,
    ! [SV531: $i,SV378: $i,SV143: $i] :
      ( ( ( SV143 = SV378 )
        = $false )
      | ( ( in @ SV531 @ SV378 )
        = $true )
      | ( ( in @ SV531 @ SV143 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2130]) ).

thf(2328,plain,
    ! [SV532: $i,SV380: $i,SV145: $i] :
      ( ( ( subset @ SV145 @ SV380 )
        = $false )
      | ( ( in @ SV532 @ SV380 )
        = $true )
      | ( ( in @ SV532 @ SV145 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2131]) ).

thf(2329,plain,
    ! [SV381: $i,SV146: $i,SV642: $i] :
      ( ( ( in @ SV642 @ SV146 )
        = $false )
      | ( ( in @ SV642 @ SV381 )
        = $true )
      | ( ( subset @ SV146 @ SV381 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2132]) ).

thf(2330,plain,
    ! [SV382: $i,SV147: $i,SV643: $i] :
      ( ( ( in @ SV643 @ SV147 )
        = $false )
      | ( ( in @ SV643 @ SV382 )
        = $true )
      | ( ( subset @ SV147 @ SV382 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2133]) ).

thf(2331,plain,
    ! [SV387: $i,SV153: $i,SV692: $i,SV644: $i] :
      ( ( ( SV644 != SV692 )
        = $true )
      | ( ( ( setadjoin @ SV153 @ SV644 )
          = ( setadjoin @ SV387 @ SV692 ) )
        = $true )
      | ( ( SV153 = SV387 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2134]) ).

thf(2332,plain,
    ! [SV388: $i,SV154: $i,SV693: $i,SV645: $i] :
      ( ( ( SV645 != SV693 )
        = $true )
      | ( ( ~ ( in @ SV645 @ SV154 )
          | ( in @ SV693 @ SV388 ) )
        = $true )
      | ( ( SV154 = SV388 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2135]) ).

thf(2333,plain,
    ! [SV390: $i > $o,SV158: $i,SV600: $i] :
      ( ( ( in @ SV600 @ SV158 )
        = $false )
      | ( ( SV390 @ SV600 )
        = $false )
      | ( ( ( dsetconstr @ SV158
            @ ^ [SY2616: $i] : ( SV390 @ SY2616 ) )
         != emptyset )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2136]) ).

thf(2334,plain,
    ! [SV399: $i,SV168: $i,SV534: $i] :
      ( ( ( in @ SV534 @ SV168 )
        = $false )
      | ( ( in @ SV399 @ ( setunion @ SV168 ) )
        = $true )
      | ( ( in @ SV399 @ SV534 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2138]) ).

thf(2335,plain,
    ! [SV169: $i,SV400: $i,SV646: $i] :
      ( ( ( in @ SV646 @ SV400 )
        = $false )
      | ( ( in @ SV646 @ SV169 )
        = $true )
      | ( ( in @ SV400 @ ( powerset @ SV169 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2139]) ).

thf(2336,plain,
    ! [SV177: $i,SV538: $i,SV404: $i > $o] :
      ( ( ( SV404 @ SV538 )
        = $false )
      | ( ( ( dsetconstr @ SV177
            @ ^ [SY2623: $i] : ( SV404 @ SY2623 ) )
         != emptyset )
        = $true )
      | ( ( in @ SV538 @ SV177 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2141]) ).

thf(2337,plain,
    ! [SV186: $i,SV544: $i,SV408: $i > $o] :
      ( ( ( SV408 @ SV544 )
        = $false )
      | ( ( in @ SV544
          @ ( dsetconstr @ SV186
            @ ^ [SY2629: $i] : ( SV408 @ SY2629 ) ) )
        = $true )
      | ( ( in @ SV544 @ SV186 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2142]) ).

thf(2338,plain,
    ! [SV409: $i,SV189: $i,SV647: $i] :
      ( ( ( in @ SV647 @ ( powerset @ SV189 ) )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK97_Xx @ SV647 @ SV409 @ SV189 ) @ SV189 )
              | ~ ~ ( ~ ( in @ ( sK97_Xx @ SV647 @ SV409 @ SV189 ) @ SV409 )
                    | ~ ~ ( in @ ( sK97_Xx @ SV647 @ SV409 @ SV189 ) @ SV647 ) ) )
          | ( subset @ SV409 @ SV647 ) )
        = $true )
      | ( ( in @ SV409 @ ( powerset @ SV189 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2143]) ).

thf(2339,plain,
    ! [SV602: $i,SV648: $i] :
      ( ( ( ~ ( in @ ( sK7_Xx @ SV648 @ SV602 ) @ SV648 )
          | ~ ~ ( in @ ( sK7_Xx @ SV648 @ SV602 ) @ SV602 ) )
        = $false )
      | ( ( in @ SV648 @ ( powerset @ SV602 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2144]) ).

thf(2340,plain,
    ! [SV603: $i,SV649: $i] :
      ( ( ( in @ SV649 @ ( powerset @ SV603 ) )
        = $false )
      | ( ( ! [SY2914: $i] :
              ( ~ ( in @ SY2914 @ SV649 )
              | ( in @ SY2914 @ SV603 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2145]) ).

thf(2341,plain,
    ! [SV545: $i,SV190: $i > $o] :
      ( ( ( SV190 @ ( sK24_SY86 @ SV545 @ SV190 ) )
        = $true )
      | ( ( ~ ( SV190 @ SV545 ) )
        = $true )
      | ( ( SV190 @ ( sK23_Xx @ SV190 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2146]) ).

thf(2342,plain,
    ! [SV190: $i > $o,SV545: $i] :
      ( ( ( SV545
         != ( sK24_SY86 @ SV545 @ SV190 ) )
        = $true )
      | ( ( ~ ( SV190 @ SV545 ) )
        = $true )
      | ( ( SV190 @ ( sK23_Xx @ SV190 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2147]) ).

thf(2343,plain,
    ! [SV546: $i,SV410: $o,SV191: $i,SV694: $i] :
      ( ( ( ~ ( in @ SV694 @ SV191 ) )
        = $true )
      | ( ( ~ SV410
          | ( in @ SV546
            @ ( dsetconstr @ SV191
              @ ^ [SY2939: $i] :
                  ( ~ ( ~ SV410
                      | ( SY2939 != SV546 ) )
                  | ~ ( ~ ~ SV410
                      | ( SY2939 != SV694 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV546 @ SV191 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2148]) ).

thf(2344,plain,
    ! [SV547: $i,SV191: $i,SV695: $i] :
      ( ( ( ~ ( in @ SV695 @ SV191 ) )
        = $true )
      | ( ( ~ $true
          | ( in @ SV547
            @ ( dsetconstr @ SV191
              @ ^ [SY2940: $i] :
                  ( ~ ( ~ $true
                      | ( SY2940 != SV547 ) )
                  | ~ ( ~ ~ $true
                      | ( SY2940 != SV695 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV547 @ SV191 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2149]) ).

thf(2345,plain,
    ! [SV548: $i,SV191: $i,SV696: $i] :
      ( ( ( ~ ( in @ SV696 @ SV191 ) )
        = $true )
      | ( ( ~ $false
          | ( in @ SV548
            @ ( dsetconstr @ SV191
              @ ^ [SY2941: $i] :
                  ( ~ ( ~ $false
                      | ( SY2941 != SV548 ) )
                  | ~ ( ~ ~ $false
                      | ( SY2941 != SV696 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV548 @ SV191 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2150]) ).

thf(2346,plain,
    ! [SV192: $i,SV411: $i,SV549: $i > $i] :
      ( ( ( in @ ( sK92_Xx @ SV549 @ SV411 @ SV192 ) @ SV192 )
        = $true )
      | ( ( ! [SY2810: $i] :
              ( ~ ( in @ SY2810 @ SV192 )
              | ( ( ap @ SV192 @ SV411
                  @ ( lam @ SV192 @ SV411
                    @ ^ [SY2811: $i] : ( SV549 @ SY2811 ) )
                  @ SY2810 )
                = ( SV549 @ SY2810 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2151]) ).

thf(2347,plain,
    ! [SV192: $i,SV411: $i,SV549: $i > $i] :
      ( ( ( ~ ( in @ ( SV549 @ ( sK92_Xx @ SV549 @ SV411 @ SV192 ) ) @ SV411 ) )
        = $true )
      | ( ( ! [SY2810: $i] :
              ( ~ ( in @ SY2810 @ SV192 )
              | ( ( ap @ SV192 @ SV411
                  @ ( lam @ SV192 @ SV411
                    @ ^ [SY2811: $i] : ( SV549 @ SY2811 ) )
                  @ SY2810 )
                = ( SV549 @ SY2810 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2152]) ).

thf(2348,plain,
    ! [SV193: $i,SV412: $i,SV550: $i] :
      ( ( ( ~ ~ ( ( SV550
                 != ( kpair @ ( sK67_Xx @ SV550 @ SV412 @ SV193 ) @ ( sK68_SY1876 @ SV550 @ SV412 @ SV193 ) ) )
                | ~ ( in @ ( sK68_SY1876 @ SV550 @ SV412 @ SV193 ) @ SV412 ) ) )
        = $false )
      | ( ( in @ SV550 @ ( cartprod @ SV193 @ SV412 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2153]) ).

thf(2349,plain,
    ! [SV193: $i,SV412: $i,SV550: $i] :
      ( ( ( ~ ( in @ ( sK67_Xx @ SV550 @ SV412 @ SV193 ) @ SV193 ) )
        = $false )
      | ( ( in @ SV550 @ ( cartprod @ SV193 @ SV412 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2153]) ).

thf(2350,plain,
    ! [SV551: $i,SV194: $i > $o] :
      ( ( ( SV194 @ ( sK57_SY248 @ SV551 @ SV194 ) )
        = $true )
      | ( ( ~ ( SV194 @ SV551 ) )
        = $true )
      | ( ( ! [SY2258: $i] :
              ( ~ ( SV194 @ SY2258 )
              | ! [SY2259: $i] :
                  ( ~ ( SV194 @ SY2259 )
                  | ( SY2258 = SY2259 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2154]) ).

thf(2351,plain,
    ! [SV194: $i > $o,SV551: $i] :
      ( ( ( SV551
         != ( sK57_SY248 @ SV551 @ SV194 ) )
        = $true )
      | ( ( ~ ( SV194 @ SV551 ) )
        = $true )
      | ( ( ! [SY2258: $i] :
              ( ~ ( SV194 @ SY2258 )
              | ! [SY2259: $i] :
                  ( ~ ( SV194 @ SY2259 )
                  | ( SY2258 = SY2259 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2155]) ).

thf(2352,plain,
    ! [SV413: $i,SV195: $i > $i > $o] :
      ( ( ( ~ ! [SY2639: $i] :
                ( ! [SY2640: $i] :
                    ( ~ ( SV195 @ SY2640 @ SY2639 )
                    | ~ ( in @ SY2640 @ SV413 ) )
                | ( in @ SY2639 @ ( sK10_B @ SV413 @ SV195 ) ) )
          | ~ ! [SY2641: $i] :
                ( ~ ( in @ SY2641 @ ( sK10_B @ SV413 @ SV195 ) )
                | ~ ( ~ ( SV195 @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SY2641 )
                    | ~ ( in @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SV413 ) ) ) )
        = $false )
      | ( ( in @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV413 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2156]) ).

thf(2353,plain,
    ! [SV725: $i,SV413: $i,SV195: $i > $i > $o] :
      ( ( ( ~ ( ~ ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
              | ~ ( ( SV725
                   != ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) ) ) )
          | ~ ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2639: $i] :
                    ( ! [SY2640: $i] :
                        ( ~ ( SV195 @ SY2640 @ SY2639 )
                        | ~ ( in @ SY2640 @ SV413 ) )
                    | ( in @ SY2639 @ ( sK10_B @ SV413 @ SV195 ) ) )
              | ~ ! [SY2641: $i] :
                    ( ~ ( in @ SY2641 @ ( sK10_B @ SV413 @ SV195 ) )
                    | ~ ( ~ ( SV195 @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SY2641 )
                        | ~ ( in @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SV413 ) ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2157]) ).

thf(2354,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( ( ~ ~ ( ~ ( ( SV552 = SV196 )
                    | ( in @ SV552 @ SV414 )
                    | ! [SX3: $o] : SX3 )
                | ~ ( ( SV552 = SV196 )
                    | ! [SX3: $o] :
                        ( ~ SX3
                        | SX3 ) ) ) )
        = $false )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2158]) ).

thf(2355,plain,
    ! [SV196: $i,SV414: $i,SV552: $i] :
      ( ( ( ~ ~ ( ~ ! [SY2814: $o] :
                      ( ~ SY2814
                      | ( in @ SV552 @ SV414 )
                      | SY2814 )
                | ~ ! [SX3: $o] :
                      ( ~ SX3
                      | ~ SX3
                      | SX3 ) ) )
        = $false )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2158]) ).

thf(2356,plain,
    ! [SV650: $i > $o,SV198: $i,SV697: $i] :
      ( ( ( ~ ( in @ SV697 @ SV198 ) )
        = $true )
      | ( ( ~ ( SV650 @ SV697 )
          | ( in @ SV697
            @ ( dsetconstr @ SV198
              @ ^ [SY2916: $i] : ( SV650 @ SY2916 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2161]) ).

thf(2357,plain,
    ! [SV651: $i > $o,SV198: $i,SV698: $i] :
      ( ( ( ~ ( in @ SV698 @ SV198 ) )
        = $true )
      | ( ( ~ ( in @ SV698
              @ ( dsetconstr @ SV198
                @ ^ [SY2918: $i] : ( SV651 @ SY2918 ) ) )
          | ( SV651 @ SV698 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2162]) ).

thf(2358,plain,
    ! [SV199: $i,SV416: $i] :
      ( ( ( in @ ( sK30_Xx @ SV416 @ SV199 ) @ SV199 )
        = $false )
      | ( ( in @ SV416 @ ( powerset @ SV199 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2164]) ).

thf(2359,plain,
    ! [SV604: $i,SV200: $i,SV417: $i > $o] :
      ( ( ( ~ ( in @ ( sK40_Xx @ SV417 @ SV200 ) @ SV200 )
          | ~ ~ ( SV417 @ ( sK40_Xx @ SV417 @ SV200 ) ) )
        = $false )
      | ( ( SV417 @ SV604 )
        = $true )
      | ( ( in @ SV604 @ SV200 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2165]) ).

thf(2360,plain,
    ! [SV201: $i,SV418: $i,SV553: $i > $i] :
      ( ( ( in @ ( sK78_Xx @ SV553 @ SV418 @ SV201 ) @ SV201 )
        = $true )
      | ( ( in
          @ ( lam @ SV201 @ SV418
            @ ^ [SY2816: $i] : ( SV553 @ SY2816 ) )
          @ ( funcSet @ SV201 @ SV418 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2166]) ).

thf(2361,plain,
    ! [SV201: $i,SV418: $i,SV553: $i > $i] :
      ( ( ( ~ ( in @ ( SV553 @ ( sK78_Xx @ SV553 @ SV418 @ SV201 ) ) @ SV418 ) )
        = $true )
      | ( ( in
          @ ( lam @ SV201 @ SV418
            @ ^ [SY2816: $i] : ( SV553 @ SY2816 ) )
          @ ( funcSet @ SV201 @ SV418 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2167]) ).

thf(2362,plain,
    ! [SV554: $i,SV419: $o,SV202: $i,SV699: $i] :
      ( ( ( ~ ( in @ SV699 @ SV202 ) )
        = $true )
      | ( ( SV419
          | ( ( dsetconstr @ SV202
              @ ^ [SY2944: $i] :
                  ( ~ ( ~ SV419
                      | ( SY2944 != SV554 ) )
                  | ~ ( ~ ~ SV419
                      | ( SY2944 != SV699 ) ) ) )
            = ( setadjoin @ SV699 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV554 @ SV202 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2168]) ).

thf(2363,plain,
    ! [SV555: $i,SV202: $i,SV700: $i] :
      ( ( ( ~ ( in @ SV700 @ SV202 ) )
        = $true )
      | ( ( $true
          | ( ( dsetconstr @ SV202
              @ ^ [SY2945: $i] :
                  ( ~ ( ~ $true
                      | ( SY2945 != SV555 ) )
                  | ~ ( ~ ~ $true
                      | ( SY2945 != SV700 ) ) ) )
            = ( setadjoin @ SV700 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV555 @ SV202 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2169]) ).

thf(2364,plain,
    ! [SV556: $i,SV202: $i,SV701: $i] :
      ( ( ( ~ ( in @ SV701 @ SV202 ) )
        = $true )
      | ( ( $false
          | ( ( dsetconstr @ SV202
              @ ^ [SY2946: $i] :
                  ( ~ ( ~ $false
                      | ( SY2946 != SV556 ) )
                  | ~ ( ~ ~ $false
                      | ( SY2946 != SV701 ) ) ) )
            = ( setadjoin @ SV701 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV556 @ SV202 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2170]) ).

thf(2365,plain,
    ! [SV605: $i > $o,SV652: $i > $o] :
      ( ( ( ( ( sK55_Xx @ SV652 @ SV605 )
           != ( sK56_SY1873 @ SV652 @ SV605 ) )
          | ~ ~ ( ~ ( ~ ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
                    | ~ ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) ) )
                | ~ ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
                    | ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) ) ) ) )
        = $false )
      | ( ( ! [SY2919: $i] :
              ( ~ ( ~ ( SV605 @ ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) )
                  | ~ ( ( SY2919
                       != ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) ) ) )
              | ~ ( SV605 @ SY2919 ) )
          | ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2171]) ).

thf(2366,plain,
    ! [SV606: $i > $o,SV653: $i > $o] :
      ( ( ( ( ( sK51_Xx @ SV653 @ SV606 )
           != ( sK52_SY1871 @ SV653 @ SV606 ) )
          | ~ ~ ( ~ ( ~ ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
                    | ~ ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) ) )
                | ~ ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
                    | ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) ) ) ) )
        = $false )
      | ( ( ! [SY2921: $i] :
              ( ~ ( ~ ( SV653 @ ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) )
                  | ~ ( ( SY2921
                       != ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) ) ) )
              | ~ ( SV653 @ SY2921 ) )
          | ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2172]) ).

thf(2367,plain,
    ! [SV420: $i > $o,SV203: $i,SV726: $i] :
      ( ( ( ~ ( in @ SV726 @ SV203 )
          | ~ ( SV420 @ SV726 ) )
        = $true )
      | ( ( SV420 @ ( sK39_Xx @ SV420 @ SV203 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2173]) ).

thf(2368,plain,
    ! [SV420: $i > $o,SV203: $i,SV727: $i] :
      ( ( ( ~ ( in @ SV727 @ SV203 )
          | ~ ( SV420 @ SV727 ) )
        = $true )
      | ( ( in @ ( sK39_Xx @ SV420 @ SV203 ) @ SV203 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2174]) ).

thf(2369,plain,
    ! [SV557: $i,SV204: $i > $o] :
      ( ( ( SV204 @ ( sK20_SY57 @ SV557 @ SV204 ) )
        = $true )
      | ( ( ~ ( SV204 @ SV557 ) )
        = $true )
      | ( ( SV204
          @ ( descr
            @ ^ [SY2291: $i] : ( SV204 @ SY2291 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2175]) ).

thf(2370,plain,
    ! [SV204: $i > $o,SV557: $i] :
      ( ( ( SV557
         != ( sK20_SY57 @ SV557 @ SV204 ) )
        = $true )
      | ( ( ~ ( SV204 @ SV557 ) )
        = $true )
      | ( ( SV204
          @ ( descr
            @ ^ [SY2291: $i] : ( SV204 @ SY2291 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2176]) ).

thf(2371,plain,
    ! [SV558: $i,SV205: $i > $o] :
      ( ( ( SV205 @ ( sK42_Xy @ SV558 @ SV205 ) )
        = $true )
      | ( ( ~ ( SV205 @ SV558 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2293: $i] :
                    ( ~ ( SV205 @ SY2293 )
                    | ( ( sK41_SY198 @ SV205 )
                      = SY2293 ) )
              | ~ ( SV205 @ ( sK41_SY198 @ SV205 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2177]) ).

thf(2372,plain,
    ! [SV205: $i > $o,SV558: $i] :
      ( ( ( SV558
         != ( sK42_Xy @ SV558 @ SV205 ) )
        = $true )
      | ( ( ~ ( SV205 @ SV558 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2293: $i] :
                    ( ~ ( SV205 @ SY2293 )
                    | ( ( sK41_SY198 @ SV205 )
                      = SY2293 ) )
              | ~ ( SV205 @ ( sK41_SY198 @ SV205 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2178]) ).

thf(2373,plain,
    ! [SV206: $i,SV421: $i,SV559: $i > $i] :
      ( ( ( in @ ( sK94_Xx @ SV559 @ SV421 @ SV206 ) @ SV206 )
        = $true )
      | ( ( ! [SY2823: $i] :
              ( ~ ( in @ SY2823 @ SV206 )
              | ( ( ap @ SV206 @ SV421
                  @ ( lam @ SV206 @ SV421
                    @ ^ [SY2824: $i] : ( SV559 @ SY2824 ) )
                  @ SY2823 )
                = ( SV559 @ SY2823 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2179]) ).

thf(2374,plain,
    ! [SV206: $i,SV421: $i,SV559: $i > $i] :
      ( ( ( ~ ( in @ ( SV559 @ ( sK94_Xx @ SV559 @ SV421 @ SV206 ) ) @ SV421 ) )
        = $true )
      | ( ( ! [SY2823: $i] :
              ( ~ ( in @ SY2823 @ SV206 )
              | ( ( ap @ SV206 @ SV421
                  @ ( lam @ SV206 @ SV421
                    @ ^ [SY2824: $i] : ( SV559 @ SY2824 ) )
                  @ SY2823 )
                = ( SV559 @ SY2823 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2180]) ).

thf(2375,plain,
    ( ( ~ ( in @ sK4_SY1829 @ ( powerset @ sK1_A ) )
      | ~ ~ ( ~ ( in @ sK5_SY1831 @ sK1_A )
            | ~ ~ ( ~ ( in @ sK5_SY1831 @ ( binintersect @ sK2_SY1822 @ sK3_SY1826 ) )
                  | ~ ~ ( in @ sK5_SY1831 @ ( binunion @ sK3_SY1826 @ sK4_SY1829 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2182]) ).

thf(2376,plain,
    ! [SV207: $i,SV422: $i,SV560: $i,SV702: $i > $o] :
      ( ( ( ~ ( ~ ( in @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ SV207 )
              | ~ ~ ( ~ ( in @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) @ SV422 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) ) @ SV560 )
                          | ~ ~ ( SV702 @ ( kpair @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) ) ) ) ) ) )
        = $true )
      | ( ( ! [SY2947: $i] :
              ( ~ ( in @ SY2947 @ SV560 )
              | ( SV702 @ SY2947 ) ) )
        = $true )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2183]) ).

thf(2377,plain,
    ! [SV561: $i,SV423: $i,SV208: $i,SV703: $i] :
      ( ( ( ~ ( subset @ SV703 @ ( cartprod @ SV208 @ SV423 ) ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ SV208 )
              | ~ ~ ( ~ ( in @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) @ SV423 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) ) @ SV561 )
                          | ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) ) @ SV703 ) ) ) )
          | ( subset @ SV561 @ SV703 ) )
        = $true )
      | ( ( subset @ SV561 @ ( cartprod @ SV208 @ SV423 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2184]) ).

thf(2378,plain,
    ! [SV209: $i,SV424: $i > $o] :
      ( ( ( ! [SY2662: $i] :
              ( ~ ( SV424 @ SY2662 )
              | ~ ( in @ SY2662 @ SV209 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV209
            @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) )
        = $true )
      | ( ( in @ ( sK70_Xx @ SV424 @ SV209 ) @ SV209 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2185]) ).

thf(2379,plain,
    ! [SV209: $i,SV424: $i > $o] :
      ( ( ( ~ ( in @ ( sK71_SY1877 @ SV424 @ SV209 ) @ SV209 )
          | ~ ~ ( ~ ( SV424 @ ( sK70_Xx @ SV424 @ SV209 ) )
                | ~ ~ ( ~ ( SV424 @ ( sK71_SY1877 @ SV424 @ SV209 ) )
                      | ~ ( ( ( sK70_Xx @ SV424 @ SV209 )
                           != ( sK71_SY1877 @ SV424 @ SV209 ) ) ) ) ) )
        = $false )
      | ( ( ! [SY2662: $i] :
              ( ~ ( SV424 @ SY2662 )
              | ~ ( in @ SY2662 @ SV209 ) )
          | ( singleton
            @ ( dsetconstr @ SV209
              @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2186]) ).

thf(2380,plain,
    ! [SV425: $i,SV210: $i] :
      ( ( ( ! [SY2664: $i,SY2665: $i] :
              ( ( SY2664 != SY2665 )
              | ~ ( in @ SY2664 @ SV210 )
              | ( in @ SY2665 @ SV425 ) ) )
        = $true )
      | ( ( SV210 = SV425 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2187]) ).

thf(2381,plain,
    ! [SV210: $i,SV425: $i] :
      ( ( ( ! [SY2666: $i,SY2667: $i] :
              ( ( SY2666 != SY2667 )
              | ~ ( in @ SY2667 @ SV425 )
              | ( in @ SY2666 @ SV210 ) ) )
        = $true )
      | ( ( SV210 = SV425 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2188]) ).

thf(2382,plain,
    ! [SV562: $i,SV211: $i > $o] :
      ( ( ( SV211 @ ( sK48_SY224 @ SV562 @ SV211 ) )
        = $true )
      | ( ( ~ ( SV211 @ SV562 ) )
        = $true )
      | ( ( ! [SY2314: $i] :
              ( ~ ( SV211 @ SY2314 )
              | ! [SY2315: $i] :
                  ( ~ ( SV211 @ SY2315 )
                  | ( SY2314 = SY2315 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2189]) ).

thf(2383,plain,
    ! [SV211: $i > $o,SV562: $i] :
      ( ( ( SV562
         != ( sK48_SY224 @ SV562 @ SV211 ) )
        = $true )
      | ( ( ~ ( SV211 @ SV562 ) )
        = $true )
      | ( ( ! [SY2314: $i] :
              ( ~ ( SV211 @ SY2314 )
              | ! [SY2315: $i] :
                  ( ~ ( SV211 @ SY2315 )
                  | ( SY2314 = SY2315 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2190]) ).

thf(2384,plain,
    ! [SV212: $i,SV426: $i,SV563: $i > $i] :
      ( ( ( in @ ( sK77_Xx @ SV563 @ SV426 @ SV212 ) @ SV212 )
        = $true )
      | ( ( func @ SV212 @ SV426
          @ ( lam @ SV212 @ SV426
            @ ^ [SY2828: $i] : ( SV563 @ SY2828 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2191]) ).

thf(2385,plain,
    ! [SV212: $i,SV426: $i,SV563: $i > $i] :
      ( ( ( ~ ( in @ ( SV563 @ ( sK77_Xx @ SV563 @ SV426 @ SV212 ) ) @ SV426 ) )
        = $true )
      | ( ( func @ SV212 @ SV426
          @ ( lam @ SV212 @ SV426
            @ ^ [SY2828: $i] : ( SV563 @ SY2828 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2192]) ).

thf(2386,plain,
    ! [SV427: $i > $o,SV213: $i > $o] :
      ( ( ( ! [SY2670: $i] :
              ( ~ ( ~ ( SV213 @ ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2670
                       != ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV213 @ SY2670 ) ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2193]) ).

thf(2387,plain,
    ! [SV427: $i > $o,SV213: $i > $o] :
      ( ( ( ~ ( ~ ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
              | ~ ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) ) )
          | ~ ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
              | ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) ) ) )
        = $false )
      | ( ( ! [SY2670: $i] :
              ( ~ ( ~ ( SV213 @ ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2670
                       != ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV213 @ SY2670 ) )
          | ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2194]) ).

thf(2388,plain,
    ! [SV428: $i,SV214: $i,SV654: $i] :
      ( ( ( in @ SV654 @ ( powerset @ SV214 ) )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK98_Xx @ SV654 @ SV428 @ SV214 ) @ SV214 )
              | ~ ~ ( ~ ( in @ ( sK98_Xx @ SV654 @ SV428 @ SV214 ) @ SV428 )
                    | ~ ~ ( in @ ( sK98_Xx @ SV654 @ SV428 @ SV214 ) @ SV654 ) ) )
          | ( in @ SV428 @ ( powerset @ SV654 ) ) )
        = $true )
      | ( ( in @ SV428 @ ( powerset @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2195]) ).

thf(2389,plain,
    ! [SV215: $i,SV655: $o,SV429: $i] :
      ( ( ( ~ ( in @ SV429 @ ( sK31_B @ SV655 @ SV429 @ SV215 ) )
          | ~ ~ ( ~ ( in @ ( sK31_B @ SV655 @ SV429 @ SV215 ) @ SV215 )
                | ~ ~ SV655 ) )
        = $false )
      | ( SV655 = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2196]) ).

thf(2390,plain,
    ! [SV215: $i,SV429: $i] :
      ( ( ( ~ ( in @ SV429 @ ( sK31_B @ $true @ SV429 @ SV215 ) )
          | ~ ~ ( ~ ( in @ ( sK31_B @ $true @ SV429 @ SV215 ) @ SV215 )
                | ~ ~ $true ) )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2197]) ).

thf(2391,plain,
    ! [SV215: $i,SV429: $i] :
      ( ( ( ~ ( in @ SV429 @ ( sK31_B @ $false @ SV429 @ SV215 ) )
          | ~ ~ ( ~ ( in @ ( sK31_B @ $false @ SV429 @ SV215 ) @ SV215 )
                | ~ ~ $false ) )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2198]) ).

thf(2392,plain,
    ! [SV216: $i,SV430: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV430 )
              | ~ ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV216 ) ) )
        = $true )
      | ( ( SV216 = SV430 )
        = $true )
      | ( ( in @ ( sK26_Xx @ SV430 @ SV216 ) @ SV216 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2199]) ).

thf(2393,plain,
    ! [SV216: $i,SV430: $i] :
      ( ( ( in @ ( sK26_Xx @ SV430 @ SV216 ) @ SV430 )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV430 )
              | ~ ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV216 ) )
          | ( SV216 = SV430 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2200]) ).

thf(2394,plain,
    ! [SV217: $i,SV431: $i] :
      ( ( ( in @ ( sK69_X @ SV431 @ SV217 ) @ SV217 )
        = $true )
      | ( ( in @ SV431 @ ( setunion @ SV217 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2201]) ).

thf(2395,plain,
    ! [SV217: $i,SV431: $i] :
      ( ( ( in @ SV431 @ ( sK69_X @ SV431 @ SV217 ) )
        = $true )
      | ( ( in @ SV431 @ ( setunion @ SV217 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2202]) ).

thf(2396,plain,
    ! [SV564: $i,SV704: $i,SV432: $i,SV218: $i] :
      ( ( ( ~ ( func @ SV218 @ SV432 @ SV704 ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) @ SV218 )
              | ~ ( ( ( ap @ SV218 @ SV432 @ SV564 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) )
                   != ( ap @ SV218 @ SV432 @ SV704 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) ) ) ) )
          | ! [SY2948: $i] :
              ( ~ ( in @ SY2948 @ SV218 )
              | ! [SY2949: $i] :
                  ( ~ ( in @ SY2949 @ SV432 )
                  | ~ ( in @ ( kpair @ SY2948 @ SY2949 ) @ SV704 )
                  | ( in @ ( kpair @ SY2948 @ SY2949 ) @ SV564 ) ) ) )
        = $true )
      | ( ( func @ SV218 @ SV432 @ SV564 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2203]) ).

thf(2397,plain,
    ! [SV433: $i,SV219: $i,SV656: $i] :
      ( ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
              | ~ ~ ( ~ ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 )
                    | ~ ~ ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 ) ) )
          | ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
              | ~ ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
                    | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) ) )
          | ( SV433 = SV656 ) )
        = $true )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2204]) ).

thf(2398,plain,
    ! [SV220: $i,SV565: $i,SV434: $i > $o] :
      ( ( ( SV434 @ SV565 )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK73_Xy @ SV565 @ SV434 @ SV220 ) @ SV220 )
              | ~ ~ ( ~ ( SV434 @ ( sK73_Xy @ SV565 @ SV434 @ SV220 ) )
                    | ~ ( ( ( sK73_Xy @ SV565 @ SV434 @ SV220 )
                         != SV565 ) ) ) )
          | ( singleton
            @ ( dsetconstr @ SV220
              @ ^ [SY2682: $i] : ( SV434 @ SY2682 ) ) ) )
        = $true )
      | ( ( in @ SV565 @ SV220 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2205]) ).

thf(2399,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ ~ ( ~ ( ( in @ SV566 @ SV221 )
                    | ~ ( in @ SV566 @ SV221 )
                    | ! [SX3: $o] : SX3 )
                | ~ ~ ( ~ ( ( in @ SV566 @ SV221 )
                          | ( in @ SV566 @ SV435 )
                          | ! [SX3: $o] : SX3 )
                      | ~ ( ( in @ SV566 @ SV221 )
                          | ! [SX3: $o] :
                              ( ~ SX3
                              | SX3 ) ) ) ) )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2206]) ).

thf(2400,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SV566 @ SV435 )
                          | ~ ( in @ SV566 @ SV221 )
                          | ! [SX3: $o] : SX3 )
                      | ~ ~ ( ~ ( ~ ( in @ SV566 @ SV435 )
                                | ( in @ SV566 @ SV435 )
                                | ! [SX3: $o] : SX3 )
                            | ~ ( ~ ( in @ SV566 @ SV435 )
                                | ! [SX3: $o] :
                                    ( ~ SX3
                                    | SX3 ) ) ) )
                | ~ ~ ( ~ ! [SY2839: $o] :
                            ( ~ SY2839
                            | ~ ( in @ SV566 @ SV221 )
                            | SY2839 )
                      | ~ ~ ( ~ ! [SY2840: $o] :
                                  ( ~ SY2840
                                  | ( in @ SV566 @ SV435 )
                                  | SY2840 )
                            | ~ ! [SX3: $o] :
                                  ( ~ SX3
                                  | ~ SX3
                                  | SX3 ) ) ) ) )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2206]) ).

thf(2401,plain,
    ! [SV222: $i,SV436: $i,SV567: $i > $i] :
      ( ( ( in @ ( sK76_Xx @ SV567 @ SV436 @ SV222 ) @ SV222 )
        = $true )
      | ( ( func @ SV222 @ SV436
          @ ( dpsetconstr @ SV222 @ SV436
            @ ^ [SY2842: $i,SY2843: $i] :
                ( ( SV567 @ SY2842 )
                = SY2843 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2207]) ).

thf(2402,plain,
    ! [SV222: $i,SV436: $i,SV567: $i > $i] :
      ( ( ( ~ ( in @ ( SV567 @ ( sK76_Xx @ SV567 @ SV436 @ SV222 ) ) @ SV436 ) )
        = $true )
      | ( ( func @ SV222 @ SV436
          @ ( dpsetconstr @ SV222 @ SV436
            @ ^ [SY2842: $i,SY2843: $i] :
                ( ( SV567 @ SY2842 )
                = SY2843 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2208]) ).

thf(2403,plain,
    ! [SV657: $i,SV223: $i,SV705: $i] :
      ( ( ( ~ ( in @ SV705 @ ( setadjoin @ SV223 @ SV657 ) ) )
        = $true )
      | ( ( ( SV705 = SV223 )
          | ( in @ SV705 @ SV657 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2209]) ).

thf(2404,plain,
    ! [SV223: $i] :
      ( ( ! [SY2357: $i,SY2358: $i] :
            ( ( SY2358 != SV223 )
            | ( in @ SY2358 @ ( setadjoin @ SV223 @ SY2357 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2210]) ).

thf(2405,plain,
    ! [SV223: $i] :
      ( ( ! [SY2359: $i,SY2360: $i] :
            ( ~ ( in @ SY2360 @ SY2359 )
            | ( in @ SY2360 @ ( setadjoin @ SV223 @ SY2359 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2211]) ).

thf(2406,plain,
    ! [SV224: $i,SV437: $i] :
      ( ( ( in @ ( sK65_Xx @ SV437 @ SV224 ) @ SV437 )
        = $false )
      | ( ( subset @ SV224 @ SV437 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2213]) ).

thf(2407,plain,
    ! [SV225: $i,SV438: $i] :
      ( ( ( ~ ( in @ ( sK6_Xx @ SV438 @ SV225 ) @ SV225 ) )
        = $true )
      | ( ( ~ ( in @ ( sK6_Xx @ SV438 @ SV225 ) @ SV438 ) )
        = $true )
      | ( ( SV225 = SV438 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2214]) ).

thf(2408,plain,
    ! [SV225: $i,SV438: $i] :
      ( ( ( in @ ( sK6_Xx @ SV438 @ SV225 ) @ SV225 )
        = $true )
      | ( ( in @ ( sK6_Xx @ SV438 @ SV225 ) @ SV438 )
        = $true )
      | ( ( SV225 = SV438 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2215]) ).

thf(2409,plain,
    ! [SV439: $i,SV226: $i] :
      ( ( ~ ! [SY2696: $i] :
              ( ~ ( in @ SY2696 @ ( binunion @ SV226 @ SV439 ) )
              | ( in @ SY2696 @ SV226 )
              | ( in @ SY2696 @ SV439 )
              | ! [SX3: $o] : SX3 ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2216]) ).

thf(2410,plain,
    ! [SV439: $i,SV226: $i] :
      ( ( ~ ! [SY2698: $i] :
              ( ~ ( in @ SY2698 @ ( binunion @ SV226 @ SV439 ) )
              | ( in @ SY2698 @ SV226 )
              | ! [SX3: $o] :
                  ( ~ SX3
                  | SX3 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2216]) ).

thf(2411,plain,
    ! [SV439: $i,SV226: $i] :
      ( ( ~ ! [SY2700: $i] :
              ( ~ ( in @ SY2700 @ ( binunion @ SV226 @ SV439 ) )
              | ! [SY2701: $o] :
                  ( ~ SY2701
                  | ( in @ SY2700 @ SV439 )
                  | SY2701 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2217]) ).

thf(2412,plain,
    ! [SV439: $i,SV226: $i] :
      ( ( ~ ( ! [SY2702: $i] :
                ~ ( in @ SY2702 @ ( binunion @ SV226 @ SV439 ) )
            | ! [SX2: $o] :
                ( ~ SX2
                | ~ SX2
                | SX2 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2217]) ).

thf(2413,plain,
    ! [SV607: $i,SV227: $i,SV440: $i > $o] :
      ( ( ( ~ ( in @ ( sK38_Xx @ SV440 @ SV227 ) @ SV227 )
          | ~ ~ ( SV440 @ ( sK38_Xx @ SV440 @ SV227 ) ) )
        = $false )
      | ( ( SV440 @ SV607 )
        = $true )
      | ( ( in @ SV607 @ SV227 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2218]) ).

thf(2414,plain,
    ! [SV228: $i > $o,SV568: $i] :
      ( ( ( ( sK47_Xy @ SV568 @ SV228 )
         != SV568 )
        = $true )
      | ( ( ~ ( SV228 @ ( sK47_Xy @ SV568 @ SV228 ) ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2375: $i] :
                    ( ~ ( SV228 @ SY2375 )
                    | ( ( sK46_SY211 @ SV228 )
                      = SY2375 ) )
              | ~ ( SV228 @ ( sK46_SY211 @ SV228 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2219]) ).

thf(2415,plain,
    ! [SV228: $i > $o,SV568: $i] :
      ( ( ( ( sK47_Xy @ SV568 @ SV228 )
          = SV568 )
        = $true )
      | ( ( SV228 @ ( sK47_Xy @ SV568 @ SV228 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2375: $i] :
                    ( ~ ( SV228 @ SY2375 )
                    | ( ( sK46_SY211 @ SV228 )
                      = SY2375 ) )
              | ~ ( SV228 @ ( sK46_SY211 @ SV228 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2220]) ).

thf(2416,plain,
    ! [SV229: $i,SV441: $i > $o] :
      ( ( ( ! [SY2705: $i] :
              ( ~ ( SV441 @ SY2705 )
              | ~ ( in @ SY2705 @ SV229 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV229
            @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) )
        = $true )
      | ( ( in @ ( sK74_Xx @ SV441 @ SV229 ) @ SV229 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2221]) ).

thf(2417,plain,
    ! [SV229: $i,SV441: $i > $o] :
      ( ( ( ~ ( in @ ( sK75_SY1878 @ SV441 @ SV229 ) @ SV229 )
          | ~ ~ ( ~ ( SV441 @ ( sK74_Xx @ SV441 @ SV229 ) )
                | ~ ~ ( ~ ( SV441 @ ( sK75_SY1878 @ SV441 @ SV229 ) )
                      | ~ ( ( ( sK74_Xx @ SV441 @ SV229 )
                           != ( sK75_SY1878 @ SV441 @ SV229 ) ) ) ) ) )
        = $false )
      | ( ( ! [SY2705: $i] :
              ( ~ ( SV441 @ SY2705 )
              | ~ ( in @ SY2705 @ SV229 ) )
          | ( singleton
            @ ( dsetconstr @ SV229
              @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2222]) ).

thf(2418,plain,
    ! [SV569: $i,SV442: $i,SV230: $i,SV706: $i] :
      ( ( ( ~ ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
              | ~ ~ ( ~ ( in @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
                          | ~ ~ ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 ) ) ) )
          | ~ ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
              | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                          | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
          | ( SV569 = SV706 ) )
        = $true )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2223]) ).

thf(2419,plain,
    ! [SV231: $i] :
      ( ( ( ~ ( in @ ( sK9_Xx @ SV231 ) @ omega )
          | ~ ( in @ ( sK9_Xx @ SV231 ) @ SV231 ) )
        = $false )
      | ( ( ~ ( in @ emptyset @ SV231 ) )
        = $true )
      | ( ( ! [SY2382: $i] :
              ( ~ ( in @ SY2382 @ omega )
              | ( in @ SY2382 @ SV231 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2224]) ).

thf(2420,plain,
    ! [SV231: $i] :
      ( ( ( in @ ( setadjoin @ ( sK9_Xx @ SV231 ) @ ( sK9_Xx @ SV231 ) ) @ SV231 )
        = $false )
      | ( ( ~ ( in @ emptyset @ SV231 ) )
        = $true )
      | ( ( ! [SY2382: $i] :
              ( ~ ( in @ SY2382 @ omega )
              | ( in @ SY2382 @ SV231 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2225]) ).

thf(2421,plain,
    ! [SV570: $i,SV443: $o,SV232: $i,SV707: $i] :
      ( ( ( ~ ( in @ SV707 @ SV232 ) )
        = $true )
      | ( ( SV443
          | ( in @ SV707
            @ ( dsetconstr @ SV232
              @ ^ [SY2950: $i] :
                  ( ~ ( ~ SV443
                      | ( SY2950 != SV570 ) )
                  | ~ ( ~ ~ SV443
                      | ( SY2950 != SV707 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV570 @ SV232 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2226]) ).

thf(2422,plain,
    ! [SV571: $i,SV232: $i,SV708: $i] :
      ( ( ( ~ ( in @ SV708 @ SV232 ) )
        = $true )
      | ( ( $true
          | ( in @ SV708
            @ ( dsetconstr @ SV232
              @ ^ [SY2951: $i] :
                  ( ~ ( ~ $true
                      | ( SY2951 != SV571 ) )
                  | ~ ( ~ ~ $true
                      | ( SY2951 != SV708 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV571 @ SV232 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2227]) ).

thf(2423,plain,
    ! [SV572: $i,SV232: $i,SV709: $i] :
      ( ( ( ~ ( in @ SV709 @ SV232 ) )
        = $true )
      | ( ( $false
          | ( in @ SV709
            @ ( dsetconstr @ SV232
              @ ^ [SY2952: $i] :
                  ( ~ ( ~ $false
                      | ( SY2952 != SV572 ) )
                  | ~ ( ~ ~ $false
                      | ( SY2952 != SV709 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV572 @ SV232 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2228]) ).

thf(2424,plain,
    ! [SV233: $i,SV658: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
              | ~ ~ ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 ) ) )
        = $true )
      | ( ( ! [SY2924: $i] :
              ~ ( in @ SY2924 @ SV658 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2925: $i] :
                    ( ~ ( in @ SY2925 @ ( sK15_B @ SV233 ) )
                    | ! [SY2926: $i] :
                        ( ~ ( in @ SY2926 @ SY2925 )
                        | ( in @ SY2926 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) )
                    | ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SY2925 ) )
              | ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) )
                          | ~ ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 ) )
                    | ~ ! [SY2927: $i] :
                          ( ~ ( in @ SY2927 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
                          | ~ ( in @ SY2927 @ SV658 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2229]) ).

thf(2425,plain,
    ! [SV233: $i] :
      ( ( ! [SY2392: $i,SY2393: $i] :
            ( ~ ( in @ SY2392 @ ( sK15_B @ SV233 ) )
            | ~ ( in @ SY2393 @ ( sK15_B @ SV233 ) )
            | ! [SX3: $i] :
                ( ~ ( in @ SX3 @ SY2392 )
                | ( in @ SX3 @ SY2393 ) )
            | ! [SX3: $i] :
                ( ~ ( in @ SX3 @ SY2393 )
                | ( in @ SX3 @ SY2392 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2230]) ).

thf(2426,plain,
    ! [SV233: $i] :
      ( ( ~ ( ~ ! [SY2396: $i] :
                  ( ~ ( in @ SY2396 @ ( sK15_B @ SV233 ) )
                  | ! [SY2397: $i] :
                      ( ~ ( in @ SY2397 @ SY2396 )
                      | ( in @ SY2397 @ SV233 ) ) )
            | ~ ! [SY2398: $i,SY2399: $i] :
                  ( ~ ( in @ SY2398 @ SV233 )
                  | ~ ( in @ SY2399 @ SV233 )
                  | ~ ( ~ ( in @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) @ ( sK15_B @ SV233 ) )
                      | ~ ~ ( ~ ( ~ ( in @ SY2398 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) )
                                | ~ ( in @ SY2399 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) ) )
                            | ~ ( ( in @ SY2398 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) )
                                | ( in @ SY2399 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) ) ) ) )
                  | ( SY2398 = SY2399 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2231]) ).

thf(2427,plain,
    ! [SV444: $i > $o,SV234: $i,SV728: $i] :
      ( ( ( ~ ( in @ SV728 @ SV234 )
          | ~ ( SV444 @ SV728 ) )
        = $true )
      | ( ( SV444 @ ( sK37_Xx @ SV444 @ SV234 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2232]) ).

thf(2428,plain,
    ! [SV444: $i > $o,SV234: $i,SV729: $i] :
      ( ( ( ~ ( in @ SV729 @ SV234 )
          | ~ ( SV444 @ SV729 ) )
        = $true )
      | ( ( in @ ( sK37_Xx @ SV444 @ SV234 ) @ SV234 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2233]) ).

thf(2429,plain,
    ! [SV573: $i,SV235: $i > $o] :
      ( ( ( SV235 @ ( sK33_SY142 @ SV573 @ SV235 ) )
        = $true )
      | ( ( ~ ( SV235 @ SV573 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2403: $i] :
                    ( ( SY2403
                     != ( sK32_Xx @ SV235 ) )
                    | ( SV235 @ SY2403 ) )
              | ~ ! [SY2404: $i] :
                    ( ~ ( SV235 @ SY2404 )
                    | ( SY2404
                      = ( sK32_Xx @ SV235 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2234]) ).

thf(2430,plain,
    ! [SV235: $i > $o,SV573: $i] :
      ( ( ( SV573
         != ( sK33_SY142 @ SV573 @ SV235 ) )
        = $true )
      | ( ( ~ ( SV235 @ SV573 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2403: $i] :
                    ( ( SY2403
                     != ( sK32_Xx @ SV235 ) )
                    | ( SV235 @ SY2403 ) )
              | ~ ! [SY2404: $i] :
                    ( ~ ( SV235 @ SY2404 )
                    | ( SY2404
                      = ( sK32_Xx @ SV235 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2235]) ).

thf(2431,plain,
    ! [SV236: $i,SV445: $i,SV574: $i,SV710: $i > $o] :
      ( ( ( ~ ( ~ ( in @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ SV236 )
              | ~ ~ ( ~ ( in @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) @ SV445 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) ) @ SV574 )
                          | ~ ~ ( SV710 @ ( kpair @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) ) ) ) ) ) )
        = $true )
      | ( ( ! [SY2953: $i] :
              ( ~ ( in @ SY2953 @ SV574 )
              | ( SV710 @ SY2953 ) ) )
        = $true )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2236]) ).

thf(2432,plain,
    ! [SV608: $i,SV237: $i,SV446: $i > $o] :
      ( ( ( ~ ( in @ ( sK35_Xx @ SV446 @ SV237 ) @ SV237 )
          | ~ ~ ( SV446 @ ( sK35_Xx @ SV446 @ SV237 ) ) )
        = $false )
      | ( ( SV446 @ SV608 )
        = $true )
      | ( ( in @ SV608 @ SV237 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2237]) ).

thf(2433,plain,
    ! [SV575: $i,SV447: $o,SV238: $i,SV711: $i] :
      ( ( ( ~ ( in @ SV711 @ SV238 ) )
        = $true )
      | ( ( ~ SV447
          | ( ( dsetconstr @ SV238
              @ ^ [SY2954: $i] :
                  ( ~ ( ~ SV447
                      | ( SY2954 != SV575 ) )
                  | ~ ( ~ ~ SV447
                      | ( SY2954 != SV711 ) ) ) )
            = ( setadjoin @ SV575 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV575 @ SV238 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2238]) ).

thf(2434,plain,
    ! [SV576: $i,SV238: $i,SV712: $i] :
      ( ( ( ~ ( in @ SV712 @ SV238 ) )
        = $true )
      | ( ( ~ $true
          | ( ( dsetconstr @ SV238
              @ ^ [SY2955: $i] :
                  ( ~ ( ~ $true
                      | ( SY2955 != SV576 ) )
                  | ~ ( ~ ~ $true
                      | ( SY2955 != SV712 ) ) ) )
            = ( setadjoin @ SV576 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV576 @ SV238 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2239]) ).

thf(2435,plain,
    ! [SV577: $i,SV238: $i,SV713: $i] :
      ( ( ( ~ ( in @ SV713 @ SV238 ) )
        = $true )
      | ( ( ~ $false
          | ( ( dsetconstr @ SV238
              @ ^ [SY2956: $i] :
                  ( ~ ( ~ $false
                      | ( SY2956 != SV577 ) )
                  | ~ ( ~ ~ $false
                      | ( SY2956 != SV713 ) ) ) )
            = ( setadjoin @ SV577 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV577 @ SV238 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2240]) ).

thf(2436,plain,
    ! [SV578: $i,SV239: $i] :
      ( ( ( in @ ( sK14_B @ SV239 ) @ SV239 )
        = $true )
      | ( ( in @ SV578 @ SV239 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2241]) ).

thf(2437,plain,
    ! [SV578: $i,SV239: $i] :
      ( ( ( ! [SY2416: $i] :
              ( ~ ( in @ SY2416 @ ( sK14_B @ SV239 ) )
              | ~ ( in @ SY2416 @ SV239 ) ) )
        = $true )
      | ( ( in @ SV578 @ SV239 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2242]) ).

thf(2438,plain,
    ! [SV579: $i,SV448: $o,SV240: $i,SV714: $i] :
      ( ( ( ~ ( in @ SV714 @ SV240 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV240
            @ ^ [SY2957: $i] :
                ( ~ ( ~ SV448
                    | ( SY2957 != SV579 ) )
                | ~ ( ~ ~ SV448
                    | ( SY2957 != SV714 ) ) ) ) )
        = $true )
      | ( ( in @ SV579 @ SV240 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2243]) ).

thf(2439,plain,
    ! [SV580: $i,SV240: $i,SV715: $i] :
      ( ( ( ~ ( in @ SV715 @ SV240 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV240
            @ ^ [SY2958: $i] :
                ( ~ ( ~ $true
                    | ( SY2958 != SV580 ) )
                | ~ ( ~ ~ $true
                    | ( SY2958 != SV715 ) ) ) ) )
        = $true )
      | ( ( in @ SV580 @ SV240 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2244]) ).

thf(2440,plain,
    ! [SV581: $i,SV240: $i,SV716: $i] :
      ( ( ( ~ ( in @ SV716 @ SV240 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV240
            @ ^ [SY2959: $i] :
                ( ~ ( ~ $false
                    | ( SY2959 != SV581 ) )
                | ~ ( ~ ~ $false
                    | ( SY2959 != SV716 ) ) ) ) )
        = $true )
      | ( ( in @ SV581 @ SV240 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2245]) ).

thf(2441,plain,
    ! [SV582: $i,SV241: $i > $o] :
      ( ( ( ~ ( SV241 @ ( sK44_Xx @ SV241 ) ) )
        = $false )
      | ( ( ~ ( ~ ! [SY2422: $i] :
                    ( ~ ( SV241 @ SY2422 )
                    | ( ( sK43_SY205 @ SV241 )
                      = SY2422 ) )
              | ~ ( SV241 @ ( sK43_SY205 @ SV241 ) ) ) )
        = $true )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2246]) ).

thf(2442,plain,
    ! [SV582: $i,SV241: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV241 @ ( sK45_SY1868 @ SV241 ) )
                | ~ ( ( ( sK44_Xx @ SV241 )
                     != ( sK45_SY1868 @ SV241 ) ) ) ) )
        = $false )
      | ( ( ~ ( ~ ! [SY2422: $i] :
                    ( ~ ( SV241 @ SY2422 )
                    | ( ( sK43_SY205 @ SV241 )
                      = SY2422 ) )
              | ~ ( SV241 @ ( sK43_SY205 @ SV241 ) ) ) )
        = $true )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2246]) ).

thf(2443,plain,
    ! [SV242: $i,SV449: $i] :
      ( ( ( in @ ( sK64_Xx @ SV449 @ SV242 ) @ SV449 )
        = $false )
      | ( ( subset @ SV242 @ SV449 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2248]) ).

thf(2444,plain,
    ! [SV609: $i,SV730: $i,SV659: $i] :
      ( ( ( ~ ( in @ SV659 @ SV730 )
          | ~ ( in @ SV730 @ SV609 ) )
        = $true )
      | ( ( in @ SV659 @ ( setunion @ SV609 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2249]) ).

thf(2445,plain,
    ! [SV610: $i,SV660: $i] :
      ( ( ( in @ SV660 @ ( setunion @ SV610 ) )
        = $false )
      | ( ( ~ ( ~ ( in @ SV660 @ ( sK8_B @ SV660 @ SV610 ) )
              | ~ ( in @ ( sK8_B @ SV660 @ SV610 ) @ SV610 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2250]) ).

thf(2446,plain,
    ! [SV583: $i,SV717: $i,SV450: $i,SV243: $i] :
      ( ( ( ~ ( func @ SV243 @ SV450 @ SV717 ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK90_Xx @ SV717 @ SV583 @ SV450 @ SV243 ) @ SV243 )
              | ~ ( ( ( ap @ SV243 @ SV450 @ SV583 @ ( sK90_Xx @ SV717 @ SV583 @ SV450 @ SV243 ) )
                   != ( ap @ SV243 @ SV450 @ SV717 @ ( sK90_Xx @ SV717 @ SV583 @ SV450 @ SV243 ) ) ) ) )
          | ( SV583 = SV717 ) )
        = $true )
      | ( ( func @ SV243 @ SV450 @ SV583 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2251]) ).

thf(2447,plain,
    ! [SV244: $i,SV584: $i,SV611: $i > $i] :
      ( ( ( in @ ( sK93_Xx @ SV611 @ SV584 @ SV244 ) @ SV244 )
        = $true )
      | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2252]) ).

thf(2448,plain,
    ! [SV244: $i,SV584: $i,SV611: $i > $i] :
      ( ( ( ~ ( in @ ( SV611 @ ( sK93_Xx @ SV611 @ SV584 @ SV244 ) ) @ SV584 ) )
        = $true )
      | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2253]) ).

thf(2449,plain,
    ! [SV585: $i,SV451: $i,SV245: $i,SV718: $i] :
      ( ( ( ~ ( in @ SV718 @ ( funcSet @ SV245 @ SV451 ) ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK91_Xx @ SV718 @ SV585 @ SV451 @ SV245 ) @ SV245 )
              | ~ ( ( ( ap @ SV245 @ SV451 @ SV585 @ ( sK91_Xx @ SV718 @ SV585 @ SV451 @ SV245 ) )
                   != ( ap @ SV245 @ SV451 @ SV718 @ ( sK91_Xx @ SV718 @ SV585 @ SV451 @ SV245 ) ) ) ) )
          | ( SV585 = SV718 ) )
        = $true )
      | ( ( in @ SV585 @ ( funcSet @ SV245 @ SV451 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2254]) ).

thf(2450,plain,
    ! [SV246: $i,SV731: $i,SV452: $i > $o] :
      ( ( ( ~ ( SV452 @ SV731 )
          | ~ ( in @ SV731 @ SV246 ) )
        = $true )
      | ( ( in @ ( sK36_Xx @ SV452 @ SV246 ) @ SV246 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2255]) ).

thf(2451,plain,
    ! [SV246: $i,SV732: $i,SV452: $i > $o] :
      ( ( ( ~ ( SV452 @ SV732 )
          | ~ ( in @ SV732 @ SV246 ) )
        = $true )
      | ( ( SV452 @ ( sK36_Xx @ SV452 @ SV246 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2256]) ).

thf(2452,plain,
    ! [SV586: $i,SV247: $i > $o] :
      ( ( ( SV247 @ ( sK22_SY74 @ SV586 @ SV247 ) )
        = $true )
      | ( ( ~ ( SV247 @ SV586 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2435: $i] :
                    ( ~ ( SV247 @ SY2435 )
                    | ( ( sK21_Xx @ SV247 )
                      = SY2435 ) )
              | ~ ( SV247 @ ( sK21_Xx @ SV247 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2257]) ).

thf(2453,plain,
    ! [SV247: $i > $o,SV586: $i] :
      ( ( ( SV586
         != ( sK22_SY74 @ SV586 @ SV247 ) )
        = $true )
      | ( ( ~ ( SV247 @ SV586 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2435: $i] :
                    ( ~ ( SV247 @ SY2435 )
                    | ( ( sK21_Xx @ SV247 )
                      = SY2435 ) )
              | ~ ( SV247 @ ( sK21_Xx @ SV247 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2258]) ).

thf(2454,plain,
    ! [SV248: $i,SV453: $i,SV661: $i > $o,SV719: $i > $o] :
      ( ( ( ~ ( ~ ( in @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) @ SV248 )
              | ~ ~ ( ~ ( in @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) @ SV453 )
                    | ~ ~ ( ( ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 )
                           != ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) )
                          | ~ ~ ( ~ ( ~ ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
                                    | ~ ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) )
                                | ~ ( ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
                                    | ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) ) ) ) ) ) )
        = $true )
      | ( ( ( dsetconstr @ SV248
            @ ^ [SY2930: $i] : ( SV661 @ SY2930 ) )
          = ( dsetconstr @ SV453
            @ ^ [SY2961: $i] : ( SV719 @ SY2961 ) ) )
        = $true )
      | ( ( SV248 = SV453 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2259]) ).

thf(2455,plain,
    ! [SV249: $i,SV454: $i > $o] :
      ( ( ( SV454 @ ( sK72_Xx @ SV454 @ SV249 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV249
            @ ^ [SY2732: $i] : ( SV454 @ SY2732 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2260]) ).

thf(2456,plain,
    ! [SV249: $i,SV454: $i > $o] :
      ( ( ( in @ ( sK72_Xx @ SV454 @ SV249 ) @ SV249 )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV249
            @ ^ [SY2732: $i] : ( SV454 @ SY2732 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2261]) ).

thf(2457,plain,
    ! [SV612: $i,SV250: $i,SV1: $i,SV733: $i] :
      ( ( ( ~ ( in @ SV733 @ ( powerset @ SV1 ) )
          | ! [SY2966: $i] :
              ( ~ ( in @ SY2966 @ SV1 )
              | ~ ( in @ SY2966 @ ( binintersect @ SV250 @ SV612 ) )
              | ( in @ SY2966 @ ( binunion @ SV250 @ SV733 ) ) ) )
        = $true )
      | ( ( in @ SV612 @ ( powerset @ SV1 ) )
        = $false )
      | ( ( in @ SV250 @ ( powerset @ SV1 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2262]) ).

thf(2458,plain,
    ! [SV613: $i,SV251: $i,SV2: $i,SV734: $i] :
      ( ( ( ~ ( in @ SV734 @ SV2 )
          | ( in @ SV734 @ ( binunion @ SV251 @ SV613 ) )
          | ~ ( in @ SV734 @ SV613 ) )
        = $true )
      | ( ( in @ SV613 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV251 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2263]) ).

thf(2459,plain,
    ! [SV614: $i,SV252: $i,SV3: $i,SV735: $i] :
      ( ( ( ~ ( in @ SV735 @ SV3 )
          | ( in @ SV735 @ ( binunion @ SV252 @ SV614 ) )
          | ~ ( in @ SV735 @ SV252 ) )
        = $true )
      | ( ( in @ SV614 @ ( powerset @ SV3 ) )
        = $false )
      | ( ( in @ SV252 @ ( powerset @ SV3 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2264]) ).

thf(2460,plain,
    ! [SV615: $i,SV4: $i,SV253: $i] :
      ( ( ( ~ ( subset @ SV253 @ ( setminus @ SV4 @ SV615 ) ) )
        = $true )
      | ( ( subset @ SV615 @ ( setminus @ SV4 @ SV253 ) )
        = $true )
      | ( ( in @ SV615 @ ( powerset @ SV4 ) )
        = $false )
      | ( ( in @ SV253 @ ( powerset @ SV4 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2265]) ).

thf(2461,plain,
    ! [SV616: $i,SV5: $i,SV254: $i] :
      ( ( ( ~ ( subset @ SV254 @ ( setminus @ SV5 @ SV616 ) ) )
        = $true )
      | ( ( ! [SY2899: $i] :
              ( ~ ( in @ SY2899 @ SV5 )
              | ~ ( in @ SY2899 @ SV616 )
              | ( in @ SY2899 @ ( setminus @ SV5 @ SV254 ) ) ) )
        = $true )
      | ( ( in @ SV616 @ ( powerset @ SV5 ) )
        = $false )
      | ( ( in @ SV254 @ ( powerset @ SV5 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2266]) ).

thf(2462,plain,
    ! [SV619: $i,SV257: $i,SV8: $i,SV736: $i] :
      ( ( ( ~ ( in @ SV736 @ SV8 )
          | ~ ( in @ SV736 @ ( setminus @ SV8 @ SV257 ) )
          | ( in @ SV736 @ ( setminus @ SV8 @ ( binintersect @ SV257 @ SV619 ) ) ) )
        = $true )
      | ( ( in @ SV619 @ ( powerset @ SV8 ) )
        = $false )
      | ( ( in @ SV257 @ ( powerset @ SV8 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2269]) ).

thf(2463,plain,
    ! [SV620: $i,SV258: $i,SV9: $i,SV737: $i] :
      ( ( ( ~ ( in @ SV737 @ SV9 )
          | ~ ( in @ SV737 @ ( setminus @ SV9 @ SV258 ) )
          | ~ ( in @ SV737 @ ( binintersect @ SV258 @ SV620 ) ) )
        = $true )
      | ( ( in @ SV620 @ ( powerset @ SV9 ) )
        = $false )
      | ( ( in @ SV258 @ ( powerset @ SV9 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2270]) ).

thf(2464,plain,
    ! [SV262: $i,SV13: $i,SV621: $i] :
      ( ( ( ~ ( in @ SV621 @ ( setminus @ SV13 @ ( setminus @ SV13 @ SV262 ) ) ) )
        = $true )
      | ( ( in @ SV621 @ SV262 )
        = $true )
      | ( ( in @ SV621 @ SV13 )
        = $false )
      | ( ( in @ SV262 @ ( powerset @ SV13 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2271]) ).

thf(2465,plain,
    ! [SV14: $i,SV263: $i,SV622: $i] :
      ( ( ( ~ ( in @ SV622 @ SV263 ) )
        = $true )
      | ( ( in @ SV622 @ ( setminus @ SV14 @ ( setminus @ SV14 @ SV263 ) ) )
        = $true )
      | ( ( in @ SV622 @ SV14 )
        = $false )
      | ( ( in @ SV263 @ ( powerset @ SV14 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2272]) ).

thf(2466,plain,
    ! [SV264: $i,SV623: $i,SV15: $i] :
      ( ( ( ~ ( subset @ ( setminus @ SV15 @ SV623 ) @ ( setminus @ SV15 @ SV264 ) ) )
        = $true )
      | ( ( subset @ SV264 @ SV623 )
        = $true )
      | ( ( in @ SV623 @ ( powerset @ SV15 ) )
        = $false )
      | ( ( in @ SV264 @ ( powerset @ SV15 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2273]) ).

thf(2467,plain,
    ! [SV16: $i,SV624: $i,SV265: $i] :
      ( ( ( ~ ( subset @ SV265 @ SV624 ) )
        = $true )
      | ( ( subset @ ( setminus @ SV16 @ SV624 ) @ ( setminus @ SV16 @ SV265 ) )
        = $true )
      | ( ( in @ SV624 @ ( powerset @ SV16 ) )
        = $false )
      | ( ( in @ SV265 @ ( powerset @ SV16 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2274]) ).

thf(2468,plain,
    ! [SV625: $i,SV266: $i,SV17: $i,SV738: $i] :
      ( ( ( ~ ( in @ SV738 @ SV17 )
          | ~ ( subset @ SV266 @ SV625 )
          | ( in @ SV738 @ SV625 )
          | ~ ( in @ SV738 @ SV266 ) )
        = $true )
      | ( ( in @ SV625 @ ( powerset @ SV17 ) )
        = $false )
      | ( ( in @ SV266 @ ( powerset @ SV17 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2275]) ).

thf(2469,plain,
    ! [SV626: $i,SV267: $i,SV18: $i,SV739: $i] :
      ( ( ( ~ ( in @ SV739 @ SV18 )
          | ~ ( subset @ SV267 @ ( setminus @ SV18 @ SV626 ) )
          | ~ ( in @ SV739 @ SV626 )
          | ~ ( in @ SV739 @ SV267 ) )
        = $true )
      | ( ( in @ SV626 @ ( powerset @ SV18 ) )
        = $false )
      | ( ( in @ SV267 @ ( powerset @ SV18 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2276]) ).

thf(2470,plain,
    ! [SV268: $i,SV627: $i,SV19: $i,SV740: $i] :
      ( ( ( ~ ( in @ SV740 @ SV19 )
          | ( in @ SV740 @ SV627 )
          | ~ ( in @ SV740 @ ( binintersect @ SV268 @ SV627 ) ) )
        = $true )
      | ( ( in @ SV627 @ ( powerset @ SV19 ) )
        = $false )
      | ( ( in @ SV268 @ ( powerset @ SV19 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2277]) ).

thf(2471,plain,
    ! [SV628: $i,SV269: $i,SV20: $i,SV741: $i] :
      ( ( ( ~ ( in @ SV741 @ SV20 )
          | ( in @ SV741 @ SV269 )
          | ~ ( in @ SV741 @ ( binintersect @ SV269 @ SV628 ) ) )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV20 ) )
        = $false )
      | ( ( in @ SV269 @ ( powerset @ SV20 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2278]) ).

thf(2472,plain,
    ! [SV270: $i,SV21: $i,SV629: $i] :
      ( ( ( in @ SV629 @ ( setminus @ SV21 @ SV270 ) )
        = $true )
      | ( ( in @ SV629 @ SV270 )
        = $true )
      | ( ( in @ SV629 @ SV21 )
        = $false )
      | ( ( in @ SV270 @ ( powerset @ SV21 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2279]) ).

thf(2473,plain,
    ! [SV22: $i,SV271: $i,SV630: $i] :
      ( ( ( ~ ( in @ SV630 @ SV271 ) )
        = $true )
      | ( ( ~ ( in @ SV630 @ ( setminus @ SV22 @ SV271 ) ) )
        = $true )
      | ( ( in @ SV630 @ SV22 )
        = $false )
      | ( ( in @ SV271 @ ( powerset @ SV22 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2280]) ).

thf(2474,plain,
    ! [SV631: $i,SV272: $i,SV23: $i,SV742: $i] :
      ( ( ( ~ ( in @ SV742 @ SV23 )
          | ~ ( in @ SV272 @ ( powerset @ SV631 ) )
          | ~ ( in @ SV742 @ SV272 )
          | ( in @ SV742 @ SV631 ) )
        = $true )
      | ( ( in @ SV631 @ ( powerset @ SV23 ) )
        = $false )
      | ( ( in @ SV272 @ ( powerset @ SV23 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2281]) ).

thf(2475,plain,
    ! [SV455: $i,SV278: $o,SV29: $i,SV662: $i] :
      ( ( ( in @ SV662 @ SV29 )
        = $false )
      | ( ( in @ ( if @ SV29 @ SV278 @ SV455 @ SV662 ) @ ( setadjoin @ SV455 @ ( setadjoin @ SV662 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV455 @ SV29 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2285]) ).

thf(2476,plain,
    ! [SV456: $i,SV29: $i,SV663: $i] :
      ( ( ( in @ SV663 @ SV29 )
        = $false )
      | ( ( in @ ( if @ SV29 @ $true @ SV456 @ SV663 ) @ ( setadjoin @ SV456 @ ( setadjoin @ SV663 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV456 @ SV29 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2286]) ).

thf(2477,plain,
    ! [SV457: $i,SV29: $i,SV664: $i] :
      ( ( ( in @ SV664 @ SV29 )
        = $false )
      | ( ( in @ ( if @ SV29 @ $false @ SV457 @ SV664 ) @ ( setadjoin @ SV457 @ ( setadjoin @ SV664 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV457 @ SV29 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2287]) ).

thf(2478,plain,
    ! [SV458: $i,SV279: $o,SV30: $i,SV665: $i] :
      ( ( ( in @ SV665 @ SV30 )
        = $false )
      | ( ( SV279
          | ( ( if @ SV30 @ SV279 @ SV458 @ SV665 )
            = SV665 ) )
        = $true )
      | ( ( in @ SV458 @ SV30 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2288]) ).

thf(2479,plain,
    ! [SV459: $i,SV30: $i,SV666: $i] :
      ( ( ( in @ SV666 @ SV30 )
        = $false )
      | ( ( $true
          | ( ( if @ SV30 @ $true @ SV459 @ SV666 )
            = SV666 ) )
        = $true )
      | ( ( in @ SV459 @ SV30 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2289]) ).

thf(2480,plain,
    ! [SV460: $i,SV30: $i,SV667: $i] :
      ( ( ( in @ SV667 @ SV30 )
        = $false )
      | ( ( $false
          | ( ( if @ SV30 @ $false @ SV460 @ SV667 )
            = SV667 ) )
        = $true )
      | ( ( in @ SV460 @ SV30 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2290]) ).

thf(2481,plain,
    ! [SV461: $i,SV280: $o,SV31: $i,SV668: $i] :
      ( ( ( in @ SV668 @ SV31 )
        = $false )
      | ( ( ~ SV280
          | ( ( if @ SV31 @ SV280 @ SV461 @ SV668 )
            = SV461 ) )
        = $true )
      | ( ( in @ SV461 @ SV31 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2291]) ).

thf(2482,plain,
    ! [SV462: $i,SV31: $i,SV669: $i] :
      ( ( ( in @ SV669 @ SV31 )
        = $false )
      | ( ( ~ $true
          | ( ( if @ SV31 @ $true @ SV462 @ SV669 )
            = SV462 ) )
        = $true )
      | ( ( in @ SV462 @ SV31 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2292]) ).

thf(2483,plain,
    ! [SV463: $i,SV31: $i,SV670: $i] :
      ( ( ( in @ SV670 @ SV31 )
        = $false )
      | ( ( ~ $false
          | ( ( if @ SV31 @ $false @ SV463 @ SV670 )
            = SV463 ) )
        = $true )
      | ( ( in @ SV463 @ SV31 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2293]) ).

thf(2484,plain,
    ! [SV464: $i,SV281: $o,SV33: $i,SV671: $i] :
      ( ( ( in @ SV671 @ SV33 )
        = $false )
      | ( ( in @ ( if @ SV33 @ SV281 @ SV464 @ SV671 ) @ SV33 )
        = $true )
      | ( ( in @ SV464 @ SV33 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2294]) ).

thf(2485,plain,
    ! [SV465: $i,SV33: $i,SV672: $i] :
      ( ( ( in @ SV672 @ SV33 )
        = $false )
      | ( ( in @ ( if @ SV33 @ $true @ SV465 @ SV672 ) @ SV33 )
        = $true )
      | ( ( in @ SV465 @ SV33 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2295]) ).

thf(2486,plain,
    ! [SV466: $i,SV33: $i,SV673: $i] :
      ( ( ( in @ SV673 @ SV33 )
        = $false )
      | ( ( in @ ( if @ SV33 @ $false @ SV466 @ SV673 ) @ SV33 )
        = $true )
      | ( ( in @ SV466 @ SV33 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2296]) ).

thf(2487,plain,
    ! [SV588: $i,SV469: $i,SV36: $i,SV720: $i] :
      ( ( ( in @ SV720 @ SV36 )
        = $false )
      | ( $true = $true )
      | ( ( func @ SV36 @ SV469 @ SV588 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2297]) ).

thf(2488,plain,
    ! [SV470: $i,SV589: $i,SV37: $i,SV721: $i] :
      ( ( ( in @ SV721 @ SV37 )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV589 @ ( funcSet @ SV37 @ SV470 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2298]) ).

thf(2489,plain,
    ! [SV471: $i,SV284: $i,SV38: $i,SV674: $i] :
      ( ( ( in @ SV674 @ SV38 )
        = $false )
      | ( ( ! [SY2932: $i] :
              ( ~ ( in @ SY2932 @ SV284 )
              | ~ ( in @ ( kpair @ SV674 @ SY2932 ) @ SV471 )
              | ( ( ap @ SV38 @ SV284 @ SV471 @ SV674 )
                = SY2932 ) ) )
        = $true )
      | ( ( in @ SV471 @ ( funcSet @ SV38 @ SV284 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2299]) ).

thf(2490,plain,
    ! [SV472: $i,SV285: $i,SV39: $i,SV675: $i] :
      ( ( ( in @ SV675 @ SV39 )
        = $false )
      | ( ( ! [SY2933: $i] :
              ( ~ ( in @ SY2933 @ SV285 )
              | ~ ( in @ ( kpair @ SV675 @ SY2933 ) @ SV472 )
              | ( ( ap @ SV39 @ SV285 @ SV472 @ SV675 )
                = SY2933 ) ) )
        = $true )
      | ( ( func @ SV39 @ SV285 @ SV472 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2300]) ).

thf(2491,plain,
    ! [SV473: $i,SV286: $i,SV40: $i,SV676: $i] :
      ( ( ( in @ SV676 @ SV40 )
        = $false )
      | ( ( in @ ( kpair @ SV676 @ ( ap @ SV40 @ SV286 @ SV473 @ SV676 ) ) @ SV473 )
        = $true )
      | ( ( in @ SV473 @ ( funcSet @ SV40 @ SV286 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2301]) ).

thf(2492,plain,
    ! [SV474: $i,SV287: $i,SV41: $i,SV677: $i] :
      ( ( ( in @ SV677 @ SV41 )
        = $false )
      | ( ( in @ ( kpair @ SV677 @ ( ap @ SV41 @ SV287 @ SV474 @ SV677 ) ) @ SV474 )
        = $true )
      | ( ( func @ SV41 @ SV287 @ SV474 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2302]) ).

thf(2493,plain,
    ! [SV635: $i,SV288: $i > $o,SV42: $i,SV743: $i] :
      ( ( ( ~ ( in @ SV743 @ SV42 )
          | ~ ( SV288 @ SV635 )
          | ~ ( SV288 @ SV743 )
          | ( SV635 = SV743 ) )
        = $true )
      | ( ( in @ SV635 @ SV42 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV42
            @ ^ [SY2500: $i] : ( SV288 @ SY2500 ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2303]) ).

thf(2494,plain,
    ! [SV476: $i,SV290: $i,SV44: $i,SV678: $i] :
      ( ( ( in @ SV678 @ SV44 )
        = $false )
      | ( ( in @ ( ap @ SV44 @ SV290 @ SV476 @ SV678 ) @ SV290 )
        = $true )
      | ( ( in @ SV476 @ ( funcSet @ SV44 @ SV290 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2304]) ).

thf(2495,plain,
    ! [SV478: $i,SV292: $i,SV46: $i,SV679: $i] :
      ( ( ( in @ SV679 @ SV46 )
        = $false )
      | ( ( in @ ( ap @ SV46 @ SV292 @ SV478 @ SV679 ) @ SV292 )
        = $true )
      | ( ( func @ SV46 @ SV292 @ SV478 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2305]) ).

thf(2496,plain,
    ! [SV479: $i,SV293: $i,SV47: $i,SV680: $i] :
      ( ( ( in @ SV680 @ SV47 )
        = $false )
      | ( ( in
          @ ( setunion
            @ ( dsetconstr @ SV293
              @ ^ [SY2934: $i] : ( in @ ( kpair @ SV680 @ SY2934 ) @ SV479 ) ) )
          @ SV293 )
        = $true )
      | ( ( func @ SV47 @ SV293 @ SV479 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2306]) ).

thf(2497,plain,
    ! [SV480: $i,SV294: $i,SV48: $i,SV681: $i] :
      ( ( ( in @ SV681 @ SV48 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV294
            @ ^ [SY2935: $i] : ( in @ ( kpair @ SV681 @ SY2935 ) @ SV480 ) ) )
        = $true )
      | ( ( func @ SV48 @ SV294 @ SV480 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2307]) ).

thf(2498,plain,
    ! [SV484: $i > $i > $o,SV52: $i,SV593: $i,SV298: $i,SV722: $i] :
      ( ( ( ~ ( in @ SV722 @ SV298 ) )
        = $true )
      | ( ( ~ ( in @ ( kpair @ SV593 @ SV722 )
              @ ( dpsetconstr @ SV52 @ SV298
                @ ^ [SY2775: $i,SY2776: $i] : ( SV484 @ SY2775 @ SY2776 ) ) )
          | ( SV484 @ SV593 @ SV722 ) )
        = $true )
      | ( ( in @ SV593 @ SV52 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2311]) ).

thf(2499,plain,
    ! [SV55: $i,SV594: $i,SV487: $i > $i > $o,SV301: $i,SV723: $i] :
      ( ( ( ~ ( in @ SV723 @ SV301 ) )
        = $true )
      | ( ( ~ ( SV487 @ SV594 @ SV723 )
          | ( in @ ( kpair @ SV594 @ SV723 )
            @ ( dpsetconstr @ SV55 @ SV301
              @ ^ [SY2783: $i,SY2784: $i] : ( SV487 @ SY2783 @ SY2784 ) ) ) )
        = $true )
      | ( ( in @ SV594 @ SV55 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2312]) ).

thf(2500,plain,
    ! [SV57: $i,SV489: $i,SV303: $i,SV683: $i] :
      ( ( ( in @ SV683 @ SV303 )
        = $false )
      | ( ( ( ksnd @ ( kpair @ SV489 @ SV683 ) )
          = SV683 )
        = $true )
      | ( ( in @ SV489 @ SV57 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2313]) ).

thf(2501,plain,
    ! [SV58: $i,SV490: $i,SV304: $i,SV684: $i] :
      ( ( ( in @ SV684 @ SV304 )
        = $false )
      | ( ( ( kfst @ ( kpair @ SV490 @ SV684 ) )
          = SV490 )
        = $true )
      | ( ( in @ SV490 @ SV58 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2314]) ).

thf(2502,plain,
    ! [SV59: $i,SV491: $i,SV685: $i,SV724: $i] :
      ( ( ( in @ SV724 @ SV685 )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV491 @ SV59 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2315]) ).

thf(2503,plain,
    ! [SV69: $i,SV312: $i,SV599: $i,SV497: $i] :
      ( ( ( SV497 = SV599 )
        = $false )
      | ( ( SV312 = SV599 )
        = $true )
      | ( ( ( setadjoin @ ( setadjoin @ SV69 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV69 @ ( setadjoin @ SV312 @ emptyset ) ) @ emptyset ) )
          = ( setadjoin @ ( setadjoin @ SV497 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV497 @ ( setadjoin @ SV599 @ emptyset ) ) @ emptyset ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2316]) ).

thf(2504,plain,
    ! [SV84: $i,SV503: $i,SV322: $i,SV686: $i] :
      ( ( ( in @ SV686 @ SV322 )
        = $false )
      | ( ( in @ ( kpair @ SV503 @ SV686 ) @ ( cartprod @ SV84 @ SV322 ) )
        = $true )
      | ( ( in @ SV503 @ SV84 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2317]) ).

thf(2505,plain,
    ! [SV85: $i,SV504: $i,SV323: $i,SV687: $i] :
      ( ( ( in @ SV687 @ SV323 )
        = $false )
      | ( ( in @ ( kpair @ SV504 @ SV687 ) @ ( powerset @ ( powerset @ ( binunion @ SV85 @ SV323 ) ) ) )
        = $true )
      | ( ( in @ SV504 @ SV85 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2318]) ).

thf(2506,plain,
    ! [SV86: $i,SV505: $i,SV324: $i,SV688: $i] :
      ( ( ( in @ SV688 @ SV324 )
        = $false )
      | ( ( in @ ( setadjoin @ ( setadjoin @ SV505 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV505 @ ( setadjoin @ SV688 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV86 @ SV324 ) ) ) )
        = $true )
      | ( ( in @ SV505 @ SV86 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2319]) ).

thf(2507,plain,
    ! [SV87: $i,SV506: $i,SV325: $i,SV689: $i] :
      ( ( ( in @ SV689 @ SV325 )
        = $false )
      | ( ( subset @ ( setadjoin @ ( setadjoin @ SV506 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV506 @ ( setadjoin @ SV689 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV87 @ SV325 ) ) )
        = $true )
      | ( ( in @ SV506 @ SV87 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2320]) ).

thf(2508,plain,
    ! [SV88: $i,SV507: $i,SV326: $i,SV690: $i] :
      ( ( ( in @ SV690 @ SV326 )
        = $false )
      | ( ( in @ ( setadjoin @ SV507 @ ( setadjoin @ SV690 @ emptyset ) ) @ ( powerset @ ( binunion @ SV88 @ SV326 ) ) )
        = $true )
      | ( ( in @ SV507 @ SV88 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2321]) ).

thf(2509,plain,
    ! [SV89: $i,SV508: $i,SV327: $i,SV691: $i] :
      ( ( ( in @ SV691 @ SV327 )
        = $false )
      | ( ( subset @ ( setadjoin @ SV508 @ ( setadjoin @ SV691 @ emptyset ) ) @ ( binunion @ SV89 @ SV327 ) )
        = $true )
      | ( ( in @ SV508 @ SV89 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2322]) ).

thf(2510,plain,
    ! [SV338: $i,SV100: $i,SV512: $i] :
      ( ( ( in @ SV512 @ ( symdiff @ SV100 @ SV338 ) )
        = $false )
      | ( ( in @ SV512 @ SV338 )
        = $false )
      | ( ( in @ SV512 @ SV100 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2323]) ).

thf(2511,plain,
    ! [SV387: $i,SV153: $i,SV692: $i,SV644: $i] :
      ( ( ( SV644 = SV692 )
        = $false )
      | ( ( ( setadjoin @ SV153 @ SV644 )
          = ( setadjoin @ SV387 @ SV692 ) )
        = $true )
      | ( ( SV153 = SV387 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2331]) ).

thf(2512,plain,
    ! [SV388: $i,SV154: $i,SV693: $i,SV645: $i] :
      ( ( ( SV645 = SV693 )
        = $false )
      | ( ( ~ ( in @ SV645 @ SV154 )
          | ( in @ SV693 @ SV388 ) )
        = $true )
      | ( ( SV154 = SV388 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2332]) ).

thf(2513,plain,
    ! [SV600: $i,SV390: $i > $o,SV158: $i] :
      ( ( ( ( dsetconstr @ SV158
            @ ^ [SY2616: $i] : ( SV390 @ SY2616 ) )
          = emptyset )
        = $false )
      | ( ( SV390 @ SV600 )
        = $false )
      | ( ( in @ SV600 @ SV158 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2333]) ).

thf(2514,plain,
    ! [SV538: $i,SV404: $i > $o,SV177: $i] :
      ( ( ( ( dsetconstr @ SV177
            @ ^ [SY2623: $i] : ( SV404 @ SY2623 ) )
          = emptyset )
        = $false )
      | ( ( SV404 @ SV538 )
        = $false )
      | ( ( in @ SV538 @ SV177 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2336]) ).

thf(2515,plain,
    ! [SV189: $i,SV409: $i,SV647: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK97_Xx @ SV647 @ SV409 @ SV189 ) @ SV189 )
              | ~ ~ ( ~ ( in @ ( sK97_Xx @ SV647 @ SV409 @ SV189 ) @ SV409 )
                    | ~ ~ ( in @ ( sK97_Xx @ SV647 @ SV409 @ SV189 ) @ SV647 ) ) ) )
        = $true )
      | ( ( subset @ SV409 @ SV647 )
        = $true )
      | ( ( in @ SV647 @ ( powerset @ SV189 ) )
        = $false )
      | ( ( in @ SV409 @ ( powerset @ SV189 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2338]) ).

thf(2516,plain,
    ! [SV602: $i,SV648: $i] :
      ( ( ( ~ ( in @ ( sK7_Xx @ SV648 @ SV602 ) @ SV648 ) )
        = $false )
      | ( ( in @ SV648 @ ( powerset @ SV602 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2339]) ).

thf(2517,plain,
    ! [SV602: $i,SV648: $i] :
      ( ( ( ~ ~ ( in @ ( sK7_Xx @ SV648 @ SV602 ) @ SV602 ) )
        = $false )
      | ( ( in @ SV648 @ ( powerset @ SV602 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2339]) ).

thf(2518,plain,
    ! [SV603: $i,SV649: $i,SV744: $i] :
      ( ( ( ~ ( in @ SV744 @ SV649 )
          | ( in @ SV744 @ SV603 ) )
        = $true )
      | ( ( in @ SV649 @ ( powerset @ SV603 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2340]) ).

thf(2519,plain,
    ! [SV545: $i,SV190: $i > $o] :
      ( ( ( SV190 @ SV545 )
        = $false )
      | ( ( SV190 @ ( sK24_SY86 @ SV545 @ SV190 ) )
        = $true )
      | ( ( SV190 @ ( sK23_Xx @ SV190 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2341]) ).

thf(2520,plain,
    ! [SV190: $i > $o,SV545: $i] :
      ( ( ( SV545
          = ( sK24_SY86 @ SV545 @ SV190 ) )
        = $false )
      | ( ( ~ ( SV190 @ SV545 ) )
        = $true )
      | ( ( SV190 @ ( sK23_Xx @ SV190 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2342]) ).

thf(2521,plain,
    ! [SV546: $i,SV410: $o,SV191: $i,SV694: $i] :
      ( ( ( in @ SV694 @ SV191 )
        = $false )
      | ( ( ~ SV410
          | ( in @ SV546
            @ ( dsetconstr @ SV191
              @ ^ [SY2939: $i] :
                  ( ~ ( ~ SV410
                      | ( SY2939 != SV546 ) )
                  | ~ ( ~ ~ SV410
                      | ( SY2939 != SV694 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV546 @ SV191 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2343]) ).

thf(2522,plain,
    ! [SV547: $i,SV191: $i,SV695: $i] :
      ( ( ( in @ SV695 @ SV191 )
        = $false )
      | ( ( ~ $true
          | ( in @ SV547
            @ ( dsetconstr @ SV191
              @ ^ [SY2940: $i] :
                  ( ~ ( ~ $true
                      | ( SY2940 != SV547 ) )
                  | ~ ( ~ ~ $true
                      | ( SY2940 != SV695 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV547 @ SV191 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2344]) ).

thf(2523,plain,
    ! [SV548: $i,SV191: $i,SV696: $i] :
      ( ( ( in @ SV696 @ SV191 )
        = $false )
      | ( ( ~ $false
          | ( in @ SV548
            @ ( dsetconstr @ SV191
              @ ^ [SY2941: $i] :
                  ( ~ ( ~ $false
                      | ( SY2941 != SV548 ) )
                  | ~ ( ~ ~ $false
                      | ( SY2941 != SV696 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV548 @ SV191 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2345]) ).

thf(2524,plain,
    ! [SV549: $i > $i,SV411: $i,SV192: $i,SV745: $i] :
      ( ( ( ~ ( in @ SV745 @ SV192 )
          | ( ( ap @ SV192 @ SV411
              @ ( lam @ SV192 @ SV411
                @ ^ [SY2811: $i] : ( SV549 @ SY2811 ) )
              @ SV745 )
            = ( SV549 @ SV745 ) ) )
        = $true )
      | ( ( in @ ( sK92_Xx @ SV549 @ SV411 @ SV192 ) @ SV192 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2346]) ).

thf(2525,plain,
    ! [SV192: $i,SV411: $i,SV549: $i > $i] :
      ( ( ( in @ ( SV549 @ ( sK92_Xx @ SV549 @ SV411 @ SV192 ) ) @ SV411 )
        = $false )
      | ( ( ! [SY2810: $i] :
              ( ~ ( in @ SY2810 @ SV192 )
              | ( ( ap @ SV192 @ SV411
                  @ ( lam @ SV192 @ SV411
                    @ ^ [SY2811: $i] : ( SV549 @ SY2811 ) )
                  @ SY2810 )
                = ( SV549 @ SY2810 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2347]) ).

thf(2526,plain,
    ! [SV193: $i,SV412: $i,SV550: $i] :
      ( ( ( ~ ( ( SV550
               != ( kpair @ ( sK67_Xx @ SV550 @ SV412 @ SV193 ) @ ( sK68_SY1876 @ SV550 @ SV412 @ SV193 ) ) )
              | ~ ( in @ ( sK68_SY1876 @ SV550 @ SV412 @ SV193 ) @ SV412 ) ) )
        = $true )
      | ( ( in @ SV550 @ ( cartprod @ SV193 @ SV412 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2348]) ).

thf(2527,plain,
    ! [SV193: $i,SV412: $i,SV550: $i] :
      ( ( ( in @ ( sK67_Xx @ SV550 @ SV412 @ SV193 ) @ SV193 )
        = $true )
      | ( ( in @ SV550 @ ( cartprod @ SV193 @ SV412 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2349]) ).

thf(2528,plain,
    ! [SV551: $i,SV194: $i > $o] :
      ( ( ( SV194 @ SV551 )
        = $false )
      | ( ( SV194 @ ( sK57_SY248 @ SV551 @ SV194 ) )
        = $true )
      | ( ( ! [SY2258: $i] :
              ( ~ ( SV194 @ SY2258 )
              | ! [SY2259: $i] :
                  ( ~ ( SV194 @ SY2259 )
                  | ( SY2258 = SY2259 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2350]) ).

thf(2529,plain,
    ! [SV194: $i > $o,SV551: $i] :
      ( ( ( SV551
          = ( sK57_SY248 @ SV551 @ SV194 ) )
        = $false )
      | ( ( ~ ( SV194 @ SV551 ) )
        = $true )
      | ( ( ! [SY2258: $i] :
              ( ~ ( SV194 @ SY2258 )
              | ! [SY2259: $i] :
                  ( ~ ( SV194 @ SY2259 )
                  | ( SY2258 = SY2259 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2351]) ).

thf(2530,plain,
    ! [SV413: $i,SV195: $i > $i > $o] :
      ( ( ( ~ ! [SY2639: $i] :
                ( ! [SY2640: $i] :
                    ( ~ ( SV195 @ SY2640 @ SY2639 )
                    | ~ ( in @ SY2640 @ SV413 ) )
                | ( in @ SY2639 @ ( sK10_B @ SV413 @ SV195 ) ) ) )
        = $false )
      | ( ( in @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV413 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2352]) ).

thf(2531,plain,
    ! [SV195: $i > $i > $o,SV413: $i] :
      ( ( ( ~ ! [SY2641: $i] :
                ( ~ ( in @ SY2641 @ ( sK10_B @ SV413 @ SV195 ) )
                | ~ ( ~ ( SV195 @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SY2641 )
                    | ~ ( in @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SV413 ) ) ) )
        = $false )
      | ( ( in @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV413 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2352]) ).

thf(2532,plain,
    ! [SV725: $i,SV413: $i,SV195: $i > $i > $o] :
      ( ( ( ~ ( ~ ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
              | ~ ( ( SV725
                   != ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2639: $i] :
                    ( ! [SY2640: $i] :
                        ( ~ ( SV195 @ SY2640 @ SY2639 )
                        | ~ ( in @ SY2640 @ SV413 ) )
                    | ( in @ SY2639 @ ( sK10_B @ SV413 @ SV195 ) ) )
              | ~ ! [SY2641: $i] :
                    ( ~ ( in @ SY2641 @ ( sK10_B @ SV413 @ SV195 ) )
                    | ~ ( ~ ( SV195 @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SY2641 )
                        | ~ ( in @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SV413 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2353]) ).

thf(2533,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( ( ~ ( ~ ( ( SV552 = SV196 )
                  | ( in @ SV552 @ SV414 )
                  | ! [SX3: $o] : SX3 )
              | ~ ( ( SV552 = SV196 )
                  | ! [SX3: $o] :
                      ( ~ SX3
                      | SX3 ) ) ) )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2354]) ).

thf(2534,plain,
    ! [SV196: $i,SV414: $i,SV552: $i] :
      ( ( ( ~ ( ~ ! [SY2814: $o] :
                    ( ~ SY2814
                    | ( in @ SV552 @ SV414 )
                    | SY2814 )
              | ~ ! [SX3: $o] :
                    ( ~ SX3
                    | ~ SX3
                    | SX3 ) ) )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2355]) ).

thf(2535,plain,
    ! [SV650: $i > $o,SV198: $i,SV697: $i] :
      ( ( ( in @ SV697 @ SV198 )
        = $false )
      | ( ( ~ ( SV650 @ SV697 )
          | ( in @ SV697
            @ ( dsetconstr @ SV198
              @ ^ [SY2916: $i] : ( SV650 @ SY2916 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2356]) ).

thf(2536,plain,
    ! [SV651: $i > $o,SV198: $i,SV698: $i] :
      ( ( ( in @ SV698 @ SV198 )
        = $false )
      | ( ( ~ ( in @ SV698
              @ ( dsetconstr @ SV198
                @ ^ [SY2918: $i] : ( SV651 @ SY2918 ) ) )
          | ( SV651 @ SV698 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2357]) ).

thf(2537,plain,
    ! [SV604: $i,SV200: $i,SV417: $i > $o] :
      ( ( ( ~ ( in @ ( sK40_Xx @ SV417 @ SV200 ) @ SV200 ) )
        = $false )
      | ( ( SV417 @ SV604 )
        = $true )
      | ( ( in @ SV604 @ SV200 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2359]) ).

thf(2538,plain,
    ! [SV604: $i,SV200: $i,SV417: $i > $o] :
      ( ( ( ~ ~ ( SV417 @ ( sK40_Xx @ SV417 @ SV200 ) ) )
        = $false )
      | ( ( SV417 @ SV604 )
        = $true )
      | ( ( in @ SV604 @ SV200 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2359]) ).

thf(2539,plain,
    ! [SV201: $i,SV418: $i,SV553: $i > $i] :
      ( ( ( in @ ( SV553 @ ( sK78_Xx @ SV553 @ SV418 @ SV201 ) ) @ SV418 )
        = $false )
      | ( ( in
          @ ( lam @ SV201 @ SV418
            @ ^ [SY2816: $i] : ( SV553 @ SY2816 ) )
          @ ( funcSet @ SV201 @ SV418 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2361]) ).

thf(2540,plain,
    ! [SV554: $i,SV419: $o,SV202: $i,SV699: $i] :
      ( ( ( in @ SV699 @ SV202 )
        = $false )
      | ( ( SV419
          | ( ( dsetconstr @ SV202
              @ ^ [SY2944: $i] :
                  ( ~ ( ~ SV419
                      | ( SY2944 != SV554 ) )
                  | ~ ( ~ ~ SV419
                      | ( SY2944 != SV699 ) ) ) )
            = ( setadjoin @ SV699 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV554 @ SV202 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2362]) ).

thf(2541,plain,
    ! [SV555: $i,SV202: $i,SV700: $i] :
      ( ( ( in @ SV700 @ SV202 )
        = $false )
      | ( ( $true
          | ( ( dsetconstr @ SV202
              @ ^ [SY2945: $i] :
                  ( ~ ( ~ $true
                      | ( SY2945 != SV555 ) )
                  | ~ ( ~ ~ $true
                      | ( SY2945 != SV700 ) ) ) )
            = ( setadjoin @ SV700 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV555 @ SV202 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2363]) ).

thf(2542,plain,
    ! [SV556: $i,SV202: $i,SV701: $i] :
      ( ( ( in @ SV701 @ SV202 )
        = $false )
      | ( ( $false
          | ( ( dsetconstr @ SV202
              @ ^ [SY2946: $i] :
                  ( ~ ( ~ $false
                      | ( SY2946 != SV556 ) )
                  | ~ ( ~ ~ $false
                      | ( SY2946 != SV701 ) ) ) )
            = ( setadjoin @ SV701 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV556 @ SV202 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2364]) ).

thf(2543,plain,
    ! [SV605: $i > $o,SV652: $i > $o] :
      ( ( ( ( sK55_Xx @ SV652 @ SV605 )
         != ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $false )
      | ( ( ! [SY2919: $i] :
              ( ~ ( ~ ( SV605 @ ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) )
                  | ~ ( ( SY2919
                       != ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) ) ) )
              | ~ ( SV605 @ SY2919 ) )
          | ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2365]) ).

thf(2544,plain,
    ! [SV652: $i > $o,SV605: $i > $o] :
      ( ( ( ~ ~ ( ~ ( ~ ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
                    | ~ ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) ) )
                | ~ ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
                    | ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) ) ) ) )
        = $false )
      | ( ( ! [SY2919: $i] :
              ( ~ ( ~ ( SV605 @ ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) )
                  | ~ ( ( SY2919
                       != ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) ) ) )
              | ~ ( SV605 @ SY2919 ) )
          | ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2365]) ).

thf(2545,plain,
    ! [SV606: $i > $o,SV653: $i > $o] :
      ( ( ( ( sK51_Xx @ SV653 @ SV606 )
         != ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $false )
      | ( ( ! [SY2921: $i] :
              ( ~ ( ~ ( SV653 @ ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) )
                  | ~ ( ( SY2921
                       != ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) ) ) )
              | ~ ( SV653 @ SY2921 ) )
          | ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2366]) ).

thf(2546,plain,
    ! [SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ~ ~ ( ~ ( ~ ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
                    | ~ ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) ) )
                | ~ ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
                    | ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) ) ) ) )
        = $false )
      | ( ( ! [SY2921: $i] :
              ( ~ ( ~ ( SV653 @ ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) )
                  | ~ ( ( SY2921
                       != ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) ) ) )
              | ~ ( SV653 @ SY2921 ) )
          | ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2366]) ).

thf(2547,plain,
    ! [SV420: $i > $o,SV203: $i,SV726: $i] :
      ( ( ( ~ ( in @ SV726 @ SV203 ) )
        = $true )
      | ( ( ~ ( SV420 @ SV726 ) )
        = $true )
      | ( ( SV420 @ ( sK39_Xx @ SV420 @ SV203 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2367]) ).

thf(2548,plain,
    ! [SV420: $i > $o,SV203: $i,SV727: $i] :
      ( ( ( ~ ( in @ SV727 @ SV203 ) )
        = $true )
      | ( ( ~ ( SV420 @ SV727 ) )
        = $true )
      | ( ( in @ ( sK39_Xx @ SV420 @ SV203 ) @ SV203 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2368]) ).

thf(2549,plain,
    ! [SV557: $i,SV204: $i > $o] :
      ( ( ( SV204 @ SV557 )
        = $false )
      | ( ( SV204 @ ( sK20_SY57 @ SV557 @ SV204 ) )
        = $true )
      | ( ( SV204
          @ ( descr
            @ ^ [SY2291: $i] : ( SV204 @ SY2291 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2369]) ).

thf(2550,plain,
    ! [SV204: $i > $o,SV557: $i] :
      ( ( ( SV557
          = ( sK20_SY57 @ SV557 @ SV204 ) )
        = $false )
      | ( ( ~ ( SV204 @ SV557 ) )
        = $true )
      | ( ( SV204
          @ ( descr
            @ ^ [SY2291: $i] : ( SV204 @ SY2291 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2370]) ).

thf(2551,plain,
    ! [SV558: $i,SV205: $i > $o] :
      ( ( ( SV205 @ SV558 )
        = $false )
      | ( ( SV205 @ ( sK42_Xy @ SV558 @ SV205 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2293: $i] :
                    ( ~ ( SV205 @ SY2293 )
                    | ( ( sK41_SY198 @ SV205 )
                      = SY2293 ) )
              | ~ ( SV205 @ ( sK41_SY198 @ SV205 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2371]) ).

thf(2552,plain,
    ! [SV205: $i > $o,SV558: $i] :
      ( ( ( SV558
          = ( sK42_Xy @ SV558 @ SV205 ) )
        = $false )
      | ( ( ~ ( SV205 @ SV558 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2293: $i] :
                    ( ~ ( SV205 @ SY2293 )
                    | ( ( sK41_SY198 @ SV205 )
                      = SY2293 ) )
              | ~ ( SV205 @ ( sK41_SY198 @ SV205 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2372]) ).

thf(2553,plain,
    ! [SV559: $i > $i,SV421: $i,SV206: $i,SV746: $i] :
      ( ( ( ~ ( in @ SV746 @ SV206 )
          | ( ( ap @ SV206 @ SV421
              @ ( lam @ SV206 @ SV421
                @ ^ [SY2824: $i] : ( SV559 @ SY2824 ) )
              @ SV746 )
            = ( SV559 @ SV746 ) ) )
        = $true )
      | ( ( in @ ( sK94_Xx @ SV559 @ SV421 @ SV206 ) @ SV206 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2373]) ).

thf(2554,plain,
    ! [SV206: $i,SV421: $i,SV559: $i > $i] :
      ( ( ( in @ ( SV559 @ ( sK94_Xx @ SV559 @ SV421 @ SV206 ) ) @ SV421 )
        = $false )
      | ( ( ! [SY2823: $i] :
              ( ~ ( in @ SY2823 @ SV206 )
              | ( ( ap @ SV206 @ SV421
                  @ ( lam @ SV206 @ SV421
                    @ ^ [SY2824: $i] : ( SV559 @ SY2824 ) )
                  @ SY2823 )
                = ( SV559 @ SY2823 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2374]) ).

thf(2555,plain,
    ( ( ~ ( in @ sK4_SY1829 @ ( powerset @ sK1_A ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2375]) ).

thf(2556,plain,
    ( ( ~ ~ ( ~ ( in @ sK5_SY1831 @ sK1_A )
            | ~ ~ ( ~ ( in @ sK5_SY1831 @ ( binintersect @ sK2_SY1822 @ sK3_SY1826 ) )
                  | ~ ~ ( in @ sK5_SY1831 @ ( binunion @ sK3_SY1826 @ sK4_SY1829 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2375]) ).

thf(2557,plain,
    ! [SV207: $i,SV422: $i,SV560: $i,SV702: $i > $o] :
      ( ( ( ~ ( in @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ SV207 )
          | ~ ~ ( ~ ( in @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) @ SV422 )
                | ~ ~ ( ~ ( in @ ( kpair @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) ) @ SV560 )
                      | ~ ~ ( SV702 @ ( kpair @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) ) ) ) ) )
        = $false )
      | ( ( ! [SY2947: $i] :
              ( ~ ( in @ SY2947 @ SV560 )
              | ( SV702 @ SY2947 ) ) )
        = $true )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2376]) ).

thf(2558,plain,
    ! [SV561: $i,SV423: $i,SV208: $i,SV703: $i] :
      ( ( ( subset @ SV703 @ ( cartprod @ SV208 @ SV423 ) )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ SV208 )
              | ~ ~ ( ~ ( in @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) @ SV423 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) ) @ SV561 )
                          | ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) ) @ SV703 ) ) ) )
          | ( subset @ SV561 @ SV703 ) )
        = $true )
      | ( ( subset @ SV561 @ ( cartprod @ SV208 @ SV423 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2377]) ).

thf(2559,plain,
    ! [SV209: $i,SV747: $i,SV424: $i > $o] :
      ( ( ( ~ ( SV424 @ SV747 )
          | ~ ( in @ SV747 @ SV209 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV209
            @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) )
        = $true )
      | ( ( in @ ( sK70_Xx @ SV424 @ SV209 ) @ SV209 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2378]) ).

thf(2560,plain,
    ! [SV209: $i,SV424: $i > $o] :
      ( ( ( ~ ( in @ ( sK71_SY1877 @ SV424 @ SV209 ) @ SV209 ) )
        = $false )
      | ( ( ! [SY2662: $i] :
              ( ~ ( SV424 @ SY2662 )
              | ~ ( in @ SY2662 @ SV209 ) )
          | ( singleton
            @ ( dsetconstr @ SV209
              @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2379]) ).

thf(2561,plain,
    ! [SV209: $i,SV424: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV424 @ ( sK70_Xx @ SV424 @ SV209 ) )
                | ~ ~ ( ~ ( SV424 @ ( sK71_SY1877 @ SV424 @ SV209 ) )
                      | ~ ( ( ( sK70_Xx @ SV424 @ SV209 )
                           != ( sK71_SY1877 @ SV424 @ SV209 ) ) ) ) ) )
        = $false )
      | ( ( ! [SY2662: $i] :
              ( ~ ( SV424 @ SY2662 )
              | ~ ( in @ SY2662 @ SV209 ) )
          | ( singleton
            @ ( dsetconstr @ SV209
              @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2379]) ).

thf(2562,plain,
    ! [SV425: $i,SV210: $i,SV748: $i] :
      ( ( ( ! [SY2969: $i] :
              ( ( SV748 != SY2969 )
              | ~ ( in @ SV748 @ SV210 )
              | ( in @ SY2969 @ SV425 ) ) )
        = $true )
      | ( ( SV210 = SV425 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2380]) ).

thf(2563,plain,
    ! [SV210: $i,SV425: $i,SV749: $i] :
      ( ( ( ! [SY2970: $i] :
              ( ( SV749 != SY2970 )
              | ~ ( in @ SY2970 @ SV425 )
              | ( in @ SV749 @ SV210 ) ) )
        = $true )
      | ( ( SV210 = SV425 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2381]) ).

thf(2564,plain,
    ! [SV562: $i,SV211: $i > $o] :
      ( ( ( SV211 @ SV562 )
        = $false )
      | ( ( SV211 @ ( sK48_SY224 @ SV562 @ SV211 ) )
        = $true )
      | ( ( ! [SY2314: $i] :
              ( ~ ( SV211 @ SY2314 )
              | ! [SY2315: $i] :
                  ( ~ ( SV211 @ SY2315 )
                  | ( SY2314 = SY2315 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2382]) ).

thf(2565,plain,
    ! [SV211: $i > $o,SV562: $i] :
      ( ( ( SV562
          = ( sK48_SY224 @ SV562 @ SV211 ) )
        = $false )
      | ( ( ~ ( SV211 @ SV562 ) )
        = $true )
      | ( ( ! [SY2314: $i] :
              ( ~ ( SV211 @ SY2314 )
              | ! [SY2315: $i] :
                  ( ~ ( SV211 @ SY2315 )
                  | ( SY2314 = SY2315 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2383]) ).

thf(2566,plain,
    ! [SV212: $i,SV426: $i,SV563: $i > $i] :
      ( ( ( in @ ( SV563 @ ( sK77_Xx @ SV563 @ SV426 @ SV212 ) ) @ SV426 )
        = $false )
      | ( ( func @ SV212 @ SV426
          @ ( lam @ SV212 @ SV426
            @ ^ [SY2828: $i] : ( SV563 @ SY2828 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2385]) ).

thf(2567,plain,
    ! [SV427: $i > $o,SV750: $i,SV213: $i > $o] :
      ( ( ( ~ ( ~ ( SV213 @ ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
              | ~ ( ( SV750
                   != ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) ) ) )
          | ~ ( SV213 @ SV750 ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2386]) ).

thf(2568,plain,
    ! [SV427: $i > $o,SV213: $i > $o] :
      ( ( ( ~ ( ~ ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
              | ~ ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) ) ) )
        = $false )
      | ( ( ! [SY2670: $i] :
              ( ~ ( ~ ( SV213 @ ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2670
                       != ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV213 @ SY2670 ) )
          | ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2387]) ).

thf(2569,plain,
    ! [SV427: $i > $o,SV213: $i > $o] :
      ( ( ( ~ ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
              | ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) ) ) )
        = $false )
      | ( ( ! [SY2670: $i] :
              ( ~ ( ~ ( SV213 @ ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2670
                       != ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV213 @ SY2670 ) )
          | ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2387]) ).

thf(2570,plain,
    ! [SV214: $i,SV428: $i,SV654: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK98_Xx @ SV654 @ SV428 @ SV214 ) @ SV214 )
              | ~ ~ ( ~ ( in @ ( sK98_Xx @ SV654 @ SV428 @ SV214 ) @ SV428 )
                    | ~ ~ ( in @ ( sK98_Xx @ SV654 @ SV428 @ SV214 ) @ SV654 ) ) ) )
        = $true )
      | ( ( in @ SV428 @ ( powerset @ SV654 ) )
        = $true )
      | ( ( in @ SV654 @ ( powerset @ SV214 ) )
        = $false )
      | ( ( in @ SV428 @ ( powerset @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2388]) ).

thf(2571,plain,
    ! [SV215: $i,SV655: $o,SV429: $i] :
      ( ( ( ~ ( in @ SV429 @ ( sK31_B @ SV655 @ SV429 @ SV215 ) ) )
        = $false )
      | ( SV655 = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2389]) ).

thf(2572,plain,
    ! [SV215: $i,SV429: $i,SV655: $o] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK31_B @ SV655 @ SV429 @ SV215 ) @ SV215 )
                | ~ ~ SV655 ) )
        = $false )
      | ( SV655 = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2389]) ).

thf(2573,plain,
    ! [SV215: $i,SV429: $i] :
      ( ( ( ~ ( in @ SV429 @ ( sK31_B @ $true @ SV429 @ SV215 ) ) )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2390]) ).

thf(2574,plain,
    ! [SV215: $i,SV429: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK31_B @ $true @ SV429 @ SV215 ) @ SV215 )
                | ~ ~ $true ) )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2390]) ).

thf(2575,plain,
    ! [SV215: $i,SV429: $i] :
      ( ( ( ~ ( in @ SV429 @ ( sK31_B @ $false @ SV429 @ SV215 ) ) )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2391]) ).

thf(2576,plain,
    ! [SV215: $i,SV429: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK31_B @ $false @ SV429 @ SV215 ) @ SV215 )
                | ~ ~ $false ) )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2391]) ).

thf(2577,plain,
    ! [SV216: $i,SV430: $i] :
      ( ( ( ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV430 )
          | ~ ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV216 ) )
        = $false )
      | ( ( SV216 = SV430 )
        = $true )
      | ( ( in @ ( sK26_Xx @ SV430 @ SV216 ) @ SV216 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2392]) ).

thf(2578,plain,
    ! [SV216: $i,SV430: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV430 )
              | ~ ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV216 ) ) )
        = $true )
      | ( ( SV216 = SV430 )
        = $true )
      | ( ( in @ ( sK26_Xx @ SV430 @ SV216 ) @ SV430 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2393]) ).

thf(2579,plain,
    ! [SV564: $i,SV704: $i,SV432: $i,SV218: $i] :
      ( ( ( func @ SV218 @ SV432 @ SV704 )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) @ SV218 )
              | ~ ( ( ( ap @ SV218 @ SV432 @ SV564 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) )
                   != ( ap @ SV218 @ SV432 @ SV704 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) ) ) ) )
          | ! [SY2948: $i] :
              ( ~ ( in @ SY2948 @ SV218 )
              | ! [SY2949: $i] :
                  ( ~ ( in @ SY2949 @ SV432 )
                  | ~ ( in @ ( kpair @ SY2948 @ SY2949 ) @ SV704 )
                  | ( in @ ( kpair @ SY2948 @ SY2949 ) @ SV564 ) ) ) )
        = $true )
      | ( ( func @ SV218 @ SV432 @ SV564 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2396]) ).

thf(2580,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
              | ~ ~ ( ~ ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 )
                    | ~ ~ ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
              | ~ ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
                    | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) ) )
          | ( SV433 = SV656 ) )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2397]) ).

thf(2581,plain,
    ! [SV220: $i,SV434: $i > $o,SV565: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK73_Xy @ SV565 @ SV434 @ SV220 ) @ SV220 )
              | ~ ~ ( ~ ( SV434 @ ( sK73_Xy @ SV565 @ SV434 @ SV220 ) )
                    | ~ ( ( ( sK73_Xy @ SV565 @ SV434 @ SV220 )
                         != SV565 ) ) ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV220
            @ ^ [SY2682: $i] : ( SV434 @ SY2682 ) ) )
        = $true )
      | ( ( SV434 @ SV565 )
        = $false )
      | ( ( in @ SV565 @ SV220 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2398]) ).

thf(2582,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ ( ~ ( ( in @ SV566 @ SV221 )
                  | ~ ( in @ SV566 @ SV221 )
                  | ! [SX3: $o] : SX3 )
              | ~ ~ ( ~ ( ( in @ SV566 @ SV221 )
                        | ( in @ SV566 @ SV435 )
                        | ! [SX3: $o] : SX3 )
                    | ~ ( ( in @ SV566 @ SV221 )
                        | ! [SX3: $o] :
                            ( ~ SX3
                            | SX3 ) ) ) ) )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2399]) ).

thf(2583,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ SV566 @ SV435 )
                        | ~ ( in @ SV566 @ SV221 )
                        | ! [SX3: $o] : SX3 )
                    | ~ ~ ( ~ ( ~ ( in @ SV566 @ SV435 )
                              | ( in @ SV566 @ SV435 )
                              | ! [SX3: $o] : SX3 )
                          | ~ ( ~ ( in @ SV566 @ SV435 )
                              | ! [SX3: $o] :
                                  ( ~ SX3
                                  | SX3 ) ) ) )
              | ~ ~ ( ~ ! [SY2839: $o] :
                          ( ~ SY2839
                          | ~ ( in @ SV566 @ SV221 )
                          | SY2839 )
                    | ~ ~ ( ~ ! [SY2840: $o] :
                                ( ~ SY2840
                                | ( in @ SV566 @ SV435 )
                                | SY2840 )
                          | ~ ! [SX3: $o] :
                                ( ~ SX3
                                | ~ SX3
                                | SX3 ) ) ) ) )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2400]) ).

thf(2584,plain,
    ! [SV222: $i,SV436: $i,SV567: $i > $i] :
      ( ( ( in @ ( SV567 @ ( sK76_Xx @ SV567 @ SV436 @ SV222 ) ) @ SV436 )
        = $false )
      | ( ( func @ SV222 @ SV436
          @ ( dpsetconstr @ SV222 @ SV436
            @ ^ [SY2842: $i,SY2843: $i] :
                ( ( SV567 @ SY2842 )
                = SY2843 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2402]) ).

thf(2585,plain,
    ! [SV657: $i,SV223: $i,SV705: $i] :
      ( ( ( in @ SV705 @ ( setadjoin @ SV223 @ SV657 ) )
        = $false )
      | ( ( ( SV705 = SV223 )
          | ( in @ SV705 @ SV657 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2403]) ).

thf(2586,plain,
    ! [SV751: $i,SV223: $i] :
      ( ( ! [SY2971: $i] :
            ( ( SY2971 != SV223 )
            | ( in @ SY2971 @ ( setadjoin @ SV223 @ SV751 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2404]) ).

thf(2587,plain,
    ! [SV223: $i,SV752: $i] :
      ( ( ! [SY2972: $i] :
            ( ~ ( in @ SY2972 @ SV752 )
            | ( in @ SY2972 @ ( setadjoin @ SV223 @ SV752 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2405]) ).

thf(2588,plain,
    ! [SV225: $i,SV438: $i] :
      ( ( ( in @ ( sK6_Xx @ SV438 @ SV225 ) @ SV225 )
        = $false )
      | ( ( ~ ( in @ ( sK6_Xx @ SV438 @ SV225 ) @ SV438 ) )
        = $true )
      | ( ( SV225 = SV438 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2407]) ).

thf(2589,plain,
    ! [SV439: $i,SV226: $i] :
      ( ( ! [SY2696: $i] :
            ( ~ ( in @ SY2696 @ ( binunion @ SV226 @ SV439 ) )
            | ( in @ SY2696 @ SV226 )
            | ( in @ SY2696 @ SV439 )
            | ! [SX3: $o] : SX3 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2409]) ).

thf(2590,plain,
    ! [SV439: $i,SV226: $i] :
      ( ( ! [SY2698: $i] :
            ( ~ ( in @ SY2698 @ ( binunion @ SV226 @ SV439 ) )
            | ( in @ SY2698 @ SV226 )
            | ! [SX3: $o] :
                ( ~ SX3
                | SX3 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2410]) ).

thf(2591,plain,
    ! [SV439: $i,SV226: $i] :
      ( ( ! [SY2700: $i] :
            ( ~ ( in @ SY2700 @ ( binunion @ SV226 @ SV439 ) )
            | ! [SY2701: $o] :
                ( ~ SY2701
                | ( in @ SY2700 @ SV439 )
                | SY2701 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2411]) ).

thf(2592,plain,
    ! [SV439: $i,SV226: $i] :
      ( ( ! [SY2702: $i] :
            ~ ( in @ SY2702 @ ( binunion @ SV226 @ SV439 ) )
        | ! [SX2: $o] :
            ( ~ SX2
            | ~ SX2
            | SX2 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2412]) ).

thf(2593,plain,
    ! [SV607: $i,SV227: $i,SV440: $i > $o] :
      ( ( ( ~ ( in @ ( sK38_Xx @ SV440 @ SV227 ) @ SV227 ) )
        = $false )
      | ( ( SV440 @ SV607 )
        = $true )
      | ( ( in @ SV607 @ SV227 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2413]) ).

thf(2594,plain,
    ! [SV607: $i,SV227: $i,SV440: $i > $o] :
      ( ( ( ~ ~ ( SV440 @ ( sK38_Xx @ SV440 @ SV227 ) ) )
        = $false )
      | ( ( SV440 @ SV607 )
        = $true )
      | ( ( in @ SV607 @ SV227 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2413]) ).

thf(2595,plain,
    ! [SV228: $i > $o,SV568: $i] :
      ( ( ( ( sK47_Xy @ SV568 @ SV228 )
          = SV568 )
        = $false )
      | ( ( ~ ( SV228 @ ( sK47_Xy @ SV568 @ SV228 ) ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2375: $i] :
                    ( ~ ( SV228 @ SY2375 )
                    | ( ( sK46_SY211 @ SV228 )
                      = SY2375 ) )
              | ~ ( SV228 @ ( sK46_SY211 @ SV228 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2414]) ).

thf(2596,plain,
    ! [SV568: $i,SV228: $i > $o] :
      ( ( ( ~ ! [SY2375: $i] :
                ( ~ ( SV228 @ SY2375 )
                | ( ( sK46_SY211 @ SV228 )
                  = SY2375 ) )
          | ~ ( SV228 @ ( sK46_SY211 @ SV228 ) ) )
        = $false )
      | ( ( SV228 @ ( sK47_Xy @ SV568 @ SV228 ) )
        = $true )
      | ( ( ( sK47_Xy @ SV568 @ SV228 )
          = SV568 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2415]) ).

thf(2597,plain,
    ! [SV229: $i,SV753: $i,SV441: $i > $o] :
      ( ( ( ~ ( SV441 @ SV753 )
          | ~ ( in @ SV753 @ SV229 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV229
            @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) )
        = $true )
      | ( ( in @ ( sK74_Xx @ SV441 @ SV229 ) @ SV229 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2416]) ).

thf(2598,plain,
    ! [SV229: $i,SV441: $i > $o] :
      ( ( ( ~ ( in @ ( sK75_SY1878 @ SV441 @ SV229 ) @ SV229 ) )
        = $false )
      | ( ( ! [SY2705: $i] :
              ( ~ ( SV441 @ SY2705 )
              | ~ ( in @ SY2705 @ SV229 ) )
          | ( singleton
            @ ( dsetconstr @ SV229
              @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2417]) ).

thf(2599,plain,
    ! [SV229: $i,SV441: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV441 @ ( sK74_Xx @ SV441 @ SV229 ) )
                | ~ ~ ( ~ ( SV441 @ ( sK75_SY1878 @ SV441 @ SV229 ) )
                      | ~ ( ( ( sK74_Xx @ SV441 @ SV229 )
                           != ( sK75_SY1878 @ SV441 @ SV229 ) ) ) ) ) )
        = $false )
      | ( ( ! [SY2705: $i] :
              ( ~ ( SV441 @ SY2705 )
              | ~ ( in @ SY2705 @ SV229 ) )
          | ( singleton
            @ ( dsetconstr @ SV229
              @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2417]) ).

thf(2600,plain,
    ! [SV569: $i,SV442: $i,SV230: $i,SV706: $i] :
      ( ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
              | ~ ~ ( ~ ( in @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
                          | ~ ~ ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 ) ) ) )
          | ~ ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
              | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                          | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
          | ( SV569 = SV706 ) )
        = $true )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2418]) ).

thf(2601,plain,
    ! [SV231: $i] :
      ( ( ( ~ ( in @ ( sK9_Xx @ SV231 ) @ omega ) )
        = $false )
      | ( ( ~ ( in @ emptyset @ SV231 ) )
        = $true )
      | ( ( ! [SY2382: $i] :
              ( ~ ( in @ SY2382 @ omega )
              | ( in @ SY2382 @ SV231 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2419]) ).

thf(2602,plain,
    ! [SV231: $i] :
      ( ( ( ~ ( in @ ( sK9_Xx @ SV231 ) @ SV231 ) )
        = $false )
      | ( ( ~ ( in @ emptyset @ SV231 ) )
        = $true )
      | ( ( ! [SY2382: $i] :
              ( ~ ( in @ SY2382 @ omega )
              | ( in @ SY2382 @ SV231 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2419]) ).

thf(2603,plain,
    ! [SV231: $i] :
      ( ( ( in @ emptyset @ SV231 )
        = $false )
      | ( ( in @ ( setadjoin @ ( sK9_Xx @ SV231 ) @ ( sK9_Xx @ SV231 ) ) @ SV231 )
        = $false )
      | ( ( ! [SY2382: $i] :
              ( ~ ( in @ SY2382 @ omega )
              | ( in @ SY2382 @ SV231 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2420]) ).

thf(2604,plain,
    ! [SV570: $i,SV443: $o,SV232: $i,SV707: $i] :
      ( ( ( in @ SV707 @ SV232 )
        = $false )
      | ( ( SV443
          | ( in @ SV707
            @ ( dsetconstr @ SV232
              @ ^ [SY2950: $i] :
                  ( ~ ( ~ SV443
                      | ( SY2950 != SV570 ) )
                  | ~ ( ~ ~ SV443
                      | ( SY2950 != SV707 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV570 @ SV232 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2421]) ).

thf(2605,plain,
    ! [SV571: $i,SV232: $i,SV708: $i] :
      ( ( ( in @ SV708 @ SV232 )
        = $false )
      | ( ( $true
          | ( in @ SV708
            @ ( dsetconstr @ SV232
              @ ^ [SY2951: $i] :
                  ( ~ ( ~ $true
                      | ( SY2951 != SV571 ) )
                  | ~ ( ~ ~ $true
                      | ( SY2951 != SV708 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV571 @ SV232 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2422]) ).

thf(2606,plain,
    ! [SV572: $i,SV232: $i,SV709: $i] :
      ( ( ( in @ SV709 @ SV232 )
        = $false )
      | ( ( $false
          | ( in @ SV709
            @ ( dsetconstr @ SV232
              @ ^ [SY2952: $i] :
                  ( ~ ( ~ $false
                      | ( SY2952 != SV572 ) )
                  | ~ ( ~ ~ $false
                      | ( SY2952 != SV709 ) ) ) ) ) )
        = $true )
      | ( ( in @ SV572 @ SV232 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2423]) ).

thf(2607,plain,
    ! [SV233: $i,SV658: $i] :
      ( ( ( ~ ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
          | ~ ~ ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 ) )
        = $false )
      | ( ( ! [SY2924: $i] :
              ~ ( in @ SY2924 @ SV658 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2925: $i] :
                    ( ~ ( in @ SY2925 @ ( sK15_B @ SV233 ) )
                    | ! [SY2926: $i] :
                        ( ~ ( in @ SY2926 @ SY2925 )
                        | ( in @ SY2926 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) )
                    | ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SY2925 ) )
              | ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) )
                          | ~ ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 ) )
                    | ~ ! [SY2927: $i] :
                          ( ~ ( in @ SY2927 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
                          | ~ ( in @ SY2927 @ SV658 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2424]) ).

thf(2608,plain,
    ! [SV233: $i,SV754: $i] :
      ( ( ! [SY2973: $i] :
            ( ~ ( in @ SV754 @ ( sK15_B @ SV233 ) )
            | ~ ( in @ SY2973 @ ( sK15_B @ SV233 ) )
            | ! [SY2974: $i] :
                ( ~ ( in @ SY2974 @ SV754 )
                | ( in @ SY2974 @ SY2973 ) )
            | ! [SY2975: $i] :
                ( ~ ( in @ SY2975 @ SY2973 )
                | ( in @ SY2975 @ SV754 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2425]) ).

thf(2609,plain,
    ! [SV233: $i] :
      ( ( ~ ! [SY2396: $i] :
              ( ~ ( in @ SY2396 @ ( sK15_B @ SV233 ) )
              | ! [SY2397: $i] :
                  ( ~ ( in @ SY2397 @ SY2396 )
                  | ( in @ SY2397 @ SV233 ) ) )
        | ~ ! [SY2398: $i,SY2399: $i] :
              ( ~ ( in @ SY2398 @ SV233 )
              | ~ ( in @ SY2399 @ SV233 )
              | ~ ( ~ ( in @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) @ ( sK15_B @ SV233 ) )
                  | ~ ~ ( ~ ( ~ ( in @ SY2398 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) )
                            | ~ ( in @ SY2399 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) ) )
                        | ~ ( ( in @ SY2398 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) )
                            | ( in @ SY2399 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) ) ) ) )
              | ( SY2398 = SY2399 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[2426]) ).

thf(2610,plain,
    ! [SV444: $i > $o,SV234: $i,SV728: $i] :
      ( ( ( ~ ( in @ SV728 @ SV234 ) )
        = $true )
      | ( ( ~ ( SV444 @ SV728 ) )
        = $true )
      | ( ( SV444 @ ( sK37_Xx @ SV444 @ SV234 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2427]) ).

thf(2611,plain,
    ! [SV444: $i > $o,SV234: $i,SV729: $i] :
      ( ( ( ~ ( in @ SV729 @ SV234 ) )
        = $true )
      | ( ( ~ ( SV444 @ SV729 ) )
        = $true )
      | ( ( in @ ( sK37_Xx @ SV444 @ SV234 ) @ SV234 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2428]) ).

thf(2612,plain,
    ! [SV573: $i,SV235: $i > $o] :
      ( ( ( SV235 @ SV573 )
        = $false )
      | ( ( SV235 @ ( sK33_SY142 @ SV573 @ SV235 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2403: $i] :
                    ( ( SY2403
                     != ( sK32_Xx @ SV235 ) )
                    | ( SV235 @ SY2403 ) )
              | ~ ! [SY2404: $i] :
                    ( ~ ( SV235 @ SY2404 )
                    | ( SY2404
                      = ( sK32_Xx @ SV235 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2429]) ).

thf(2613,plain,
    ! [SV235: $i > $o,SV573: $i] :
      ( ( ( SV573
          = ( sK33_SY142 @ SV573 @ SV235 ) )
        = $false )
      | ( ( ~ ( SV235 @ SV573 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2403: $i] :
                    ( ( SY2403
                     != ( sK32_Xx @ SV235 ) )
                    | ( SV235 @ SY2403 ) )
              | ~ ! [SY2404: $i] :
                    ( ~ ( SV235 @ SY2404 )
                    | ( SY2404
                      = ( sK32_Xx @ SV235 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2430]) ).

thf(2614,plain,
    ! [SV236: $i,SV445: $i,SV574: $i,SV710: $i > $o] :
      ( ( ( ~ ( in @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ SV236 )
          | ~ ~ ( ~ ( in @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) @ SV445 )
                | ~ ~ ( ~ ( in @ ( kpair @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) ) @ SV574 )
                      | ~ ~ ( SV710 @ ( kpair @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) ) ) ) ) )
        = $false )
      | ( ( ! [SY2953: $i] :
              ( ~ ( in @ SY2953 @ SV574 )
              | ( SV710 @ SY2953 ) ) )
        = $true )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2431]) ).

thf(2615,plain,
    ! [SV608: $i,SV237: $i,SV446: $i > $o] :
      ( ( ( ~ ( in @ ( sK35_Xx @ SV446 @ SV237 ) @ SV237 ) )
        = $false )
      | ( ( SV446 @ SV608 )
        = $true )
      | ( ( in @ SV608 @ SV237 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2432]) ).

thf(2616,plain,
    ! [SV608: $i,SV237: $i,SV446: $i > $o] :
      ( ( ( ~ ~ ( SV446 @ ( sK35_Xx @ SV446 @ SV237 ) ) )
        = $false )
      | ( ( SV446 @ SV608 )
        = $true )
      | ( ( in @ SV608 @ SV237 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2432]) ).

thf(2617,plain,
    ! [SV575: $i,SV447: $o,SV238: $i,SV711: $i] :
      ( ( ( in @ SV711 @ SV238 )
        = $false )
      | ( ( ~ SV447
          | ( ( dsetconstr @ SV238
              @ ^ [SY2954: $i] :
                  ( ~ ( ~ SV447
                      | ( SY2954 != SV575 ) )
                  | ~ ( ~ ~ SV447
                      | ( SY2954 != SV711 ) ) ) )
            = ( setadjoin @ SV575 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV575 @ SV238 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2433]) ).

thf(2618,plain,
    ! [SV576: $i,SV238: $i,SV712: $i] :
      ( ( ( in @ SV712 @ SV238 )
        = $false )
      | ( ( ~ $true
          | ( ( dsetconstr @ SV238
              @ ^ [SY2955: $i] :
                  ( ~ ( ~ $true
                      | ( SY2955 != SV576 ) )
                  | ~ ( ~ ~ $true
                      | ( SY2955 != SV712 ) ) ) )
            = ( setadjoin @ SV576 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV576 @ SV238 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2434]) ).

thf(2619,plain,
    ! [SV577: $i,SV238: $i,SV713: $i] :
      ( ( ( in @ SV713 @ SV238 )
        = $false )
      | ( ( ~ $false
          | ( ( dsetconstr @ SV238
              @ ^ [SY2956: $i] :
                  ( ~ ( ~ $false
                      | ( SY2956 != SV577 ) )
                  | ~ ( ~ ~ $false
                      | ( SY2956 != SV713 ) ) ) )
            = ( setadjoin @ SV577 @ emptyset ) ) )
        = $true )
      | ( ( in @ SV577 @ SV238 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2435]) ).

thf(2620,plain,
    ! [SV578: $i,SV239: $i,SV755: $i] :
      ( ( ( ~ ( in @ SV755 @ ( sK14_B @ SV239 ) )
          | ~ ( in @ SV755 @ SV239 ) )
        = $true )
      | ( ( in @ SV578 @ SV239 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2437]) ).

thf(2621,plain,
    ! [SV579: $i,SV448: $o,SV240: $i,SV714: $i] :
      ( ( ( in @ SV714 @ SV240 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV240
            @ ^ [SY2957: $i] :
                ( ~ ( ~ SV448
                    | ( SY2957 != SV579 ) )
                | ~ ( ~ ~ SV448
                    | ( SY2957 != SV714 ) ) ) ) )
        = $true )
      | ( ( in @ SV579 @ SV240 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2438]) ).

thf(2622,plain,
    ! [SV580: $i,SV240: $i,SV715: $i] :
      ( ( ( in @ SV715 @ SV240 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV240
            @ ^ [SY2958: $i] :
                ( ~ ( ~ $true
                    | ( SY2958 != SV580 ) )
                | ~ ( ~ ~ $true
                    | ( SY2958 != SV715 ) ) ) ) )
        = $true )
      | ( ( in @ SV580 @ SV240 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2439]) ).

thf(2623,plain,
    ! [SV581: $i,SV240: $i,SV716: $i] :
      ( ( ( in @ SV716 @ SV240 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV240
            @ ^ [SY2959: $i] :
                ( ~ ( ~ $false
                    | ( SY2959 != SV581 ) )
                | ~ ( ~ ~ $false
                    | ( SY2959 != SV716 ) ) ) ) )
        = $true )
      | ( ( in @ SV581 @ SV240 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2440]) ).

thf(2624,plain,
    ! [SV582: $i,SV241: $i > $o] :
      ( ( ( SV241 @ ( sK44_Xx @ SV241 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2422: $i] :
                    ( ~ ( SV241 @ SY2422 )
                    | ( ( sK43_SY205 @ SV241 )
                      = SY2422 ) )
              | ~ ( SV241 @ ( sK43_SY205 @ SV241 ) ) ) )
        = $true )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2441]) ).

thf(2625,plain,
    ! [SV582: $i,SV241: $i > $o] :
      ( ( ( ~ ( ~ ( SV241 @ ( sK45_SY1868 @ SV241 ) )
              | ~ ( ( ( sK44_Xx @ SV241 )
                   != ( sK45_SY1868 @ SV241 ) ) ) ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2422: $i] :
                    ( ~ ( SV241 @ SY2422 )
                    | ( ( sK43_SY205 @ SV241 )
                      = SY2422 ) )
              | ~ ( SV241 @ ( sK43_SY205 @ SV241 ) ) ) )
        = $true )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2442]) ).

thf(2626,plain,
    ! [SV609: $i,SV730: $i,SV659: $i] :
      ( ( ( ~ ( in @ SV659 @ SV730 ) )
        = $true )
      | ( ( ~ ( in @ SV730 @ SV609 ) )
        = $true )
      | ( ( in @ SV659 @ ( setunion @ SV609 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2444]) ).

thf(2627,plain,
    ! [SV610: $i,SV660: $i] :
      ( ( ( ~ ( in @ SV660 @ ( sK8_B @ SV660 @ SV610 ) )
          | ~ ( in @ ( sK8_B @ SV660 @ SV610 ) @ SV610 ) )
        = $false )
      | ( ( in @ SV660 @ ( setunion @ SV610 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2445]) ).

thf(2628,plain,
    ! [SV583: $i,SV717: $i,SV450: $i,SV243: $i] :
      ( ( ( func @ SV243 @ SV450 @ SV717 )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK90_Xx @ SV717 @ SV583 @ SV450 @ SV243 ) @ SV243 )
              | ~ ( ( ( ap @ SV243 @ SV450 @ SV583 @ ( sK90_Xx @ SV717 @ SV583 @ SV450 @ SV243 ) )
                   != ( ap @ SV243 @ SV450 @ SV717 @ ( sK90_Xx @ SV717 @ SV583 @ SV450 @ SV243 ) ) ) ) )
          | ( SV583 = SV717 ) )
        = $true )
      | ( ( func @ SV243 @ SV450 @ SV583 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2446]) ).

thf(2629,plain,
    ! [SV244: $i,SV584: $i,SV611: $i > $i] :
      ( ( ( in @ ( SV611 @ ( sK93_Xx @ SV611 @ SV584 @ SV244 ) ) @ SV584 )
        = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2448]) ).

thf(2630,plain,
    ! [SV585: $i,SV451: $i,SV245: $i,SV718: $i] :
      ( ( ( in @ SV718 @ ( funcSet @ SV245 @ SV451 ) )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK91_Xx @ SV718 @ SV585 @ SV451 @ SV245 ) @ SV245 )
              | ~ ( ( ( ap @ SV245 @ SV451 @ SV585 @ ( sK91_Xx @ SV718 @ SV585 @ SV451 @ SV245 ) )
                   != ( ap @ SV245 @ SV451 @ SV718 @ ( sK91_Xx @ SV718 @ SV585 @ SV451 @ SV245 ) ) ) ) )
          | ( SV585 = SV718 ) )
        = $true )
      | ( ( in @ SV585 @ ( funcSet @ SV245 @ SV451 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2449]) ).

thf(2631,plain,
    ! [SV246: $i,SV731: $i,SV452: $i > $o] :
      ( ( ( ~ ( SV452 @ SV731 ) )
        = $true )
      | ( ( ~ ( in @ SV731 @ SV246 ) )
        = $true )
      | ( ( in @ ( sK36_Xx @ SV452 @ SV246 ) @ SV246 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2450]) ).

thf(2632,plain,
    ! [SV246: $i,SV732: $i,SV452: $i > $o] :
      ( ( ( ~ ( SV452 @ SV732 ) )
        = $true )
      | ( ( ~ ( in @ SV732 @ SV246 ) )
        = $true )
      | ( ( SV452 @ ( sK36_Xx @ SV452 @ SV246 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2451]) ).

thf(2633,plain,
    ! [SV586: $i,SV247: $i > $o] :
      ( ( ( SV247 @ SV586 )
        = $false )
      | ( ( SV247 @ ( sK22_SY74 @ SV586 @ SV247 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2435: $i] :
                    ( ~ ( SV247 @ SY2435 )
                    | ( ( sK21_Xx @ SV247 )
                      = SY2435 ) )
              | ~ ( SV247 @ ( sK21_Xx @ SV247 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2452]) ).

thf(2634,plain,
    ! [SV247: $i > $o,SV586: $i] :
      ( ( ( SV586
          = ( sK22_SY74 @ SV586 @ SV247 ) )
        = $false )
      | ( ( ~ ( SV247 @ SV586 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2435: $i] :
                    ( ~ ( SV247 @ SY2435 )
                    | ( ( sK21_Xx @ SV247 )
                      = SY2435 ) )
              | ~ ( SV247 @ ( sK21_Xx @ SV247 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2453]) ).

thf(2635,plain,
    ! [SV248: $i,SV453: $i,SV661: $i > $o,SV719: $i > $o] :
      ( ( ( ~ ( in @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) @ SV248 )
          | ~ ~ ( ~ ( in @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) @ SV453 )
                | ~ ~ ( ( ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 )
                       != ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) )
                      | ~ ~ ( ~ ( ~ ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
                                | ~ ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) )
                            | ~ ( ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
                                | ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) ) ) ) ) )
        = $false )
      | ( ( ( dsetconstr @ SV248
            @ ^ [SY2930: $i] : ( SV661 @ SY2930 ) )
          = ( dsetconstr @ SV453
            @ ^ [SY2961: $i] : ( SV719 @ SY2961 ) ) )
        = $true )
      | ( ( SV248 = SV453 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2454]) ).

thf(2636,plain,
    ! [SV612: $i,SV250: $i,SV1: $i,SV733: $i] :
      ( ( ( ~ ( in @ SV733 @ ( powerset @ SV1 ) ) )
        = $true )
      | ( ( ! [SY2966: $i] :
              ( ~ ( in @ SY2966 @ SV1 )
              | ~ ( in @ SY2966 @ ( binintersect @ SV250 @ SV612 ) )
              | ( in @ SY2966 @ ( binunion @ SV250 @ SV733 ) ) ) )
        = $true )
      | ( ( in @ SV612 @ ( powerset @ SV1 ) )
        = $false )
      | ( ( in @ SV250 @ ( powerset @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2457]) ).

thf(2637,plain,
    ! [SV613: $i,SV251: $i,SV2: $i,SV734: $i] :
      ( ( ( ~ ( in @ SV734 @ SV2 ) )
        = $true )
      | ( ( ( in @ SV734 @ ( binunion @ SV251 @ SV613 ) )
          | ~ ( in @ SV734 @ SV613 ) )
        = $true )
      | ( ( in @ SV613 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV251 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2458]) ).

thf(2638,plain,
    ! [SV614: $i,SV252: $i,SV3: $i,SV735: $i] :
      ( ( ( ~ ( in @ SV735 @ SV3 ) )
        = $true )
      | ( ( ( in @ SV735 @ ( binunion @ SV252 @ SV614 ) )
          | ~ ( in @ SV735 @ SV252 ) )
        = $true )
      | ( ( in @ SV614 @ ( powerset @ SV3 ) )
        = $false )
      | ( ( in @ SV252 @ ( powerset @ SV3 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2459]) ).

thf(2639,plain,
    ! [SV615: $i,SV4: $i,SV253: $i] :
      ( ( ( subset @ SV253 @ ( setminus @ SV4 @ SV615 ) )
        = $false )
      | ( ( subset @ SV615 @ ( setminus @ SV4 @ SV253 ) )
        = $true )
      | ( ( in @ SV615 @ ( powerset @ SV4 ) )
        = $false )
      | ( ( in @ SV253 @ ( powerset @ SV4 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2460]) ).

thf(2640,plain,
    ! [SV616: $i,SV5: $i,SV254: $i] :
      ( ( ( subset @ SV254 @ ( setminus @ SV5 @ SV616 ) )
        = $false )
      | ( ( ! [SY2899: $i] :
              ( ~ ( in @ SY2899 @ SV5 )
              | ~ ( in @ SY2899 @ SV616 )
              | ( in @ SY2899 @ ( setminus @ SV5 @ SV254 ) ) ) )
        = $true )
      | ( ( in @ SV616 @ ( powerset @ SV5 ) )
        = $false )
      | ( ( in @ SV254 @ ( powerset @ SV5 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2461]) ).

thf(2641,plain,
    ! [SV619: $i,SV257: $i,SV8: $i,SV736: $i] :
      ( ( ( ~ ( in @ SV736 @ SV8 ) )
        = $true )
      | ( ( ~ ( in @ SV736 @ ( setminus @ SV8 @ SV257 ) )
          | ( in @ SV736 @ ( setminus @ SV8 @ ( binintersect @ SV257 @ SV619 ) ) ) )
        = $true )
      | ( ( in @ SV619 @ ( powerset @ SV8 ) )
        = $false )
      | ( ( in @ SV257 @ ( powerset @ SV8 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2462]) ).

thf(2642,plain,
    ! [SV620: $i,SV258: $i,SV9: $i,SV737: $i] :
      ( ( ( ~ ( in @ SV737 @ SV9 ) )
        = $true )
      | ( ( ~ ( in @ SV737 @ ( setminus @ SV9 @ SV258 ) )
          | ~ ( in @ SV737 @ ( binintersect @ SV258 @ SV620 ) ) )
        = $true )
      | ( ( in @ SV620 @ ( powerset @ SV9 ) )
        = $false )
      | ( ( in @ SV258 @ ( powerset @ SV9 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2463]) ).

thf(2643,plain,
    ! [SV262: $i,SV13: $i,SV621: $i] :
      ( ( ( in @ SV621 @ ( setminus @ SV13 @ ( setminus @ SV13 @ SV262 ) ) )
        = $false )
      | ( ( in @ SV621 @ SV262 )
        = $true )
      | ( ( in @ SV621 @ SV13 )
        = $false )
      | ( ( in @ SV262 @ ( powerset @ SV13 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2464]) ).

thf(2644,plain,
    ! [SV14: $i,SV263: $i,SV622: $i] :
      ( ( ( in @ SV622 @ SV263 )
        = $false )
      | ( ( in @ SV622 @ ( setminus @ SV14 @ ( setminus @ SV14 @ SV263 ) ) )
        = $true )
      | ( ( in @ SV622 @ SV14 )
        = $false )
      | ( ( in @ SV263 @ ( powerset @ SV14 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2465]) ).

thf(2645,plain,
    ! [SV264: $i,SV623: $i,SV15: $i] :
      ( ( ( subset @ ( setminus @ SV15 @ SV623 ) @ ( setminus @ SV15 @ SV264 ) )
        = $false )
      | ( ( subset @ SV264 @ SV623 )
        = $true )
      | ( ( in @ SV623 @ ( powerset @ SV15 ) )
        = $false )
      | ( ( in @ SV264 @ ( powerset @ SV15 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2466]) ).

thf(2646,plain,
    ! [SV16: $i,SV624: $i,SV265: $i] :
      ( ( ( subset @ SV265 @ SV624 )
        = $false )
      | ( ( subset @ ( setminus @ SV16 @ SV624 ) @ ( setminus @ SV16 @ SV265 ) )
        = $true )
      | ( ( in @ SV624 @ ( powerset @ SV16 ) )
        = $false )
      | ( ( in @ SV265 @ ( powerset @ SV16 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2467]) ).

thf(2647,plain,
    ! [SV625: $i,SV266: $i,SV17: $i,SV738: $i] :
      ( ( ( ~ ( in @ SV738 @ SV17 ) )
        = $true )
      | ( ( ~ ( subset @ SV266 @ SV625 )
          | ( in @ SV738 @ SV625 )
          | ~ ( in @ SV738 @ SV266 ) )
        = $true )
      | ( ( in @ SV625 @ ( powerset @ SV17 ) )
        = $false )
      | ( ( in @ SV266 @ ( powerset @ SV17 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2468]) ).

thf(2648,plain,
    ! [SV626: $i,SV267: $i,SV18: $i,SV739: $i] :
      ( ( ( ~ ( in @ SV739 @ SV18 ) )
        = $true )
      | ( ( ~ ( subset @ SV267 @ ( setminus @ SV18 @ SV626 ) )
          | ~ ( in @ SV739 @ SV626 )
          | ~ ( in @ SV739 @ SV267 ) )
        = $true )
      | ( ( in @ SV626 @ ( powerset @ SV18 ) )
        = $false )
      | ( ( in @ SV267 @ ( powerset @ SV18 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2469]) ).

thf(2649,plain,
    ! [SV268: $i,SV627: $i,SV19: $i,SV740: $i] :
      ( ( ( ~ ( in @ SV740 @ SV19 ) )
        = $true )
      | ( ( ( in @ SV740 @ SV627 )
          | ~ ( in @ SV740 @ ( binintersect @ SV268 @ SV627 ) ) )
        = $true )
      | ( ( in @ SV627 @ ( powerset @ SV19 ) )
        = $false )
      | ( ( in @ SV268 @ ( powerset @ SV19 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2470]) ).

thf(2650,plain,
    ! [SV628: $i,SV269: $i,SV20: $i,SV741: $i] :
      ( ( ( ~ ( in @ SV741 @ SV20 ) )
        = $true )
      | ( ( ( in @ SV741 @ SV269 )
          | ~ ( in @ SV741 @ ( binintersect @ SV269 @ SV628 ) ) )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV20 ) )
        = $false )
      | ( ( in @ SV269 @ ( powerset @ SV20 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2471]) ).

thf(2651,plain,
    ! [SV22: $i,SV271: $i,SV630: $i] :
      ( ( ( in @ SV630 @ SV271 )
        = $false )
      | ( ( ~ ( in @ SV630 @ ( setminus @ SV22 @ SV271 ) ) )
        = $true )
      | ( ( in @ SV630 @ SV22 )
        = $false )
      | ( ( in @ SV271 @ ( powerset @ SV22 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2473]) ).

thf(2652,plain,
    ! [SV631: $i,SV272: $i,SV23: $i,SV742: $i] :
      ( ( ( ~ ( in @ SV742 @ SV23 ) )
        = $true )
      | ( ( ~ ( in @ SV272 @ ( powerset @ SV631 ) )
          | ~ ( in @ SV742 @ SV272 )
          | ( in @ SV742 @ SV631 ) )
        = $true )
      | ( ( in @ SV631 @ ( powerset @ SV23 ) )
        = $false )
      | ( ( in @ SV272 @ ( powerset @ SV23 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2474]) ).

thf(2653,plain,
    ! [SV665: $i,SV458: $i,SV30: $i,SV279: $o] :
      ( ( SV279 = $true )
      | ( ( ( if @ SV30 @ SV279 @ SV458 @ SV665 )
          = SV665 )
        = $true )
      | ( ( in @ SV665 @ SV30 )
        = $false )
      | ( ( in @ SV458 @ SV30 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2478]) ).

thf(2654,plain,
    ! [SV666: $i,SV459: $i,SV30: $i] :
      ( ( $true = $true )
      | ( ( ( if @ SV30 @ $true @ SV459 @ SV666 )
          = SV666 )
        = $true )
      | ( ( in @ SV666 @ SV30 )
        = $false )
      | ( ( in @ SV459 @ SV30 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2479]) ).

thf(2655,plain,
    ! [SV667: $i,SV460: $i,SV30: $i] :
      ( ( $false = $true )
      | ( ( ( if @ SV30 @ $false @ SV460 @ SV667 )
          = SV667 )
        = $true )
      | ( ( in @ SV667 @ SV30 )
        = $false )
      | ( ( in @ SV460 @ SV30 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2480]) ).

thf(2656,plain,
    ! [SV668: $i,SV461: $i,SV31: $i,SV280: $o] :
      ( ( ( ~ SV280 ) = $true )
      | ( ( ( if @ SV31 @ SV280 @ SV461 @ SV668 )
          = SV461 )
        = $true )
      | ( ( in @ SV668 @ SV31 )
        = $false )
      | ( ( in @ SV461 @ SV31 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2481]) ).

thf(2657,plain,
    ! [SV669: $i,SV462: $i,SV31: $i] :
      ( ( ( ~ $true ) = $true )
      | ( ( ( if @ SV31 @ $true @ SV462 @ SV669 )
          = SV462 )
        = $true )
      | ( ( in @ SV669 @ SV31 )
        = $false )
      | ( ( in @ SV462 @ SV31 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2482]) ).

thf(2658,plain,
    ! [SV670: $i,SV463: $i,SV31: $i] :
      ( ( ( ~ $false ) = $true )
      | ( ( ( if @ SV31 @ $false @ SV463 @ SV670 )
          = SV463 )
        = $true )
      | ( ( in @ SV670 @ SV31 )
        = $false )
      | ( ( in @ SV463 @ SV31 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2483]) ).

thf(2659,plain,
    ! [SV38: $i,SV471: $i,SV674: $i,SV284: $i,SV756: $i] :
      ( ( ( ~ ( in @ SV756 @ SV284 )
          | ~ ( in @ ( kpair @ SV674 @ SV756 ) @ SV471 )
          | ( ( ap @ SV38 @ SV284 @ SV471 @ SV674 )
            = SV756 ) )
        = $true )
      | ( ( in @ SV674 @ SV38 )
        = $false )
      | ( ( in @ SV471 @ ( funcSet @ SV38 @ SV284 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2489]) ).

thf(2660,plain,
    ! [SV39: $i,SV472: $i,SV675: $i,SV285: $i,SV757: $i] :
      ( ( ( ~ ( in @ SV757 @ SV285 )
          | ~ ( in @ ( kpair @ SV675 @ SV757 ) @ SV472 )
          | ( ( ap @ SV39 @ SV285 @ SV472 @ SV675 )
            = SV757 ) )
        = $true )
      | ( ( in @ SV675 @ SV39 )
        = $false )
      | ( ( func @ SV39 @ SV285 @ SV472 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2490]) ).

thf(2661,plain,
    ! [SV635: $i,SV288: $i > $o,SV42: $i,SV743: $i] :
      ( ( ( ~ ( in @ SV743 @ SV42 ) )
        = $true )
      | ( ( ~ ( SV288 @ SV635 )
          | ~ ( SV288 @ SV743 )
          | ( SV635 = SV743 ) )
        = $true )
      | ( ( in @ SV635 @ SV42 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV42
            @ ^ [SY2500: $i] : ( SV288 @ SY2500 ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2493]) ).

thf(2662,plain,
    ! [SV484: $i > $i > $o,SV52: $i,SV593: $i,SV298: $i,SV722: $i] :
      ( ( ( in @ SV722 @ SV298 )
        = $false )
      | ( ( ~ ( in @ ( kpair @ SV593 @ SV722 )
              @ ( dpsetconstr @ SV52 @ SV298
                @ ^ [SY2775: $i,SY2776: $i] : ( SV484 @ SY2775 @ SY2776 ) ) )
          | ( SV484 @ SV593 @ SV722 ) )
        = $true )
      | ( ( in @ SV593 @ SV52 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2498]) ).

thf(2663,plain,
    ! [SV55: $i,SV594: $i,SV487: $i > $i > $o,SV301: $i,SV723: $i] :
      ( ( ( in @ SV723 @ SV301 )
        = $false )
      | ( ( ~ ( SV487 @ SV594 @ SV723 )
          | ( in @ ( kpair @ SV594 @ SV723 )
            @ ( dpsetconstr @ SV55 @ SV301
              @ ^ [SY2783: $i,SY2784: $i] : ( SV487 @ SY2783 @ SY2784 ) ) ) )
        = $true )
      | ( ( in @ SV594 @ SV55 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2499]) ).

thf(2664,plain,
    ! [SV388: $i,SV693: $i,SV154: $i,SV645: $i] :
      ( ( ( ~ ( in @ SV645 @ SV154 ) )
        = $true )
      | ( ( in @ SV693 @ SV388 )
        = $true )
      | ( ( SV645 = SV693 )
        = $false )
      | ( ( SV154 = SV388 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2512]) ).

thf(2665,plain,
    ! [SV189: $i,SV409: $i,SV647: $i] :
      ( ( ( ~ ( in @ ( sK97_Xx @ SV647 @ SV409 @ SV189 ) @ SV189 )
          | ~ ~ ( ~ ( in @ ( sK97_Xx @ SV647 @ SV409 @ SV189 ) @ SV409 )
                | ~ ~ ( in @ ( sK97_Xx @ SV647 @ SV409 @ SV189 ) @ SV647 ) ) )
        = $false )
      | ( ( subset @ SV409 @ SV647 )
        = $true )
      | ( ( in @ SV647 @ ( powerset @ SV189 ) )
        = $false )
      | ( ( in @ SV409 @ ( powerset @ SV189 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2515]) ).

thf(2666,plain,
    ! [SV602: $i,SV648: $i] :
      ( ( ( in @ ( sK7_Xx @ SV648 @ SV602 ) @ SV648 )
        = $true )
      | ( ( in @ SV648 @ ( powerset @ SV602 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2516]) ).

thf(2667,plain,
    ! [SV602: $i,SV648: $i] :
      ( ( ( ~ ( in @ ( sK7_Xx @ SV648 @ SV602 ) @ SV602 ) )
        = $true )
      | ( ( in @ SV648 @ ( powerset @ SV602 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2517]) ).

thf(2668,plain,
    ! [SV603: $i,SV649: $i,SV744: $i] :
      ( ( ( ~ ( in @ SV744 @ SV649 ) )
        = $true )
      | ( ( in @ SV744 @ SV603 )
        = $true )
      | ( ( in @ SV649 @ ( powerset @ SV603 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2518]) ).

thf(2669,plain,
    ! [SV545: $i,SV190: $i > $o] :
      ( ( ( SV190 @ SV545 )
        = $false )
      | ( ( SV545
          = ( sK24_SY86 @ SV545 @ SV190 ) )
        = $false )
      | ( ( SV190 @ ( sK23_Xx @ SV190 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2520]) ).

thf(2670,plain,
    ! [SV694: $i,SV191: $i,SV546: $i,SV410: $o] :
      ( ( ( ~ SV410 ) = $true )
      | ( ( in @ SV546
          @ ( dsetconstr @ SV191
            @ ^ [SY2939: $i] :
                ( ~ ( ~ SV410
                    | ( SY2939 != SV546 ) )
                | ~ ( ~ ~ SV410
                    | ( SY2939 != SV694 ) ) ) ) )
        = $true )
      | ( ( in @ SV694 @ SV191 )
        = $false )
      | ( ( in @ SV546 @ SV191 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2521]) ).

thf(2671,plain,
    ! [SV695: $i,SV191: $i,SV547: $i] :
      ( ( ( ~ $true ) = $true )
      | ( ( in @ SV547
          @ ( dsetconstr @ SV191
            @ ^ [SY2940: $i] :
                ( ~ ( ~ $true
                    | ( SY2940 != SV547 ) )
                | ~ ( ~ ~ $true
                    | ( SY2940 != SV695 ) ) ) ) )
        = $true )
      | ( ( in @ SV695 @ SV191 )
        = $false )
      | ( ( in @ SV547 @ SV191 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2522]) ).

thf(2672,plain,
    ! [SV696: $i,SV191: $i,SV548: $i] :
      ( ( ( ~ $false ) = $true )
      | ( ( in @ SV548
          @ ( dsetconstr @ SV191
            @ ^ [SY2941: $i] :
                ( ~ ( ~ $false
                    | ( SY2941 != SV548 ) )
                | ~ ( ~ ~ $false
                    | ( SY2941 != SV696 ) ) ) ) )
        = $true )
      | ( ( in @ SV696 @ SV191 )
        = $false )
      | ( ( in @ SV548 @ SV191 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2523]) ).

thf(2673,plain,
    ! [SV549: $i > $i,SV411: $i,SV192: $i,SV745: $i] :
      ( ( ( ~ ( in @ SV745 @ SV192 ) )
        = $true )
      | ( ( ( ap @ SV192 @ SV411
            @ ( lam @ SV192 @ SV411
              @ ^ [SY2811: $i] : ( SV549 @ SY2811 ) )
            @ SV745 )
          = ( SV549 @ SV745 ) )
        = $true )
      | ( ( in @ ( sK92_Xx @ SV549 @ SV411 @ SV192 ) @ SV192 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2524]) ).

thf(2674,plain,
    ! [SV549: $i > $i,SV411: $i,SV192: $i,SV758: $i] :
      ( ( ( ~ ( in @ SV758 @ SV192 )
          | ( ( ap @ SV192 @ SV411
              @ ( lam @ SV192 @ SV411
                @ ^ [SY2811: $i] : ( SV549 @ SY2811 ) )
              @ SV758 )
            = ( SV549 @ SV758 ) ) )
        = $true )
      | ( ( in @ ( SV549 @ ( sK92_Xx @ SV549 @ SV411 @ SV192 ) ) @ SV411 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2525]) ).

thf(2675,plain,
    ! [SV193: $i,SV412: $i,SV550: $i] :
      ( ( ( ( SV550
           != ( kpair @ ( sK67_Xx @ SV550 @ SV412 @ SV193 ) @ ( sK68_SY1876 @ SV550 @ SV412 @ SV193 ) ) )
          | ~ ( in @ ( sK68_SY1876 @ SV550 @ SV412 @ SV193 ) @ SV412 ) )
        = $false )
      | ( ( in @ SV550 @ ( cartprod @ SV193 @ SV412 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2526]) ).

thf(2676,plain,
    ! [SV551: $i,SV759: $i,SV194: $i > $o] :
      ( ( ( ~ ( SV194 @ SV759 )
          | ! [SY2977: $i] :
              ( ~ ( SV194 @ SY2977 )
              | ( SV759 = SY2977 ) ) )
        = $true )
      | ( ( SV194 @ ( sK57_SY248 @ SV551 @ SV194 ) )
        = $true )
      | ( ( SV194 @ SV551 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2528]) ).

thf(2677,plain,
    ! [SV551: $i,SV194: $i > $o] :
      ( ( ( SV194 @ SV551 )
        = $false )
      | ( ( SV551
          = ( sK57_SY248 @ SV551 @ SV194 ) )
        = $false )
      | ( ( ! [SY2258: $i] :
              ( ~ ( SV194 @ SY2258 )
              | ! [SY2259: $i] :
                  ( ~ ( SV194 @ SY2259 )
                  | ( SY2258 = SY2259 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2529]) ).

thf(2678,plain,
    ! [SV413: $i,SV195: $i > $i > $o] :
      ( ( ( ! [SY2639: $i] :
              ( ! [SY2640: $i] :
                  ( ~ ( SV195 @ SY2640 @ SY2639 )
                  | ~ ( in @ SY2640 @ SV413 ) )
              | ( in @ SY2639 @ ( sK10_B @ SV413 @ SV195 ) ) ) )
        = $true )
      | ( ( in @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV413 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2530]) ).

thf(2679,plain,
    ! [SV195: $i > $i > $o,SV413: $i] :
      ( ( ( ! [SY2641: $i] :
              ( ~ ( in @ SY2641 @ ( sK10_B @ SV413 @ SV195 ) )
              | ~ ( ~ ( SV195 @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SY2641 )
                  | ~ ( in @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SV413 ) ) ) )
        = $true )
      | ( ( in @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV413 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2531]) ).

thf(2680,plain,
    ! [SV725: $i,SV413: $i,SV195: $i > $i > $o] :
      ( ( ( ~ ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
          | ~ ( ( SV725
               != ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) ) ) )
        = $false )
      | ( ( ~ ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2639: $i] :
                    ( ! [SY2640: $i] :
                        ( ~ ( SV195 @ SY2640 @ SY2639 )
                        | ~ ( in @ SY2640 @ SV413 ) )
                    | ( in @ SY2639 @ ( sK10_B @ SV413 @ SV195 ) ) )
              | ~ ! [SY2641: $i] :
                    ( ~ ( in @ SY2641 @ ( sK10_B @ SV413 @ SV195 ) )
                    | ~ ( ~ ( SV195 @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SY2641 )
                        | ~ ( in @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SV413 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2532]) ).

thf(2681,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( ( ~ ( ( SV552 = SV196 )
              | ( in @ SV552 @ SV414 )
              | ! [SX3: $o] : SX3 )
          | ~ ( ( SV552 = SV196 )
              | ! [SX3: $o] :
                  ( ~ SX3
                  | SX3 ) ) )
        = $false )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2533]) ).

thf(2682,plain,
    ! [SV196: $i,SV414: $i,SV552: $i] :
      ( ( ( ~ ! [SY2814: $o] :
                ( ~ SY2814
                | ( in @ SV552 @ SV414 )
                | SY2814 )
          | ~ ! [SX3: $o] :
                ( ~ SX3
                | ~ SX3
                | SX3 ) )
        = $false )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2534]) ).

thf(2683,plain,
    ! [SV198: $i,SV697: $i,SV650: $i > $o] :
      ( ( ( ~ ( SV650 @ SV697 ) )
        = $true )
      | ( ( in @ SV697
          @ ( dsetconstr @ SV198
            @ ^ [SY2916: $i] : ( SV650 @ SY2916 ) ) )
        = $true )
      | ( ( in @ SV697 @ SV198 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2535]) ).

thf(2684,plain,
    ! [SV651: $i > $o,SV198: $i,SV698: $i] :
      ( ( ( ~ ( in @ SV698
              @ ( dsetconstr @ SV198
                @ ^ [SY2918: $i] : ( SV651 @ SY2918 ) ) ) )
        = $true )
      | ( ( SV651 @ SV698 )
        = $true )
      | ( ( in @ SV698 @ SV198 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2536]) ).

thf(2685,plain,
    ! [SV604: $i,SV200: $i,SV417: $i > $o] :
      ( ( ( in @ ( sK40_Xx @ SV417 @ SV200 ) @ SV200 )
        = $true )
      | ( ( SV417 @ SV604 )
        = $true )
      | ( ( in @ SV604 @ SV200 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2537]) ).

thf(2686,plain,
    ! [SV604: $i,SV200: $i,SV417: $i > $o] :
      ( ( ( ~ ( SV417 @ ( sK40_Xx @ SV417 @ SV200 ) ) )
        = $true )
      | ( ( SV417 @ SV604 )
        = $true )
      | ( ( in @ SV604 @ SV200 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2538]) ).

thf(2687,plain,
    ! [SV699: $i,SV554: $i,SV202: $i,SV419: $o] :
      ( ( SV419 = $true )
      | ( ( ( dsetconstr @ SV202
            @ ^ [SY2944: $i] :
                ( ~ ( ~ SV419
                    | ( SY2944 != SV554 ) )
                | ~ ( ~ ~ SV419
                    | ( SY2944 != SV699 ) ) ) )
          = ( setadjoin @ SV699 @ emptyset ) )
        = $true )
      | ( ( in @ SV699 @ SV202 )
        = $false )
      | ( ( in @ SV554 @ SV202 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2540]) ).

thf(2688,plain,
    ! [SV700: $i,SV555: $i,SV202: $i] :
      ( ( $true = $true )
      | ( ( ( dsetconstr @ SV202
            @ ^ [SY2945: $i] :
                ( ~ ( ~ $true
                    | ( SY2945 != SV555 ) )
                | ~ ( ~ ~ $true
                    | ( SY2945 != SV700 ) ) ) )
          = ( setadjoin @ SV700 @ emptyset ) )
        = $true )
      | ( ( in @ SV700 @ SV202 )
        = $false )
      | ( ( in @ SV555 @ SV202 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2541]) ).

thf(2689,plain,
    ! [SV701: $i,SV556: $i,SV202: $i] :
      ( ( $false = $true )
      | ( ( ( dsetconstr @ SV202
            @ ^ [SY2946: $i] :
                ( ~ ( ~ $false
                    | ( SY2946 != SV556 ) )
                | ~ ( ~ ~ $false
                    | ( SY2946 != SV701 ) ) ) )
          = ( setadjoin @ SV701 @ emptyset ) )
        = $true )
      | ( ( in @ SV701 @ SV202 )
        = $false )
      | ( ( in @ SV556 @ SV202 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2542]) ).

thf(2690,plain,
    ! [SV605: $i > $o,SV652: $i > $o] :
      ( ( ( ( sK55_Xx @ SV652 @ SV605 )
          = ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true )
      | ( ( ! [SY2919: $i] :
              ( ~ ( ~ ( SV605 @ ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) )
                  | ~ ( ( SY2919
                       != ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) ) ) )
              | ~ ( SV605 @ SY2919 ) )
          | ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2543]) ).

thf(2691,plain,
    ! [SV652: $i > $o,SV605: $i > $o] :
      ( ( ( ~ ( ~ ( ~ ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
                  | ~ ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) ) )
              | ~ ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
                  | ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) ) ) ) )
        = $true )
      | ( ( ! [SY2919: $i] :
              ( ~ ( ~ ( SV605 @ ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) )
                  | ~ ( ( SY2919
                       != ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) ) ) )
              | ~ ( SV605 @ SY2919 ) )
          | ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2544]) ).

thf(2692,plain,
    ! [SV606: $i > $o,SV653: $i > $o] :
      ( ( ( ( sK51_Xx @ SV653 @ SV606 )
          = ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true )
      | ( ( ! [SY2921: $i] :
              ( ~ ( ~ ( SV653 @ ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) )
                  | ~ ( ( SY2921
                       != ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) ) ) )
              | ~ ( SV653 @ SY2921 ) )
          | ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2545]) ).

thf(2693,plain,
    ! [SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ~ ( ~ ( ~ ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
                  | ~ ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) ) )
              | ~ ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
                  | ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) ) ) ) )
        = $true )
      | ( ( ! [SY2921: $i] :
              ( ~ ( ~ ( SV653 @ ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) )
                  | ~ ( ( SY2921
                       != ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) ) ) )
              | ~ ( SV653 @ SY2921 ) )
          | ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2546]) ).

thf(2694,plain,
    ! [SV420: $i > $o,SV203: $i,SV726: $i] :
      ( ( ( in @ SV726 @ SV203 )
        = $false )
      | ( ( ~ ( SV420 @ SV726 ) )
        = $true )
      | ( ( SV420 @ ( sK39_Xx @ SV420 @ SV203 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2547]) ).

thf(2695,plain,
    ! [SV420: $i > $o,SV203: $i,SV727: $i] :
      ( ( ( in @ SV727 @ SV203 )
        = $false )
      | ( ( ~ ( SV420 @ SV727 ) )
        = $true )
      | ( ( in @ ( sK39_Xx @ SV420 @ SV203 ) @ SV203 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2548]) ).

thf(2696,plain,
    ! [SV557: $i,SV204: $i > $o] :
      ( ( ( SV204 @ SV557 )
        = $false )
      | ( ( SV557
          = ( sK20_SY57 @ SV557 @ SV204 ) )
        = $false )
      | ( ( SV204
          @ ( descr
            @ ^ [SY2291: $i] : ( SV204 @ SY2291 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2550]) ).

thf(2697,plain,
    ! [SV558: $i,SV205: $i > $o] :
      ( ( ( ~ ! [SY2293: $i] :
                ( ~ ( SV205 @ SY2293 )
                | ( ( sK41_SY198 @ SV205 )
                  = SY2293 ) )
          | ~ ( SV205 @ ( sK41_SY198 @ SV205 ) ) )
        = $false )
      | ( ( SV205 @ ( sK42_Xy @ SV558 @ SV205 ) )
        = $true )
      | ( ( SV205 @ SV558 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2551]) ).

thf(2698,plain,
    ! [SV558: $i,SV205: $i > $o] :
      ( ( ( SV205 @ SV558 )
        = $false )
      | ( ( SV558
          = ( sK42_Xy @ SV558 @ SV205 ) )
        = $false )
      | ( ( ~ ( ~ ! [SY2293: $i] :
                    ( ~ ( SV205 @ SY2293 )
                    | ( ( sK41_SY198 @ SV205 )
                      = SY2293 ) )
              | ~ ( SV205 @ ( sK41_SY198 @ SV205 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2552]) ).

thf(2699,plain,
    ! [SV559: $i > $i,SV421: $i,SV206: $i,SV746: $i] :
      ( ( ( ~ ( in @ SV746 @ SV206 ) )
        = $true )
      | ( ( ( ap @ SV206 @ SV421
            @ ( lam @ SV206 @ SV421
              @ ^ [SY2824: $i] : ( SV559 @ SY2824 ) )
            @ SV746 )
          = ( SV559 @ SV746 ) )
        = $true )
      | ( ( in @ ( sK94_Xx @ SV559 @ SV421 @ SV206 ) @ SV206 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2553]) ).

thf(2700,plain,
    ! [SV559: $i > $i,SV421: $i,SV206: $i,SV760: $i] :
      ( ( ( ~ ( in @ SV760 @ SV206 )
          | ( ( ap @ SV206 @ SV421
              @ ( lam @ SV206 @ SV421
                @ ^ [SY2824: $i] : ( SV559 @ SY2824 ) )
              @ SV760 )
            = ( SV559 @ SV760 ) ) )
        = $true )
      | ( ( in @ ( SV559 @ ( sK94_Xx @ SV559 @ SV421 @ SV206 ) ) @ SV421 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2554]) ).

thf(2701,plain,
    ( ( in @ sK4_SY1829 @ ( powerset @ sK1_A ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2555]) ).

thf(2702,plain,
    ( ( ~ ( ~ ( in @ sK5_SY1831 @ sK1_A )
          | ~ ~ ( ~ ( in @ sK5_SY1831 @ ( binintersect @ sK2_SY1822 @ sK3_SY1826 ) )
                | ~ ~ ( in @ sK5_SY1831 @ ( binunion @ sK3_SY1826 @ sK4_SY1829 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2556]) ).

thf(2703,plain,
    ! [SV207: $i,SV422: $i,SV560: $i,SV702: $i > $o] :
      ( ( ( ~ ( in @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ SV207 ) )
        = $false )
      | ( ( ! [SY2947: $i] :
              ( ~ ( in @ SY2947 @ SV560 )
              | ( SV702 @ SY2947 ) ) )
        = $true )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2557]) ).

thf(2704,plain,
    ! [SV207: $i,SV422: $i,SV560: $i,SV702: $i > $o] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) @ SV422 )
                | ~ ~ ( ~ ( in @ ( kpair @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) ) @ SV560 )
                      | ~ ~ ( SV702 @ ( kpair @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) ) ) ) ) )
        = $false )
      | ( ( ! [SY2947: $i] :
              ( ~ ( in @ SY2947 @ SV560 )
              | ( SV702 @ SY2947 ) ) )
        = $true )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2557]) ).

thf(2705,plain,
    ! [SV208: $i,SV423: $i,SV561: $i,SV703: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ SV208 )
              | ~ ~ ( ~ ( in @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) @ SV423 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) ) @ SV561 )
                          | ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) ) @ SV703 ) ) ) ) )
        = $true )
      | ( ( subset @ SV561 @ SV703 )
        = $true )
      | ( ( subset @ SV703 @ ( cartprod @ SV208 @ SV423 ) )
        = $false )
      | ( ( subset @ SV561 @ ( cartprod @ SV208 @ SV423 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2558]) ).

thf(2706,plain,
    ! [SV209: $i,SV747: $i,SV424: $i > $o] :
      ( ( ( ~ ( SV424 @ SV747 ) )
        = $true )
      | ( ( ~ ( in @ SV747 @ SV209 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV209
            @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) )
        = $true )
      | ( ( in @ ( sK70_Xx @ SV424 @ SV209 ) @ SV209 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2559]) ).

thf(2707,plain,
    ! [SV209: $i,SV424: $i > $o] :
      ( ( ( in @ ( sK71_SY1877 @ SV424 @ SV209 ) @ SV209 )
        = $true )
      | ( ( ! [SY2662: $i] :
              ( ~ ( SV424 @ SY2662 )
              | ~ ( in @ SY2662 @ SV209 ) )
          | ( singleton
            @ ( dsetconstr @ SV209
              @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2560]) ).

thf(2708,plain,
    ! [SV209: $i,SV424: $i > $o] :
      ( ( ( ~ ( ~ ( SV424 @ ( sK70_Xx @ SV424 @ SV209 ) )
              | ~ ~ ( ~ ( SV424 @ ( sK71_SY1877 @ SV424 @ SV209 ) )
                    | ~ ( ( ( sK70_Xx @ SV424 @ SV209 )
                         != ( sK71_SY1877 @ SV424 @ SV209 ) ) ) ) ) )
        = $true )
      | ( ( ! [SY2662: $i] :
              ( ~ ( SV424 @ SY2662 )
              | ~ ( in @ SY2662 @ SV209 ) )
          | ( singleton
            @ ( dsetconstr @ SV209
              @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2561]) ).

thf(2709,plain,
    ! [SV425: $i,SV210: $i,SV761: $i,SV748: $i] :
      ( ( ( ( SV748 != SV761 )
          | ~ ( in @ SV748 @ SV210 )
          | ( in @ SV761 @ SV425 ) )
        = $true )
      | ( ( SV210 = SV425 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2562]) ).

thf(2710,plain,
    ! [SV210: $i,SV425: $i,SV762: $i,SV749: $i] :
      ( ( ( ( SV749 != SV762 )
          | ~ ( in @ SV762 @ SV425 )
          | ( in @ SV749 @ SV210 ) )
        = $true )
      | ( ( SV210 = SV425 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2563]) ).

thf(2711,plain,
    ! [SV562: $i,SV763: $i,SV211: $i > $o] :
      ( ( ( ~ ( SV211 @ SV763 )
          | ! [SY2979: $i] :
              ( ~ ( SV211 @ SY2979 )
              | ( SV763 = SY2979 ) ) )
        = $true )
      | ( ( SV211 @ ( sK48_SY224 @ SV562 @ SV211 ) )
        = $true )
      | ( ( SV211 @ SV562 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2564]) ).

thf(2712,plain,
    ! [SV562: $i,SV211: $i > $o] :
      ( ( ( SV211 @ SV562 )
        = $false )
      | ( ( SV562
          = ( sK48_SY224 @ SV562 @ SV211 ) )
        = $false )
      | ( ( ! [SY2314: $i] :
              ( ~ ( SV211 @ SY2314 )
              | ! [SY2315: $i] :
                  ( ~ ( SV211 @ SY2315 )
                  | ( SY2314 = SY2315 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2565]) ).

thf(2713,plain,
    ! [SV427: $i > $o,SV750: $i,SV213: $i > $o] :
      ( ( ( ~ ( ~ ( SV213 @ ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
              | ~ ( ( SV750
                   != ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV213 @ SV750 ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2567]) ).

thf(2714,plain,
    ! [SV427: $i > $o,SV213: $i > $o] :
      ( ( ( ~ ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
          | ~ ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) ) )
        = $true )
      | ( ( ! [SY2670: $i] :
              ( ~ ( ~ ( SV213 @ ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2670
                       != ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV213 @ SY2670 ) )
          | ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2568]) ).

thf(2715,plain,
    ! [SV427: $i > $o,SV213: $i > $o] :
      ( ( ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
          | ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) ) )
        = $true )
      | ( ( ! [SY2670: $i] :
              ( ~ ( ~ ( SV213 @ ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2670
                       != ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV213 @ SY2670 ) )
          | ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2569]) ).

thf(2716,plain,
    ! [SV214: $i,SV428: $i,SV654: $i] :
      ( ( ( ~ ( in @ ( sK98_Xx @ SV654 @ SV428 @ SV214 ) @ SV214 )
          | ~ ~ ( ~ ( in @ ( sK98_Xx @ SV654 @ SV428 @ SV214 ) @ SV428 )
                | ~ ~ ( in @ ( sK98_Xx @ SV654 @ SV428 @ SV214 ) @ SV654 ) ) )
        = $false )
      | ( ( in @ SV428 @ ( powerset @ SV654 ) )
        = $true )
      | ( ( in @ SV654 @ ( powerset @ SV214 ) )
        = $false )
      | ( ( in @ SV428 @ ( powerset @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2570]) ).

thf(2717,plain,
    ! [SV215: $i,SV655: $o,SV429: $i] :
      ( ( ( in @ SV429 @ ( sK31_B @ SV655 @ SV429 @ SV215 ) )
        = $true )
      | ( SV655 = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2571]) ).

thf(2718,plain,
    ! [SV215: $i,SV429: $i,SV655: $o] :
      ( ( ( ~ ( ~ ( in @ ( sK31_B @ SV655 @ SV429 @ SV215 ) @ SV215 )
              | ~ ~ SV655 ) )
        = $true )
      | ( SV655 = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2572]) ).

thf(2719,plain,
    ! [SV215: $i,SV429: $i] :
      ( ( ( in @ SV429 @ ( sK31_B @ $true @ SV429 @ SV215 ) )
        = $true )
      | ( $true = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2573]) ).

thf(2720,plain,
    ! [SV215: $i,SV429: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK31_B @ $true @ SV429 @ SV215 ) @ SV215 )
              | ~ ~ $true ) )
        = $true )
      | ( $true = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2574]) ).

thf(2721,plain,
    ! [SV215: $i,SV429: $i] :
      ( ( ( in @ SV429 @ ( sK31_B @ $false @ SV429 @ SV215 ) )
        = $true )
      | ( $false = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2575]) ).

thf(2722,plain,
    ! [SV215: $i,SV429: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK31_B @ $false @ SV429 @ SV215 ) @ SV215 )
              | ~ ~ $false ) )
        = $true )
      | ( $false = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2576]) ).

thf(2723,plain,
    ! [SV216: $i,SV430: $i] :
      ( ( ( ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV430 ) )
        = $false )
      | ( ( SV216 = SV430 )
        = $true )
      | ( ( in @ ( sK26_Xx @ SV430 @ SV216 ) @ SV216 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2577]) ).

thf(2724,plain,
    ! [SV216: $i,SV430: $i] :
      ( ( ( ~ ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV216 ) )
        = $false )
      | ( ( SV216 = SV430 )
        = $true )
      | ( ( in @ ( sK26_Xx @ SV430 @ SV216 ) @ SV216 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2577]) ).

thf(2725,plain,
    ! [SV216: $i,SV430: $i] :
      ( ( ( ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV430 )
          | ~ ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV216 ) )
        = $false )
      | ( ( SV216 = SV430 )
        = $true )
      | ( ( in @ ( sK26_Xx @ SV430 @ SV216 ) @ SV430 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2578]) ).

thf(2726,plain,
    ! [SV218: $i,SV432: $i,SV564: $i,SV704: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) @ SV218 )
              | ~ ( ( ( ap @ SV218 @ SV432 @ SV564 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) )
                   != ( ap @ SV218 @ SV432 @ SV704 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) ) ) ) ) )
        = $true )
      | ( ( ! [SY2948: $i] :
              ( ~ ( in @ SY2948 @ SV218 )
              | ! [SY2949: $i] :
                  ( ~ ( in @ SY2949 @ SV432 )
                  | ~ ( in @ ( kpair @ SY2948 @ SY2949 ) @ SV704 )
                  | ( in @ ( kpair @ SY2948 @ SY2949 ) @ SV564 ) ) ) )
        = $true )
      | ( ( func @ SV218 @ SV432 @ SV704 )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV564 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2579]) ).

thf(2727,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
          | ~ ~ ( ~ ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 )
                | ~ ~ ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 ) ) )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
              | ~ ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
                    | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) ) )
          | ( SV433 = SV656 ) )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2580]) ).

thf(2728,plain,
    ! [SV220: $i,SV434: $i > $o,SV565: $i] :
      ( ( ( ~ ( in @ ( sK73_Xy @ SV565 @ SV434 @ SV220 ) @ SV220 )
          | ~ ~ ( ~ ( SV434 @ ( sK73_Xy @ SV565 @ SV434 @ SV220 ) )
                | ~ ( ( ( sK73_Xy @ SV565 @ SV434 @ SV220 )
                     != SV565 ) ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV220
            @ ^ [SY2682: $i] : ( SV434 @ SY2682 ) ) )
        = $true )
      | ( ( SV434 @ SV565 )
        = $false )
      | ( ( in @ SV565 @ SV220 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2581]) ).

thf(2729,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ ( ( in @ SV566 @ SV221 )
              | ~ ( in @ SV566 @ SV221 )
              | ! [SX3: $o] : SX3 )
          | ~ ~ ( ~ ( ( in @ SV566 @ SV221 )
                    | ( in @ SV566 @ SV435 )
                    | ! [SX3: $o] : SX3 )
                | ~ ( ( in @ SV566 @ SV221 )
                    | ! [SX3: $o] :
                        ( ~ SX3
                        | SX3 ) ) ) )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2582]) ).

thf(2730,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ ~ ( ~ ( ~ ( in @ SV566 @ SV435 )
                    | ~ ( in @ SV566 @ SV221 )
                    | ! [SX3: $o] : SX3 )
                | ~ ~ ( ~ ( ~ ( in @ SV566 @ SV435 )
                          | ( in @ SV566 @ SV435 )
                          | ! [SX3: $o] : SX3 )
                      | ~ ( ~ ( in @ SV566 @ SV435 )
                          | ! [SX3: $o] :
                              ( ~ SX3
                              | SX3 ) ) ) )
          | ~ ~ ( ~ ! [SY2839: $o] :
                      ( ~ SY2839
                      | ~ ( in @ SV566 @ SV221 )
                      | SY2839 )
                | ~ ~ ( ~ ! [SY2840: $o] :
                            ( ~ SY2840
                            | ( in @ SV566 @ SV435 )
                            | SY2840 )
                      | ~ ! [SX3: $o] :
                            ( ~ SX3
                            | ~ SX3
                            | SX3 ) ) ) )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2583]) ).

thf(2731,plain,
    ! [SV657: $i,SV223: $i,SV705: $i] :
      ( ( ( SV705 = SV223 )
        = $true )
      | ( ( in @ SV705 @ SV657 )
        = $true )
      | ( ( in @ SV705 @ ( setadjoin @ SV223 @ SV657 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2585]) ).

thf(2732,plain,
    ! [SV751: $i,SV223: $i,SV764: $i] :
      ( ( ( SV764 != SV223 )
        | ( in @ SV764 @ ( setadjoin @ SV223 @ SV751 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2586]) ).

thf(2733,plain,
    ! [SV223: $i,SV752: $i,SV765: $i] :
      ( ( ~ ( in @ SV765 @ SV752 )
        | ( in @ SV765 @ ( setadjoin @ SV223 @ SV752 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2587]) ).

thf(2734,plain,
    ! [SV225: $i,SV438: $i] :
      ( ( ( in @ ( sK6_Xx @ SV438 @ SV225 ) @ SV438 )
        = $false )
      | ( ( in @ ( sK6_Xx @ SV438 @ SV225 ) @ SV225 )
        = $false )
      | ( ( SV225 = SV438 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2588]) ).

thf(2735,plain,
    ! [SV439: $i,SV226: $i,SV766: $i] :
      ( ( ~ ( in @ SV766 @ ( binunion @ SV226 @ SV439 ) )
        | ( in @ SV766 @ SV226 )
        | ( in @ SV766 @ SV439 )
        | ! [SX3: $o] : SX3 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2589]) ).

thf(2736,plain,
    ! [SV439: $i,SV226: $i,SV767: $i] :
      ( ( ~ ( in @ SV767 @ ( binunion @ SV226 @ SV439 ) )
        | ( in @ SV767 @ SV226 )
        | ! [SX3: $o] :
            ( ~ SX3
            | SX3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2590]) ).

thf(2737,plain,
    ! [SV439: $i,SV226: $i,SV768: $i] :
      ( ( ~ ( in @ SV768 @ ( binunion @ SV226 @ SV439 ) )
        | ! [SY2982: $o] :
            ( ~ SY2982
            | ( in @ SV768 @ SV439 )
            | SY2982 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2591]) ).

thf(2738,plain,
    ! [SV439: $i,SV226: $i] :
      ( ( ( ! [SY2702: $i] :
              ~ ( in @ SY2702 @ ( binunion @ SV226 @ SV439 ) ) )
        = $true )
      | ( ( ! [SX2: $o] :
              ( ~ SX2
              | ~ SX2
              | SX2 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2592]) ).

thf(2739,plain,
    ! [SV607: $i,SV227: $i,SV440: $i > $o] :
      ( ( ( in @ ( sK38_Xx @ SV440 @ SV227 ) @ SV227 )
        = $true )
      | ( ( SV440 @ SV607 )
        = $true )
      | ( ( in @ SV607 @ SV227 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2593]) ).

thf(2740,plain,
    ! [SV607: $i,SV227: $i,SV440: $i > $o] :
      ( ( ( ~ ( SV440 @ ( sK38_Xx @ SV440 @ SV227 ) ) )
        = $true )
      | ( ( SV440 @ SV607 )
        = $true )
      | ( ( in @ SV607 @ SV227 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2594]) ).

thf(2741,plain,
    ! [SV568: $i,SV228: $i > $o] :
      ( ( ( SV228 @ ( sK47_Xy @ SV568 @ SV228 ) )
        = $false )
      | ( ( ( sK47_Xy @ SV568 @ SV228 )
          = SV568 )
        = $false )
      | ( ( ~ ( ~ ! [SY2375: $i] :
                    ( ~ ( SV228 @ SY2375 )
                    | ( ( sK46_SY211 @ SV228 )
                      = SY2375 ) )
              | ~ ( SV228 @ ( sK46_SY211 @ SV228 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2595]) ).

thf(2742,plain,
    ! [SV568: $i,SV228: $i > $o] :
      ( ( ( ~ ! [SY2375: $i] :
                ( ~ ( SV228 @ SY2375 )
                | ( ( sK46_SY211 @ SV228 )
                  = SY2375 ) ) )
        = $false )
      | ( ( SV228 @ ( sK47_Xy @ SV568 @ SV228 ) )
        = $true )
      | ( ( ( sK47_Xy @ SV568 @ SV228 )
          = SV568 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2596]) ).

thf(2743,plain,
    ! [SV568: $i,SV228: $i > $o] :
      ( ( ( ~ ( SV228 @ ( sK46_SY211 @ SV228 ) ) )
        = $false )
      | ( ( SV228 @ ( sK47_Xy @ SV568 @ SV228 ) )
        = $true )
      | ( ( ( sK47_Xy @ SV568 @ SV228 )
          = SV568 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2596]) ).

thf(2744,plain,
    ! [SV229: $i,SV753: $i,SV441: $i > $o] :
      ( ( ( ~ ( SV441 @ SV753 ) )
        = $true )
      | ( ( ~ ( in @ SV753 @ SV229 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV229
            @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) )
        = $true )
      | ( ( in @ ( sK74_Xx @ SV441 @ SV229 ) @ SV229 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2597]) ).

thf(2745,plain,
    ! [SV229: $i,SV441: $i > $o] :
      ( ( ( in @ ( sK75_SY1878 @ SV441 @ SV229 ) @ SV229 )
        = $true )
      | ( ( ! [SY2705: $i] :
              ( ~ ( SV441 @ SY2705 )
              | ~ ( in @ SY2705 @ SV229 ) )
          | ( singleton
            @ ( dsetconstr @ SV229
              @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2598]) ).

thf(2746,plain,
    ! [SV229: $i,SV441: $i > $o] :
      ( ( ( ~ ( ~ ( SV441 @ ( sK74_Xx @ SV441 @ SV229 ) )
              | ~ ~ ( ~ ( SV441 @ ( sK75_SY1878 @ SV441 @ SV229 ) )
                    | ~ ( ( ( sK74_Xx @ SV441 @ SV229 )
                         != ( sK75_SY1878 @ SV441 @ SV229 ) ) ) ) ) )
        = $true )
      | ( ( ! [SY2705: $i] :
              ( ~ ( SV441 @ SY2705 )
              | ~ ( in @ SY2705 @ SV229 ) )
          | ( singleton
            @ ( dsetconstr @ SV229
              @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2599]) ).

thf(2747,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
              | ~ ~ ( ~ ( in @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
                          | ~ ~ ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 ) ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
              | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                          | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
          | ( SV569 = SV706 ) )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2600]) ).

thf(2748,plain,
    ! [SV231: $i] :
      ( ( ( in @ ( sK9_Xx @ SV231 ) @ omega )
        = $true )
      | ( ( ~ ( in @ emptyset @ SV231 ) )
        = $true )
      | ( ( ! [SY2382: $i] :
              ( ~ ( in @ SY2382 @ omega )
              | ( in @ SY2382 @ SV231 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2601]) ).

thf(2749,plain,
    ! [SV231: $i] :
      ( ( ( in @ ( sK9_Xx @ SV231 ) @ SV231 )
        = $true )
      | ( ( ~ ( in @ emptyset @ SV231 ) )
        = $true )
      | ( ( ! [SY2382: $i] :
              ( ~ ( in @ SY2382 @ omega )
              | ( in @ SY2382 @ SV231 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2602]) ).

thf(2750,plain,
    ! [SV231: $i,SV769: $i] :
      ( ( ( ~ ( in @ SV769 @ omega )
          | ( in @ SV769 @ SV231 ) )
        = $true )
      | ( ( in @ ( setadjoin @ ( sK9_Xx @ SV231 ) @ ( sK9_Xx @ SV231 ) ) @ SV231 )
        = $false )
      | ( ( in @ emptyset @ SV231 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2603]) ).

thf(2751,plain,
    ! [SV570: $i,SV232: $i,SV707: $i,SV443: $o] :
      ( ( SV443 = $true )
      | ( ( in @ SV707
          @ ( dsetconstr @ SV232
            @ ^ [SY2950: $i] :
                ( ~ ( ~ SV443
                    | ( SY2950 != SV570 ) )
                | ~ ( ~ ~ SV443
                    | ( SY2950 != SV707 ) ) ) ) )
        = $true )
      | ( ( in @ SV707 @ SV232 )
        = $false )
      | ( ( in @ SV570 @ SV232 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2604]) ).

thf(2752,plain,
    ! [SV571: $i,SV232: $i,SV708: $i] :
      ( ( $true = $true )
      | ( ( in @ SV708
          @ ( dsetconstr @ SV232
            @ ^ [SY2951: $i] :
                ( ~ ( ~ $true
                    | ( SY2951 != SV571 ) )
                | ~ ( ~ ~ $true
                    | ( SY2951 != SV708 ) ) ) ) )
        = $true )
      | ( ( in @ SV708 @ SV232 )
        = $false )
      | ( ( in @ SV571 @ SV232 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2605]) ).

thf(2753,plain,
    ! [SV572: $i,SV232: $i,SV709: $i] :
      ( ( $false = $true )
      | ( ( in @ SV709
          @ ( dsetconstr @ SV232
            @ ^ [SY2952: $i] :
                ( ~ ( ~ $false
                    | ( SY2952 != SV572 ) )
                | ~ ( ~ ~ $false
                    | ( SY2952 != SV709 ) ) ) ) )
        = $true )
      | ( ( in @ SV709 @ SV232 )
        = $false )
      | ( ( in @ SV572 @ SV232 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2606]) ).

thf(2754,plain,
    ! [SV233: $i,SV658: $i] :
      ( ( ( ~ ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 ) )
        = $false )
      | ( ( ! [SY2924: $i] :
              ~ ( in @ SY2924 @ SV658 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2925: $i] :
                    ( ~ ( in @ SY2925 @ ( sK15_B @ SV233 ) )
                    | ! [SY2926: $i] :
                        ( ~ ( in @ SY2926 @ SY2925 )
                        | ( in @ SY2926 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) )
                    | ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SY2925 ) )
              | ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) )
                          | ~ ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 ) )
                    | ~ ! [SY2927: $i] :
                          ( ~ ( in @ SY2927 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
                          | ~ ( in @ SY2927 @ SV658 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2607]) ).

thf(2755,plain,
    ! [SV233: $i,SV658: $i] :
      ( ( ( ~ ~ ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 ) )
        = $false )
      | ( ( ! [SY2924: $i] :
              ~ ( in @ SY2924 @ SV658 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2925: $i] :
                    ( ~ ( in @ SY2925 @ ( sK15_B @ SV233 ) )
                    | ! [SY2926: $i] :
                        ( ~ ( in @ SY2926 @ SY2925 )
                        | ( in @ SY2926 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) )
                    | ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SY2925 ) )
              | ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) )
                          | ~ ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 ) )
                    | ~ ! [SY2927: $i] :
                          ( ~ ( in @ SY2927 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
                          | ~ ( in @ SY2927 @ SV658 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2607]) ).

thf(2756,plain,
    ! [SV770: $i,SV233: $i,SV754: $i] :
      ( ( ~ ( in @ SV754 @ ( sK15_B @ SV233 ) )
        | ~ ( in @ SV770 @ ( sK15_B @ SV233 ) )
        | ! [SY2983: $i] :
            ( ~ ( in @ SY2983 @ SV754 )
            | ( in @ SY2983 @ SV770 ) )
        | ! [SY2984: $i] :
            ( ~ ( in @ SY2984 @ SV770 )
            | ( in @ SY2984 @ SV754 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2608]) ).

thf(2757,plain,
    ! [SV233: $i] :
      ( ( ~ ! [SY2396: $i] :
              ( ~ ( in @ SY2396 @ ( sK15_B @ SV233 ) )
              | ! [SY2397: $i] :
                  ( ~ ( in @ SY2397 @ SY2396 )
                  | ( in @ SY2397 @ SV233 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2609]) ).

thf(2758,plain,
    ! [SV233: $i] :
      ( ( ~ ! [SY2398: $i,SY2399: $i] :
              ( ~ ( in @ SY2398 @ SV233 )
              | ~ ( in @ SY2399 @ SV233 )
              | ~ ( ~ ( in @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) @ ( sK15_B @ SV233 ) )
                  | ~ ~ ( ~ ( ~ ( in @ SY2398 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) )
                            | ~ ( in @ SY2399 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) ) )
                        | ~ ( ( in @ SY2398 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) )
                            | ( in @ SY2399 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) ) ) ) )
              | ( SY2398 = SY2399 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2609]) ).

thf(2759,plain,
    ! [SV444: $i > $o,SV234: $i,SV728: $i] :
      ( ( ( in @ SV728 @ SV234 )
        = $false )
      | ( ( ~ ( SV444 @ SV728 ) )
        = $true )
      | ( ( SV444 @ ( sK37_Xx @ SV444 @ SV234 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2610]) ).

thf(2760,plain,
    ! [SV444: $i > $o,SV234: $i,SV729: $i] :
      ( ( ( in @ SV729 @ SV234 )
        = $false )
      | ( ( ~ ( SV444 @ SV729 ) )
        = $true )
      | ( ( in @ ( sK37_Xx @ SV444 @ SV234 ) @ SV234 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2611]) ).

thf(2761,plain,
    ! [SV573: $i,SV235: $i > $o] :
      ( ( ( ~ ! [SY2403: $i] :
                ( ( SY2403
                 != ( sK32_Xx @ SV235 ) )
                | ( SV235 @ SY2403 ) )
          | ~ ! [SY2404: $i] :
                ( ~ ( SV235 @ SY2404 )
                | ( SY2404
                  = ( sK32_Xx @ SV235 ) ) ) )
        = $false )
      | ( ( SV235 @ ( sK33_SY142 @ SV573 @ SV235 ) )
        = $true )
      | ( ( SV235 @ SV573 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2612]) ).

thf(2762,plain,
    ! [SV573: $i,SV235: $i > $o] :
      ( ( ( SV235 @ SV573 )
        = $false )
      | ( ( SV573
          = ( sK33_SY142 @ SV573 @ SV235 ) )
        = $false )
      | ( ( ~ ( ~ ! [SY2403: $i] :
                    ( ( SY2403
                     != ( sK32_Xx @ SV235 ) )
                    | ( SV235 @ SY2403 ) )
              | ~ ! [SY2404: $i] :
                    ( ~ ( SV235 @ SY2404 )
                    | ( SY2404
                      = ( sK32_Xx @ SV235 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2613]) ).

thf(2763,plain,
    ! [SV236: $i,SV445: $i,SV574: $i,SV710: $i > $o] :
      ( ( ( ~ ( in @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ SV236 ) )
        = $false )
      | ( ( ! [SY2953: $i] :
              ( ~ ( in @ SY2953 @ SV574 )
              | ( SV710 @ SY2953 ) ) )
        = $true )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2614]) ).

thf(2764,plain,
    ! [SV236: $i,SV445: $i,SV574: $i,SV710: $i > $o] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) @ SV445 )
                | ~ ~ ( ~ ( in @ ( kpair @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) ) @ SV574 )
                      | ~ ~ ( SV710 @ ( kpair @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) ) ) ) ) )
        = $false )
      | ( ( ! [SY2953: $i] :
              ( ~ ( in @ SY2953 @ SV574 )
              | ( SV710 @ SY2953 ) ) )
        = $true )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2614]) ).

thf(2765,plain,
    ! [SV608: $i,SV237: $i,SV446: $i > $o] :
      ( ( ( in @ ( sK35_Xx @ SV446 @ SV237 ) @ SV237 )
        = $true )
      | ( ( SV446 @ SV608 )
        = $true )
      | ( ( in @ SV608 @ SV237 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2615]) ).

thf(2766,plain,
    ! [SV608: $i,SV237: $i,SV446: $i > $o] :
      ( ( ( ~ ( SV446 @ ( sK35_Xx @ SV446 @ SV237 ) ) )
        = $true )
      | ( ( SV446 @ SV608 )
        = $true )
      | ( ( in @ SV608 @ SV237 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2616]) ).

thf(2767,plain,
    ! [SV711: $i,SV575: $i,SV238: $i,SV447: $o] :
      ( ( ( ~ SV447 ) = $true )
      | ( ( ( dsetconstr @ SV238
            @ ^ [SY2954: $i] :
                ( ~ ( ~ SV447
                    | ( SY2954 != SV575 ) )
                | ~ ( ~ ~ SV447
                    | ( SY2954 != SV711 ) ) ) )
          = ( setadjoin @ SV575 @ emptyset ) )
        = $true )
      | ( ( in @ SV711 @ SV238 )
        = $false )
      | ( ( in @ SV575 @ SV238 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2617]) ).

thf(2768,plain,
    ! [SV712: $i,SV576: $i,SV238: $i] :
      ( ( ( ~ $true ) = $true )
      | ( ( ( dsetconstr @ SV238
            @ ^ [SY2955: $i] :
                ( ~ ( ~ $true
                    | ( SY2955 != SV576 ) )
                | ~ ( ~ ~ $true
                    | ( SY2955 != SV712 ) ) ) )
          = ( setadjoin @ SV576 @ emptyset ) )
        = $true )
      | ( ( in @ SV712 @ SV238 )
        = $false )
      | ( ( in @ SV576 @ SV238 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2618]) ).

thf(2769,plain,
    ! [SV713: $i,SV577: $i,SV238: $i] :
      ( ( ( ~ $false ) = $true )
      | ( ( ( dsetconstr @ SV238
            @ ^ [SY2956: $i] :
                ( ~ ( ~ $false
                    | ( SY2956 != SV577 ) )
                | ~ ( ~ ~ $false
                    | ( SY2956 != SV713 ) ) ) )
          = ( setadjoin @ SV577 @ emptyset ) )
        = $true )
      | ( ( in @ SV713 @ SV238 )
        = $false )
      | ( ( in @ SV577 @ SV238 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2619]) ).

thf(2770,plain,
    ! [SV578: $i,SV239: $i,SV755: $i] :
      ( ( ( ~ ( in @ SV755 @ ( sK14_B @ SV239 ) ) )
        = $true )
      | ( ( ~ ( in @ SV755 @ SV239 ) )
        = $true )
      | ( ( in @ SV578 @ SV239 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2620]) ).

thf(2771,plain,
    ! [SV582: $i,SV241: $i > $o] :
      ( ( ( ~ ! [SY2422: $i] :
                ( ~ ( SV241 @ SY2422 )
                | ( ( sK43_SY205 @ SV241 )
                  = SY2422 ) )
          | ~ ( SV241 @ ( sK43_SY205 @ SV241 ) ) )
        = $false )
      | ( ( SV241 @ ( sK44_Xx @ SV241 ) )
        = $true )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2624]) ).

thf(2772,plain,
    ! [SV582: $i,SV241: $i > $o] :
      ( ( ( ~ ( SV241 @ ( sK45_SY1868 @ SV241 ) )
          | ~ ( ( ( sK44_Xx @ SV241 )
               != ( sK45_SY1868 @ SV241 ) ) ) )
        = $false )
      | ( ( ~ ( ~ ! [SY2422: $i] :
                    ( ~ ( SV241 @ SY2422 )
                    | ( ( sK43_SY205 @ SV241 )
                      = SY2422 ) )
              | ~ ( SV241 @ ( sK43_SY205 @ SV241 ) ) ) )
        = $true )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2625]) ).

thf(2773,plain,
    ! [SV609: $i,SV730: $i,SV659: $i] :
      ( ( ( in @ SV659 @ SV730 )
        = $false )
      | ( ( ~ ( in @ SV730 @ SV609 ) )
        = $true )
      | ( ( in @ SV659 @ ( setunion @ SV609 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2626]) ).

thf(2774,plain,
    ! [SV610: $i,SV660: $i] :
      ( ( ( ~ ( in @ SV660 @ ( sK8_B @ SV660 @ SV610 ) ) )
        = $false )
      | ( ( in @ SV660 @ ( setunion @ SV610 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2627]) ).

thf(2775,plain,
    ! [SV610: $i,SV660: $i] :
      ( ( ( ~ ( in @ ( sK8_B @ SV660 @ SV610 ) @ SV610 ) )
        = $false )
      | ( ( in @ SV660 @ ( setunion @ SV610 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2627]) ).

thf(2776,plain,
    ! [SV243: $i,SV450: $i,SV583: $i,SV717: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK90_Xx @ SV717 @ SV583 @ SV450 @ SV243 ) @ SV243 )
              | ~ ( ( ( ap @ SV243 @ SV450 @ SV583 @ ( sK90_Xx @ SV717 @ SV583 @ SV450 @ SV243 ) )
                   != ( ap @ SV243 @ SV450 @ SV717 @ ( sK90_Xx @ SV717 @ SV583 @ SV450 @ SV243 ) ) ) ) ) )
        = $true )
      | ( ( SV583 = SV717 )
        = $true )
      | ( ( func @ SV243 @ SV450 @ SV717 )
        = $false )
      | ( ( func @ SV243 @ SV450 @ SV583 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2628]) ).

thf(2777,plain,
    ! [SV245: $i,SV451: $i,SV585: $i,SV718: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK91_Xx @ SV718 @ SV585 @ SV451 @ SV245 ) @ SV245 )
              | ~ ( ( ( ap @ SV245 @ SV451 @ SV585 @ ( sK91_Xx @ SV718 @ SV585 @ SV451 @ SV245 ) )
                   != ( ap @ SV245 @ SV451 @ SV718 @ ( sK91_Xx @ SV718 @ SV585 @ SV451 @ SV245 ) ) ) ) ) )
        = $true )
      | ( ( SV585 = SV718 )
        = $true )
      | ( ( in @ SV718 @ ( funcSet @ SV245 @ SV451 ) )
        = $false )
      | ( ( in @ SV585 @ ( funcSet @ SV245 @ SV451 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2630]) ).

thf(2778,plain,
    ! [SV246: $i,SV731: $i,SV452: $i > $o] :
      ( ( ( SV452 @ SV731 )
        = $false )
      | ( ( ~ ( in @ SV731 @ SV246 ) )
        = $true )
      | ( ( in @ ( sK36_Xx @ SV452 @ SV246 ) @ SV246 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2631]) ).

thf(2779,plain,
    ! [SV246: $i,SV732: $i,SV452: $i > $o] :
      ( ( ( SV452 @ SV732 )
        = $false )
      | ( ( ~ ( in @ SV732 @ SV246 ) )
        = $true )
      | ( ( SV452 @ ( sK36_Xx @ SV452 @ SV246 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2632]) ).

thf(2780,plain,
    ! [SV586: $i,SV247: $i > $o] :
      ( ( ( ~ ! [SY2435: $i] :
                ( ~ ( SV247 @ SY2435 )
                | ( ( sK21_Xx @ SV247 )
                  = SY2435 ) )
          | ~ ( SV247 @ ( sK21_Xx @ SV247 ) ) )
        = $false )
      | ( ( SV247 @ ( sK22_SY74 @ SV586 @ SV247 ) )
        = $true )
      | ( ( SV247 @ SV586 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2633]) ).

thf(2781,plain,
    ! [SV586: $i,SV247: $i > $o] :
      ( ( ( SV247 @ SV586 )
        = $false )
      | ( ( SV586
          = ( sK22_SY74 @ SV586 @ SV247 ) )
        = $false )
      | ( ( ~ ( ~ ! [SY2435: $i] :
                    ( ~ ( SV247 @ SY2435 )
                    | ( ( sK21_Xx @ SV247 )
                      = SY2435 ) )
              | ~ ( SV247 @ ( sK21_Xx @ SV247 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2634]) ).

thf(2782,plain,
    ! [SV248: $i,SV453: $i,SV661: $i > $o,SV719: $i > $o] :
      ( ( ( ~ ( in @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) @ SV248 ) )
        = $false )
      | ( ( ( dsetconstr @ SV248
            @ ^ [SY2930: $i] : ( SV661 @ SY2930 ) )
          = ( dsetconstr @ SV453
            @ ^ [SY2961: $i] : ( SV719 @ SY2961 ) ) )
        = $true )
      | ( ( SV248 = SV453 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2635]) ).

thf(2783,plain,
    ! [SV248: $i,SV453: $i,SV661: $i > $o,SV719: $i > $o] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) @ SV453 )
                | ~ ~ ( ( ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 )
                       != ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) )
                      | ~ ~ ( ~ ( ~ ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
                                | ~ ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) )
                            | ~ ( ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
                                | ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) ) ) ) ) )
        = $false )
      | ( ( ( dsetconstr @ SV248
            @ ^ [SY2930: $i] : ( SV661 @ SY2930 ) )
          = ( dsetconstr @ SV453
            @ ^ [SY2961: $i] : ( SV719 @ SY2961 ) ) )
        = $true )
      | ( ( SV248 = SV453 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2635]) ).

thf(2784,plain,
    ! [SV612: $i,SV250: $i,SV1: $i,SV733: $i] :
      ( ( ( in @ SV733 @ ( powerset @ SV1 ) )
        = $false )
      | ( ( ! [SY2966: $i] :
              ( ~ ( in @ SY2966 @ SV1 )
              | ~ ( in @ SY2966 @ ( binintersect @ SV250 @ SV612 ) )
              | ( in @ SY2966 @ ( binunion @ SV250 @ SV733 ) ) ) )
        = $true )
      | ( ( in @ SV612 @ ( powerset @ SV1 ) )
        = $false )
      | ( ( in @ SV250 @ ( powerset @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2636]) ).

thf(2785,plain,
    ! [SV613: $i,SV251: $i,SV2: $i,SV734: $i] :
      ( ( ( in @ SV734 @ SV2 )
        = $false )
      | ( ( ( in @ SV734 @ ( binunion @ SV251 @ SV613 ) )
          | ~ ( in @ SV734 @ SV613 ) )
        = $true )
      | ( ( in @ SV613 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV251 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2637]) ).

thf(2786,plain,
    ! [SV614: $i,SV252: $i,SV3: $i,SV735: $i] :
      ( ( ( in @ SV735 @ SV3 )
        = $false )
      | ( ( ( in @ SV735 @ ( binunion @ SV252 @ SV614 ) )
          | ~ ( in @ SV735 @ SV252 ) )
        = $true )
      | ( ( in @ SV614 @ ( powerset @ SV3 ) )
        = $false )
      | ( ( in @ SV252 @ ( powerset @ SV3 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2638]) ).

thf(2787,plain,
    ! [SV254: $i,SV616: $i,SV5: $i,SV771: $i] :
      ( ( ( ~ ( in @ SV771 @ SV5 )
          | ~ ( in @ SV771 @ SV616 )
          | ( in @ SV771 @ ( setminus @ SV5 @ SV254 ) ) )
        = $true )
      | ( ( subset @ SV254 @ ( setminus @ SV5 @ SV616 ) )
        = $false )
      | ( ( in @ SV616 @ ( powerset @ SV5 ) )
        = $false )
      | ( ( in @ SV254 @ ( powerset @ SV5 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2640]) ).

thf(2788,plain,
    ! [SV619: $i,SV257: $i,SV8: $i,SV736: $i] :
      ( ( ( in @ SV736 @ SV8 )
        = $false )
      | ( ( ~ ( in @ SV736 @ ( setminus @ SV8 @ SV257 ) )
          | ( in @ SV736 @ ( setminus @ SV8 @ ( binintersect @ SV257 @ SV619 ) ) ) )
        = $true )
      | ( ( in @ SV619 @ ( powerset @ SV8 ) )
        = $false )
      | ( ( in @ SV257 @ ( powerset @ SV8 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2641]) ).

thf(2789,plain,
    ! [SV620: $i,SV258: $i,SV9: $i,SV737: $i] :
      ( ( ( in @ SV737 @ SV9 )
        = $false )
      | ( ( ~ ( in @ SV737 @ ( setminus @ SV9 @ SV258 ) )
          | ~ ( in @ SV737 @ ( binintersect @ SV258 @ SV620 ) ) )
        = $true )
      | ( ( in @ SV620 @ ( powerset @ SV9 ) )
        = $false )
      | ( ( in @ SV258 @ ( powerset @ SV9 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2642]) ).

thf(2790,plain,
    ! [SV625: $i,SV266: $i,SV17: $i,SV738: $i] :
      ( ( ( in @ SV738 @ SV17 )
        = $false )
      | ( ( ~ ( subset @ SV266 @ SV625 )
          | ( in @ SV738 @ SV625 )
          | ~ ( in @ SV738 @ SV266 ) )
        = $true )
      | ( ( in @ SV625 @ ( powerset @ SV17 ) )
        = $false )
      | ( ( in @ SV266 @ ( powerset @ SV17 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2647]) ).

thf(2791,plain,
    ! [SV626: $i,SV267: $i,SV18: $i,SV739: $i] :
      ( ( ( in @ SV739 @ SV18 )
        = $false )
      | ( ( ~ ( subset @ SV267 @ ( setminus @ SV18 @ SV626 ) )
          | ~ ( in @ SV739 @ SV626 )
          | ~ ( in @ SV739 @ SV267 ) )
        = $true )
      | ( ( in @ SV626 @ ( powerset @ SV18 ) )
        = $false )
      | ( ( in @ SV267 @ ( powerset @ SV18 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2648]) ).

thf(2792,plain,
    ! [SV268: $i,SV627: $i,SV19: $i,SV740: $i] :
      ( ( ( in @ SV740 @ SV19 )
        = $false )
      | ( ( ( in @ SV740 @ SV627 )
          | ~ ( in @ SV740 @ ( binintersect @ SV268 @ SV627 ) ) )
        = $true )
      | ( ( in @ SV627 @ ( powerset @ SV19 ) )
        = $false )
      | ( ( in @ SV268 @ ( powerset @ SV19 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2649]) ).

thf(2793,plain,
    ! [SV628: $i,SV269: $i,SV20: $i,SV741: $i] :
      ( ( ( in @ SV741 @ SV20 )
        = $false )
      | ( ( ( in @ SV741 @ SV269 )
          | ~ ( in @ SV741 @ ( binintersect @ SV269 @ SV628 ) ) )
        = $true )
      | ( ( in @ SV628 @ ( powerset @ SV20 ) )
        = $false )
      | ( ( in @ SV269 @ ( powerset @ SV20 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2650]) ).

thf(2794,plain,
    ! [SV271: $i,SV22: $i,SV630: $i] :
      ( ( ( in @ SV630 @ ( setminus @ SV22 @ SV271 ) )
        = $false )
      | ( ( in @ SV630 @ SV271 )
        = $false )
      | ( ( in @ SV630 @ SV22 )
        = $false )
      | ( ( in @ SV271 @ ( powerset @ SV22 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2651]) ).

thf(2795,plain,
    ! [SV631: $i,SV272: $i,SV23: $i,SV742: $i] :
      ( ( ( in @ SV742 @ SV23 )
        = $false )
      | ( ( ~ ( in @ SV272 @ ( powerset @ SV631 ) )
          | ~ ( in @ SV742 @ SV272 )
          | ( in @ SV742 @ SV631 ) )
        = $true )
      | ( ( in @ SV631 @ ( powerset @ SV23 ) )
        = $false )
      | ( ( in @ SV272 @ ( powerset @ SV23 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2652]) ).

thf(2796,plain,
    ! [SV668: $i,SV461: $i,SV31: $i,SV280: $o] :
      ( ( SV280 = $false )
      | ( ( ( if @ SV31 @ SV280 @ SV461 @ SV668 )
          = SV461 )
        = $true )
      | ( ( in @ SV668 @ SV31 )
        = $false )
      | ( ( in @ SV461 @ SV31 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2656]) ).

thf(2797,plain,
    ! [SV669: $i,SV462: $i,SV31: $i] :
      ( ( $true = $false )
      | ( ( ( if @ SV31 @ $true @ SV462 @ SV669 )
          = SV462 )
        = $true )
      | ( ( in @ SV669 @ SV31 )
        = $false )
      | ( ( in @ SV462 @ SV31 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2657]) ).

thf(2798,plain,
    ! [SV670: $i,SV463: $i,SV31: $i] :
      ( ( $false = $false )
      | ( ( ( if @ SV31 @ $false @ SV463 @ SV670 )
          = SV463 )
        = $true )
      | ( ( in @ SV670 @ SV31 )
        = $false )
      | ( ( in @ SV463 @ SV31 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2658]) ).

thf(2799,plain,
    ! [SV38: $i,SV471: $i,SV674: $i,SV284: $i,SV756: $i] :
      ( ( ( ~ ( in @ SV756 @ SV284 ) )
        = $true )
      | ( ( ~ ( in @ ( kpair @ SV674 @ SV756 ) @ SV471 )
          | ( ( ap @ SV38 @ SV284 @ SV471 @ SV674 )
            = SV756 ) )
        = $true )
      | ( ( in @ SV674 @ SV38 )
        = $false )
      | ( ( in @ SV471 @ ( funcSet @ SV38 @ SV284 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2659]) ).

thf(2800,plain,
    ! [SV39: $i,SV472: $i,SV675: $i,SV285: $i,SV757: $i] :
      ( ( ( ~ ( in @ SV757 @ SV285 ) )
        = $true )
      | ( ( ~ ( in @ ( kpair @ SV675 @ SV757 ) @ SV472 )
          | ( ( ap @ SV39 @ SV285 @ SV472 @ SV675 )
            = SV757 ) )
        = $true )
      | ( ( in @ SV675 @ SV39 )
        = $false )
      | ( ( func @ SV39 @ SV285 @ SV472 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2660]) ).

thf(2801,plain,
    ! [SV635: $i,SV288: $i > $o,SV42: $i,SV743: $i] :
      ( ( ( in @ SV743 @ SV42 )
        = $false )
      | ( ( ~ ( SV288 @ SV635 )
          | ~ ( SV288 @ SV743 )
          | ( SV635 = SV743 ) )
        = $true )
      | ( ( in @ SV635 @ SV42 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV42
            @ ^ [SY2500: $i] : ( SV288 @ SY2500 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2661]) ).

thf(2802,plain,
    ! [SV484: $i > $i > $o,SV298: $i,SV52: $i,SV722: $i,SV593: $i] :
      ( ( ( ~ ( in @ ( kpair @ SV593 @ SV722 )
              @ ( dpsetconstr @ SV52 @ SV298
                @ ^ [SY2775: $i,SY2776: $i] : ( SV484 @ SY2775 @ SY2776 ) ) ) )
        = $true )
      | ( ( SV484 @ SV593 @ SV722 )
        = $true )
      | ( ( in @ SV722 @ SV298 )
        = $false )
      | ( ( in @ SV593 @ SV52 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2662]) ).

thf(2803,plain,
    ! [SV301: $i,SV55: $i,SV723: $i,SV594: $i,SV487: $i > $i > $o] :
      ( ( ( ~ ( SV487 @ SV594 @ SV723 ) )
        = $true )
      | ( ( in @ ( kpair @ SV594 @ SV723 )
          @ ( dpsetconstr @ SV55 @ SV301
            @ ^ [SY2783: $i,SY2784: $i] : ( SV487 @ SY2783 @ SY2784 ) ) )
        = $true )
      | ( ( in @ SV723 @ SV301 )
        = $false )
      | ( ( in @ SV594 @ SV55 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2663]) ).

thf(2804,plain,
    ! [SV388: $i,SV693: $i,SV154: $i,SV645: $i] :
      ( ( ( in @ SV645 @ SV154 )
        = $false )
      | ( ( in @ SV693 @ SV388 )
        = $true )
      | ( ( SV645 = SV693 )
        = $false )
      | ( ( SV154 = SV388 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2664]) ).

thf(2805,plain,
    ! [SV189: $i,SV409: $i,SV647: $i] :
      ( ( ( ~ ( in @ ( sK97_Xx @ SV647 @ SV409 @ SV189 ) @ SV189 ) )
        = $false )
      | ( ( subset @ SV409 @ SV647 )
        = $true )
      | ( ( in @ SV647 @ ( powerset @ SV189 ) )
        = $false )
      | ( ( in @ SV409 @ ( powerset @ SV189 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2665]) ).

thf(2806,plain,
    ! [SV189: $i,SV409: $i,SV647: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK97_Xx @ SV647 @ SV409 @ SV189 ) @ SV409 )
                | ~ ~ ( in @ ( sK97_Xx @ SV647 @ SV409 @ SV189 ) @ SV647 ) ) )
        = $false )
      | ( ( subset @ SV409 @ SV647 )
        = $true )
      | ( ( in @ SV647 @ ( powerset @ SV189 ) )
        = $false )
      | ( ( in @ SV409 @ ( powerset @ SV189 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2665]) ).

thf(2807,plain,
    ! [SV602: $i,SV648: $i] :
      ( ( ( in @ ( sK7_Xx @ SV648 @ SV602 ) @ SV602 )
        = $false )
      | ( ( in @ SV648 @ ( powerset @ SV602 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2667]) ).

thf(2808,plain,
    ! [SV603: $i,SV649: $i,SV744: $i] :
      ( ( ( in @ SV744 @ SV649 )
        = $false )
      | ( ( in @ SV744 @ SV603 )
        = $true )
      | ( ( in @ SV649 @ ( powerset @ SV603 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2668]) ).

thf(2809,plain,
    ! [SV694: $i,SV191: $i,SV546: $i,SV410: $o] :
      ( ( SV410 = $false )
      | ( ( in @ SV546
          @ ( dsetconstr @ SV191
            @ ^ [SY2939: $i] :
                ( ~ ( ~ SV410
                    | ( SY2939 != SV546 ) )
                | ~ ( ~ ~ SV410
                    | ( SY2939 != SV694 ) ) ) ) )
        = $true )
      | ( ( in @ SV694 @ SV191 )
        = $false )
      | ( ( in @ SV546 @ SV191 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2670]) ).

thf(2810,plain,
    ! [SV695: $i,SV191: $i,SV547: $i] :
      ( ( $true = $false )
      | ( ( in @ SV547
          @ ( dsetconstr @ SV191
            @ ^ [SY2940: $i] :
                ( ~ ( ~ $true
                    | ( SY2940 != SV547 ) )
                | ~ ( ~ ~ $true
                    | ( SY2940 != SV695 ) ) ) ) )
        = $true )
      | ( ( in @ SV695 @ SV191 )
        = $false )
      | ( ( in @ SV547 @ SV191 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2671]) ).

thf(2811,plain,
    ! [SV696: $i,SV191: $i,SV548: $i] :
      ( ( $false = $false )
      | ( ( in @ SV548
          @ ( dsetconstr @ SV191
            @ ^ [SY2941: $i] :
                ( ~ ( ~ $false
                    | ( SY2941 != SV548 ) )
                | ~ ( ~ ~ $false
                    | ( SY2941 != SV696 ) ) ) ) )
        = $true )
      | ( ( in @ SV696 @ SV191 )
        = $false )
      | ( ( in @ SV548 @ SV191 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2672]) ).

thf(2812,plain,
    ! [SV549: $i > $i,SV411: $i,SV192: $i,SV745: $i] :
      ( ( ( in @ SV745 @ SV192 )
        = $false )
      | ( ( ( ap @ SV192 @ SV411
            @ ( lam @ SV192 @ SV411
              @ ^ [SY2811: $i] : ( SV549 @ SY2811 ) )
            @ SV745 )
          = ( SV549 @ SV745 ) )
        = $true )
      | ( ( in @ ( sK92_Xx @ SV549 @ SV411 @ SV192 ) @ SV192 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2673]) ).

thf(2813,plain,
    ! [SV549: $i > $i,SV411: $i,SV192: $i,SV758: $i] :
      ( ( ( ~ ( in @ SV758 @ SV192 ) )
        = $true )
      | ( ( ( ap @ SV192 @ SV411
            @ ( lam @ SV192 @ SV411
              @ ^ [SY2811: $i] : ( SV549 @ SY2811 ) )
            @ SV758 )
          = ( SV549 @ SV758 ) )
        = $true )
      | ( ( in @ ( SV549 @ ( sK92_Xx @ SV549 @ SV411 @ SV192 ) ) @ SV411 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2674]) ).

thf(2814,plain,
    ! [SV193: $i,SV412: $i,SV550: $i] :
      ( ( ( SV550
         != ( kpair @ ( sK67_Xx @ SV550 @ SV412 @ SV193 ) @ ( sK68_SY1876 @ SV550 @ SV412 @ SV193 ) ) )
        = $false )
      | ( ( in @ SV550 @ ( cartprod @ SV193 @ SV412 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2675]) ).

thf(2815,plain,
    ! [SV193: $i,SV412: $i,SV550: $i] :
      ( ( ( ~ ( in @ ( sK68_SY1876 @ SV550 @ SV412 @ SV193 ) @ SV412 ) )
        = $false )
      | ( ( in @ SV550 @ ( cartprod @ SV193 @ SV412 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2675]) ).

thf(2816,plain,
    ! [SV551: $i,SV759: $i,SV194: $i > $o] :
      ( ( ( ~ ( SV194 @ SV759 ) )
        = $true )
      | ( ( ! [SY2977: $i] :
              ( ~ ( SV194 @ SY2977 )
              | ( SV759 = SY2977 ) ) )
        = $true )
      | ( ( SV194 @ ( sK57_SY248 @ SV551 @ SV194 ) )
        = $true )
      | ( ( SV194 @ SV551 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2676]) ).

thf(2817,plain,
    ! [SV551: $i,SV772: $i,SV194: $i > $o] :
      ( ( ( ~ ( SV194 @ SV772 )
          | ! [SY2985: $i] :
              ( ~ ( SV194 @ SY2985 )
              | ( SV772 = SY2985 ) ) )
        = $true )
      | ( ( SV551
          = ( sK57_SY248 @ SV551 @ SV194 ) )
        = $false )
      | ( ( SV194 @ SV551 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2677]) ).

thf(2818,plain,
    ! [SV413: $i,SV773: $i,SV195: $i > $i > $o] :
      ( ( ( ! [SY2986: $i] :
              ( ~ ( SV195 @ SY2986 @ SV773 )
              | ~ ( in @ SY2986 @ SV413 ) )
          | ( in @ SV773 @ ( sK10_B @ SV413 @ SV195 ) ) )
        = $true )
      | ( ( in @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV413 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2678]) ).

thf(2819,plain,
    ! [SV195: $i > $i > $o,SV413: $i,SV774: $i] :
      ( ( ( ~ ( in @ SV774 @ ( sK10_B @ SV413 @ SV195 ) )
          | ~ ( ~ ( SV195 @ ( sK11_Xy @ SV774 @ SV413 @ SV195 ) @ SV774 )
              | ~ ( in @ ( sK11_Xy @ SV774 @ SV413 @ SV195 ) @ SV413 ) ) )
        = $true )
      | ( ( in @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV413 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2679]) ).

thf(2820,plain,
    ! [SV725: $i,SV413: $i,SV195: $i > $i > $o] :
      ( ( ( ~ ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) ) )
        = $false )
      | ( ( ~ ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2639: $i] :
                    ( ! [SY2640: $i] :
                        ( ~ ( SV195 @ SY2640 @ SY2639 )
                        | ~ ( in @ SY2640 @ SV413 ) )
                    | ( in @ SY2639 @ ( sK10_B @ SV413 @ SV195 ) ) )
              | ~ ! [SY2641: $i] :
                    ( ~ ( in @ SY2641 @ ( sK10_B @ SV413 @ SV195 ) )
                    | ~ ( ~ ( SV195 @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SY2641 )
                        | ~ ( in @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SV413 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2680]) ).

thf(2821,plain,
    ! [SV195: $i > $i > $o,SV413: $i,SV725: $i] :
      ( ( ( ~ ( ( SV725
               != ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) ) ) )
        = $false )
      | ( ( ~ ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2639: $i] :
                    ( ! [SY2640: $i] :
                        ( ~ ( SV195 @ SY2640 @ SY2639 )
                        | ~ ( in @ SY2640 @ SV413 ) )
                    | ( in @ SY2639 @ ( sK10_B @ SV413 @ SV195 ) ) )
              | ~ ! [SY2641: $i] :
                    ( ~ ( in @ SY2641 @ ( sK10_B @ SV413 @ SV195 ) )
                    | ~ ( ~ ( SV195 @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SY2641 )
                        | ~ ( in @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SV413 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2680]) ).

thf(2822,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( ( ~ ( ( SV552 = SV196 )
              | ( in @ SV552 @ SV414 )
              | ! [SX3: $o] : SX3 ) )
        = $false )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2681]) ).

thf(2823,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( ( ~ ( ( SV552 = SV196 )
              | ! [SX3: $o] :
                  ( ~ SX3
                  | SX3 ) ) )
        = $false )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2681]) ).

thf(2824,plain,
    ! [SV196: $i,SV414: $i,SV552: $i] :
      ( ( ( ~ ! [SY2814: $o] :
                ( ~ SY2814
                | ( in @ SV552 @ SV414 )
                | SY2814 ) )
        = $false )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2682]) ).

thf(2825,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( ( ~ ! [SX3: $o] :
                ( ~ SX3
                | ~ SX3
                | SX3 ) )
        = $false )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2682]) ).

thf(2826,plain,
    ! [SV198: $i,SV697: $i,SV650: $i > $o] :
      ( ( ( SV650 @ SV697 )
        = $false )
      | ( ( in @ SV697
          @ ( dsetconstr @ SV198
            @ ^ [SY2916: $i] : ( SV650 @ SY2916 ) ) )
        = $true )
      | ( ( in @ SV697 @ SV198 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2683]) ).

thf(2827,plain,
    ! [SV651: $i > $o,SV198: $i,SV698: $i] :
      ( ( ( in @ SV698
          @ ( dsetconstr @ SV198
            @ ^ [SY2918: $i] : ( SV651 @ SY2918 ) ) )
        = $false )
      | ( ( SV651 @ SV698 )
        = $true )
      | ( ( in @ SV698 @ SV198 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2684]) ).

thf(2828,plain,
    ! [SV604: $i,SV200: $i,SV417: $i > $o] :
      ( ( ( SV417 @ ( sK40_Xx @ SV417 @ SV200 ) )
        = $false )
      | ( ( SV417 @ SV604 )
        = $true )
      | ( ( in @ SV604 @ SV200 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2686]) ).

thf(2829,plain,
    ! [SV652: $i > $o,SV605: $i > $o] :
      ( ( ( ! [SY2919: $i] :
              ( ~ ( ~ ( SV605 @ ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) )
                  | ~ ( ( SY2919
                       != ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) ) ) )
              | ~ ( SV605 @ SY2919 ) ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( ( sK55_Xx @ SV652 @ SV605 )
          = ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2690]) ).

thf(2830,plain,
    ! [SV652: $i > $o,SV605: $i > $o] :
      ( ( ( ~ ( ~ ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
              | ~ ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) ) )
          | ~ ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
              | ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) ) ) )
        = $false )
      | ( ( ! [SY2919: $i] :
              ( ~ ( ~ ( SV605 @ ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) )
                  | ~ ( ( SY2919
                       != ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) ) ) )
              | ~ ( SV605 @ SY2919 ) )
          | ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2691]) ).

thf(2831,plain,
    ! [SV606: $i > $o,SV653: $i > $o] :
      ( ( ( ! [SY2921: $i] :
              ( ~ ( ~ ( SV653 @ ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) )
                  | ~ ( ( SY2921
                       != ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) ) ) )
              | ~ ( SV653 @ SY2921 ) ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( ( sK51_Xx @ SV653 @ SV606 )
          = ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2692]) ).

thf(2832,plain,
    ! [SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ~ ( ~ ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
              | ~ ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) ) )
          | ~ ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
              | ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) ) ) )
        = $false )
      | ( ( ! [SY2921: $i] :
              ( ~ ( ~ ( SV653 @ ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) )
                  | ~ ( ( SY2921
                       != ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) ) ) )
              | ~ ( SV653 @ SY2921 ) )
          | ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2693]) ).

thf(2833,plain,
    ! [SV203: $i,SV726: $i,SV420: $i > $o] :
      ( ( ( SV420 @ SV726 )
        = $false )
      | ( ( in @ SV726 @ SV203 )
        = $false )
      | ( ( SV420 @ ( sK39_Xx @ SV420 @ SV203 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2694]) ).

thf(2834,plain,
    ! [SV203: $i,SV727: $i,SV420: $i > $o] :
      ( ( ( SV420 @ SV727 )
        = $false )
      | ( ( in @ SV727 @ SV203 )
        = $false )
      | ( ( in @ ( sK39_Xx @ SV420 @ SV203 ) @ SV203 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2695]) ).

thf(2835,plain,
    ! [SV558: $i,SV205: $i > $o] :
      ( ( ( ~ ! [SY2293: $i] :
                ( ~ ( SV205 @ SY2293 )
                | ( ( sK41_SY198 @ SV205 )
                  = SY2293 ) ) )
        = $false )
      | ( ( SV205 @ ( sK42_Xy @ SV558 @ SV205 ) )
        = $true )
      | ( ( SV205 @ SV558 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2697]) ).

thf(2836,plain,
    ! [SV558: $i,SV205: $i > $o] :
      ( ( ( ~ ( SV205 @ ( sK41_SY198 @ SV205 ) ) )
        = $false )
      | ( ( SV205 @ ( sK42_Xy @ SV558 @ SV205 ) )
        = $true )
      | ( ( SV205 @ SV558 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2697]) ).

thf(2837,plain,
    ! [SV558: $i,SV205: $i > $o] :
      ( ( ( ~ ! [SY2293: $i] :
                ( ~ ( SV205 @ SY2293 )
                | ( ( sK41_SY198 @ SV205 )
                  = SY2293 ) )
          | ~ ( SV205 @ ( sK41_SY198 @ SV205 ) ) )
        = $false )
      | ( ( SV558
          = ( sK42_Xy @ SV558 @ SV205 ) )
        = $false )
      | ( ( SV205 @ SV558 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2698]) ).

thf(2838,plain,
    ! [SV559: $i > $i,SV421: $i,SV206: $i,SV746: $i] :
      ( ( ( in @ SV746 @ SV206 )
        = $false )
      | ( ( ( ap @ SV206 @ SV421
            @ ( lam @ SV206 @ SV421
              @ ^ [SY2824: $i] : ( SV559 @ SY2824 ) )
            @ SV746 )
          = ( SV559 @ SV746 ) )
        = $true )
      | ( ( in @ ( sK94_Xx @ SV559 @ SV421 @ SV206 ) @ SV206 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2699]) ).

thf(2839,plain,
    ! [SV559: $i > $i,SV421: $i,SV206: $i,SV760: $i] :
      ( ( ( ~ ( in @ SV760 @ SV206 ) )
        = $true )
      | ( ( ( ap @ SV206 @ SV421
            @ ( lam @ SV206 @ SV421
              @ ^ [SY2824: $i] : ( SV559 @ SY2824 ) )
            @ SV760 )
          = ( SV559 @ SV760 ) )
        = $true )
      | ( ( in @ ( SV559 @ ( sK94_Xx @ SV559 @ SV421 @ SV206 ) ) @ SV421 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2700]) ).

thf(2840,plain,
    ( ( ~ ( in @ sK5_SY1831 @ sK1_A )
      | ~ ~ ( ~ ( in @ sK5_SY1831 @ ( binintersect @ sK2_SY1822 @ sK3_SY1826 ) )
            | ~ ~ ( in @ sK5_SY1831 @ ( binunion @ sK3_SY1826 @ sK4_SY1829 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[2702]) ).

thf(2841,plain,
    ! [SV207: $i,SV422: $i,SV560: $i,SV702: $i > $o] :
      ( ( ( in @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ SV207 )
        = $true )
      | ( ( ! [SY2947: $i] :
              ( ~ ( in @ SY2947 @ SV560 )
              | ( SV702 @ SY2947 ) ) )
        = $true )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2703]) ).

thf(2842,plain,
    ! [SV207: $i,SV422: $i,SV560: $i,SV702: $i > $o] :
      ( ( ( ~ ( ~ ( in @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) @ SV422 )
              | ~ ~ ( ~ ( in @ ( kpair @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) ) @ SV560 )
                    | ~ ~ ( SV702 @ ( kpair @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) ) ) ) ) )
        = $true )
      | ( ( ! [SY2947: $i] :
              ( ~ ( in @ SY2947 @ SV560 )
              | ( SV702 @ SY2947 ) ) )
        = $true )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2704]) ).

thf(2843,plain,
    ! [SV208: $i,SV423: $i,SV561: $i,SV703: $i] :
      ( ( ( ~ ( in @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ SV208 )
          | ~ ~ ( ~ ( in @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) @ SV423 )
                | ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) ) @ SV561 )
                      | ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) ) @ SV703 ) ) ) )
        = $false )
      | ( ( subset @ SV561 @ SV703 )
        = $true )
      | ( ( subset @ SV703 @ ( cartprod @ SV208 @ SV423 ) )
        = $false )
      | ( ( subset @ SV561 @ ( cartprod @ SV208 @ SV423 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2705]) ).

thf(2844,plain,
    ! [SV209: $i,SV747: $i,SV424: $i > $o] :
      ( ( ( SV424 @ SV747 )
        = $false )
      | ( ( ~ ( in @ SV747 @ SV209 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV209
            @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) )
        = $true )
      | ( ( in @ ( sK70_Xx @ SV424 @ SV209 ) @ SV209 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2706]) ).

thf(2845,plain,
    ! [SV209: $i,SV424: $i > $o] :
      ( ( ( ! [SY2662: $i] :
              ( ~ ( SV424 @ SY2662 )
              | ~ ( in @ SY2662 @ SV209 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV209
            @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) )
        = $true )
      | ( ( in @ ( sK71_SY1877 @ SV424 @ SV209 ) @ SV209 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2707]) ).

thf(2846,plain,
    ! [SV209: $i,SV424: $i > $o] :
      ( ( ( ~ ( SV424 @ ( sK70_Xx @ SV424 @ SV209 ) )
          | ~ ~ ( ~ ( SV424 @ ( sK71_SY1877 @ SV424 @ SV209 ) )
                | ~ ( ( ( sK70_Xx @ SV424 @ SV209 )
                     != ( sK71_SY1877 @ SV424 @ SV209 ) ) ) ) )
        = $false )
      | ( ( ! [SY2662: $i] :
              ( ~ ( SV424 @ SY2662 )
              | ~ ( in @ SY2662 @ SV209 ) )
          | ( singleton
            @ ( dsetconstr @ SV209
              @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2708]) ).

thf(2847,plain,
    ! [SV425: $i,SV210: $i,SV761: $i,SV748: $i] :
      ( ( ( SV748 != SV761 )
        = $true )
      | ( ( ~ ( in @ SV748 @ SV210 )
          | ( in @ SV761 @ SV425 ) )
        = $true )
      | ( ( SV210 = SV425 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2709]) ).

thf(2848,plain,
    ! [SV210: $i,SV425: $i,SV762: $i,SV749: $i] :
      ( ( ( SV749 != SV762 )
        = $true )
      | ( ( ~ ( in @ SV762 @ SV425 )
          | ( in @ SV749 @ SV210 ) )
        = $true )
      | ( ( SV210 = SV425 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2710]) ).

thf(2849,plain,
    ! [SV562: $i,SV763: $i,SV211: $i > $o] :
      ( ( ( ~ ( SV211 @ SV763 ) )
        = $true )
      | ( ( ! [SY2979: $i] :
              ( ~ ( SV211 @ SY2979 )
              | ( SV763 = SY2979 ) ) )
        = $true )
      | ( ( SV211 @ ( sK48_SY224 @ SV562 @ SV211 ) )
        = $true )
      | ( ( SV211 @ SV562 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2711]) ).

thf(2850,plain,
    ! [SV562: $i,SV775: $i,SV211: $i > $o] :
      ( ( ( ~ ( SV211 @ SV775 )
          | ! [SY2987: $i] :
              ( ~ ( SV211 @ SY2987 )
              | ( SV775 = SY2987 ) ) )
        = $true )
      | ( ( SV562
          = ( sK48_SY224 @ SV562 @ SV211 ) )
        = $false )
      | ( ( SV211 @ SV562 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2712]) ).

thf(2851,plain,
    ! [SV427: $i > $o,SV750: $i,SV213: $i > $o] :
      ( ( ( ~ ( SV213 @ ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
          | ~ ( ( SV750
               != ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) ) ) )
        = $false )
      | ( ( ~ ( SV213 @ SV750 ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2713]) ).

thf(2852,plain,
    ! [SV427: $i > $o,SV213: $i > $o] :
      ( ( ( ~ ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) ) )
        = $true )
      | ( ( ~ ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) ) )
        = $true )
      | ( ( ! [SY2670: $i] :
              ( ~ ( ~ ( SV213 @ ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2670
                       != ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV213 @ SY2670 ) )
          | ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2714]) ).

thf(2853,plain,
    ! [SV427: $i > $o,SV213: $i > $o] :
      ( ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( ! [SY2670: $i] :
              ( ~ ( ~ ( SV213 @ ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2670
                       != ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV213 @ SY2670 ) )
          | ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2715]) ).

thf(2854,plain,
    ! [SV214: $i,SV428: $i,SV654: $i] :
      ( ( ( ~ ( in @ ( sK98_Xx @ SV654 @ SV428 @ SV214 ) @ SV214 ) )
        = $false )
      | ( ( in @ SV428 @ ( powerset @ SV654 ) )
        = $true )
      | ( ( in @ SV654 @ ( powerset @ SV214 ) )
        = $false )
      | ( ( in @ SV428 @ ( powerset @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2716]) ).

thf(2855,plain,
    ! [SV214: $i,SV428: $i,SV654: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK98_Xx @ SV654 @ SV428 @ SV214 ) @ SV428 )
                | ~ ~ ( in @ ( sK98_Xx @ SV654 @ SV428 @ SV214 ) @ SV654 ) ) )
        = $false )
      | ( ( in @ SV428 @ ( powerset @ SV654 ) )
        = $true )
      | ( ( in @ SV654 @ ( powerset @ SV214 ) )
        = $false )
      | ( ( in @ SV428 @ ( powerset @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2716]) ).

thf(2856,plain,
    ! [SV215: $i,SV429: $i,SV655: $o] :
      ( ( ( ~ ( in @ ( sK31_B @ SV655 @ SV429 @ SV215 ) @ SV215 )
          | ~ ~ SV655 )
        = $false )
      | ( SV655 = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2718]) ).

thf(2857,plain,
    ! [SV215: $i,SV429: $i] :
      ( ( ( ~ ( in @ ( sK31_B @ $true @ SV429 @ SV215 ) @ SV215 )
          | ~ ~ $true )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2720]) ).

thf(2858,plain,
    ! [SV215: $i,SV429: $i] :
      ( ( ( ~ ( in @ ( sK31_B @ $false @ SV429 @ SV215 ) @ SV215 )
          | ~ ~ $false )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2722]) ).

thf(2859,plain,
    ! [SV216: $i,SV430: $i] :
      ( ( ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV430 )
        = $true )
      | ( ( SV216 = SV430 )
        = $true )
      | ( ( in @ ( sK26_Xx @ SV430 @ SV216 ) @ SV216 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2723]) ).

thf(2860,plain,
    ! [SV216: $i,SV430: $i] :
      ( ( ( ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV216 ) )
        = $true )
      | ( ( SV216 = SV430 )
        = $true )
      | ( ( in @ ( sK26_Xx @ SV430 @ SV216 ) @ SV216 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2724]) ).

thf(2861,plain,
    ! [SV216: $i,SV430: $i] :
      ( ( ( ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV430 ) )
        = $false )
      | ( ( SV216 = SV430 )
        = $true )
      | ( ( in @ ( sK26_Xx @ SV430 @ SV216 ) @ SV430 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2725]) ).

thf(2862,plain,
    ! [SV216: $i,SV430: $i] :
      ( ( ( ~ ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV216 ) )
        = $false )
      | ( ( SV216 = SV430 )
        = $true )
      | ( ( in @ ( sK26_Xx @ SV430 @ SV216 ) @ SV430 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2725]) ).

thf(2863,plain,
    ! [SV218: $i,SV432: $i,SV564: $i,SV704: $i] :
      ( ( ( ~ ( in @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) @ SV218 )
          | ~ ( ( ( ap @ SV218 @ SV432 @ SV564 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) )
               != ( ap @ SV218 @ SV432 @ SV704 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) ) ) ) )
        = $false )
      | ( ( ! [SY2948: $i] :
              ( ~ ( in @ SY2948 @ SV218 )
              | ! [SY2949: $i] :
                  ( ~ ( in @ SY2949 @ SV432 )
                  | ~ ( in @ ( kpair @ SY2948 @ SY2949 ) @ SV704 )
                  | ( in @ ( kpair @ SY2948 @ SY2949 ) @ SV564 ) ) ) )
        = $true )
      | ( ( func @ SV218 @ SV432 @ SV704 )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV564 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2726]) ).

thf(2864,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 ) )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
              | ~ ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
                    | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) ) )
          | ( SV433 = SV656 ) )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2727]) ).

thf(2865,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 )
                | ~ ~ ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 ) ) )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
              | ~ ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
                    | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) ) )
          | ( SV433 = SV656 ) )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2727]) ).

thf(2866,plain,
    ! [SV220: $i,SV434: $i > $o,SV565: $i] :
      ( ( ( ~ ( in @ ( sK73_Xy @ SV565 @ SV434 @ SV220 ) @ SV220 ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV220
            @ ^ [SY2682: $i] : ( SV434 @ SY2682 ) ) )
        = $true )
      | ( ( SV434 @ SV565 )
        = $false )
      | ( ( in @ SV565 @ SV220 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2728]) ).

thf(2867,plain,
    ! [SV220: $i,SV565: $i,SV434: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV434 @ ( sK73_Xy @ SV565 @ SV434 @ SV220 ) )
                | ~ ( ( ( sK73_Xy @ SV565 @ SV434 @ SV220 )
                     != SV565 ) ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV220
            @ ^ [SY2682: $i] : ( SV434 @ SY2682 ) ) )
        = $true )
      | ( ( SV434 @ SV565 )
        = $false )
      | ( ( in @ SV565 @ SV220 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2728]) ).

thf(2868,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ ( ( in @ SV566 @ SV221 )
              | ~ ( in @ SV566 @ SV221 )
              | ! [SX3: $o] : SX3 ) )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2729]) ).

thf(2869,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ ~ ( ~ ( ( in @ SV566 @ SV221 )
                    | ( in @ SV566 @ SV435 )
                    | ! [SX3: $o] : SX3 )
                | ~ ( ( in @ SV566 @ SV221 )
                    | ! [SX3: $o] :
                        ( ~ SX3
                        | SX3 ) ) ) )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2729]) ).

thf(2870,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ ~ ( ~ ( ~ ( in @ SV566 @ SV435 )
                    | ~ ( in @ SV566 @ SV221 )
                    | ! [SX3: $o] : SX3 )
                | ~ ~ ( ~ ( ~ ( in @ SV566 @ SV435 )
                          | ( in @ SV566 @ SV435 )
                          | ! [SX3: $o] : SX3 )
                      | ~ ( ~ ( in @ SV566 @ SV435 )
                          | ! [SX3: $o] :
                              ( ~ SX3
                              | SX3 ) ) ) ) )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2730]) ).

thf(2871,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ ~ ( ~ ! [SY2839: $o] :
                      ( ~ SY2839
                      | ~ ( in @ SV566 @ SV221 )
                      | SY2839 )
                | ~ ~ ( ~ ! [SY2840: $o] :
                            ( ~ SY2840
                            | ( in @ SV566 @ SV435 )
                            | SY2840 )
                      | ~ ! [SX3: $o] :
                            ( ~ SX3
                            | ~ SX3
                            | SX3 ) ) ) )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2730]) ).

thf(2872,plain,
    ! [SV751: $i,SV223: $i,SV764: $i] :
      ( ( ( SV764 != SV223 )
        = $true )
      | ( ( in @ SV764 @ ( setadjoin @ SV223 @ SV751 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2732]) ).

thf(2873,plain,
    ! [SV223: $i,SV752: $i,SV765: $i] :
      ( ( ( ~ ( in @ SV765 @ SV752 ) )
        = $true )
      | ( ( in @ SV765 @ ( setadjoin @ SV223 @ SV752 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2733]) ).

thf(2874,plain,
    ! [SV439: $i,SV226: $i,SV766: $i] :
      ( ( ( ~ ( in @ SV766 @ ( binunion @ SV226 @ SV439 ) ) )
        = $true )
      | ( ( ( in @ SV766 @ SV226 )
          | ( in @ SV766 @ SV439 )
          | ! [SX3: $o] : SX3 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2735]) ).

thf(2875,plain,
    ! [SV439: $i,SV226: $i,SV767: $i] :
      ( ( ( ~ ( in @ SV767 @ ( binunion @ SV226 @ SV439 ) ) )
        = $true )
      | ( ( ( in @ SV767 @ SV226 )
          | ! [SX3: $o] :
              ( ~ SX3
              | SX3 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2736]) ).

thf(2876,plain,
    ! [SV439: $i,SV226: $i,SV768: $i] :
      ( ( ( ~ ( in @ SV768 @ ( binunion @ SV226 @ SV439 ) ) )
        = $true )
      | ( ( ! [SY2982: $o] :
              ( ~ SY2982
              | ( in @ SV768 @ SV439 )
              | SY2982 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2737]) ).

thf(2877,plain,
    ! [SV439: $i,SV226: $i,SV776: $i] :
      ( ( ( ~ ( in @ SV776 @ ( binunion @ SV226 @ SV439 ) ) )
        = $true )
      | ( ( ! [SX2: $o] :
              ( ~ SX2
              | ~ SX2
              | SX2 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2738]) ).

thf(2878,plain,
    ! [SV607: $i,SV227: $i,SV440: $i > $o] :
      ( ( ( SV440 @ ( sK38_Xx @ SV440 @ SV227 ) )
        = $false )
      | ( ( SV440 @ SV607 )
        = $true )
      | ( ( in @ SV607 @ SV227 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2740]) ).

thf(2879,plain,
    ! [SV568: $i,SV228: $i > $o] :
      ( ( ( ~ ! [SY2375: $i] :
                ( ~ ( SV228 @ SY2375 )
                | ( ( sK46_SY211 @ SV228 )
                  = SY2375 ) )
          | ~ ( SV228 @ ( sK46_SY211 @ SV228 ) ) )
        = $false )
      | ( ( ( sK47_Xy @ SV568 @ SV228 )
          = SV568 )
        = $false )
      | ( ( SV228 @ ( sK47_Xy @ SV568 @ SV228 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2741]) ).

thf(2880,plain,
    ! [SV568: $i,SV228: $i > $o] :
      ( ( ( ! [SY2375: $i] :
              ( ~ ( SV228 @ SY2375 )
              | ( ( sK46_SY211 @ SV228 )
                = SY2375 ) ) )
        = $true )
      | ( ( SV228 @ ( sK47_Xy @ SV568 @ SV228 ) )
        = $true )
      | ( ( ( sK47_Xy @ SV568 @ SV228 )
          = SV568 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2742]) ).

thf(2881,plain,
    ! [SV568: $i,SV228: $i > $o] :
      ( ( ( SV228 @ ( sK46_SY211 @ SV228 ) )
        = $true )
      | ( ( SV228 @ ( sK47_Xy @ SV568 @ SV228 ) )
        = $true )
      | ( ( ( sK47_Xy @ SV568 @ SV228 )
          = SV568 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2743]) ).

thf(2882,plain,
    ! [SV229: $i,SV753: $i,SV441: $i > $o] :
      ( ( ( SV441 @ SV753 )
        = $false )
      | ( ( ~ ( in @ SV753 @ SV229 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV229
            @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) )
        = $true )
      | ( ( in @ ( sK74_Xx @ SV441 @ SV229 ) @ SV229 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2744]) ).

thf(2883,plain,
    ! [SV229: $i,SV441: $i > $o] :
      ( ( ( ! [SY2705: $i] :
              ( ~ ( SV441 @ SY2705 )
              | ~ ( in @ SY2705 @ SV229 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV229
            @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) )
        = $true )
      | ( ( in @ ( sK75_SY1878 @ SV441 @ SV229 ) @ SV229 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2745]) ).

thf(2884,plain,
    ! [SV229: $i,SV441: $i > $o] :
      ( ( ( ~ ( SV441 @ ( sK74_Xx @ SV441 @ SV229 ) )
          | ~ ~ ( ~ ( SV441 @ ( sK75_SY1878 @ SV441 @ SV229 ) )
                | ~ ( ( ( sK74_Xx @ SV441 @ SV229 )
                     != ( sK75_SY1878 @ SV441 @ SV229 ) ) ) ) )
        = $false )
      | ( ( ! [SY2705: $i] :
              ( ~ ( SV441 @ SY2705 )
              | ~ ( in @ SY2705 @ SV229 ) )
          | ( singleton
            @ ( dsetconstr @ SV229
              @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2746]) ).

thf(2885,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
          | ~ ~ ( ~ ( in @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                | ~ ~ ( ~ ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
                      | ~ ~ ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 ) ) ) )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
              | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                          | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
          | ( SV569 = SV706 ) )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2747]) ).

thf(2886,plain,
    ! [SV231: $i] :
      ( ( ( in @ emptyset @ SV231 )
        = $false )
      | ( ( in @ ( sK9_Xx @ SV231 ) @ omega )
        = $true )
      | ( ( ! [SY2382: $i] :
              ( ~ ( in @ SY2382 @ omega )
              | ( in @ SY2382 @ SV231 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2748]) ).

thf(2887,plain,
    ! [SV231: $i] :
      ( ( ( in @ emptyset @ SV231 )
        = $false )
      | ( ( in @ ( sK9_Xx @ SV231 ) @ SV231 )
        = $true )
      | ( ( ! [SY2382: $i] :
              ( ~ ( in @ SY2382 @ omega )
              | ( in @ SY2382 @ SV231 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2749]) ).

thf(2888,plain,
    ! [SV231: $i,SV769: $i] :
      ( ( ( ~ ( in @ SV769 @ omega ) )
        = $true )
      | ( ( in @ SV769 @ SV231 )
        = $true )
      | ( ( in @ ( setadjoin @ ( sK9_Xx @ SV231 ) @ ( sK9_Xx @ SV231 ) ) @ SV231 )
        = $false )
      | ( ( in @ emptyset @ SV231 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2750]) ).

thf(2889,plain,
    ! [SV233: $i,SV658: $i] :
      ( ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( ! [SY2924: $i] :
              ~ ( in @ SY2924 @ SV658 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2925: $i] :
                    ( ~ ( in @ SY2925 @ ( sK15_B @ SV233 ) )
                    | ! [SY2926: $i] :
                        ( ~ ( in @ SY2926 @ SY2925 )
                        | ( in @ SY2926 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) )
                    | ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SY2925 ) )
              | ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) )
                          | ~ ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 ) )
                    | ~ ! [SY2927: $i] :
                          ( ~ ( in @ SY2927 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
                          | ~ ( in @ SY2927 @ SV658 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2754]) ).

thf(2890,plain,
    ! [SV233: $i,SV658: $i] :
      ( ( ( ~ ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 ) )
        = $true )
      | ( ( ! [SY2924: $i] :
              ~ ( in @ SY2924 @ SV658 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2925: $i] :
                    ( ~ ( in @ SY2925 @ ( sK15_B @ SV233 ) )
                    | ! [SY2926: $i] :
                        ( ~ ( in @ SY2926 @ SY2925 )
                        | ( in @ SY2926 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) )
                    | ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SY2925 ) )
              | ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) )
                          | ~ ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 ) )
                    | ~ ! [SY2927: $i] :
                          ( ~ ( in @ SY2927 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
                          | ~ ( in @ SY2927 @ SV658 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2755]) ).

thf(2891,plain,
    ! [SV770: $i,SV233: $i,SV754: $i] :
      ( ( ( ~ ( in @ SV754 @ ( sK15_B @ SV233 ) )
          | ~ ( in @ SV770 @ ( sK15_B @ SV233 ) ) )
        = $true )
      | ( ( ! [SY2983: $i] :
              ( ~ ( in @ SY2983 @ SV754 )
              | ( in @ SY2983 @ SV770 ) )
          | ! [SY2984: $i] :
              ( ~ ( in @ SY2984 @ SV770 )
              | ( in @ SY2984 @ SV754 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2756]) ).

thf(2892,plain,
    ! [SV233: $i] :
      ( ( ! [SY2396: $i] :
            ( ~ ( in @ SY2396 @ ( sK15_B @ SV233 ) )
            | ! [SY2397: $i] :
                ( ~ ( in @ SY2397 @ SY2396 )
                | ( in @ SY2397 @ SV233 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2757]) ).

thf(2893,plain,
    ! [SV233: $i] :
      ( ( ! [SY2398: $i,SY2399: $i] :
            ( ~ ( in @ SY2398 @ SV233 )
            | ~ ( in @ SY2399 @ SV233 )
            | ~ ( ~ ( in @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) @ ( sK15_B @ SV233 ) )
                | ~ ~ ( ~ ( ~ ( in @ SY2398 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) )
                          | ~ ( in @ SY2399 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) ) )
                      | ~ ( ( in @ SY2398 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) )
                          | ( in @ SY2399 @ ( sK16_SY1855 @ SY2399 @ SY2398 @ SV233 ) ) ) ) )
            | ( SY2398 = SY2399 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2758]) ).

thf(2894,plain,
    ! [SV234: $i,SV728: $i,SV444: $i > $o] :
      ( ( ( SV444 @ SV728 )
        = $false )
      | ( ( in @ SV728 @ SV234 )
        = $false )
      | ( ( SV444 @ ( sK37_Xx @ SV444 @ SV234 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2759]) ).

thf(2895,plain,
    ! [SV234: $i,SV729: $i,SV444: $i > $o] :
      ( ( ( SV444 @ SV729 )
        = $false )
      | ( ( in @ SV729 @ SV234 )
        = $false )
      | ( ( in @ ( sK37_Xx @ SV444 @ SV234 ) @ SV234 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2760]) ).

thf(2896,plain,
    ! [SV573: $i,SV235: $i > $o] :
      ( ( ( ~ ! [SY2403: $i] :
                ( ( SY2403
                 != ( sK32_Xx @ SV235 ) )
                | ( SV235 @ SY2403 ) ) )
        = $false )
      | ( ( SV235 @ ( sK33_SY142 @ SV573 @ SV235 ) )
        = $true )
      | ( ( SV235 @ SV573 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2761]) ).

thf(2897,plain,
    ! [SV573: $i,SV235: $i > $o] :
      ( ( ( ~ ! [SY2404: $i] :
                ( ~ ( SV235 @ SY2404 )
                | ( SY2404
                  = ( sK32_Xx @ SV235 ) ) ) )
        = $false )
      | ( ( SV235 @ ( sK33_SY142 @ SV573 @ SV235 ) )
        = $true )
      | ( ( SV235 @ SV573 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2761]) ).

thf(2898,plain,
    ! [SV573: $i,SV235: $i > $o] :
      ( ( ( ~ ! [SY2403: $i] :
                ( ( SY2403
                 != ( sK32_Xx @ SV235 ) )
                | ( SV235 @ SY2403 ) )
          | ~ ! [SY2404: $i] :
                ( ~ ( SV235 @ SY2404 )
                | ( SY2404
                  = ( sK32_Xx @ SV235 ) ) ) )
        = $false )
      | ( ( SV573
          = ( sK33_SY142 @ SV573 @ SV235 ) )
        = $false )
      | ( ( SV235 @ SV573 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2762]) ).

thf(2899,plain,
    ! [SV236: $i,SV445: $i,SV574: $i,SV710: $i > $o] :
      ( ( ( in @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ SV236 )
        = $true )
      | ( ( ! [SY2953: $i] :
              ( ~ ( in @ SY2953 @ SV574 )
              | ( SV710 @ SY2953 ) ) )
        = $true )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2763]) ).

thf(2900,plain,
    ! [SV236: $i,SV445: $i,SV574: $i,SV710: $i > $o] :
      ( ( ( ~ ( ~ ( in @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) @ SV445 )
              | ~ ~ ( ~ ( in @ ( kpair @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) ) @ SV574 )
                    | ~ ~ ( SV710 @ ( kpair @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) ) ) ) ) )
        = $true )
      | ( ( ! [SY2953: $i] :
              ( ~ ( in @ SY2953 @ SV574 )
              | ( SV710 @ SY2953 ) ) )
        = $true )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2764]) ).

thf(2901,plain,
    ! [SV608: $i,SV237: $i,SV446: $i > $o] :
      ( ( ( SV446 @ ( sK35_Xx @ SV446 @ SV237 ) )
        = $false )
      | ( ( SV446 @ SV608 )
        = $true )
      | ( ( in @ SV608 @ SV237 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2766]) ).

thf(2902,plain,
    ! [SV711: $i,SV575: $i,SV238: $i,SV447: $o] :
      ( ( SV447 = $false )
      | ( ( ( dsetconstr @ SV238
            @ ^ [SY2954: $i] :
                ( ~ ( ~ SV447
                    | ( SY2954 != SV575 ) )
                | ~ ( ~ ~ SV447
                    | ( SY2954 != SV711 ) ) ) )
          = ( setadjoin @ SV575 @ emptyset ) )
        = $true )
      | ( ( in @ SV711 @ SV238 )
        = $false )
      | ( ( in @ SV575 @ SV238 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2767]) ).

thf(2903,plain,
    ! [SV712: $i,SV576: $i,SV238: $i] :
      ( ( $true = $false )
      | ( ( ( dsetconstr @ SV238
            @ ^ [SY2955: $i] :
                ( ~ ( ~ $true
                    | ( SY2955 != SV576 ) )
                | ~ ( ~ ~ $true
                    | ( SY2955 != SV712 ) ) ) )
          = ( setadjoin @ SV576 @ emptyset ) )
        = $true )
      | ( ( in @ SV712 @ SV238 )
        = $false )
      | ( ( in @ SV576 @ SV238 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2768]) ).

thf(2904,plain,
    ! [SV713: $i,SV577: $i,SV238: $i] :
      ( ( $false = $false )
      | ( ( ( dsetconstr @ SV238
            @ ^ [SY2956: $i] :
                ( ~ ( ~ $false
                    | ( SY2956 != SV577 ) )
                | ~ ( ~ ~ $false
                    | ( SY2956 != SV713 ) ) ) )
          = ( setadjoin @ SV577 @ emptyset ) )
        = $true )
      | ( ( in @ SV713 @ SV238 )
        = $false )
      | ( ( in @ SV577 @ SV238 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2769]) ).

thf(2905,plain,
    ! [SV578: $i,SV239: $i,SV755: $i] :
      ( ( ( in @ SV755 @ ( sK14_B @ SV239 ) )
        = $false )
      | ( ( ~ ( in @ SV755 @ SV239 ) )
        = $true )
      | ( ( in @ SV578 @ SV239 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2770]) ).

thf(2906,plain,
    ! [SV582: $i,SV241: $i > $o] :
      ( ( ( ~ ! [SY2422: $i] :
                ( ~ ( SV241 @ SY2422 )
                | ( ( sK43_SY205 @ SV241 )
                  = SY2422 ) ) )
        = $false )
      | ( ( SV241 @ ( sK44_Xx @ SV241 ) )
        = $true )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2771]) ).

thf(2907,plain,
    ! [SV582: $i,SV241: $i > $o] :
      ( ( ( ~ ( SV241 @ ( sK43_SY205 @ SV241 ) ) )
        = $false )
      | ( ( SV241 @ ( sK44_Xx @ SV241 ) )
        = $true )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2771]) ).

thf(2908,plain,
    ! [SV582: $i,SV241: $i > $o] :
      ( ( ( ~ ( SV241 @ ( sK45_SY1868 @ SV241 ) ) )
        = $false )
      | ( ( ~ ( ~ ! [SY2422: $i] :
                    ( ~ ( SV241 @ SY2422 )
                    | ( ( sK43_SY205 @ SV241 )
                      = SY2422 ) )
              | ~ ( SV241 @ ( sK43_SY205 @ SV241 ) ) ) )
        = $true )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2772]) ).

thf(2909,plain,
    ! [SV582: $i,SV241: $i > $o] :
      ( ( ( ~ ( ( ( sK44_Xx @ SV241 )
               != ( sK45_SY1868 @ SV241 ) ) ) )
        = $false )
      | ( ( ~ ( ~ ! [SY2422: $i] :
                    ( ~ ( SV241 @ SY2422 )
                    | ( ( sK43_SY205 @ SV241 )
                      = SY2422 ) )
              | ~ ( SV241 @ ( sK43_SY205 @ SV241 ) ) ) )
        = $true )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2772]) ).

thf(2910,plain,
    ! [SV659: $i,SV609: $i,SV730: $i] :
      ( ( ( in @ SV730 @ SV609 )
        = $false )
      | ( ( in @ SV659 @ SV730 )
        = $false )
      | ( ( in @ SV659 @ ( setunion @ SV609 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2773]) ).

thf(2911,plain,
    ! [SV610: $i,SV660: $i] :
      ( ( ( in @ SV660 @ ( sK8_B @ SV660 @ SV610 ) )
        = $true )
      | ( ( in @ SV660 @ ( setunion @ SV610 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2774]) ).

thf(2912,plain,
    ! [SV610: $i,SV660: $i] :
      ( ( ( in @ ( sK8_B @ SV660 @ SV610 ) @ SV610 )
        = $true )
      | ( ( in @ SV660 @ ( setunion @ SV610 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2775]) ).

thf(2913,plain,
    ! [SV243: $i,SV450: $i,SV583: $i,SV717: $i] :
      ( ( ( ~ ( in @ ( sK90_Xx @ SV717 @ SV583 @ SV450 @ SV243 ) @ SV243 )
          | ~ ( ( ( ap @ SV243 @ SV450 @ SV583 @ ( sK90_Xx @ SV717 @ SV583 @ SV450 @ SV243 ) )
               != ( ap @ SV243 @ SV450 @ SV717 @ ( sK90_Xx @ SV717 @ SV583 @ SV450 @ SV243 ) ) ) ) )
        = $false )
      | ( ( SV583 = SV717 )
        = $true )
      | ( ( func @ SV243 @ SV450 @ SV717 )
        = $false )
      | ( ( func @ SV243 @ SV450 @ SV583 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2776]) ).

thf(2914,plain,
    ! [SV245: $i,SV451: $i,SV585: $i,SV718: $i] :
      ( ( ( ~ ( in @ ( sK91_Xx @ SV718 @ SV585 @ SV451 @ SV245 ) @ SV245 )
          | ~ ( ( ( ap @ SV245 @ SV451 @ SV585 @ ( sK91_Xx @ SV718 @ SV585 @ SV451 @ SV245 ) )
               != ( ap @ SV245 @ SV451 @ SV718 @ ( sK91_Xx @ SV718 @ SV585 @ SV451 @ SV245 ) ) ) ) )
        = $false )
      | ( ( SV585 = SV718 )
        = $true )
      | ( ( in @ SV718 @ ( funcSet @ SV245 @ SV451 ) )
        = $false )
      | ( ( in @ SV585 @ ( funcSet @ SV245 @ SV451 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2777]) ).

thf(2915,plain,
    ! [SV452: $i > $o,SV246: $i,SV731: $i] :
      ( ( ( in @ SV731 @ SV246 )
        = $false )
      | ( ( SV452 @ SV731 )
        = $false )
      | ( ( in @ ( sK36_Xx @ SV452 @ SV246 ) @ SV246 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2778]) ).

thf(2916,plain,
    ! [SV452: $i > $o,SV246: $i,SV732: $i] :
      ( ( ( in @ SV732 @ SV246 )
        = $false )
      | ( ( SV452 @ SV732 )
        = $false )
      | ( ( SV452 @ ( sK36_Xx @ SV452 @ SV246 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2779]) ).

thf(2917,plain,
    ! [SV586: $i,SV247: $i > $o] :
      ( ( ( ~ ! [SY2435: $i] :
                ( ~ ( SV247 @ SY2435 )
                | ( ( sK21_Xx @ SV247 )
                  = SY2435 ) ) )
        = $false )
      | ( ( SV247 @ ( sK22_SY74 @ SV586 @ SV247 ) )
        = $true )
      | ( ( SV247 @ SV586 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2780]) ).

thf(2918,plain,
    ! [SV586: $i,SV247: $i > $o] :
      ( ( ( ~ ( SV247 @ ( sK21_Xx @ SV247 ) ) )
        = $false )
      | ( ( SV247 @ ( sK22_SY74 @ SV586 @ SV247 ) )
        = $true )
      | ( ( SV247 @ SV586 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2780]) ).

thf(2919,plain,
    ! [SV586: $i,SV247: $i > $o] :
      ( ( ( ~ ! [SY2435: $i] :
                ( ~ ( SV247 @ SY2435 )
                | ( ( sK21_Xx @ SV247 )
                  = SY2435 ) )
          | ~ ( SV247 @ ( sK21_Xx @ SV247 ) ) )
        = $false )
      | ( ( SV586
          = ( sK22_SY74 @ SV586 @ SV247 ) )
        = $false )
      | ( ( SV247 @ SV586 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2781]) ).

thf(2920,plain,
    ! [SV248: $i,SV453: $i,SV661: $i > $o,SV719: $i > $o] :
      ( ( ( in @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) @ SV248 )
        = $true )
      | ( ( ( dsetconstr @ SV248
            @ ^ [SY2930: $i] : ( SV661 @ SY2930 ) )
          = ( dsetconstr @ SV453
            @ ^ [SY2961: $i] : ( SV719 @ SY2961 ) ) )
        = $true )
      | ( ( SV248 = SV453 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2782]) ).

thf(2921,plain,
    ! [SV248: $i,SV453: $i,SV661: $i > $o,SV719: $i > $o] :
      ( ( ( ~ ( ~ ( in @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) @ SV453 )
              | ~ ~ ( ( ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 )
                     != ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) )
                    | ~ ~ ( ~ ( ~ ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
                              | ~ ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) )
                          | ~ ( ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
                              | ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) ) ) ) ) )
        = $true )
      | ( ( ( dsetconstr @ SV248
            @ ^ [SY2930: $i] : ( SV661 @ SY2930 ) )
          = ( dsetconstr @ SV453
            @ ^ [SY2961: $i] : ( SV719 @ SY2961 ) ) )
        = $true )
      | ( ( SV248 = SV453 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2783]) ).

thf(2922,plain,
    ! [SV733: $i,SV612: $i,SV250: $i,SV1: $i,SV777: $i] :
      ( ( ( ~ ( in @ SV777 @ SV1 )
          | ~ ( in @ SV777 @ ( binintersect @ SV250 @ SV612 ) )
          | ( in @ SV777 @ ( binunion @ SV250 @ SV733 ) ) )
        = $true )
      | ( ( in @ SV733 @ ( powerset @ SV1 ) )
        = $false )
      | ( ( in @ SV612 @ ( powerset @ SV1 ) )
        = $false )
      | ( ( in @ SV250 @ ( powerset @ SV1 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2784]) ).

thf(2923,plain,
    ! [SV2: $i,SV613: $i,SV251: $i,SV734: $i] :
      ( ( ( in @ SV734 @ ( binunion @ SV251 @ SV613 ) )
        = $true )
      | ( ( ~ ( in @ SV734 @ SV613 ) )
        = $true )
      | ( ( in @ SV734 @ SV2 )
        = $false )
      | ( ( in @ SV613 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV251 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2785]) ).

thf(2924,plain,
    ! [SV3: $i,SV614: $i,SV252: $i,SV735: $i] :
      ( ( ( in @ SV735 @ ( binunion @ SV252 @ SV614 ) )
        = $true )
      | ( ( ~ ( in @ SV735 @ SV252 ) )
        = $true )
      | ( ( in @ SV735 @ SV3 )
        = $false )
      | ( ( in @ SV614 @ ( powerset @ SV3 ) )
        = $false )
      | ( ( in @ SV252 @ ( powerset @ SV3 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2786]) ).

thf(2925,plain,
    ! [SV254: $i,SV616: $i,SV5: $i,SV771: $i] :
      ( ( ( ~ ( in @ SV771 @ SV5 ) )
        = $true )
      | ( ( ~ ( in @ SV771 @ SV616 )
          | ( in @ SV771 @ ( setminus @ SV5 @ SV254 ) ) )
        = $true )
      | ( ( subset @ SV254 @ ( setminus @ SV5 @ SV616 ) )
        = $false )
      | ( ( in @ SV616 @ ( powerset @ SV5 ) )
        = $false )
      | ( ( in @ SV254 @ ( powerset @ SV5 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2787]) ).

thf(2926,plain,
    ! [SV619: $i,SV257: $i,SV8: $i,SV736: $i] :
      ( ( ( ~ ( in @ SV736 @ ( setminus @ SV8 @ SV257 ) ) )
        = $true )
      | ( ( in @ SV736 @ ( setminus @ SV8 @ ( binintersect @ SV257 @ SV619 ) ) )
        = $true )
      | ( ( in @ SV736 @ SV8 )
        = $false )
      | ( ( in @ SV619 @ ( powerset @ SV8 ) )
        = $false )
      | ( ( in @ SV257 @ ( powerset @ SV8 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2788]) ).

thf(2927,plain,
    ! [SV620: $i,SV258: $i,SV9: $i,SV737: $i] :
      ( ( ( ~ ( in @ SV737 @ ( setminus @ SV9 @ SV258 ) ) )
        = $true )
      | ( ( ~ ( in @ SV737 @ ( binintersect @ SV258 @ SV620 ) ) )
        = $true )
      | ( ( in @ SV737 @ SV9 )
        = $false )
      | ( ( in @ SV620 @ ( powerset @ SV9 ) )
        = $false )
      | ( ( in @ SV258 @ ( powerset @ SV9 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2789]) ).

thf(2928,plain,
    ! [SV17: $i,SV738: $i,SV625: $i,SV266: $i] :
      ( ( ( ~ ( subset @ SV266 @ SV625 ) )
        = $true )
      | ( ( ( in @ SV738 @ SV625 )
          | ~ ( in @ SV738 @ SV266 ) )
        = $true )
      | ( ( in @ SV738 @ SV17 )
        = $false )
      | ( ( in @ SV625 @ ( powerset @ SV17 ) )
        = $false )
      | ( ( in @ SV266 @ ( powerset @ SV17 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2790]) ).

thf(2929,plain,
    ! [SV739: $i,SV626: $i,SV18: $i,SV267: $i] :
      ( ( ( ~ ( subset @ SV267 @ ( setminus @ SV18 @ SV626 ) ) )
        = $true )
      | ( ( ~ ( in @ SV739 @ SV626 )
          | ~ ( in @ SV739 @ SV267 ) )
        = $true )
      | ( ( in @ SV739 @ SV18 )
        = $false )
      | ( ( in @ SV626 @ ( powerset @ SV18 ) )
        = $false )
      | ( ( in @ SV267 @ ( powerset @ SV18 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2791]) ).

thf(2930,plain,
    ! [SV19: $i,SV268: $i,SV627: $i,SV740: $i] :
      ( ( ( in @ SV740 @ SV627 )
        = $true )
      | ( ( ~ ( in @ SV740 @ ( binintersect @ SV268 @ SV627 ) ) )
        = $true )
      | ( ( in @ SV740 @ SV19 )
        = $false )
      | ( ( in @ SV627 @ ( powerset @ SV19 ) )
        = $false )
      | ( ( in @ SV268 @ ( powerset @ SV19 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2792]) ).

thf(2931,plain,
    ! [SV20: $i,SV628: $i,SV269: $i,SV741: $i] :
      ( ( ( in @ SV741 @ SV269 )
        = $true )
      | ( ( ~ ( in @ SV741 @ ( binintersect @ SV269 @ SV628 ) ) )
        = $true )
      | ( ( in @ SV741 @ SV20 )
        = $false )
      | ( ( in @ SV628 @ ( powerset @ SV20 ) )
        = $false )
      | ( ( in @ SV269 @ ( powerset @ SV20 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2793]) ).

thf(2932,plain,
    ! [SV23: $i,SV742: $i,SV631: $i,SV272: $i] :
      ( ( ( ~ ( in @ SV272 @ ( powerset @ SV631 ) ) )
        = $true )
      | ( ( ~ ( in @ SV742 @ SV272 )
          | ( in @ SV742 @ SV631 ) )
        = $true )
      | ( ( in @ SV742 @ SV23 )
        = $false )
      | ( ( in @ SV631 @ ( powerset @ SV23 ) )
        = $false )
      | ( ( in @ SV272 @ ( powerset @ SV23 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2795]) ).

thf(2933,plain,
    ! [SV38: $i,SV471: $i,SV674: $i,SV284: $i,SV756: $i] :
      ( ( ( in @ SV756 @ SV284 )
        = $false )
      | ( ( ~ ( in @ ( kpair @ SV674 @ SV756 ) @ SV471 )
          | ( ( ap @ SV38 @ SV284 @ SV471 @ SV674 )
            = SV756 ) )
        = $true )
      | ( ( in @ SV674 @ SV38 )
        = $false )
      | ( ( in @ SV471 @ ( funcSet @ SV38 @ SV284 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2799]) ).

thf(2934,plain,
    ! [SV39: $i,SV472: $i,SV675: $i,SV285: $i,SV757: $i] :
      ( ( ( in @ SV757 @ SV285 )
        = $false )
      | ( ( ~ ( in @ ( kpair @ SV675 @ SV757 ) @ SV472 )
          | ( ( ap @ SV39 @ SV285 @ SV472 @ SV675 )
            = SV757 ) )
        = $true )
      | ( ( in @ SV675 @ SV39 )
        = $false )
      | ( ( func @ SV39 @ SV285 @ SV472 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2800]) ).

thf(2935,plain,
    ! [SV42: $i,SV743: $i,SV635: $i,SV288: $i > $o] :
      ( ( ( ~ ( SV288 @ SV635 ) )
        = $true )
      | ( ( ~ ( SV288 @ SV743 )
          | ( SV635 = SV743 ) )
        = $true )
      | ( ( in @ SV743 @ SV42 )
        = $false )
      | ( ( in @ SV635 @ SV42 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV42
            @ ^ [SY2500: $i] : ( SV288 @ SY2500 ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2801]) ).

thf(2936,plain,
    ! [SV484: $i > $i > $o,SV298: $i,SV52: $i,SV722: $i,SV593: $i] :
      ( ( ( in @ ( kpair @ SV593 @ SV722 )
          @ ( dpsetconstr @ SV52 @ SV298
            @ ^ [SY2775: $i,SY2776: $i] : ( SV484 @ SY2775 @ SY2776 ) ) )
        = $false )
      | ( ( SV484 @ SV593 @ SV722 )
        = $true )
      | ( ( in @ SV722 @ SV298 )
        = $false )
      | ( ( in @ SV593 @ SV52 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2802]) ).

thf(2937,plain,
    ! [SV301: $i,SV55: $i,SV723: $i,SV594: $i,SV487: $i > $i > $o] :
      ( ( ( SV487 @ SV594 @ SV723 )
        = $false )
      | ( ( in @ ( kpair @ SV594 @ SV723 )
          @ ( dpsetconstr @ SV55 @ SV301
            @ ^ [SY2783: $i,SY2784: $i] : ( SV487 @ SY2783 @ SY2784 ) ) )
        = $true )
      | ( ( in @ SV723 @ SV301 )
        = $false )
      | ( ( in @ SV594 @ SV55 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2803]) ).

thf(2938,plain,
    ! [SV189: $i,SV409: $i,SV647: $i] :
      ( ( ( in @ ( sK97_Xx @ SV647 @ SV409 @ SV189 ) @ SV189 )
        = $true )
      | ( ( subset @ SV409 @ SV647 )
        = $true )
      | ( ( in @ SV647 @ ( powerset @ SV189 ) )
        = $false )
      | ( ( in @ SV409 @ ( powerset @ SV189 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2805]) ).

thf(2939,plain,
    ! [SV189: $i,SV409: $i,SV647: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK97_Xx @ SV647 @ SV409 @ SV189 ) @ SV409 )
              | ~ ~ ( in @ ( sK97_Xx @ SV647 @ SV409 @ SV189 ) @ SV647 ) ) )
        = $true )
      | ( ( subset @ SV409 @ SV647 )
        = $true )
      | ( ( in @ SV647 @ ( powerset @ SV189 ) )
        = $false )
      | ( ( in @ SV409 @ ( powerset @ SV189 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2806]) ).

thf(2940,plain,
    ! [SV549: $i > $i,SV411: $i,SV192: $i,SV758: $i] :
      ( ( ( in @ SV758 @ SV192 )
        = $false )
      | ( ( ( ap @ SV192 @ SV411
            @ ( lam @ SV192 @ SV411
              @ ^ [SY2811: $i] : ( SV549 @ SY2811 ) )
            @ SV758 )
          = ( SV549 @ SV758 ) )
        = $true )
      | ( ( in @ ( SV549 @ ( sK92_Xx @ SV549 @ SV411 @ SV192 ) ) @ SV411 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2813]) ).

thf(2941,plain,
    ! [SV193: $i,SV412: $i,SV550: $i] :
      ( ( ( SV550
          = ( kpair @ ( sK67_Xx @ SV550 @ SV412 @ SV193 ) @ ( sK68_SY1876 @ SV550 @ SV412 @ SV193 ) ) )
        = $true )
      | ( ( in @ SV550 @ ( cartprod @ SV193 @ SV412 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2814]) ).

thf(2942,plain,
    ! [SV193: $i,SV412: $i,SV550: $i] :
      ( ( ( in @ ( sK68_SY1876 @ SV550 @ SV412 @ SV193 ) @ SV412 )
        = $true )
      | ( ( in @ SV550 @ ( cartprod @ SV193 @ SV412 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2815]) ).

thf(2943,plain,
    ! [SV551: $i,SV759: $i,SV194: $i > $o] :
      ( ( ( SV194 @ SV759 )
        = $false )
      | ( ( ! [SY2977: $i] :
              ( ~ ( SV194 @ SY2977 )
              | ( SV759 = SY2977 ) ) )
        = $true )
      | ( ( SV194 @ ( sK57_SY248 @ SV551 @ SV194 ) )
        = $true )
      | ( ( SV194 @ SV551 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2816]) ).

thf(2944,plain,
    ! [SV551: $i,SV772: $i,SV194: $i > $o] :
      ( ( ( ~ ( SV194 @ SV772 ) )
        = $true )
      | ( ( ! [SY2985: $i] :
              ( ~ ( SV194 @ SY2985 )
              | ( SV772 = SY2985 ) ) )
        = $true )
      | ( ( SV551
          = ( sK57_SY248 @ SV551 @ SV194 ) )
        = $false )
      | ( ( SV194 @ SV551 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2817]) ).

thf(2945,plain,
    ! [SV413: $i,SV773: $i,SV195: $i > $i > $o] :
      ( ( ( ! [SY2986: $i] :
              ( ~ ( SV195 @ SY2986 @ SV773 )
              | ~ ( in @ SY2986 @ SV413 ) ) )
        = $true )
      | ( ( in @ SV773 @ ( sK10_B @ SV413 @ SV195 ) )
        = $true )
      | ( ( in @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV413 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2818]) ).

thf(2946,plain,
    ! [SV195: $i > $i > $o,SV413: $i,SV774: $i] :
      ( ( ( ~ ( in @ SV774 @ ( sK10_B @ SV413 @ SV195 ) ) )
        = $true )
      | ( ( ~ ( ~ ( SV195 @ ( sK11_Xy @ SV774 @ SV413 @ SV195 ) @ SV774 )
              | ~ ( in @ ( sK11_Xy @ SV774 @ SV413 @ SV195 ) @ SV413 ) ) )
        = $true )
      | ( ( in @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV413 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2819]) ).

thf(2947,plain,
    ! [SV725: $i,SV413: $i,SV195: $i > $i > $o] :
      ( ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $true )
      | ( ( ~ ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2639: $i] :
                    ( ! [SY2640: $i] :
                        ( ~ ( SV195 @ SY2640 @ SY2639 )
                        | ~ ( in @ SY2640 @ SV413 ) )
                    | ( in @ SY2639 @ ( sK10_B @ SV413 @ SV195 ) ) )
              | ~ ! [SY2641: $i] :
                    ( ~ ( in @ SY2641 @ ( sK10_B @ SV413 @ SV195 ) )
                    | ~ ( ~ ( SV195 @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SY2641 )
                        | ~ ( in @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SV413 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2820]) ).

thf(2948,plain,
    ! [SV195: $i > $i > $o,SV413: $i,SV725: $i] :
      ( ( ( SV725
         != ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $true )
      | ( ( ~ ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2639: $i] :
                    ( ! [SY2640: $i] :
                        ( ~ ( SV195 @ SY2640 @ SY2639 )
                        | ~ ( in @ SY2640 @ SV413 ) )
                    | ( in @ SY2639 @ ( sK10_B @ SV413 @ SV195 ) ) )
              | ~ ! [SY2641: $i] :
                    ( ~ ( in @ SY2641 @ ( sK10_B @ SV413 @ SV195 ) )
                    | ~ ( ~ ( SV195 @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SY2641 )
                        | ~ ( in @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SV413 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2821]) ).

thf(2949,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( ( ( SV552 = SV196 )
          | ( in @ SV552 @ SV414 )
          | ! [SX3: $o] : SX3 )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2822]) ).

thf(2950,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( ( ( SV552 = SV196 )
          | ! [SX3: $o] :
              ( ~ SX3
              | SX3 ) )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2823]) ).

thf(2951,plain,
    ! [SV196: $i,SV414: $i,SV552: $i] :
      ( ( ( ! [SY2814: $o] :
              ( ~ SY2814
              | ( in @ SV552 @ SV414 )
              | SY2814 ) )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2824]) ).

thf(2952,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( ( ! [SX3: $o] :
              ( ~ SX3
              | ~ SX3
              | SX3 ) )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2825]) ).

thf(2953,plain,
    ! [SV652: $i > $o,SV778: $i,SV605: $i > $o] :
      ( ( ( ~ ( ~ ( SV605 @ ( sK54_SY233 @ SV778 @ SV652 @ SV605 ) )
              | ~ ( ( SV778
                   != ( sK54_SY233 @ SV778 @ SV652 @ SV605 ) ) ) )
          | ~ ( SV605 @ SV778 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( ( sK55_Xx @ SV652 @ SV605 )
          = ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2829]) ).

thf(2954,plain,
    ! [SV652: $i > $o,SV605: $i > $o] :
      ( ( ( ~ ( ~ ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
              | ~ ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) ) ) )
        = $false )
      | ( ( ! [SY2919: $i] :
              ( ~ ( ~ ( SV605 @ ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) )
                  | ~ ( ( SY2919
                       != ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) ) ) )
              | ~ ( SV605 @ SY2919 ) )
          | ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2830]) ).

thf(2955,plain,
    ! [SV652: $i > $o,SV605: $i > $o] :
      ( ( ( ~ ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
              | ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) ) ) )
        = $false )
      | ( ( ! [SY2919: $i] :
              ( ~ ( ~ ( SV605 @ ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) )
                  | ~ ( ( SY2919
                       != ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) ) ) )
              | ~ ( SV605 @ SY2919 ) )
          | ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2830]) ).

thf(2956,plain,
    ! [SV606: $i > $o,SV779: $i,SV653: $i > $o] :
      ( ( ( ~ ( ~ ( SV653 @ ( sK50_SY236 @ SV779 @ SV653 @ SV606 ) )
              | ~ ( ( SV779
                   != ( sK50_SY236 @ SV779 @ SV653 @ SV606 ) ) ) )
          | ~ ( SV653 @ SV779 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( ( sK51_Xx @ SV653 @ SV606 )
          = ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2831]) ).

thf(2957,plain,
    ! [SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ~ ( ~ ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
              | ~ ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) ) ) )
        = $false )
      | ( ( ! [SY2921: $i] :
              ( ~ ( ~ ( SV653 @ ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) )
                  | ~ ( ( SY2921
                       != ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) ) ) )
              | ~ ( SV653 @ SY2921 ) )
          | ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2832]) ).

thf(2958,plain,
    ! [SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ~ ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
              | ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) ) ) )
        = $false )
      | ( ( ! [SY2921: $i] :
              ( ~ ( ~ ( SV653 @ ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) )
                  | ~ ( ( SY2921
                       != ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) ) ) )
              | ~ ( SV653 @ SY2921 ) )
          | ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2832]) ).

thf(2959,plain,
    ! [SV558: $i,SV205: $i > $o] :
      ( ( ( ! [SY2293: $i] :
              ( ~ ( SV205 @ SY2293 )
              | ( ( sK41_SY198 @ SV205 )
                = SY2293 ) ) )
        = $true )
      | ( ( SV205 @ ( sK42_Xy @ SV558 @ SV205 ) )
        = $true )
      | ( ( SV205 @ SV558 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2835]) ).

thf(2960,plain,
    ! [SV558: $i,SV205: $i > $o] :
      ( ( ( SV205 @ ( sK41_SY198 @ SV205 ) )
        = $true )
      | ( ( SV205 @ ( sK42_Xy @ SV558 @ SV205 ) )
        = $true )
      | ( ( SV205 @ SV558 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2836]) ).

thf(2961,plain,
    ! [SV558: $i,SV205: $i > $o] :
      ( ( ( ~ ! [SY2293: $i] :
                ( ~ ( SV205 @ SY2293 )
                | ( ( sK41_SY198 @ SV205 )
                  = SY2293 ) ) )
        = $false )
      | ( ( SV558
          = ( sK42_Xy @ SV558 @ SV205 ) )
        = $false )
      | ( ( SV205 @ SV558 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2837]) ).

thf(2962,plain,
    ! [SV558: $i,SV205: $i > $o] :
      ( ( ( ~ ( SV205 @ ( sK41_SY198 @ SV205 ) ) )
        = $false )
      | ( ( SV558
          = ( sK42_Xy @ SV558 @ SV205 ) )
        = $false )
      | ( ( SV205 @ SV558 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2837]) ).

thf(2963,plain,
    ! [SV559: $i > $i,SV421: $i,SV206: $i,SV760: $i] :
      ( ( ( in @ SV760 @ SV206 )
        = $false )
      | ( ( ( ap @ SV206 @ SV421
            @ ( lam @ SV206 @ SV421
              @ ^ [SY2824: $i] : ( SV559 @ SY2824 ) )
            @ SV760 )
          = ( SV559 @ SV760 ) )
        = $true )
      | ( ( in @ ( SV559 @ ( sK94_Xx @ SV559 @ SV421 @ SV206 ) ) @ SV421 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2839]) ).

thf(2964,plain,
    ( ( ~ ( in @ sK5_SY1831 @ sK1_A ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2840]) ).

thf(2965,plain,
    ( ( ~ ~ ( ~ ( in @ sK5_SY1831 @ ( binintersect @ sK2_SY1822 @ sK3_SY1826 ) )
            | ~ ~ ( in @ sK5_SY1831 @ ( binunion @ sK3_SY1826 @ sK4_SY1829 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[2840]) ).

thf(2966,plain,
    ! [SV207: $i,SV422: $i,SV702: $i > $o,SV560: $i,SV780: $i] :
      ( ( ( ~ ( in @ SV780 @ SV560 )
          | ( SV702 @ SV780 ) )
        = $true )
      | ( ( in @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ SV207 )
        = $true )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2841]) ).

thf(2967,plain,
    ! [SV207: $i,SV422: $i,SV560: $i,SV702: $i > $o] :
      ( ( ( ~ ( in @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) @ SV422 )
          | ~ ~ ( ~ ( in @ ( kpair @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) ) @ SV560 )
                | ~ ~ ( SV702 @ ( kpair @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) ) ) ) )
        = $false )
      | ( ( ! [SY2947: $i] :
              ( ~ ( in @ SY2947 @ SV560 )
              | ( SV702 @ SY2947 ) ) )
        = $true )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2842]) ).

thf(2968,plain,
    ! [SV208: $i,SV423: $i,SV561: $i,SV703: $i] :
      ( ( ( ~ ( in @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ SV208 ) )
        = $false )
      | ( ( subset @ SV561 @ SV703 )
        = $true )
      | ( ( subset @ SV703 @ ( cartprod @ SV208 @ SV423 ) )
        = $false )
      | ( ( subset @ SV561 @ ( cartprod @ SV208 @ SV423 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2843]) ).

thf(2969,plain,
    ! [SV208: $i,SV423: $i,SV561: $i,SV703: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) @ SV423 )
                | ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) ) @ SV561 )
                      | ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) ) @ SV703 ) ) ) )
        = $false )
      | ( ( subset @ SV561 @ SV703 )
        = $true )
      | ( ( subset @ SV703 @ ( cartprod @ SV208 @ SV423 ) )
        = $false )
      | ( ( subset @ SV561 @ ( cartprod @ SV208 @ SV423 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2843]) ).

thf(2970,plain,
    ! [SV424: $i > $o,SV209: $i,SV747: $i] :
      ( ( ( in @ SV747 @ SV209 )
        = $false )
      | ( ( SV424 @ SV747 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV209
            @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) )
        = $true )
      | ( ( in @ ( sK70_Xx @ SV424 @ SV209 ) @ SV209 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2844]) ).

thf(2971,plain,
    ! [SV209: $i,SV781: $i,SV424: $i > $o] :
      ( ( ( ~ ( SV424 @ SV781 )
          | ~ ( in @ SV781 @ SV209 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV209
            @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) )
        = $true )
      | ( ( in @ ( sK71_SY1877 @ SV424 @ SV209 ) @ SV209 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2845]) ).

thf(2972,plain,
    ! [SV209: $i,SV424: $i > $o] :
      ( ( ( ~ ( SV424 @ ( sK70_Xx @ SV424 @ SV209 ) ) )
        = $false )
      | ( ( ! [SY2662: $i] :
              ( ~ ( SV424 @ SY2662 )
              | ~ ( in @ SY2662 @ SV209 ) )
          | ( singleton
            @ ( dsetconstr @ SV209
              @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2846]) ).

thf(2973,plain,
    ! [SV209: $i,SV424: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV424 @ ( sK71_SY1877 @ SV424 @ SV209 ) )
                | ~ ( ( ( sK70_Xx @ SV424 @ SV209 )
                     != ( sK71_SY1877 @ SV424 @ SV209 ) ) ) ) )
        = $false )
      | ( ( ! [SY2662: $i] :
              ( ~ ( SV424 @ SY2662 )
              | ~ ( in @ SY2662 @ SV209 ) )
          | ( singleton
            @ ( dsetconstr @ SV209
              @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2846]) ).

thf(2974,plain,
    ! [SV425: $i,SV210: $i,SV761: $i,SV748: $i] :
      ( ( ( SV748 = SV761 )
        = $false )
      | ( ( ~ ( in @ SV748 @ SV210 )
          | ( in @ SV761 @ SV425 ) )
        = $true )
      | ( ( SV210 = SV425 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2847]) ).

thf(2975,plain,
    ! [SV210: $i,SV425: $i,SV762: $i,SV749: $i] :
      ( ( ( SV749 = SV762 )
        = $false )
      | ( ( ~ ( in @ SV762 @ SV425 )
          | ( in @ SV749 @ SV210 ) )
        = $true )
      | ( ( SV210 = SV425 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2848]) ).

thf(2976,plain,
    ! [SV562: $i,SV763: $i,SV211: $i > $o] :
      ( ( ( SV211 @ SV763 )
        = $false )
      | ( ( ! [SY2979: $i] :
              ( ~ ( SV211 @ SY2979 )
              | ( SV763 = SY2979 ) ) )
        = $true )
      | ( ( SV211 @ ( sK48_SY224 @ SV562 @ SV211 ) )
        = $true )
      | ( ( SV211 @ SV562 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2849]) ).

thf(2977,plain,
    ! [SV562: $i,SV775: $i,SV211: $i > $o] :
      ( ( ( ~ ( SV211 @ SV775 ) )
        = $true )
      | ( ( ! [SY2987: $i] :
              ( ~ ( SV211 @ SY2987 )
              | ( SV775 = SY2987 ) ) )
        = $true )
      | ( ( SV562
          = ( sK48_SY224 @ SV562 @ SV211 ) )
        = $false )
      | ( ( SV211 @ SV562 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2850]) ).

thf(2978,plain,
    ! [SV427: $i > $o,SV750: $i,SV213: $i > $o] :
      ( ( ( ~ ( SV213 @ ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) ) )
        = $false )
      | ( ( ~ ( SV213 @ SV750 ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2851]) ).

thf(2979,plain,
    ! [SV213: $i > $o,SV427: $i > $o,SV750: $i] :
      ( ( ( ~ ( ( SV750
               != ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) ) ) )
        = $false )
      | ( ( ~ ( SV213 @ SV750 ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2851]) ).

thf(2980,plain,
    ! [SV427: $i > $o,SV213: $i > $o] :
      ( ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( ~ ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) ) )
        = $true )
      | ( ( ! [SY2670: $i] :
              ( ~ ( ~ ( SV213 @ ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2670
                       != ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV213 @ SY2670 ) )
          | ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2852]) ).

thf(2981,plain,
    ! [SV427: $i > $o,SV213: $i > $o] :
      ( ( ( ! [SY2670: $i] :
              ( ~ ( ~ ( SV213 @ ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2670
                       != ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV213 @ SY2670 ) ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2853]) ).

thf(2982,plain,
    ! [SV214: $i,SV428: $i,SV654: $i] :
      ( ( ( in @ ( sK98_Xx @ SV654 @ SV428 @ SV214 ) @ SV214 )
        = $true )
      | ( ( in @ SV428 @ ( powerset @ SV654 ) )
        = $true )
      | ( ( in @ SV654 @ ( powerset @ SV214 ) )
        = $false )
      | ( ( in @ SV428 @ ( powerset @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2854]) ).

thf(2983,plain,
    ! [SV214: $i,SV428: $i,SV654: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK98_Xx @ SV654 @ SV428 @ SV214 ) @ SV428 )
              | ~ ~ ( in @ ( sK98_Xx @ SV654 @ SV428 @ SV214 ) @ SV654 ) ) )
        = $true )
      | ( ( in @ SV428 @ ( powerset @ SV654 ) )
        = $true )
      | ( ( in @ SV654 @ ( powerset @ SV214 ) )
        = $false )
      | ( ( in @ SV428 @ ( powerset @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2855]) ).

thf(2984,plain,
    ! [SV215: $i,SV429: $i,SV655: $o] :
      ( ( ( ~ ( in @ ( sK31_B @ SV655 @ SV429 @ SV215 ) @ SV215 ) )
        = $false )
      | ( SV655 = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2856]) ).

thf(2985,plain,
    ! [SV215: $i,SV429: $i,SV655: $o] :
      ( ( ( ~ ~ SV655 )
        = $false )
      | ( SV655 = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2856]) ).

thf(2986,plain,
    ! [SV215: $i,SV429: $i] :
      ( ( ( ~ ( in @ ( sK31_B @ $true @ SV429 @ SV215 ) @ SV215 ) )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2857]) ).

thf(2987,plain,
    ! [SV215: $i,SV429: $i] :
      ( ( ( ~ ~ $true )
        = $false )
      | ( $true = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2857]) ).

thf(2988,plain,
    ! [SV215: $i,SV429: $i] :
      ( ( ( ~ ( in @ ( sK31_B @ $false @ SV429 @ SV215 ) @ SV215 ) )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2858]) ).

thf(2989,plain,
    ! [SV215: $i,SV429: $i] :
      ( ( ( ~ ~ $false )
        = $false )
      | ( $false = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2858]) ).

thf(2990,plain,
    ! [SV216: $i,SV430: $i] :
      ( ( ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV216 )
        = $false )
      | ( ( SV216 = SV430 )
        = $true )
      | ( ( in @ ( sK26_Xx @ SV430 @ SV216 ) @ SV216 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2860]) ).

thf(2991,plain,
    ! [SV216: $i,SV430: $i] :
      ( ( ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV430 )
        = $true )
      | ( ( SV216 = SV430 )
        = $true )
      | ( ( in @ ( sK26_Xx @ SV430 @ SV216 ) @ SV430 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2861]) ).

thf(2992,plain,
    ! [SV216: $i,SV430: $i] :
      ( ( ( ~ ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV216 ) )
        = $true )
      | ( ( SV216 = SV430 )
        = $true )
      | ( ( in @ ( sK26_Xx @ SV430 @ SV216 ) @ SV430 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2862]) ).

thf(2993,plain,
    ! [SV218: $i,SV432: $i,SV564: $i,SV704: $i] :
      ( ( ( ~ ( in @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) @ SV218 ) )
        = $false )
      | ( ( ! [SY2948: $i] :
              ( ~ ( in @ SY2948 @ SV218 )
              | ! [SY2949: $i] :
                  ( ~ ( in @ SY2949 @ SV432 )
                  | ~ ( in @ ( kpair @ SY2948 @ SY2949 ) @ SV704 )
                  | ( in @ ( kpair @ SY2948 @ SY2949 ) @ SV564 ) ) ) )
        = $true )
      | ( ( func @ SV218 @ SV432 @ SV704 )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV564 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2863]) ).

thf(2994,plain,
    ! [SV704: $i,SV564: $i,SV432: $i,SV218: $i] :
      ( ( ( ~ ( ( ( ap @ SV218 @ SV432 @ SV564 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) )
               != ( ap @ SV218 @ SV432 @ SV704 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) ) ) ) )
        = $false )
      | ( ( ! [SY2948: $i] :
              ( ~ ( in @ SY2948 @ SV218 )
              | ! [SY2949: $i] :
                  ( ~ ( in @ SY2949 @ SV432 )
                  | ~ ( in @ ( kpair @ SY2948 @ SY2949 ) @ SV704 )
                  | ( in @ ( kpair @ SY2948 @ SY2949 ) @ SV564 ) ) ) )
        = $true )
      | ( ( func @ SV218 @ SV432 @ SV704 )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV564 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2863]) ).

thf(2995,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
              | ~ ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
                    | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) ) )
          | ( SV433 = SV656 ) )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2864]) ).

thf(2996,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 )
              | ~ ~ ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 ) ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
              | ~ ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
                    | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) ) )
          | ( SV433 = SV656 ) )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2865]) ).

thf(2997,plain,
    ! [SV220: $i,SV434: $i > $o,SV565: $i] :
      ( ( ( in @ ( sK73_Xy @ SV565 @ SV434 @ SV220 ) @ SV220 )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV220
            @ ^ [SY2682: $i] : ( SV434 @ SY2682 ) ) )
        = $true )
      | ( ( SV434 @ SV565 )
        = $false )
      | ( ( in @ SV565 @ SV220 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2866]) ).

thf(2998,plain,
    ! [SV220: $i,SV565: $i,SV434: $i > $o] :
      ( ( ( ~ ( ~ ( SV434 @ ( sK73_Xy @ SV565 @ SV434 @ SV220 ) )
              | ~ ( ( ( sK73_Xy @ SV565 @ SV434 @ SV220 )
                   != SV565 ) ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV220
            @ ^ [SY2682: $i] : ( SV434 @ SY2682 ) ) )
        = $true )
      | ( ( SV434 @ SV565 )
        = $false )
      | ( ( in @ SV565 @ SV220 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2867]) ).

thf(2999,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ( in @ SV566 @ SV221 )
          | ~ ( in @ SV566 @ SV221 )
          | ! [SX3: $o] : SX3 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2868]) ).

thf(3000,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ ( ~ ( ( in @ SV566 @ SV221 )
                  | ( in @ SV566 @ SV435 )
                  | ! [SX3: $o] : SX3 )
              | ~ ( ( in @ SV566 @ SV221 )
                  | ! [SX3: $o] :
                      ( ~ SX3
                      | SX3 ) ) ) )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2869]) ).

thf(3001,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ ( ~ ( ~ ( in @ SV566 @ SV435 )
                  | ~ ( in @ SV566 @ SV221 )
                  | ! [SX3: $o] : SX3 )
              | ~ ~ ( ~ ( ~ ( in @ SV566 @ SV435 )
                        | ( in @ SV566 @ SV435 )
                        | ! [SX3: $o] : SX3 )
                    | ~ ( ~ ( in @ SV566 @ SV435 )
                        | ! [SX3: $o] :
                            ( ~ SX3
                            | SX3 ) ) ) ) )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2870]) ).

thf(3002,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ ( ~ ! [SY2839: $o] :
                    ( ~ SY2839
                    | ~ ( in @ SV566 @ SV221 )
                    | SY2839 )
              | ~ ~ ( ~ ! [SY2840: $o] :
                          ( ~ SY2840
                          | ( in @ SV566 @ SV435 )
                          | SY2840 )
                    | ~ ! [SX3: $o] :
                          ( ~ SX3
                          | ~ SX3
                          | SX3 ) ) ) )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2871]) ).

thf(3003,plain,
    ! [SV751: $i,SV223: $i,SV764: $i] :
      ( ( ( SV764 = SV223 )
        = $false )
      | ( ( in @ SV764 @ ( setadjoin @ SV223 @ SV751 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2872]) ).

thf(3004,plain,
    ! [SV223: $i,SV752: $i,SV765: $i] :
      ( ( ( in @ SV765 @ SV752 )
        = $false )
      | ( ( in @ SV765 @ ( setadjoin @ SV223 @ SV752 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2873]) ).

thf(3005,plain,
    ! [SV439: $i,SV226: $i,SV766: $i] :
      ( ( ( in @ SV766 @ ( binunion @ SV226 @ SV439 ) )
        = $false )
      | ( ( ( in @ SV766 @ SV226 )
          | ( in @ SV766 @ SV439 )
          | ! [SX3: $o] : SX3 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2874]) ).

thf(3006,plain,
    ! [SV439: $i,SV226: $i,SV767: $i] :
      ( ( ( in @ SV767 @ ( binunion @ SV226 @ SV439 ) )
        = $false )
      | ( ( ( in @ SV767 @ SV226 )
          | ! [SX3: $o] :
              ( ~ SX3
              | SX3 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2875]) ).

thf(3007,plain,
    ! [SV439: $i,SV226: $i,SV768: $i] :
      ( ( ( in @ SV768 @ ( binunion @ SV226 @ SV439 ) )
        = $false )
      | ( ( ! [SY2982: $o] :
              ( ~ SY2982
              | ( in @ SV768 @ SV439 )
              | SY2982 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2876]) ).

thf(3008,plain,
    ! [SV439: $i,SV226: $i,SV776: $i] :
      ( ( ( in @ SV776 @ ( binunion @ SV226 @ SV439 ) )
        = $false )
      | ( ( ! [SX2: $o] :
              ( ~ SX2
              | ~ SX2
              | SX2 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2877]) ).

thf(3009,plain,
    ! [SV568: $i,SV228: $i > $o] :
      ( ( ( ~ ! [SY2375: $i] :
                ( ~ ( SV228 @ SY2375 )
                | ( ( sK46_SY211 @ SV228 )
                  = SY2375 ) ) )
        = $false )
      | ( ( ( sK47_Xy @ SV568 @ SV228 )
          = SV568 )
        = $false )
      | ( ( SV228 @ ( sK47_Xy @ SV568 @ SV228 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2879]) ).

thf(3010,plain,
    ! [SV568: $i,SV228: $i > $o] :
      ( ( ( ~ ( SV228 @ ( sK46_SY211 @ SV228 ) ) )
        = $false )
      | ( ( ( sK47_Xy @ SV568 @ SV228 )
          = SV568 )
        = $false )
      | ( ( SV228 @ ( sK47_Xy @ SV568 @ SV228 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2879]) ).

thf(3011,plain,
    ! [SV568: $i,SV782: $i,SV228: $i > $o] :
      ( ( ( ~ ( SV228 @ SV782 )
          | ( ( sK46_SY211 @ SV228 )
            = SV782 ) )
        = $true )
      | ( ( SV228 @ ( sK47_Xy @ SV568 @ SV228 ) )
        = $true )
      | ( ( ( sK47_Xy @ SV568 @ SV228 )
          = SV568 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2880]) ).

thf(3012,plain,
    ! [SV441: $i > $o,SV229: $i,SV753: $i] :
      ( ( ( in @ SV753 @ SV229 )
        = $false )
      | ( ( SV441 @ SV753 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV229
            @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) )
        = $true )
      | ( ( in @ ( sK74_Xx @ SV441 @ SV229 ) @ SV229 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2882]) ).

thf(3013,plain,
    ! [SV229: $i,SV783: $i,SV441: $i > $o] :
      ( ( ( ~ ( SV441 @ SV783 )
          | ~ ( in @ SV783 @ SV229 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV229
            @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) )
        = $true )
      | ( ( in @ ( sK75_SY1878 @ SV441 @ SV229 ) @ SV229 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2883]) ).

thf(3014,plain,
    ! [SV229: $i,SV441: $i > $o] :
      ( ( ( ~ ( SV441 @ ( sK74_Xx @ SV441 @ SV229 ) ) )
        = $false )
      | ( ( ! [SY2705: $i] :
              ( ~ ( SV441 @ SY2705 )
              | ~ ( in @ SY2705 @ SV229 ) )
          | ( singleton
            @ ( dsetconstr @ SV229
              @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2884]) ).

thf(3015,plain,
    ! [SV229: $i,SV441: $i > $o] :
      ( ( ( ~ ~ ( ~ ( SV441 @ ( sK75_SY1878 @ SV441 @ SV229 ) )
                | ~ ( ( ( sK74_Xx @ SV441 @ SV229 )
                     != ( sK75_SY1878 @ SV441 @ SV229 ) ) ) ) )
        = $false )
      | ( ( ! [SY2705: $i] :
              ( ~ ( SV441 @ SY2705 )
              | ~ ( in @ SY2705 @ SV229 ) )
          | ( singleton
            @ ( dsetconstr @ SV229
              @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2884]) ).

thf(3016,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 ) )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
              | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                          | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
          | ( SV569 = SV706 ) )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2885]) ).

thf(3017,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                | ~ ~ ( ~ ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
                      | ~ ~ ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 ) ) ) )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
              | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                          | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
          | ( SV569 = SV706 ) )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2885]) ).

thf(3018,plain,
    ! [SV231: $i,SV784: $i] :
      ( ( ( ~ ( in @ SV784 @ omega )
          | ( in @ SV784 @ SV231 ) )
        = $true )
      | ( ( in @ ( sK9_Xx @ SV231 ) @ omega )
        = $true )
      | ( ( in @ emptyset @ SV231 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2886]) ).

thf(3019,plain,
    ! [SV231: $i,SV785: $i] :
      ( ( ( ~ ( in @ SV785 @ omega )
          | ( in @ SV785 @ SV231 ) )
        = $true )
      | ( ( in @ ( sK9_Xx @ SV231 ) @ SV231 )
        = $true )
      | ( ( in @ emptyset @ SV231 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2887]) ).

thf(3020,plain,
    ! [SV231: $i,SV769: $i] :
      ( ( ( in @ SV769 @ omega )
        = $false )
      | ( ( in @ SV769 @ SV231 )
        = $true )
      | ( ( in @ ( setadjoin @ ( sK9_Xx @ SV231 ) @ ( sK9_Xx @ SV231 ) ) @ SV231 )
        = $false )
      | ( ( in @ emptyset @ SV231 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2888]) ).

thf(3021,plain,
    ! [SV233: $i,SV658: $i,SV786: $i] :
      ( ( ( ~ ( in @ SV786 @ SV658 ) )
        = $true )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( ~ ( ~ ! [SY2925: $i] :
                    ( ~ ( in @ SY2925 @ ( sK15_B @ SV233 ) )
                    | ! [SY2926: $i] :
                        ( ~ ( in @ SY2926 @ SY2925 )
                        | ( in @ SY2926 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) )
                    | ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SY2925 ) )
              | ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) )
                          | ~ ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 ) )
                    | ~ ! [SY2927: $i] :
                          ( ~ ( in @ SY2927 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
                          | ~ ( in @ SY2927 @ SV658 ) ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2889]) ).

thf(3022,plain,
    ! [SV233: $i,SV658: $i] :
      ( ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 )
        = $false )
      | ( ( ! [SY2924: $i] :
              ~ ( in @ SY2924 @ SV658 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2925: $i] :
                    ( ~ ( in @ SY2925 @ ( sK15_B @ SV233 ) )
                    | ! [SY2926: $i] :
                        ( ~ ( in @ SY2926 @ SY2925 )
                        | ( in @ SY2926 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) )
                    | ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SY2925 ) )
              | ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) )
                          | ~ ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 ) )
                    | ~ ! [SY2927: $i] :
                          ( ~ ( in @ SY2927 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
                          | ~ ( in @ SY2927 @ SV658 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2890]) ).

thf(3023,plain,
    ! [SV770: $i,SV233: $i,SV754: $i] :
      ( ( ( ~ ( in @ SV754 @ ( sK15_B @ SV233 ) ) )
        = $true )
      | ( ( ~ ( in @ SV770 @ ( sK15_B @ SV233 ) ) )
        = $true )
      | ( ( ! [SY2983: $i] :
              ( ~ ( in @ SY2983 @ SV754 )
              | ( in @ SY2983 @ SV770 ) )
          | ! [SY2984: $i] :
              ( ~ ( in @ SY2984 @ SV770 )
              | ( in @ SY2984 @ SV754 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2891]) ).

thf(3024,plain,
    ! [SV233: $i,SV787: $i] :
      ( ( ~ ( in @ SV787 @ ( sK15_B @ SV233 ) )
        | ! [SY2988: $i] :
            ( ~ ( in @ SY2988 @ SV787 )
            | ( in @ SY2988 @ SV233 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2892]) ).

thf(3025,plain,
    ! [SV233: $i,SV788: $i] :
      ( ( ! [SY2989: $i] :
            ( ~ ( in @ SV788 @ SV233 )
            | ~ ( in @ SY2989 @ SV233 )
            | ~ ( ~ ( in @ ( sK16_SY1855 @ SY2989 @ SV788 @ SV233 ) @ ( sK15_B @ SV233 ) )
                | ~ ~ ( ~ ( ~ ( in @ SV788 @ ( sK16_SY1855 @ SY2989 @ SV788 @ SV233 ) )
                          | ~ ( in @ SY2989 @ ( sK16_SY1855 @ SY2989 @ SV788 @ SV233 ) ) )
                      | ~ ( ( in @ SV788 @ ( sK16_SY1855 @ SY2989 @ SV788 @ SV233 ) )
                          | ( in @ SY2989 @ ( sK16_SY1855 @ SY2989 @ SV788 @ SV233 ) ) ) ) )
            | ( SV788 = SY2989 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2893]) ).

thf(3026,plain,
    ! [SV573: $i,SV235: $i > $o] :
      ( ( ( ! [SY2403: $i] :
              ( ( SY2403
               != ( sK32_Xx @ SV235 ) )
              | ( SV235 @ SY2403 ) ) )
        = $true )
      | ( ( SV235 @ ( sK33_SY142 @ SV573 @ SV235 ) )
        = $true )
      | ( ( SV235 @ SV573 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2896]) ).

thf(3027,plain,
    ! [SV573: $i,SV235: $i > $o] :
      ( ( ( ! [SY2404: $i] :
              ( ~ ( SV235 @ SY2404 )
              | ( SY2404
                = ( sK32_Xx @ SV235 ) ) ) )
        = $true )
      | ( ( SV235 @ ( sK33_SY142 @ SV573 @ SV235 ) )
        = $true )
      | ( ( SV235 @ SV573 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2897]) ).

thf(3028,plain,
    ! [SV573: $i,SV235: $i > $o] :
      ( ( ( ~ ! [SY2403: $i] :
                ( ( SY2403
                 != ( sK32_Xx @ SV235 ) )
                | ( SV235 @ SY2403 ) ) )
        = $false )
      | ( ( SV573
          = ( sK33_SY142 @ SV573 @ SV235 ) )
        = $false )
      | ( ( SV235 @ SV573 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2898]) ).

thf(3029,plain,
    ! [SV573: $i,SV235: $i > $o] :
      ( ( ( ~ ! [SY2404: $i] :
                ( ~ ( SV235 @ SY2404 )
                | ( SY2404
                  = ( sK32_Xx @ SV235 ) ) ) )
        = $false )
      | ( ( SV573
          = ( sK33_SY142 @ SV573 @ SV235 ) )
        = $false )
      | ( ( SV235 @ SV573 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2898]) ).

thf(3030,plain,
    ! [SV236: $i,SV445: $i,SV710: $i > $o,SV574: $i,SV789: $i] :
      ( ( ( ~ ( in @ SV789 @ SV574 )
          | ( SV710 @ SV789 ) )
        = $true )
      | ( ( in @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ SV236 )
        = $true )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2899]) ).

thf(3031,plain,
    ! [SV236: $i,SV445: $i,SV574: $i,SV710: $i > $o] :
      ( ( ( ~ ( in @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) @ SV445 )
          | ~ ~ ( ~ ( in @ ( kpair @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) ) @ SV574 )
                | ~ ~ ( SV710 @ ( kpair @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) ) ) ) )
        = $false )
      | ( ( ! [SY2953: $i] :
              ( ~ ( in @ SY2953 @ SV574 )
              | ( SV710 @ SY2953 ) ) )
        = $true )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2900]) ).

thf(3032,plain,
    ! [SV578: $i,SV239: $i,SV755: $i] :
      ( ( ( in @ SV755 @ SV239 )
        = $false )
      | ( ( in @ SV755 @ ( sK14_B @ SV239 ) )
        = $false )
      | ( ( in @ SV578 @ SV239 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2905]) ).

thf(3033,plain,
    ! [SV582: $i,SV241: $i > $o] :
      ( ( ( ! [SY2422: $i] :
              ( ~ ( SV241 @ SY2422 )
              | ( ( sK43_SY205 @ SV241 )
                = SY2422 ) ) )
        = $true )
      | ( ( SV241 @ ( sK44_Xx @ SV241 ) )
        = $true )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2906]) ).

thf(3034,plain,
    ! [SV582: $i,SV241: $i > $o] :
      ( ( ( SV241 @ ( sK43_SY205 @ SV241 ) )
        = $true )
      | ( ( SV241 @ ( sK44_Xx @ SV241 ) )
        = $true )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2907]) ).

thf(3035,plain,
    ! [SV582: $i,SV241: $i > $o] :
      ( ( ( SV241 @ ( sK45_SY1868 @ SV241 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2422: $i] :
                    ( ~ ( SV241 @ SY2422 )
                    | ( ( sK43_SY205 @ SV241 )
                      = SY2422 ) )
              | ~ ( SV241 @ ( sK43_SY205 @ SV241 ) ) ) )
        = $true )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2908]) ).

thf(3036,plain,
    ! [SV582: $i,SV241: $i > $o] :
      ( ( ( ( sK44_Xx @ SV241 )
         != ( sK45_SY1868 @ SV241 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2422: $i] :
                    ( ~ ( SV241 @ SY2422 )
                    | ( ( sK43_SY205 @ SV241 )
                      = SY2422 ) )
              | ~ ( SV241 @ ( sK43_SY205 @ SV241 ) ) ) )
        = $true )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2909]) ).

thf(3037,plain,
    ! [SV243: $i,SV450: $i,SV583: $i,SV717: $i] :
      ( ( ( ~ ( in @ ( sK90_Xx @ SV717 @ SV583 @ SV450 @ SV243 ) @ SV243 ) )
        = $false )
      | ( ( SV583 = SV717 )
        = $true )
      | ( ( func @ SV243 @ SV450 @ SV717 )
        = $false )
      | ( ( func @ SV243 @ SV450 @ SV583 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2913]) ).

thf(3038,plain,
    ! [SV717: $i,SV583: $i,SV450: $i,SV243: $i] :
      ( ( ( ~ ( ( ( ap @ SV243 @ SV450 @ SV583 @ ( sK90_Xx @ SV717 @ SV583 @ SV450 @ SV243 ) )
               != ( ap @ SV243 @ SV450 @ SV717 @ ( sK90_Xx @ SV717 @ SV583 @ SV450 @ SV243 ) ) ) ) )
        = $false )
      | ( ( SV583 = SV717 )
        = $true )
      | ( ( func @ SV243 @ SV450 @ SV717 )
        = $false )
      | ( ( func @ SV243 @ SV450 @ SV583 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2913]) ).

thf(3039,plain,
    ! [SV245: $i,SV451: $i,SV585: $i,SV718: $i] :
      ( ( ( ~ ( in @ ( sK91_Xx @ SV718 @ SV585 @ SV451 @ SV245 ) @ SV245 ) )
        = $false )
      | ( ( SV585 = SV718 )
        = $true )
      | ( ( in @ SV718 @ ( funcSet @ SV245 @ SV451 ) )
        = $false )
      | ( ( in @ SV585 @ ( funcSet @ SV245 @ SV451 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2914]) ).

thf(3040,plain,
    ! [SV718: $i,SV585: $i,SV451: $i,SV245: $i] :
      ( ( ( ~ ( ( ( ap @ SV245 @ SV451 @ SV585 @ ( sK91_Xx @ SV718 @ SV585 @ SV451 @ SV245 ) )
               != ( ap @ SV245 @ SV451 @ SV718 @ ( sK91_Xx @ SV718 @ SV585 @ SV451 @ SV245 ) ) ) ) )
        = $false )
      | ( ( SV585 = SV718 )
        = $true )
      | ( ( in @ SV718 @ ( funcSet @ SV245 @ SV451 ) )
        = $false )
      | ( ( in @ SV585 @ ( funcSet @ SV245 @ SV451 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2914]) ).

thf(3041,plain,
    ! [SV586: $i,SV247: $i > $o] :
      ( ( ( ! [SY2435: $i] :
              ( ~ ( SV247 @ SY2435 )
              | ( ( sK21_Xx @ SV247 )
                = SY2435 ) ) )
        = $true )
      | ( ( SV247 @ ( sK22_SY74 @ SV586 @ SV247 ) )
        = $true )
      | ( ( SV247 @ SV586 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2917]) ).

thf(3042,plain,
    ! [SV586: $i,SV247: $i > $o] :
      ( ( ( SV247 @ ( sK21_Xx @ SV247 ) )
        = $true )
      | ( ( SV247 @ ( sK22_SY74 @ SV586 @ SV247 ) )
        = $true )
      | ( ( SV247 @ SV586 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2918]) ).

thf(3043,plain,
    ! [SV586: $i,SV247: $i > $o] :
      ( ( ( ~ ! [SY2435: $i] :
                ( ~ ( SV247 @ SY2435 )
                | ( ( sK21_Xx @ SV247 )
                  = SY2435 ) ) )
        = $false )
      | ( ( SV586
          = ( sK22_SY74 @ SV586 @ SV247 ) )
        = $false )
      | ( ( SV247 @ SV586 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2919]) ).

thf(3044,plain,
    ! [SV586: $i,SV247: $i > $o] :
      ( ( ( ~ ( SV247 @ ( sK21_Xx @ SV247 ) ) )
        = $false )
      | ( ( SV586
          = ( sK22_SY74 @ SV586 @ SV247 ) )
        = $false )
      | ( ( SV247 @ SV586 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2919]) ).

thf(3045,plain,
    ! [SV248: $i,SV453: $i,SV661: $i > $o,SV719: $i > $o] :
      ( ( ( ~ ( in @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) @ SV453 )
          | ~ ~ ( ( ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 )
                 != ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) )
                | ~ ~ ( ~ ( ~ ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
                          | ~ ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) )
                      | ~ ( ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
                          | ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) ) ) ) )
        = $false )
      | ( ( ( dsetconstr @ SV248
            @ ^ [SY2930: $i] : ( SV661 @ SY2930 ) )
          = ( dsetconstr @ SV453
            @ ^ [SY2961: $i] : ( SV719 @ SY2961 ) ) )
        = $true )
      | ( ( SV248 = SV453 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2921]) ).

thf(3046,plain,
    ! [SV733: $i,SV612: $i,SV250: $i,SV1: $i,SV777: $i] :
      ( ( ( ~ ( in @ SV777 @ SV1 ) )
        = $true )
      | ( ( ~ ( in @ SV777 @ ( binintersect @ SV250 @ SV612 ) )
          | ( in @ SV777 @ ( binunion @ SV250 @ SV733 ) ) )
        = $true )
      | ( ( in @ SV733 @ ( powerset @ SV1 ) )
        = $false )
      | ( ( in @ SV612 @ ( powerset @ SV1 ) )
        = $false )
      | ( ( in @ SV250 @ ( powerset @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2922]) ).

thf(3047,plain,
    ! [SV2: $i,SV251: $i,SV613: $i,SV734: $i] :
      ( ( ( in @ SV734 @ SV613 )
        = $false )
      | ( ( in @ SV734 @ ( binunion @ SV251 @ SV613 ) )
        = $true )
      | ( ( in @ SV734 @ SV2 )
        = $false )
      | ( ( in @ SV613 @ ( powerset @ SV2 ) )
        = $false )
      | ( ( in @ SV251 @ ( powerset @ SV2 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2923]) ).

thf(3048,plain,
    ! [SV3: $i,SV614: $i,SV252: $i,SV735: $i] :
      ( ( ( in @ SV735 @ SV252 )
        = $false )
      | ( ( in @ SV735 @ ( binunion @ SV252 @ SV614 ) )
        = $true )
      | ( ( in @ SV735 @ SV3 )
        = $false )
      | ( ( in @ SV614 @ ( powerset @ SV3 ) )
        = $false )
      | ( ( in @ SV252 @ ( powerset @ SV3 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2924]) ).

thf(3049,plain,
    ! [SV254: $i,SV616: $i,SV5: $i,SV771: $i] :
      ( ( ( in @ SV771 @ SV5 )
        = $false )
      | ( ( ~ ( in @ SV771 @ SV616 )
          | ( in @ SV771 @ ( setminus @ SV5 @ SV254 ) ) )
        = $true )
      | ( ( subset @ SV254 @ ( setminus @ SV5 @ SV616 ) )
        = $false )
      | ( ( in @ SV616 @ ( powerset @ SV5 ) )
        = $false )
      | ( ( in @ SV254 @ ( powerset @ SV5 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2925]) ).

thf(3050,plain,
    ! [SV619: $i,SV257: $i,SV8: $i,SV736: $i] :
      ( ( ( in @ SV736 @ ( setminus @ SV8 @ SV257 ) )
        = $false )
      | ( ( in @ SV736 @ ( setminus @ SV8 @ ( binintersect @ SV257 @ SV619 ) ) )
        = $true )
      | ( ( in @ SV736 @ SV8 )
        = $false )
      | ( ( in @ SV619 @ ( powerset @ SV8 ) )
        = $false )
      | ( ( in @ SV257 @ ( powerset @ SV8 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2926]) ).

thf(3051,plain,
    ! [SV620: $i,SV258: $i,SV9: $i,SV737: $i] :
      ( ( ( in @ SV737 @ ( setminus @ SV9 @ SV258 ) )
        = $false )
      | ( ( ~ ( in @ SV737 @ ( binintersect @ SV258 @ SV620 ) ) )
        = $true )
      | ( ( in @ SV737 @ SV9 )
        = $false )
      | ( ( in @ SV620 @ ( powerset @ SV9 ) )
        = $false )
      | ( ( in @ SV258 @ ( powerset @ SV9 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2927]) ).

thf(3052,plain,
    ! [SV17: $i,SV738: $i,SV625: $i,SV266: $i] :
      ( ( ( subset @ SV266 @ SV625 )
        = $false )
      | ( ( ( in @ SV738 @ SV625 )
          | ~ ( in @ SV738 @ SV266 ) )
        = $true )
      | ( ( in @ SV738 @ SV17 )
        = $false )
      | ( ( in @ SV625 @ ( powerset @ SV17 ) )
        = $false )
      | ( ( in @ SV266 @ ( powerset @ SV17 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2928]) ).

thf(3053,plain,
    ! [SV739: $i,SV626: $i,SV18: $i,SV267: $i] :
      ( ( ( subset @ SV267 @ ( setminus @ SV18 @ SV626 ) )
        = $false )
      | ( ( ~ ( in @ SV739 @ SV626 )
          | ~ ( in @ SV739 @ SV267 ) )
        = $true )
      | ( ( in @ SV739 @ SV18 )
        = $false )
      | ( ( in @ SV626 @ ( powerset @ SV18 ) )
        = $false )
      | ( ( in @ SV267 @ ( powerset @ SV18 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2929]) ).

thf(3054,plain,
    ! [SV19: $i,SV627: $i,SV268: $i,SV740: $i] :
      ( ( ( in @ SV740 @ ( binintersect @ SV268 @ SV627 ) )
        = $false )
      | ( ( in @ SV740 @ SV627 )
        = $true )
      | ( ( in @ SV740 @ SV19 )
        = $false )
      | ( ( in @ SV627 @ ( powerset @ SV19 ) )
        = $false )
      | ( ( in @ SV268 @ ( powerset @ SV19 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2930]) ).

thf(3055,plain,
    ! [SV20: $i,SV628: $i,SV269: $i,SV741: $i] :
      ( ( ( in @ SV741 @ ( binintersect @ SV269 @ SV628 ) )
        = $false )
      | ( ( in @ SV741 @ SV269 )
        = $true )
      | ( ( in @ SV741 @ SV20 )
        = $false )
      | ( ( in @ SV628 @ ( powerset @ SV20 ) )
        = $false )
      | ( ( in @ SV269 @ ( powerset @ SV20 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2931]) ).

thf(3056,plain,
    ! [SV23: $i,SV742: $i,SV631: $i,SV272: $i] :
      ( ( ( in @ SV272 @ ( powerset @ SV631 ) )
        = $false )
      | ( ( ~ ( in @ SV742 @ SV272 )
          | ( in @ SV742 @ SV631 ) )
        = $true )
      | ( ( in @ SV742 @ SV23 )
        = $false )
      | ( ( in @ SV631 @ ( powerset @ SV23 ) )
        = $false )
      | ( ( in @ SV272 @ ( powerset @ SV23 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2932]) ).

thf(3057,plain,
    ! [SV284: $i,SV38: $i,SV471: $i,SV756: $i,SV674: $i] :
      ( ( ( ~ ( in @ ( kpair @ SV674 @ SV756 ) @ SV471 ) )
        = $true )
      | ( ( ( ap @ SV38 @ SV284 @ SV471 @ SV674 )
          = SV756 )
        = $true )
      | ( ( in @ SV756 @ SV284 )
        = $false )
      | ( ( in @ SV674 @ SV38 )
        = $false )
      | ( ( in @ SV471 @ ( funcSet @ SV38 @ SV284 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2933]) ).

thf(3058,plain,
    ! [SV285: $i,SV39: $i,SV472: $i,SV757: $i,SV675: $i] :
      ( ( ( ~ ( in @ ( kpair @ SV675 @ SV757 ) @ SV472 ) )
        = $true )
      | ( ( ( ap @ SV39 @ SV285 @ SV472 @ SV675 )
          = SV757 )
        = $true )
      | ( ( in @ SV757 @ SV285 )
        = $false )
      | ( ( in @ SV675 @ SV39 )
        = $false )
      | ( ( func @ SV39 @ SV285 @ SV472 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2934]) ).

thf(3059,plain,
    ! [SV42: $i,SV743: $i,SV635: $i,SV288: $i > $o] :
      ( ( ( SV288 @ SV635 )
        = $false )
      | ( ( ~ ( SV288 @ SV743 )
          | ( SV635 = SV743 ) )
        = $true )
      | ( ( in @ SV743 @ SV42 )
        = $false )
      | ( ( in @ SV635 @ SV42 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV42
            @ ^ [SY2500: $i] : ( SV288 @ SY2500 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2935]) ).

thf(3060,plain,
    ! [SV189: $i,SV409: $i,SV647: $i] :
      ( ( ( ~ ( in @ ( sK97_Xx @ SV647 @ SV409 @ SV189 ) @ SV409 )
          | ~ ~ ( in @ ( sK97_Xx @ SV647 @ SV409 @ SV189 ) @ SV647 ) )
        = $false )
      | ( ( subset @ SV409 @ SV647 )
        = $true )
      | ( ( in @ SV647 @ ( powerset @ SV189 ) )
        = $false )
      | ( ( in @ SV409 @ ( powerset @ SV189 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2939]) ).

thf(3061,plain,
    ! [SV551: $i,SV759: $i,SV790: $i,SV194: $i > $o] :
      ( ( ( ~ ( SV194 @ SV790 )
          | ( SV759 = SV790 ) )
        = $true )
      | ( ( SV194 @ SV759 )
        = $false )
      | ( ( SV194 @ ( sK57_SY248 @ SV551 @ SV194 ) )
        = $true )
      | ( ( SV194 @ SV551 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2943]) ).

thf(3062,plain,
    ! [SV551: $i,SV772: $i,SV194: $i > $o] :
      ( ( ( SV194 @ SV772 )
        = $false )
      | ( ( ! [SY2985: $i] :
              ( ~ ( SV194 @ SY2985 )
              | ( SV772 = SY2985 ) ) )
        = $true )
      | ( ( SV551
          = ( sK57_SY248 @ SV551 @ SV194 ) )
        = $false )
      | ( ( SV194 @ SV551 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2944]) ).

thf(3063,plain,
    ! [SV413: $i,SV773: $i,SV791: $i,SV195: $i > $i > $o] :
      ( ( ( ~ ( SV195 @ SV791 @ SV773 )
          | ~ ( in @ SV791 @ SV413 ) )
        = $true )
      | ( ( in @ SV773 @ ( sK10_B @ SV413 @ SV195 ) )
        = $true )
      | ( ( in @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV413 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2945]) ).

thf(3064,plain,
    ! [SV195: $i > $i > $o,SV413: $i,SV774: $i] :
      ( ( ( in @ SV774 @ ( sK10_B @ SV413 @ SV195 ) )
        = $false )
      | ( ( ~ ( ~ ( SV195 @ ( sK11_Xy @ SV774 @ SV413 @ SV195 ) @ SV774 )
              | ~ ( in @ ( sK11_Xy @ SV774 @ SV413 @ SV195 ) @ SV413 ) ) )
        = $true )
      | ( ( in @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV413 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2946]) ).

thf(3065,plain,
    ! [SV725: $i,SV413: $i,SV195: $i > $i > $o] :
      ( ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2639: $i] :
                    ( ! [SY2640: $i] :
                        ( ~ ( SV195 @ SY2640 @ SY2639 )
                        | ~ ( in @ SY2640 @ SV413 ) )
                    | ( in @ SY2639 @ ( sK10_B @ SV413 @ SV195 ) ) )
              | ~ ! [SY2641: $i] :
                    ( ~ ( in @ SY2641 @ ( sK10_B @ SV413 @ SV195 ) )
                    | ~ ( ~ ( SV195 @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SY2641 )
                        | ~ ( in @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SV413 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2947]) ).

thf(3066,plain,
    ! [SV195: $i > $i > $o,SV413: $i,SV725: $i] :
      ( ( ( SV725
          = ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $false )
      | ( ( ~ ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2639: $i] :
                    ( ! [SY2640: $i] :
                        ( ~ ( SV195 @ SY2640 @ SY2639 )
                        | ~ ( in @ SY2640 @ SV413 ) )
                    | ( in @ SY2639 @ ( sK10_B @ SV413 @ SV195 ) ) )
              | ~ ! [SY2641: $i] :
                    ( ~ ( in @ SY2641 @ ( sK10_B @ SV413 @ SV195 ) )
                    | ~ ( ~ ( SV195 @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SY2641 )
                        | ~ ( in @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SV413 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2948]) ).

thf(3067,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( ( SV552 = SV196 )
        = $true )
      | ( ( ( in @ SV552 @ SV414 )
          | ! [SX3: $o] : SX3 )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2949]) ).

thf(3068,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( ( SV552 = SV196 )
        = $true )
      | ( ( ! [SX3: $o] :
              ( ~ SX3
              | SX3 ) )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2950]) ).

thf(3069,plain,
    ! [SV196: $i,SV414: $i,SV552: $i,SV792: $o] :
      ( ( ( ~ SV792
          | ( in @ SV552 @ SV414 )
          | SV792 )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[2951]) ).

thf(3070,plain,
    ! [SV196: $i,SV414: $i,SV552: $i] :
      ( ( ( ~ $true
          | ( in @ SV552 @ SV414 )
          | $true )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[2951]) ).

thf(3071,plain,
    ! [SV196: $i,SV414: $i,SV552: $i] :
      ( ( ( ~ $false
          | ( in @ SV552 @ SV414 )
          | $false )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[2951]) ).

thf(3072,plain,
    ! [SV414: $i,SV196: $i,SV552: $i,SV793: $o] :
      ( ( ( ~ SV793
          | ~ SV793
          | SV793 )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[2952]) ).

thf(3073,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( ( ~ $true
          | ~ $true
          | $true )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[2952]) ).

thf(3074,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( ( ~ $false
          | ~ $false
          | $false )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[2952]) ).

thf(3075,plain,
    ! [SV652: $i > $o,SV778: $i,SV605: $i > $o] :
      ( ( ( ~ ( ~ ( SV605 @ ( sK54_SY233 @ SV778 @ SV652 @ SV605 ) )
              | ~ ( ( SV778
                   != ( sK54_SY233 @ SV778 @ SV652 @ SV605 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV605 @ SV778 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( ( sK55_Xx @ SV652 @ SV605 )
          = ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2953]) ).

thf(3076,plain,
    ! [SV652: $i > $o,SV605: $i > $o] :
      ( ( ( ~ ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
          | ~ ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) ) )
        = $true )
      | ( ( ! [SY2919: $i] :
              ( ~ ( ~ ( SV605 @ ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) )
                  | ~ ( ( SY2919
                       != ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) ) ) )
              | ~ ( SV605 @ SY2919 ) )
          | ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2954]) ).

thf(3077,plain,
    ! [SV652: $i > $o,SV605: $i > $o] :
      ( ( ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
          | ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) ) )
        = $true )
      | ( ( ! [SY2919: $i] :
              ( ~ ( ~ ( SV605 @ ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) )
                  | ~ ( ( SY2919
                       != ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) ) ) )
              | ~ ( SV605 @ SY2919 ) )
          | ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2955]) ).

thf(3078,plain,
    ! [SV606: $i > $o,SV779: $i,SV653: $i > $o] :
      ( ( ( ~ ( ~ ( SV653 @ ( sK50_SY236 @ SV779 @ SV653 @ SV606 ) )
              | ~ ( ( SV779
                   != ( sK50_SY236 @ SV779 @ SV653 @ SV606 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV653 @ SV779 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( ( sK51_Xx @ SV653 @ SV606 )
          = ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2956]) ).

thf(3079,plain,
    ! [SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ~ ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
          | ~ ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) ) )
        = $true )
      | ( ( ! [SY2921: $i] :
              ( ~ ( ~ ( SV653 @ ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) )
                  | ~ ( ( SY2921
                       != ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) ) ) )
              | ~ ( SV653 @ SY2921 ) )
          | ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2957]) ).

thf(3080,plain,
    ! [SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
          | ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) ) )
        = $true )
      | ( ( ! [SY2921: $i] :
              ( ~ ( ~ ( SV653 @ ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) )
                  | ~ ( ( SY2921
                       != ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) ) ) )
              | ~ ( SV653 @ SY2921 ) )
          | ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2958]) ).

thf(3081,plain,
    ! [SV558: $i,SV794: $i,SV205: $i > $o] :
      ( ( ( ~ ( SV205 @ SV794 )
          | ( ( sK41_SY198 @ SV205 )
            = SV794 ) )
        = $true )
      | ( ( SV205 @ ( sK42_Xy @ SV558 @ SV205 ) )
        = $true )
      | ( ( SV205 @ SV558 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2959]) ).

thf(3082,plain,
    ! [SV558: $i,SV205: $i > $o] :
      ( ( ( ! [SY2293: $i] :
              ( ~ ( SV205 @ SY2293 )
              | ( ( sK41_SY198 @ SV205 )
                = SY2293 ) ) )
        = $true )
      | ( ( SV558
          = ( sK42_Xy @ SV558 @ SV205 ) )
        = $false )
      | ( ( SV205 @ SV558 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2961]) ).

thf(3083,plain,
    ! [SV558: $i,SV205: $i > $o] :
      ( ( ( SV205 @ ( sK41_SY198 @ SV205 ) )
        = $true )
      | ( ( SV558
          = ( sK42_Xy @ SV558 @ SV205 ) )
        = $false )
      | ( ( SV205 @ SV558 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2962]) ).

thf(3084,plain,
    ( ( in @ sK5_SY1831 @ sK1_A )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2964]) ).

thf(3085,plain,
    ( ( ~ ( ~ ( in @ sK5_SY1831 @ ( binintersect @ sK2_SY1822 @ sK3_SY1826 ) )
          | ~ ~ ( in @ sK5_SY1831 @ ( binunion @ sK3_SY1826 @ sK4_SY1829 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[2965]) ).

thf(3086,plain,
    ! [SV207: $i,SV422: $i,SV702: $i > $o,SV560: $i,SV780: $i] :
      ( ( ( ~ ( in @ SV780 @ SV560 ) )
        = $true )
      | ( ( SV702 @ SV780 )
        = $true )
      | ( ( in @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ SV207 )
        = $true )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2966]) ).

thf(3087,plain,
    ! [SV207: $i,SV422: $i,SV560: $i,SV702: $i > $o] :
      ( ( ( ~ ( in @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) @ SV422 ) )
        = $false )
      | ( ( ! [SY2947: $i] :
              ( ~ ( in @ SY2947 @ SV560 )
              | ( SV702 @ SY2947 ) ) )
        = $true )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2967]) ).

thf(3088,plain,
    ! [SV207: $i,SV422: $i,SV560: $i,SV702: $i > $o] :
      ( ( ( ~ ~ ( ~ ( in @ ( kpair @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) ) @ SV560 )
                | ~ ~ ( SV702 @ ( kpair @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) ) ) ) )
        = $false )
      | ( ( ! [SY2947: $i] :
              ( ~ ( in @ SY2947 @ SV560 )
              | ( SV702 @ SY2947 ) ) )
        = $true )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2967]) ).

thf(3089,plain,
    ! [SV208: $i,SV423: $i,SV561: $i,SV703: $i] :
      ( ( ( in @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ SV208 )
        = $true )
      | ( ( subset @ SV561 @ SV703 )
        = $true )
      | ( ( subset @ SV703 @ ( cartprod @ SV208 @ SV423 ) )
        = $false )
      | ( ( subset @ SV561 @ ( cartprod @ SV208 @ SV423 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2968]) ).

thf(3090,plain,
    ! [SV208: $i,SV423: $i,SV561: $i,SV703: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) @ SV423 )
              | ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) ) @ SV561 )
                    | ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) ) @ SV703 ) ) ) )
        = $true )
      | ( ( subset @ SV561 @ SV703 )
        = $true )
      | ( ( subset @ SV703 @ ( cartprod @ SV208 @ SV423 ) )
        = $false )
      | ( ( subset @ SV561 @ ( cartprod @ SV208 @ SV423 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2969]) ).

thf(3091,plain,
    ! [SV209: $i,SV781: $i,SV424: $i > $o] :
      ( ( ( ~ ( SV424 @ SV781 ) )
        = $true )
      | ( ( ~ ( in @ SV781 @ SV209 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV209
            @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) )
        = $true )
      | ( ( in @ ( sK71_SY1877 @ SV424 @ SV209 ) @ SV209 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2971]) ).

thf(3092,plain,
    ! [SV209: $i,SV424: $i > $o] :
      ( ( ( SV424 @ ( sK70_Xx @ SV424 @ SV209 ) )
        = $true )
      | ( ( ! [SY2662: $i] :
              ( ~ ( SV424 @ SY2662 )
              | ~ ( in @ SY2662 @ SV209 ) )
          | ( singleton
            @ ( dsetconstr @ SV209
              @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2972]) ).

thf(3093,plain,
    ! [SV209: $i,SV424: $i > $o] :
      ( ( ( ~ ( ~ ( SV424 @ ( sK71_SY1877 @ SV424 @ SV209 ) )
              | ~ ( ( ( sK70_Xx @ SV424 @ SV209 )
                   != ( sK71_SY1877 @ SV424 @ SV209 ) ) ) ) )
        = $true )
      | ( ( ! [SY2662: $i] :
              ( ~ ( SV424 @ SY2662 )
              | ~ ( in @ SY2662 @ SV209 ) )
          | ( singleton
            @ ( dsetconstr @ SV209
              @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2973]) ).

thf(3094,plain,
    ! [SV425: $i,SV761: $i,SV210: $i,SV748: $i] :
      ( ( ( ~ ( in @ SV748 @ SV210 ) )
        = $true )
      | ( ( in @ SV761 @ SV425 )
        = $true )
      | ( ( SV748 = SV761 )
        = $false )
      | ( ( SV210 = SV425 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2974]) ).

thf(3095,plain,
    ! [SV210: $i,SV749: $i,SV425: $i,SV762: $i] :
      ( ( ( ~ ( in @ SV762 @ SV425 ) )
        = $true )
      | ( ( in @ SV749 @ SV210 )
        = $true )
      | ( ( SV749 = SV762 )
        = $false )
      | ( ( SV210 = SV425 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2975]) ).

thf(3096,plain,
    ! [SV562: $i,SV763: $i,SV795: $i,SV211: $i > $o] :
      ( ( ( ~ ( SV211 @ SV795 )
          | ( SV763 = SV795 ) )
        = $true )
      | ( ( SV211 @ SV763 )
        = $false )
      | ( ( SV211 @ ( sK48_SY224 @ SV562 @ SV211 ) )
        = $true )
      | ( ( SV211 @ SV562 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2976]) ).

thf(3097,plain,
    ! [SV562: $i,SV775: $i,SV211: $i > $o] :
      ( ( ( SV211 @ SV775 )
        = $false )
      | ( ( ! [SY2987: $i] :
              ( ~ ( SV211 @ SY2987 )
              | ( SV775 = SY2987 ) ) )
        = $true )
      | ( ( SV562
          = ( sK48_SY224 @ SV562 @ SV211 ) )
        = $false )
      | ( ( SV211 @ SV562 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2977]) ).

thf(3098,plain,
    ! [SV427: $i > $o,SV750: $i,SV213: $i > $o] :
      ( ( ( SV213 @ ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
        = $true )
      | ( ( ~ ( SV213 @ SV750 ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2978]) ).

thf(3099,plain,
    ! [SV213: $i > $o,SV427: $i > $o,SV750: $i] :
      ( ( ( SV750
         != ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
        = $true )
      | ( ( ~ ( SV213 @ SV750 ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2979]) ).

thf(3100,plain,
    ! [SV213: $i > $o,SV427: $i > $o] :
      ( ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( ! [SY2670: $i] :
              ( ~ ( ~ ( SV213 @ ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2670
                       != ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV213 @ SY2670 ) )
          | ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2980]) ).

thf(3101,plain,
    ! [SV427: $i > $o,SV796: $i,SV213: $i > $o] :
      ( ( ( ~ ( ~ ( SV213 @ ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
              | ~ ( ( SV796
                   != ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) ) ) )
          | ~ ( SV213 @ SV796 ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[2981]) ).

thf(3102,plain,
    ! [SV214: $i,SV428: $i,SV654: $i] :
      ( ( ( ~ ( in @ ( sK98_Xx @ SV654 @ SV428 @ SV214 ) @ SV428 )
          | ~ ~ ( in @ ( sK98_Xx @ SV654 @ SV428 @ SV214 ) @ SV654 ) )
        = $false )
      | ( ( in @ SV428 @ ( powerset @ SV654 ) )
        = $true )
      | ( ( in @ SV654 @ ( powerset @ SV214 ) )
        = $false )
      | ( ( in @ SV428 @ ( powerset @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2983]) ).

thf(3103,plain,
    ! [SV215: $i,SV429: $i,SV655: $o] :
      ( ( ( in @ ( sK31_B @ SV655 @ SV429 @ SV215 ) @ SV215 )
        = $true )
      | ( SV655 = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2984]) ).

thf(3104,plain,
    ! [SV215: $i,SV429: $i,SV655: $o] :
      ( ( ( ~ SV655 ) = $true )
      | ( SV655 = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2985]) ).

thf(3105,plain,
    ! [SV215: $i,SV429: $i] :
      ( ( ( in @ ( sK31_B @ $true @ SV429 @ SV215 ) @ SV215 )
        = $true )
      | ( $true = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2986]) ).

thf(3106,plain,
    ! [SV215: $i,SV429: $i] :
      ( ( ( ~ $true ) = $true )
      | ( $true = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2987]) ).

thf(3107,plain,
    ! [SV215: $i,SV429: $i] :
      ( ( ( in @ ( sK31_B @ $false @ SV429 @ SV215 ) @ SV215 )
        = $true )
      | ( $false = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2988]) ).

thf(3108,plain,
    ! [SV215: $i,SV429: $i] :
      ( ( ( ~ $false ) = $true )
      | ( $false = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2989]) ).

thf(3109,plain,
    ! [SV216: $i,SV430: $i] :
      ( ( ( in @ ( sK25_Xx @ SV430 @ SV216 ) @ SV216 )
        = $false )
      | ( ( SV216 = SV430 )
        = $true )
      | ( ( in @ ( sK26_Xx @ SV430 @ SV216 ) @ SV430 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2992]) ).

thf(3110,plain,
    ! [SV218: $i,SV432: $i,SV564: $i,SV704: $i] :
      ( ( ( in @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) @ SV218 )
        = $true )
      | ( ( ! [SY2948: $i] :
              ( ~ ( in @ SY2948 @ SV218 )
              | ! [SY2949: $i] :
                  ( ~ ( in @ SY2949 @ SV432 )
                  | ~ ( in @ ( kpair @ SY2948 @ SY2949 ) @ SV704 )
                  | ( in @ ( kpair @ SY2948 @ SY2949 ) @ SV564 ) ) ) )
        = $true )
      | ( ( func @ SV218 @ SV432 @ SV704 )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV564 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2993]) ).

thf(3111,plain,
    ! [SV704: $i,SV564: $i,SV432: $i,SV218: $i] :
      ( ( ( ( ap @ SV218 @ SV432 @ SV564 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) )
         != ( ap @ SV218 @ SV432 @ SV704 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) ) )
        = $true )
      | ( ( ! [SY2948: $i] :
              ( ~ ( in @ SY2948 @ SV218 )
              | ! [SY2949: $i] :
                  ( ~ ( in @ SY2949 @ SV432 )
                  | ~ ( in @ ( kpair @ SY2948 @ SY2949 ) @ SV704 )
                  | ( in @ ( kpair @ SY2948 @ SY2949 ) @ SV564 ) ) ) )
        = $true )
      | ( ( func @ SV218 @ SV432 @ SV704 )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV564 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2994]) ).

thf(3112,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
              | ~ ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
                    | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) ) ) )
        = $true )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2995]) ).

thf(3113,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 )
          | ~ ~ ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 ) )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
              | ~ ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
                    | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) ) )
          | ( SV433 = SV656 ) )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2996]) ).

thf(3114,plain,
    ! [SV220: $i,SV565: $i,SV434: $i > $o] :
      ( ( ( ~ ( SV434 @ ( sK73_Xy @ SV565 @ SV434 @ SV220 ) )
          | ~ ( ( ( sK73_Xy @ SV565 @ SV434 @ SV220 )
               != SV565 ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV220
            @ ^ [SY2682: $i] : ( SV434 @ SY2682 ) ) )
        = $true )
      | ( ( SV434 @ SV565 )
        = $false )
      | ( ( in @ SV565 @ SV220 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2998]) ).

thf(3115,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( in @ SV566 @ SV221 )
        = $true )
      | ( ( ~ ( in @ SV566 @ SV221 )
          | ! [SX3: $o] : SX3 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2999]) ).

thf(3116,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ ( ( in @ SV566 @ SV221 )
              | ( in @ SV566 @ SV435 )
              | ! [SX3: $o] : SX3 )
          | ~ ( ( in @ SV566 @ SV221 )
              | ! [SX3: $o] :
                  ( ~ SX3
                  | SX3 ) ) )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3000]) ).

thf(3117,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ ( ~ ( in @ SV566 @ SV435 )
              | ~ ( in @ SV566 @ SV221 )
              | ! [SX3: $o] : SX3 )
          | ~ ~ ( ~ ( ~ ( in @ SV566 @ SV435 )
                    | ( in @ SV566 @ SV435 )
                    | ! [SX3: $o] : SX3 )
                | ~ ( ~ ( in @ SV566 @ SV435 )
                    | ! [SX3: $o] :
                        ( ~ SX3
                        | SX3 ) ) ) )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3001]) ).

thf(3118,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ ! [SY2839: $o] :
                ( ~ SY2839
                | ~ ( in @ SV566 @ SV221 )
                | SY2839 )
          | ~ ~ ( ~ ! [SY2840: $o] :
                      ( ~ SY2840
                      | ( in @ SV566 @ SV435 )
                      | SY2840 )
                | ~ ! [SX3: $o] :
                      ( ~ SX3
                      | ~ SX3
                      | SX3 ) ) )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3002]) ).

thf(3119,plain,
    ! [SV439: $i,SV226: $i,SV766: $i] :
      ( ( ( in @ SV766 @ SV226 )
        = $true )
      | ( ( ( in @ SV766 @ SV439 )
          | ! [SX3: $o] : SX3 )
        = $true )
      | ( ( in @ SV766 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3005]) ).

thf(3120,plain,
    ! [SV439: $i,SV226: $i,SV767: $i] :
      ( ( ( in @ SV767 @ SV226 )
        = $true )
      | ( ( ! [SX3: $o] :
              ( ~ SX3
              | SX3 ) )
        = $true )
      | ( ( in @ SV767 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3006]) ).

thf(3121,plain,
    ! [SV226: $i,SV439: $i,SV768: $i,SV797: $o] :
      ( ( ( ~ SV797
          | ( in @ SV768 @ SV439 )
          | SV797 )
        = $true )
      | ( ( in @ SV768 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3007]) ).

thf(3122,plain,
    ! [SV226: $i,SV439: $i,SV768: $i] :
      ( ( ( ~ $true
          | ( in @ SV768 @ SV439 )
          | $true )
        = $true )
      | ( ( in @ SV768 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3007]) ).

thf(3123,plain,
    ! [SV226: $i,SV439: $i,SV768: $i] :
      ( ( ( ~ $false
          | ( in @ SV768 @ SV439 )
          | $false )
        = $true )
      | ( ( in @ SV768 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3007]) ).

thf(3124,plain,
    ! [SV439: $i,SV226: $i,SV776: $i,SV798: $o] :
      ( ( ( ~ SV798
          | ~ SV798
          | SV798 )
        = $true )
      | ( ( in @ SV776 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3008]) ).

thf(3125,plain,
    ! [SV439: $i,SV226: $i,SV776: $i] :
      ( ( ( ~ $true
          | ~ $true
          | $true )
        = $true )
      | ( ( in @ SV776 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3008]) ).

thf(3126,plain,
    ! [SV439: $i,SV226: $i,SV776: $i] :
      ( ( ( ~ $false
          | ~ $false
          | $false )
        = $true )
      | ( ( in @ SV776 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3008]) ).

thf(3127,plain,
    ! [SV568: $i,SV228: $i > $o] :
      ( ( ( ! [SY2375: $i] :
              ( ~ ( SV228 @ SY2375 )
              | ( ( sK46_SY211 @ SV228 )
                = SY2375 ) ) )
        = $true )
      | ( ( ( sK47_Xy @ SV568 @ SV228 )
          = SV568 )
        = $false )
      | ( ( SV228 @ ( sK47_Xy @ SV568 @ SV228 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3009]) ).

thf(3128,plain,
    ! [SV568: $i,SV228: $i > $o] :
      ( ( ( SV228 @ ( sK46_SY211 @ SV228 ) )
        = $true )
      | ( ( ( sK47_Xy @ SV568 @ SV228 )
          = SV568 )
        = $false )
      | ( ( SV228 @ ( sK47_Xy @ SV568 @ SV228 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3010]) ).

thf(3129,plain,
    ! [SV568: $i,SV782: $i,SV228: $i > $o] :
      ( ( ( ~ ( SV228 @ SV782 ) )
        = $true )
      | ( ( ( sK46_SY211 @ SV228 )
          = SV782 )
        = $true )
      | ( ( SV228 @ ( sK47_Xy @ SV568 @ SV228 ) )
        = $true )
      | ( ( ( sK47_Xy @ SV568 @ SV228 )
          = SV568 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3011]) ).

thf(3130,plain,
    ! [SV229: $i,SV783: $i,SV441: $i > $o] :
      ( ( ( ~ ( SV441 @ SV783 ) )
        = $true )
      | ( ( ~ ( in @ SV783 @ SV229 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV229
            @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) )
        = $true )
      | ( ( in @ ( sK75_SY1878 @ SV441 @ SV229 ) @ SV229 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3013]) ).

thf(3131,plain,
    ! [SV229: $i,SV441: $i > $o] :
      ( ( ( SV441 @ ( sK74_Xx @ SV441 @ SV229 ) )
        = $true )
      | ( ( ! [SY2705: $i] :
              ( ~ ( SV441 @ SY2705 )
              | ~ ( in @ SY2705 @ SV229 ) )
          | ( singleton
            @ ( dsetconstr @ SV229
              @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3014]) ).

thf(3132,plain,
    ! [SV229: $i,SV441: $i > $o] :
      ( ( ( ~ ( ~ ( SV441 @ ( sK75_SY1878 @ SV441 @ SV229 ) )
              | ~ ( ( ( sK74_Xx @ SV441 @ SV229 )
                   != ( sK75_SY1878 @ SV441 @ SV229 ) ) ) ) )
        = $true )
      | ( ( ! [SY2705: $i] :
              ( ~ ( SV441 @ SY2705 )
              | ~ ( in @ SY2705 @ SV229 ) )
          | ( singleton
            @ ( dsetconstr @ SV229
              @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3015]) ).

thf(3133,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( in @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
              | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                          | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
          | ( SV569 = SV706 ) )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3016]) ).

thf(3134,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
              | ~ ~ ( ~ ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
                    | ~ ~ ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
              | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                          | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
          | ( SV569 = SV706 ) )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3017]) ).

thf(3135,plain,
    ! [SV231: $i,SV784: $i] :
      ( ( ( ~ ( in @ SV784 @ omega ) )
        = $true )
      | ( ( in @ SV784 @ SV231 )
        = $true )
      | ( ( in @ ( sK9_Xx @ SV231 ) @ omega )
        = $true )
      | ( ( in @ emptyset @ SV231 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3018]) ).

thf(3136,plain,
    ! [SV231: $i,SV785: $i] :
      ( ( ( ~ ( in @ SV785 @ omega ) )
        = $true )
      | ( ( in @ SV785 @ SV231 )
        = $true )
      | ( ( in @ ( sK9_Xx @ SV231 ) @ SV231 )
        = $true )
      | ( ( in @ emptyset @ SV231 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3019]) ).

thf(3137,plain,
    ! [SV233: $i,SV658: $i,SV786: $i] :
      ( ( ( in @ SV786 @ SV658 )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( ~ ( ~ ! [SY2925: $i] :
                    ( ~ ( in @ SY2925 @ ( sK15_B @ SV233 ) )
                    | ! [SY2926: $i] :
                        ( ~ ( in @ SY2926 @ SY2925 )
                        | ( in @ SY2926 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) )
                    | ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SY2925 ) )
              | ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) )
                          | ~ ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 ) )
                    | ~ ! [SY2927: $i] :
                          ( ~ ( in @ SY2927 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
                          | ~ ( in @ SY2927 @ SV658 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3021]) ).

thf(3138,plain,
    ! [SV233: $i,SV658: $i,SV799: $i] :
      ( ( ( ~ ( in @ SV799 @ SV658 ) )
        = $true )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 )
        = $false )
      | ( ( ~ ( ~ ! [SY2925: $i] :
                    ( ~ ( in @ SY2925 @ ( sK15_B @ SV233 ) )
                    | ! [SY2926: $i] :
                        ( ~ ( in @ SY2926 @ SY2925 )
                        | ( in @ SY2926 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) )
                    | ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SY2925 ) )
              | ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) )
                          | ~ ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 ) )
                    | ~ ! [SY2927: $i] :
                          ( ~ ( in @ SY2927 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
                          | ~ ( in @ SY2927 @ SV658 ) ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3022]) ).

thf(3139,plain,
    ! [SV770: $i,SV233: $i,SV754: $i] :
      ( ( ( in @ SV754 @ ( sK15_B @ SV233 ) )
        = $false )
      | ( ( ~ ( in @ SV770 @ ( sK15_B @ SV233 ) ) )
        = $true )
      | ( ( ! [SY2983: $i] :
              ( ~ ( in @ SY2983 @ SV754 )
              | ( in @ SY2983 @ SV770 ) )
          | ! [SY2984: $i] :
              ( ~ ( in @ SY2984 @ SV770 )
              | ( in @ SY2984 @ SV754 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3023]) ).

thf(3140,plain,
    ! [SV233: $i,SV787: $i] :
      ( ( ( ~ ( in @ SV787 @ ( sK15_B @ SV233 ) ) )
        = $true )
      | ( ( ! [SY2988: $i] :
              ( ~ ( in @ SY2988 @ SV787 )
              | ( in @ SY2988 @ SV233 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3024]) ).

thf(3141,plain,
    ! [SV800: $i,SV233: $i,SV788: $i] :
      ( ( ~ ( in @ SV788 @ SV233 )
        | ~ ( in @ SV800 @ SV233 )
        | ~ ( ~ ( in @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) @ ( sK15_B @ SV233 ) )
            | ~ ~ ( ~ ( ~ ( in @ SV788 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) )
                      | ~ ( in @ SV800 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) ) )
                  | ~ ( ( in @ SV788 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) )
                      | ( in @ SV800 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) ) ) ) )
        | ( SV788 = SV800 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[3025]) ).

thf(3142,plain,
    ! [SV573: $i,SV235: $i > $o,SV801: $i] :
      ( ( ( ( SV801
           != ( sK32_Xx @ SV235 ) )
          | ( SV235 @ SV801 ) )
        = $true )
      | ( ( SV235 @ ( sK33_SY142 @ SV573 @ SV235 ) )
        = $true )
      | ( ( SV235 @ SV573 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3026]) ).

thf(3143,plain,
    ! [SV573: $i,SV802: $i,SV235: $i > $o] :
      ( ( ( ~ ( SV235 @ SV802 )
          | ( SV802
            = ( sK32_Xx @ SV235 ) ) )
        = $true )
      | ( ( SV235 @ ( sK33_SY142 @ SV573 @ SV235 ) )
        = $true )
      | ( ( SV235 @ SV573 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3027]) ).

thf(3144,plain,
    ! [SV573: $i,SV235: $i > $o] :
      ( ( ( ! [SY2403: $i] :
              ( ( SY2403
               != ( sK32_Xx @ SV235 ) )
              | ( SV235 @ SY2403 ) ) )
        = $true )
      | ( ( SV573
          = ( sK33_SY142 @ SV573 @ SV235 ) )
        = $false )
      | ( ( SV235 @ SV573 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3028]) ).

thf(3145,plain,
    ! [SV573: $i,SV235: $i > $o] :
      ( ( ( ! [SY2404: $i] :
              ( ~ ( SV235 @ SY2404 )
              | ( SY2404
                = ( sK32_Xx @ SV235 ) ) ) )
        = $true )
      | ( ( SV573
          = ( sK33_SY142 @ SV573 @ SV235 ) )
        = $false )
      | ( ( SV235 @ SV573 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3029]) ).

thf(3146,plain,
    ! [SV236: $i,SV445: $i,SV710: $i > $o,SV574: $i,SV789: $i] :
      ( ( ( ~ ( in @ SV789 @ SV574 ) )
        = $true )
      | ( ( SV710 @ SV789 )
        = $true )
      | ( ( in @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ SV236 )
        = $true )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3030]) ).

thf(3147,plain,
    ! [SV236: $i,SV445: $i,SV574: $i,SV710: $i > $o] :
      ( ( ( ~ ( in @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) @ SV445 ) )
        = $false )
      | ( ( ! [SY2953: $i] :
              ( ~ ( in @ SY2953 @ SV574 )
              | ( SV710 @ SY2953 ) ) )
        = $true )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3031]) ).

thf(3148,plain,
    ! [SV236: $i,SV445: $i,SV574: $i,SV710: $i > $o] :
      ( ( ( ~ ~ ( ~ ( in @ ( kpair @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) ) @ SV574 )
                | ~ ~ ( SV710 @ ( kpair @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) ) ) ) )
        = $false )
      | ( ( ! [SY2953: $i] :
              ( ~ ( in @ SY2953 @ SV574 )
              | ( SV710 @ SY2953 ) ) )
        = $true )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3031]) ).

thf(3149,plain,
    ! [SV582: $i,SV803: $i,SV241: $i > $o] :
      ( ( ( ~ ( SV241 @ SV803 )
          | ( ( sK43_SY205 @ SV241 )
            = SV803 ) )
        = $true )
      | ( ( SV241 @ ( sK44_Xx @ SV241 ) )
        = $true )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3033]) ).

thf(3150,plain,
    ! [SV582: $i,SV241: $i > $o] :
      ( ( ( ~ ! [SY2422: $i] :
                ( ~ ( SV241 @ SY2422 )
                | ( ( sK43_SY205 @ SV241 )
                  = SY2422 ) )
          | ~ ( SV241 @ ( sK43_SY205 @ SV241 ) ) )
        = $false )
      | ( ( SV241 @ ( sK45_SY1868 @ SV241 ) )
        = $true )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3035]) ).

thf(3151,plain,
    ! [SV582: $i,SV241: $i > $o] :
      ( ( ( ( sK44_Xx @ SV241 )
          = ( sK45_SY1868 @ SV241 ) )
        = $false )
      | ( ( ~ ( ~ ! [SY2422: $i] :
                    ( ~ ( SV241 @ SY2422 )
                    | ( ( sK43_SY205 @ SV241 )
                      = SY2422 ) )
              | ~ ( SV241 @ ( sK43_SY205 @ SV241 ) ) ) )
        = $true )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3036]) ).

thf(3152,plain,
    ! [SV243: $i,SV450: $i,SV583: $i,SV717: $i] :
      ( ( ( in @ ( sK90_Xx @ SV717 @ SV583 @ SV450 @ SV243 ) @ SV243 )
        = $true )
      | ( ( SV583 = SV717 )
        = $true )
      | ( ( func @ SV243 @ SV450 @ SV717 )
        = $false )
      | ( ( func @ SV243 @ SV450 @ SV583 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3037]) ).

thf(3153,plain,
    ! [SV717: $i,SV583: $i,SV450: $i,SV243: $i] :
      ( ( ( ( ap @ SV243 @ SV450 @ SV583 @ ( sK90_Xx @ SV717 @ SV583 @ SV450 @ SV243 ) )
         != ( ap @ SV243 @ SV450 @ SV717 @ ( sK90_Xx @ SV717 @ SV583 @ SV450 @ SV243 ) ) )
        = $true )
      | ( ( SV583 = SV717 )
        = $true )
      | ( ( func @ SV243 @ SV450 @ SV717 )
        = $false )
      | ( ( func @ SV243 @ SV450 @ SV583 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3038]) ).

thf(3154,plain,
    ! [SV245: $i,SV451: $i,SV585: $i,SV718: $i] :
      ( ( ( in @ ( sK91_Xx @ SV718 @ SV585 @ SV451 @ SV245 ) @ SV245 )
        = $true )
      | ( ( SV585 = SV718 )
        = $true )
      | ( ( in @ SV718 @ ( funcSet @ SV245 @ SV451 ) )
        = $false )
      | ( ( in @ SV585 @ ( funcSet @ SV245 @ SV451 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3039]) ).

thf(3155,plain,
    ! [SV718: $i,SV585: $i,SV451: $i,SV245: $i] :
      ( ( ( ( ap @ SV245 @ SV451 @ SV585 @ ( sK91_Xx @ SV718 @ SV585 @ SV451 @ SV245 ) )
         != ( ap @ SV245 @ SV451 @ SV718 @ ( sK91_Xx @ SV718 @ SV585 @ SV451 @ SV245 ) ) )
        = $true )
      | ( ( SV585 = SV718 )
        = $true )
      | ( ( in @ SV718 @ ( funcSet @ SV245 @ SV451 ) )
        = $false )
      | ( ( in @ SV585 @ ( funcSet @ SV245 @ SV451 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3040]) ).

thf(3156,plain,
    ! [SV586: $i,SV804: $i,SV247: $i > $o] :
      ( ( ( ~ ( SV247 @ SV804 )
          | ( ( sK21_Xx @ SV247 )
            = SV804 ) )
        = $true )
      | ( ( SV247 @ ( sK22_SY74 @ SV586 @ SV247 ) )
        = $true )
      | ( ( SV247 @ SV586 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3041]) ).

thf(3157,plain,
    ! [SV586: $i,SV247: $i > $o] :
      ( ( ( ! [SY2435: $i] :
              ( ~ ( SV247 @ SY2435 )
              | ( ( sK21_Xx @ SV247 )
                = SY2435 ) ) )
        = $true )
      | ( ( SV586
          = ( sK22_SY74 @ SV586 @ SV247 ) )
        = $false )
      | ( ( SV247 @ SV586 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3043]) ).

thf(3158,plain,
    ! [SV586: $i,SV247: $i > $o] :
      ( ( ( SV247 @ ( sK21_Xx @ SV247 ) )
        = $true )
      | ( ( SV586
          = ( sK22_SY74 @ SV586 @ SV247 ) )
        = $false )
      | ( ( SV247 @ SV586 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3044]) ).

thf(3159,plain,
    ! [SV248: $i,SV453: $i,SV661: $i > $o,SV719: $i > $o] :
      ( ( ( ~ ( in @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) @ SV453 ) )
        = $false )
      | ( ( ( dsetconstr @ SV248
            @ ^ [SY2930: $i] : ( SV661 @ SY2930 ) )
          = ( dsetconstr @ SV453
            @ ^ [SY2961: $i] : ( SV719 @ SY2961 ) ) )
        = $true )
      | ( ( SV248 = SV453 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3045]) ).

thf(3160,plain,
    ! [SV248: $i,SV453: $i,SV661: $i > $o,SV719: $i > $o] :
      ( ( ( ~ ~ ( ( ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 )
                 != ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) )
                | ~ ~ ( ~ ( ~ ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
                          | ~ ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) )
                      | ~ ( ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
                          | ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) ) ) ) )
        = $false )
      | ( ( ( dsetconstr @ SV248
            @ ^ [SY2930: $i] : ( SV661 @ SY2930 ) )
          = ( dsetconstr @ SV453
            @ ^ [SY2961: $i] : ( SV719 @ SY2961 ) ) )
        = $true )
      | ( ( SV248 = SV453 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3045]) ).

thf(3161,plain,
    ! [SV733: $i,SV612: $i,SV250: $i,SV1: $i,SV777: $i] :
      ( ( ( in @ SV777 @ SV1 )
        = $false )
      | ( ( ~ ( in @ SV777 @ ( binintersect @ SV250 @ SV612 ) )
          | ( in @ SV777 @ ( binunion @ SV250 @ SV733 ) ) )
        = $true )
      | ( ( in @ SV733 @ ( powerset @ SV1 ) )
        = $false )
      | ( ( in @ SV612 @ ( powerset @ SV1 ) )
        = $false )
      | ( ( in @ SV250 @ ( powerset @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3046]) ).

thf(3162,plain,
    ! [SV254: $i,SV5: $i,SV616: $i,SV771: $i] :
      ( ( ( ~ ( in @ SV771 @ SV616 ) )
        = $true )
      | ( ( in @ SV771 @ ( setminus @ SV5 @ SV254 ) )
        = $true )
      | ( ( in @ SV771 @ SV5 )
        = $false )
      | ( ( subset @ SV254 @ ( setminus @ SV5 @ SV616 ) )
        = $false )
      | ( ( in @ SV616 @ ( powerset @ SV5 ) )
        = $false )
      | ( ( in @ SV254 @ ( powerset @ SV5 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3049]) ).

thf(3163,plain,
    ! [SV9: $i,SV620: $i,SV258: $i,SV737: $i] :
      ( ( ( in @ SV737 @ ( binintersect @ SV258 @ SV620 ) )
        = $false )
      | ( ( in @ SV737 @ ( setminus @ SV9 @ SV258 ) )
        = $false )
      | ( ( in @ SV737 @ SV9 )
        = $false )
      | ( ( in @ SV620 @ ( powerset @ SV9 ) )
        = $false )
      | ( ( in @ SV258 @ ( powerset @ SV9 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3051]) ).

thf(3164,plain,
    ! [SV17: $i,SV266: $i,SV625: $i,SV738: $i] :
      ( ( ( in @ SV738 @ SV625 )
        = $true )
      | ( ( ~ ( in @ SV738 @ SV266 ) )
        = $true )
      | ( ( subset @ SV266 @ SV625 )
        = $false )
      | ( ( in @ SV738 @ SV17 )
        = $false )
      | ( ( in @ SV625 @ ( powerset @ SV17 ) )
        = $false )
      | ( ( in @ SV266 @ ( powerset @ SV17 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3052]) ).

thf(3165,plain,
    ! [SV18: $i,SV267: $i,SV626: $i,SV739: $i] :
      ( ( ( ~ ( in @ SV739 @ SV626 ) )
        = $true )
      | ( ( ~ ( in @ SV739 @ SV267 ) )
        = $true )
      | ( ( subset @ SV267 @ ( setminus @ SV18 @ SV626 ) )
        = $false )
      | ( ( in @ SV739 @ SV18 )
        = $false )
      | ( ( in @ SV626 @ ( powerset @ SV18 ) )
        = $false )
      | ( ( in @ SV267 @ ( powerset @ SV18 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3053]) ).

thf(3166,plain,
    ! [SV23: $i,SV631: $i,SV272: $i,SV742: $i] :
      ( ( ( ~ ( in @ SV742 @ SV272 ) )
        = $true )
      | ( ( in @ SV742 @ SV631 )
        = $true )
      | ( ( in @ SV272 @ ( powerset @ SV631 ) )
        = $false )
      | ( ( in @ SV742 @ SV23 )
        = $false )
      | ( ( in @ SV631 @ ( powerset @ SV23 ) )
        = $false )
      | ( ( in @ SV272 @ ( powerset @ SV23 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3056]) ).

thf(3167,plain,
    ! [SV284: $i,SV38: $i,SV471: $i,SV756: $i,SV674: $i] :
      ( ( ( in @ ( kpair @ SV674 @ SV756 ) @ SV471 )
        = $false )
      | ( ( ( ap @ SV38 @ SV284 @ SV471 @ SV674 )
          = SV756 )
        = $true )
      | ( ( in @ SV756 @ SV284 )
        = $false )
      | ( ( in @ SV674 @ SV38 )
        = $false )
      | ( ( in @ SV471 @ ( funcSet @ SV38 @ SV284 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3057]) ).

thf(3168,plain,
    ! [SV285: $i,SV39: $i,SV472: $i,SV757: $i,SV675: $i] :
      ( ( ( in @ ( kpair @ SV675 @ SV757 ) @ SV472 )
        = $false )
      | ( ( ( ap @ SV39 @ SV285 @ SV472 @ SV675 )
          = SV757 )
        = $true )
      | ( ( in @ SV757 @ SV285 )
        = $false )
      | ( ( in @ SV675 @ SV39 )
        = $false )
      | ( ( func @ SV39 @ SV285 @ SV472 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3058]) ).

thf(3169,plain,
    ! [SV42: $i,SV635: $i,SV743: $i,SV288: $i > $o] :
      ( ( ( ~ ( SV288 @ SV743 ) )
        = $true )
      | ( ( SV635 = SV743 )
        = $true )
      | ( ( SV288 @ SV635 )
        = $false )
      | ( ( in @ SV743 @ SV42 )
        = $false )
      | ( ( in @ SV635 @ SV42 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV42
            @ ^ [SY2500: $i] : ( SV288 @ SY2500 ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3059]) ).

thf(3170,plain,
    ! [SV189: $i,SV409: $i,SV647: $i] :
      ( ( ( ~ ( in @ ( sK97_Xx @ SV647 @ SV409 @ SV189 ) @ SV409 ) )
        = $false )
      | ( ( subset @ SV409 @ SV647 )
        = $true )
      | ( ( in @ SV647 @ ( powerset @ SV189 ) )
        = $false )
      | ( ( in @ SV409 @ ( powerset @ SV189 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3060]) ).

thf(3171,plain,
    ! [SV189: $i,SV409: $i,SV647: $i] :
      ( ( ( ~ ~ ( in @ ( sK97_Xx @ SV647 @ SV409 @ SV189 ) @ SV647 ) )
        = $false )
      | ( ( subset @ SV409 @ SV647 )
        = $true )
      | ( ( in @ SV647 @ ( powerset @ SV189 ) )
        = $false )
      | ( ( in @ SV409 @ ( powerset @ SV189 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3060]) ).

thf(3172,plain,
    ! [SV551: $i,SV759: $i,SV790: $i,SV194: $i > $o] :
      ( ( ( ~ ( SV194 @ SV790 ) )
        = $true )
      | ( ( SV759 = SV790 )
        = $true )
      | ( ( SV194 @ SV759 )
        = $false )
      | ( ( SV194 @ ( sK57_SY248 @ SV551 @ SV194 ) )
        = $true )
      | ( ( SV194 @ SV551 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3061]) ).

thf(3173,plain,
    ! [SV551: $i,SV772: $i,SV805: $i,SV194: $i > $o] :
      ( ( ( ~ ( SV194 @ SV805 )
          | ( SV772 = SV805 ) )
        = $true )
      | ( ( SV194 @ SV772 )
        = $false )
      | ( ( SV551
          = ( sK57_SY248 @ SV551 @ SV194 ) )
        = $false )
      | ( ( SV194 @ SV551 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3062]) ).

thf(3174,plain,
    ! [SV413: $i,SV773: $i,SV791: $i,SV195: $i > $i > $o] :
      ( ( ( ~ ( SV195 @ SV791 @ SV773 ) )
        = $true )
      | ( ( ~ ( in @ SV791 @ SV413 ) )
        = $true )
      | ( ( in @ SV773 @ ( sK10_B @ SV413 @ SV195 ) )
        = $true )
      | ( ( in @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV413 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3063]) ).

thf(3175,plain,
    ! [SV413: $i,SV774: $i,SV195: $i > $i > $o] :
      ( ( ( ~ ( SV195 @ ( sK11_Xy @ SV774 @ SV413 @ SV195 ) @ SV774 )
          | ~ ( in @ ( sK11_Xy @ SV774 @ SV413 @ SV195 ) @ SV413 ) )
        = $false )
      | ( ( in @ SV774 @ ( sK10_B @ SV413 @ SV195 ) )
        = $false )
      | ( ( in @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV413 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3064]) ).

thf(3176,plain,
    ! [SV725: $i,SV413: $i,SV195: $i > $i > $o] :
      ( ( ( ~ ! [SY2639: $i] :
                ( ! [SY2640: $i] :
                    ( ~ ( SV195 @ SY2640 @ SY2639 )
                    | ~ ( in @ SY2640 @ SV413 ) )
                | ( in @ SY2639 @ ( sK10_B @ SV413 @ SV195 ) ) )
          | ~ ! [SY2641: $i] :
                ( ~ ( in @ SY2641 @ ( sK10_B @ SV413 @ SV195 ) )
                | ~ ( ~ ( SV195 @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SY2641 )
                    | ~ ( in @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SV413 ) ) ) )
        = $false )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3065]) ).

thf(3177,plain,
    ! [SV725: $i,SV413: $i,SV195: $i > $i > $o] :
      ( ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false )
      | ( ( SV725
          = ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $false )
      | ( ( ~ ( ~ ! [SY2639: $i] :
                    ( ! [SY2640: $i] :
                        ( ~ ( SV195 @ SY2640 @ SY2639 )
                        | ~ ( in @ SY2640 @ SV413 ) )
                    | ( in @ SY2639 @ ( sK10_B @ SV413 @ SV195 ) ) )
              | ~ ! [SY2641: $i] :
                    ( ~ ( in @ SY2641 @ ( sK10_B @ SV413 @ SV195 ) )
                    | ~ ( ~ ( SV195 @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SY2641 )
                        | ~ ( in @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SV413 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3066]) ).

thf(3178,plain,
    ! [SV196: $i,SV414: $i,SV552: $i] :
      ( ( ( in @ SV552 @ SV414 )
        = $true )
      | ( ( ! [SX3: $o] : SX3 )
        = $true )
      | ( ( SV552 = SV196 )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3067]) ).

thf(3179,plain,
    ! [SV414: $i,SV196: $i,SV552: $i,SV806: $o] :
      ( ( ( ~ SV806
          | SV806 )
        = $true )
      | ( ( SV552 = SV196 )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3068]) ).

thf(3180,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( ( ~ $true
          | $true )
        = $true )
      | ( ( SV552 = SV196 )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3068]) ).

thf(3181,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( ( ~ $false
          | $false )
        = $true )
      | ( ( SV552 = SV196 )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3068]) ).

thf(3182,plain,
    ! [SV196: $i,SV414: $i,SV552: $i,SV792: $o] :
      ( ( ( ~ SV792 ) = $true )
      | ( ( ( in @ SV552 @ SV414 )
          | SV792 )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3069]) ).

thf(3183,plain,
    ! [SV196: $i,SV414: $i,SV552: $i] :
      ( ( ( ~ $true ) = $true )
      | ( ( ( in @ SV552 @ SV414 )
          | $true )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3070]) ).

thf(3184,plain,
    ! [SV196: $i,SV414: $i,SV552: $i] :
      ( ( ( ~ $false ) = $true )
      | ( ( ( in @ SV552 @ SV414 )
          | $false )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3071]) ).

thf(3185,plain,
    ! [SV414: $i,SV196: $i,SV552: $i,SV793: $o] :
      ( ( ( ~ SV793 ) = $true )
      | ( ( ~ SV793
          | SV793 )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3072]) ).

thf(3186,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( ( ~ $true ) = $true )
      | ( ( ~ $true
          | $true )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3073]) ).

thf(3187,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( ( ~ $false ) = $true )
      | ( ( ~ $false
          | $false )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3074]) ).

thf(3188,plain,
    ! [SV652: $i > $o,SV778: $i,SV605: $i > $o] :
      ( ( ( ~ ( SV605 @ ( sK54_SY233 @ SV778 @ SV652 @ SV605 ) )
          | ~ ( ( SV778
               != ( sK54_SY233 @ SV778 @ SV652 @ SV605 ) ) ) )
        = $false )
      | ( ( ~ ( SV605 @ SV778 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( ( sK55_Xx @ SV652 @ SV605 )
          = ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3075]) ).

thf(3189,plain,
    ! [SV652: $i > $o,SV605: $i > $o] :
      ( ( ( ~ ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) ) )
        = $true )
      | ( ( ~ ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) ) )
        = $true )
      | ( ( ! [SY2919: $i] :
              ( ~ ( ~ ( SV605 @ ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) )
                  | ~ ( ( SY2919
                       != ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) ) ) )
              | ~ ( SV605 @ SY2919 ) )
          | ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3076]) ).

thf(3190,plain,
    ! [SV652: $i > $o,SV605: $i > $o] :
      ( ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true )
      | ( ( ! [SY2919: $i] :
              ( ~ ( ~ ( SV605 @ ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) )
                  | ~ ( ( SY2919
                       != ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) ) ) )
              | ~ ( SV605 @ SY2919 ) )
          | ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3077]) ).

thf(3191,plain,
    ! [SV606: $i > $o,SV779: $i,SV653: $i > $o] :
      ( ( ( ~ ( SV653 @ ( sK50_SY236 @ SV779 @ SV653 @ SV606 ) )
          | ~ ( ( SV779
               != ( sK50_SY236 @ SV779 @ SV653 @ SV606 ) ) ) )
        = $false )
      | ( ( ~ ( SV653 @ SV779 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( ( sK51_Xx @ SV653 @ SV606 )
          = ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3078]) ).

thf(3192,plain,
    ! [SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ~ ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) ) )
        = $true )
      | ( ( ~ ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) ) )
        = $true )
      | ( ( ! [SY2921: $i] :
              ( ~ ( ~ ( SV653 @ ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) )
                  | ~ ( ( SY2921
                       != ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) ) ) )
              | ~ ( SV653 @ SY2921 ) )
          | ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3079]) ).

thf(3193,plain,
    ! [SV653: $i > $o,SV606: $i > $o] :
      ( ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true )
      | ( ( ! [SY2921: $i] :
              ( ~ ( ~ ( SV653 @ ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) )
                  | ~ ( ( SY2921
                       != ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) ) ) )
              | ~ ( SV653 @ SY2921 ) )
          | ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3080]) ).

thf(3194,plain,
    ! [SV558: $i,SV794: $i,SV205: $i > $o] :
      ( ( ( ~ ( SV205 @ SV794 ) )
        = $true )
      | ( ( ( sK41_SY198 @ SV205 )
          = SV794 )
        = $true )
      | ( ( SV205 @ ( sK42_Xy @ SV558 @ SV205 ) )
        = $true )
      | ( ( SV205 @ SV558 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3081]) ).

thf(3195,plain,
    ! [SV558: $i,SV807: $i,SV205: $i > $o] :
      ( ( ( ~ ( SV205 @ SV807 )
          | ( ( sK41_SY198 @ SV205 )
            = SV807 ) )
        = $true )
      | ( ( SV558
          = ( sK42_Xy @ SV558 @ SV205 ) )
        = $false )
      | ( ( SV205 @ SV558 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3082]) ).

thf(3196,plain,
    ( ( ~ ( in @ sK5_SY1831 @ ( binintersect @ sK2_SY1822 @ sK3_SY1826 ) )
      | ~ ~ ( in @ sK5_SY1831 @ ( binunion @ sK3_SY1826 @ sK4_SY1829 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[3085]) ).

thf(3197,plain,
    ! [SV207: $i,SV422: $i,SV702: $i > $o,SV560: $i,SV780: $i] :
      ( ( ( in @ SV780 @ SV560 )
        = $false )
      | ( ( SV702 @ SV780 )
        = $true )
      | ( ( in @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ SV207 )
        = $true )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3086]) ).

thf(3198,plain,
    ! [SV207: $i,SV422: $i,SV560: $i,SV702: $i > $o] :
      ( ( ( in @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) @ SV422 )
        = $true )
      | ( ( ! [SY2947: $i] :
              ( ~ ( in @ SY2947 @ SV560 )
              | ( SV702 @ SY2947 ) ) )
        = $true )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3087]) ).

thf(3199,plain,
    ! [SV207: $i,SV422: $i,SV560: $i,SV702: $i > $o] :
      ( ( ( ~ ( ~ ( in @ ( kpair @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) ) @ SV560 )
              | ~ ~ ( SV702 @ ( kpair @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) ) ) ) )
        = $true )
      | ( ( ! [SY2947: $i] :
              ( ~ ( in @ SY2947 @ SV560 )
              | ( SV702 @ SY2947 ) ) )
        = $true )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3088]) ).

thf(3200,plain,
    ! [SV208: $i,SV423: $i,SV561: $i,SV703: $i] :
      ( ( ( ~ ( in @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) @ SV423 )
          | ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) ) @ SV561 )
                | ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) ) @ SV703 ) ) )
        = $false )
      | ( ( subset @ SV561 @ SV703 )
        = $true )
      | ( ( subset @ SV703 @ ( cartprod @ SV208 @ SV423 ) )
        = $false )
      | ( ( subset @ SV561 @ ( cartprod @ SV208 @ SV423 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3090]) ).

thf(3201,plain,
    ! [SV209: $i,SV781: $i,SV424: $i > $o] :
      ( ( ( SV424 @ SV781 )
        = $false )
      | ( ( ~ ( in @ SV781 @ SV209 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV209
            @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) )
        = $true )
      | ( ( in @ ( sK71_SY1877 @ SV424 @ SV209 ) @ SV209 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3091]) ).

thf(3202,plain,
    ! [SV209: $i,SV424: $i > $o] :
      ( ( ( ! [SY2662: $i] :
              ( ~ ( SV424 @ SY2662 )
              | ~ ( in @ SY2662 @ SV209 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV209
            @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) )
        = $true )
      | ( ( SV424 @ ( sK70_Xx @ SV424 @ SV209 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3092]) ).

thf(3203,plain,
    ! [SV209: $i,SV424: $i > $o] :
      ( ( ( ~ ( SV424 @ ( sK71_SY1877 @ SV424 @ SV209 ) )
          | ~ ( ( ( sK70_Xx @ SV424 @ SV209 )
               != ( sK71_SY1877 @ SV424 @ SV209 ) ) ) )
        = $false )
      | ( ( ! [SY2662: $i] :
              ( ~ ( SV424 @ SY2662 )
              | ~ ( in @ SY2662 @ SV209 ) )
          | ( singleton
            @ ( dsetconstr @ SV209
              @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3093]) ).

thf(3204,plain,
    ! [SV425: $i,SV761: $i,SV210: $i,SV748: $i] :
      ( ( ( in @ SV748 @ SV210 )
        = $false )
      | ( ( in @ SV761 @ SV425 )
        = $true )
      | ( ( SV748 = SV761 )
        = $false )
      | ( ( SV210 = SV425 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3094]) ).

thf(3205,plain,
    ! [SV210: $i,SV749: $i,SV425: $i,SV762: $i] :
      ( ( ( in @ SV762 @ SV425 )
        = $false )
      | ( ( in @ SV749 @ SV210 )
        = $true )
      | ( ( SV749 = SV762 )
        = $false )
      | ( ( SV210 = SV425 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3095]) ).

thf(3206,plain,
    ! [SV562: $i,SV763: $i,SV795: $i,SV211: $i > $o] :
      ( ( ( ~ ( SV211 @ SV795 ) )
        = $true )
      | ( ( SV763 = SV795 )
        = $true )
      | ( ( SV211 @ SV763 )
        = $false )
      | ( ( SV211 @ ( sK48_SY224 @ SV562 @ SV211 ) )
        = $true )
      | ( ( SV211 @ SV562 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3096]) ).

thf(3207,plain,
    ! [SV562: $i,SV775: $i,SV808: $i,SV211: $i > $o] :
      ( ( ( ~ ( SV211 @ SV808 )
          | ( SV775 = SV808 ) )
        = $true )
      | ( ( SV211 @ SV775 )
        = $false )
      | ( ( SV562
          = ( sK48_SY224 @ SV562 @ SV211 ) )
        = $false )
      | ( ( SV211 @ SV562 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3097]) ).

thf(3208,plain,
    ! [SV427: $i > $o,SV750: $i,SV213: $i > $o] :
      ( ( ( SV213 @ SV750 )
        = $false )
      | ( ( SV213 @ ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3098]) ).

thf(3209,plain,
    ! [SV213: $i > $o,SV427: $i > $o,SV750: $i] :
      ( ( ( SV750
          = ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
        = $false )
      | ( ( ~ ( SV213 @ SV750 ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3099]) ).

thf(3210,plain,
    ! [SV427: $i > $o,SV213: $i > $o] :
      ( ( ( ! [SY2670: $i] :
              ( ~ ( ~ ( SV213 @ ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2670
                       != ( sK59_SY257 @ SY2670 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV213 @ SY2670 ) ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3100]) ).

thf(3211,plain,
    ! [SV427: $i > $o,SV796: $i,SV213: $i > $o] :
      ( ( ( ~ ( ~ ( SV213 @ ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
              | ~ ( ( SV796
                   != ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV213 @ SV796 ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3101]) ).

thf(3212,plain,
    ! [SV214: $i,SV428: $i,SV654: $i] :
      ( ( ( ~ ( in @ ( sK98_Xx @ SV654 @ SV428 @ SV214 ) @ SV428 ) )
        = $false )
      | ( ( in @ SV428 @ ( powerset @ SV654 ) )
        = $true )
      | ( ( in @ SV654 @ ( powerset @ SV214 ) )
        = $false )
      | ( ( in @ SV428 @ ( powerset @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3102]) ).

thf(3213,plain,
    ! [SV214: $i,SV428: $i,SV654: $i] :
      ( ( ( ~ ~ ( in @ ( sK98_Xx @ SV654 @ SV428 @ SV214 ) @ SV654 ) )
        = $false )
      | ( ( in @ SV428 @ ( powerset @ SV654 ) )
        = $true )
      | ( ( in @ SV654 @ ( powerset @ SV214 ) )
        = $false )
      | ( ( in @ SV428 @ ( powerset @ SV214 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3102]) ).

thf(3214,plain,
    ! [SV215: $i,SV429: $i,SV655: $o] :
      ( ( SV655 = $false )
      | ( SV655 = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3104]) ).

thf(3215,plain,
    ! [SV215: $i,SV429: $i] :
      ( ( $true = $false )
      | ( $true = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3106]) ).

thf(3216,plain,
    ! [SV215: $i,SV429: $i] :
      ( ( $false = $false )
      | ( $false = $true )
      | ( ( in @ SV429 @ ( setunion @ SV215 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3108]) ).

thf(3217,plain,
    ! [SV564: $i,SV704: $i,SV432: $i,SV218: $i,SV809: $i] :
      ( ( ( ~ ( in @ SV809 @ SV218 )
          | ! [SY2990: $i] :
              ( ~ ( in @ SY2990 @ SV432 )
              | ~ ( in @ ( kpair @ SV809 @ SY2990 ) @ SV704 )
              | ( in @ ( kpair @ SV809 @ SY2990 ) @ SV564 ) ) )
        = $true )
      | ( ( in @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) @ SV218 )
        = $true )
      | ( ( func @ SV218 @ SV432 @ SV704 )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV564 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3110]) ).

thf(3218,plain,
    ! [SV704: $i,SV564: $i,SV432: $i,SV218: $i] :
      ( ( ( ( ap @ SV218 @ SV432 @ SV564 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) )
          = ( ap @ SV218 @ SV432 @ SV704 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) ) )
        = $false )
      | ( ( ! [SY2948: $i] :
              ( ~ ( in @ SY2948 @ SV218 )
              | ! [SY2949: $i] :
                  ( ~ ( in @ SY2949 @ SV432 )
                  | ~ ( in @ ( kpair @ SY2948 @ SY2949 ) @ SV704 )
                  | ( in @ ( kpair @ SY2948 @ SY2949 ) @ SV564 ) ) ) )
        = $true )
      | ( ( func @ SV218 @ SV432 @ SV704 )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV564 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3111]) ).

thf(3219,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
          | ~ ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
                | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) ) )
        = $false )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3112]) ).

thf(3220,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
              | ~ ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
                    | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) ) )
          | ( SV433 = SV656 ) )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3113]) ).

thf(3221,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ~ ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 ) )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
              | ~ ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
                    | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) ) )
          | ( SV433 = SV656 ) )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3113]) ).

thf(3222,plain,
    ! [SV220: $i,SV565: $i,SV434: $i > $o] :
      ( ( ( ~ ( SV434 @ ( sK73_Xy @ SV565 @ SV434 @ SV220 ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV220
            @ ^ [SY2682: $i] : ( SV434 @ SY2682 ) ) )
        = $true )
      | ( ( SV434 @ SV565 )
        = $false )
      | ( ( in @ SV565 @ SV220 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3114]) ).

thf(3223,plain,
    ! [SV220: $i,SV434: $i > $o,SV565: $i] :
      ( ( ( ~ ( ( ( sK73_Xy @ SV565 @ SV434 @ SV220 )
               != SV565 ) ) )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV220
            @ ^ [SY2682: $i] : ( SV434 @ SY2682 ) ) )
        = $true )
      | ( ( SV434 @ SV565 )
        = $false )
      | ( ( in @ SV565 @ SV220 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3114]) ).

thf(3224,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ ( in @ SV566 @ SV221 ) )
        = $true )
      | ( ( ! [SX3: $o] : SX3 )
        = $true )
      | ( ( in @ SV566 @ SV221 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3115]) ).

thf(3225,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ ( ( in @ SV566 @ SV221 )
              | ( in @ SV566 @ SV435 )
              | ! [SX3: $o] : SX3 ) )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3116]) ).

thf(3226,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ ( ( in @ SV566 @ SV221 )
              | ! [SX3: $o] :
                  ( ~ SX3
                  | SX3 ) ) )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3116]) ).

thf(3227,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ ( ~ ( in @ SV566 @ SV435 )
              | ~ ( in @ SV566 @ SV221 )
              | ! [SX3: $o] : SX3 ) )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3117]) ).

thf(3228,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ ~ ( ~ ( ~ ( in @ SV566 @ SV435 )
                    | ( in @ SV566 @ SV435 )
                    | ! [SX3: $o] : SX3 )
                | ~ ( ~ ( in @ SV566 @ SV435 )
                    | ! [SX3: $o] :
                        ( ~ SX3
                        | SX3 ) ) ) )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3117]) ).

thf(3229,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ ! [SY2839: $o] :
                ( ~ SY2839
                | ~ ( in @ SV566 @ SV221 )
                | SY2839 ) )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3118]) ).

thf(3230,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ ~ ( ~ ! [SY2840: $o] :
                      ( ~ SY2840
                      | ( in @ SV566 @ SV435 )
                      | SY2840 )
                | ~ ! [SX3: $o] :
                      ( ~ SX3
                      | ~ SX3
                      | SX3 ) ) )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3118]) ).

thf(3231,plain,
    ! [SV226: $i,SV439: $i,SV766: $i] :
      ( ( ( in @ SV766 @ SV439 )
        = $true )
      | ( ( ! [SX3: $o] : SX3 )
        = $true )
      | ( ( in @ SV766 @ SV226 )
        = $true )
      | ( ( in @ SV766 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3119]) ).

thf(3232,plain,
    ! [SV439: $i,SV226: $i,SV767: $i,SV810: $o] :
      ( ( ( ~ SV810
          | SV810 )
        = $true )
      | ( ( in @ SV767 @ SV226 )
        = $true )
      | ( ( in @ SV767 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3120]) ).

thf(3233,plain,
    ! [SV439: $i,SV226: $i,SV767: $i] :
      ( ( ( ~ $true
          | $true )
        = $true )
      | ( ( in @ SV767 @ SV226 )
        = $true )
      | ( ( in @ SV767 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3120]) ).

thf(3234,plain,
    ! [SV439: $i,SV226: $i,SV767: $i] :
      ( ( ( ~ $false
          | $false )
        = $true )
      | ( ( in @ SV767 @ SV226 )
        = $true )
      | ( ( in @ SV767 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3120]) ).

thf(3235,plain,
    ! [SV226: $i,SV439: $i,SV768: $i,SV797: $o] :
      ( ( ( ~ SV797 ) = $true )
      | ( ( ( in @ SV768 @ SV439 )
          | SV797 )
        = $true )
      | ( ( in @ SV768 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3121]) ).

thf(3236,plain,
    ! [SV226: $i,SV439: $i,SV768: $i] :
      ( ( ( ~ $true ) = $true )
      | ( ( ( in @ SV768 @ SV439 )
          | $true )
        = $true )
      | ( ( in @ SV768 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3122]) ).

thf(3237,plain,
    ! [SV226: $i,SV439: $i,SV768: $i] :
      ( ( ( ~ $false ) = $true )
      | ( ( ( in @ SV768 @ SV439 )
          | $false )
        = $true )
      | ( ( in @ SV768 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3123]) ).

thf(3238,plain,
    ! [SV439: $i,SV226: $i,SV776: $i,SV798: $o] :
      ( ( ( ~ SV798 ) = $true )
      | ( ( ~ SV798
          | SV798 )
        = $true )
      | ( ( in @ SV776 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3124]) ).

thf(3239,plain,
    ! [SV439: $i,SV226: $i,SV776: $i] :
      ( ( ( ~ $true ) = $true )
      | ( ( ~ $true
          | $true )
        = $true )
      | ( ( in @ SV776 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3125]) ).

thf(3240,plain,
    ! [SV439: $i,SV226: $i,SV776: $i] :
      ( ( ( ~ $false ) = $true )
      | ( ( ~ $false
          | $false )
        = $true )
      | ( ( in @ SV776 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3126]) ).

thf(3241,plain,
    ! [SV568: $i,SV811: $i,SV228: $i > $o] :
      ( ( ( ~ ( SV228 @ SV811 )
          | ( ( sK46_SY211 @ SV228 )
            = SV811 ) )
        = $true )
      | ( ( ( sK47_Xy @ SV568 @ SV228 )
          = SV568 )
        = $false )
      | ( ( SV228 @ ( sK47_Xy @ SV568 @ SV228 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3127]) ).

thf(3242,plain,
    ! [SV568: $i,SV782: $i,SV228: $i > $o] :
      ( ( ( SV228 @ SV782 )
        = $false )
      | ( ( ( sK46_SY211 @ SV228 )
          = SV782 )
        = $true )
      | ( ( SV228 @ ( sK47_Xy @ SV568 @ SV228 ) )
        = $true )
      | ( ( ( sK47_Xy @ SV568 @ SV228 )
          = SV568 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3129]) ).

thf(3243,plain,
    ! [SV229: $i,SV783: $i,SV441: $i > $o] :
      ( ( ( SV441 @ SV783 )
        = $false )
      | ( ( ~ ( in @ SV783 @ SV229 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV229
            @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) )
        = $true )
      | ( ( in @ ( sK75_SY1878 @ SV441 @ SV229 ) @ SV229 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3130]) ).

thf(3244,plain,
    ! [SV229: $i,SV441: $i > $o] :
      ( ( ( ! [SY2705: $i] :
              ( ~ ( SV441 @ SY2705 )
              | ~ ( in @ SY2705 @ SV229 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV229
            @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) )
        = $true )
      | ( ( SV441 @ ( sK74_Xx @ SV441 @ SV229 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3131]) ).

thf(3245,plain,
    ! [SV229: $i,SV441: $i > $o] :
      ( ( ( ~ ( SV441 @ ( sK75_SY1878 @ SV441 @ SV229 ) )
          | ~ ( ( ( sK74_Xx @ SV441 @ SV229 )
               != ( sK75_SY1878 @ SV441 @ SV229 ) ) ) )
        = $false )
      | ( ( ! [SY2705: $i] :
              ( ~ ( SV441 @ SY2705 )
              | ~ ( in @ SY2705 @ SV229 ) )
          | ( singleton
            @ ( dsetconstr @ SV229
              @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3132]) ).

thf(3246,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
              | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                          | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) ) )
        = $true )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3133]) ).

thf(3247,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
          | ~ ~ ( ~ ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
                | ~ ~ ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 ) ) )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
              | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                          | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
          | ( SV569 = SV706 ) )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3134]) ).

thf(3248,plain,
    ! [SV231: $i,SV784: $i] :
      ( ( ( in @ SV784 @ omega )
        = $false )
      | ( ( in @ SV784 @ SV231 )
        = $true )
      | ( ( in @ ( sK9_Xx @ SV231 ) @ omega )
        = $true )
      | ( ( in @ emptyset @ SV231 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3135]) ).

thf(3249,plain,
    ! [SV231: $i,SV785: $i] :
      ( ( ( in @ SV785 @ omega )
        = $false )
      | ( ( in @ SV785 @ SV231 )
        = $true )
      | ( ( in @ ( sK9_Xx @ SV231 ) @ SV231 )
        = $true )
      | ( ( in @ emptyset @ SV231 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3136]) ).

thf(3250,plain,
    ! [SV786: $i,SV658: $i,SV233: $i] :
      ( ( ( ~ ! [SY2925: $i] :
                ( ~ ( in @ SY2925 @ ( sK15_B @ SV233 ) )
                | ! [SY2926: $i] :
                    ( ~ ( in @ SY2926 @ SY2925 )
                    | ( in @ SY2926 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) )
                | ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SY2925 ) )
          | ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) )
                      | ~ ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 ) )
                | ~ ! [SY2927: $i] :
                      ( ~ ( in @ SY2927 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
                      | ~ ( in @ SY2927 @ SV658 ) ) ) )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( in @ SV786 @ SV658 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3137]) ).

thf(3251,plain,
    ! [SV233: $i,SV658: $i,SV799: $i] :
      ( ( ( in @ SV799 @ SV658 )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 )
        = $false )
      | ( ( ~ ( ~ ! [SY2925: $i] :
                    ( ~ ( in @ SY2925 @ ( sK15_B @ SV233 ) )
                    | ! [SY2926: $i] :
                        ( ~ ( in @ SY2926 @ SY2925 )
                        | ( in @ SY2926 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) )
                    | ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SY2925 ) )
              | ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) )
                          | ~ ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 ) )
                    | ~ ! [SY2927: $i] :
                          ( ~ ( in @ SY2927 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
                          | ~ ( in @ SY2927 @ SV658 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3138]) ).

thf(3252,plain,
    ! [SV754: $i,SV233: $i,SV770: $i] :
      ( ( ( in @ SV770 @ ( sK15_B @ SV233 ) )
        = $false )
      | ( ( in @ SV754 @ ( sK15_B @ SV233 ) )
        = $false )
      | ( ( ! [SY2983: $i] :
              ( ~ ( in @ SY2983 @ SV754 )
              | ( in @ SY2983 @ SV770 ) )
          | ! [SY2984: $i] :
              ( ~ ( in @ SY2984 @ SV770 )
              | ( in @ SY2984 @ SV754 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3139]) ).

thf(3253,plain,
    ! [SV233: $i,SV787: $i] :
      ( ( ( in @ SV787 @ ( sK15_B @ SV233 ) )
        = $false )
      | ( ( ! [SY2988: $i] :
              ( ~ ( in @ SY2988 @ SV787 )
              | ( in @ SY2988 @ SV233 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3140]) ).

thf(3254,plain,
    ! [SV800: $i,SV233: $i,SV788: $i] :
      ( ( ( ~ ( in @ SV788 @ SV233 )
          | ~ ( in @ SV800 @ SV233 ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) @ ( sK15_B @ SV233 ) )
              | ~ ~ ( ~ ( ~ ( in @ SV788 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) )
                        | ~ ( in @ SV800 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) ) )
                    | ~ ( ( in @ SV788 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) )
                        | ( in @ SV800 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) ) ) ) )
          | ( SV788 = SV800 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3141]) ).

thf(3255,plain,
    ! [SV573: $i,SV235: $i > $o,SV801: $i] :
      ( ( ( SV801
         != ( sK32_Xx @ SV235 ) )
        = $true )
      | ( ( SV235 @ SV801 )
        = $true )
      | ( ( SV235 @ ( sK33_SY142 @ SV573 @ SV235 ) )
        = $true )
      | ( ( SV235 @ SV573 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3142]) ).

thf(3256,plain,
    ! [SV573: $i,SV802: $i,SV235: $i > $o] :
      ( ( ( ~ ( SV235 @ SV802 ) )
        = $true )
      | ( ( SV802
          = ( sK32_Xx @ SV235 ) )
        = $true )
      | ( ( SV235 @ ( sK33_SY142 @ SV573 @ SV235 ) )
        = $true )
      | ( ( SV235 @ SV573 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3143]) ).

thf(3257,plain,
    ! [SV573: $i,SV235: $i > $o,SV812: $i] :
      ( ( ( ( SV812
           != ( sK32_Xx @ SV235 ) )
          | ( SV235 @ SV812 ) )
        = $true )
      | ( ( SV573
          = ( sK33_SY142 @ SV573 @ SV235 ) )
        = $false )
      | ( ( SV235 @ SV573 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3144]) ).

thf(3258,plain,
    ! [SV573: $i,SV813: $i,SV235: $i > $o] :
      ( ( ( ~ ( SV235 @ SV813 )
          | ( SV813
            = ( sK32_Xx @ SV235 ) ) )
        = $true )
      | ( ( SV573
          = ( sK33_SY142 @ SV573 @ SV235 ) )
        = $false )
      | ( ( SV235 @ SV573 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3145]) ).

thf(3259,plain,
    ! [SV236: $i,SV445: $i,SV710: $i > $o,SV574: $i,SV789: $i] :
      ( ( ( in @ SV789 @ SV574 )
        = $false )
      | ( ( SV710 @ SV789 )
        = $true )
      | ( ( in @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ SV236 )
        = $true )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3146]) ).

thf(3260,plain,
    ! [SV236: $i,SV445: $i,SV574: $i,SV710: $i > $o] :
      ( ( ( in @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) @ SV445 )
        = $true )
      | ( ( ! [SY2953: $i] :
              ( ~ ( in @ SY2953 @ SV574 )
              | ( SV710 @ SY2953 ) ) )
        = $true )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3147]) ).

thf(3261,plain,
    ! [SV236: $i,SV445: $i,SV574: $i,SV710: $i > $o] :
      ( ( ( ~ ( ~ ( in @ ( kpair @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) ) @ SV574 )
              | ~ ~ ( SV710 @ ( kpair @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) ) ) ) )
        = $true )
      | ( ( ! [SY2953: $i] :
              ( ~ ( in @ SY2953 @ SV574 )
              | ( SV710 @ SY2953 ) ) )
        = $true )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3148]) ).

thf(3262,plain,
    ! [SV582: $i,SV803: $i,SV241: $i > $o] :
      ( ( ( ~ ( SV241 @ SV803 ) )
        = $true )
      | ( ( ( sK43_SY205 @ SV241 )
          = SV803 )
        = $true )
      | ( ( SV241 @ ( sK44_Xx @ SV241 ) )
        = $true )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3149]) ).

thf(3263,plain,
    ! [SV582: $i,SV241: $i > $o] :
      ( ( ( ~ ! [SY2422: $i] :
                ( ~ ( SV241 @ SY2422 )
                | ( ( sK43_SY205 @ SV241 )
                  = SY2422 ) ) )
        = $false )
      | ( ( SV241 @ ( sK45_SY1868 @ SV241 ) )
        = $true )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3150]) ).

thf(3264,plain,
    ! [SV582: $i,SV241: $i > $o] :
      ( ( ( ~ ( SV241 @ ( sK43_SY205 @ SV241 ) ) )
        = $false )
      | ( ( SV241 @ ( sK45_SY1868 @ SV241 ) )
        = $true )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3150]) ).

thf(3265,plain,
    ! [SV582: $i,SV241: $i > $o] :
      ( ( ( ~ ! [SY2422: $i] :
                ( ~ ( SV241 @ SY2422 )
                | ( ( sK43_SY205 @ SV241 )
                  = SY2422 ) )
          | ~ ( SV241 @ ( sK43_SY205 @ SV241 ) ) )
        = $false )
      | ( ( ( sK44_Xx @ SV241 )
          = ( sK45_SY1868 @ SV241 ) )
        = $false )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3151]) ).

thf(3266,plain,
    ! [SV717: $i,SV583: $i,SV450: $i,SV243: $i] :
      ( ( ( ( ap @ SV243 @ SV450 @ SV583 @ ( sK90_Xx @ SV717 @ SV583 @ SV450 @ SV243 ) )
          = ( ap @ SV243 @ SV450 @ SV717 @ ( sK90_Xx @ SV717 @ SV583 @ SV450 @ SV243 ) ) )
        = $false )
      | ( ( SV583 = SV717 )
        = $true )
      | ( ( func @ SV243 @ SV450 @ SV717 )
        = $false )
      | ( ( func @ SV243 @ SV450 @ SV583 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3153]) ).

thf(3267,plain,
    ! [SV718: $i,SV585: $i,SV451: $i,SV245: $i] :
      ( ( ( ( ap @ SV245 @ SV451 @ SV585 @ ( sK91_Xx @ SV718 @ SV585 @ SV451 @ SV245 ) )
          = ( ap @ SV245 @ SV451 @ SV718 @ ( sK91_Xx @ SV718 @ SV585 @ SV451 @ SV245 ) ) )
        = $false )
      | ( ( SV585 = SV718 )
        = $true )
      | ( ( in @ SV718 @ ( funcSet @ SV245 @ SV451 ) )
        = $false )
      | ( ( in @ SV585 @ ( funcSet @ SV245 @ SV451 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3155]) ).

thf(3268,plain,
    ! [SV586: $i,SV804: $i,SV247: $i > $o] :
      ( ( ( ~ ( SV247 @ SV804 ) )
        = $true )
      | ( ( ( sK21_Xx @ SV247 )
          = SV804 )
        = $true )
      | ( ( SV247 @ ( sK22_SY74 @ SV586 @ SV247 ) )
        = $true )
      | ( ( SV247 @ SV586 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3156]) ).

thf(3269,plain,
    ! [SV586: $i,SV814: $i,SV247: $i > $o] :
      ( ( ( ~ ( SV247 @ SV814 )
          | ( ( sK21_Xx @ SV247 )
            = SV814 ) )
        = $true )
      | ( ( SV586
          = ( sK22_SY74 @ SV586 @ SV247 ) )
        = $false )
      | ( ( SV247 @ SV586 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3157]) ).

thf(3270,plain,
    ! [SV248: $i,SV453: $i,SV661: $i > $o,SV719: $i > $o] :
      ( ( ( in @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) @ SV453 )
        = $true )
      | ( ( ( dsetconstr @ SV248
            @ ^ [SY2930: $i] : ( SV661 @ SY2930 ) )
          = ( dsetconstr @ SV453
            @ ^ [SY2961: $i] : ( SV719 @ SY2961 ) ) )
        = $true )
      | ( ( SV248 = SV453 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3159]) ).

thf(3271,plain,
    ! [SV248: $i,SV453: $i,SV661: $i > $o,SV719: $i > $o] :
      ( ( ( ~ ( ( ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 )
               != ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) )
              | ~ ~ ( ~ ( ~ ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
                        | ~ ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) )
                    | ~ ( ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
                        | ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) ) ) ) )
        = $true )
      | ( ( ( dsetconstr @ SV248
            @ ^ [SY2930: $i] : ( SV661 @ SY2930 ) )
          = ( dsetconstr @ SV453
            @ ^ [SY2961: $i] : ( SV719 @ SY2961 ) ) )
        = $true )
      | ( ( SV248 = SV453 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3160]) ).

thf(3272,plain,
    ! [SV1: $i,SV733: $i,SV612: $i,SV250: $i,SV777: $i] :
      ( ( ( ~ ( in @ SV777 @ ( binintersect @ SV250 @ SV612 ) ) )
        = $true )
      | ( ( in @ SV777 @ ( binunion @ SV250 @ SV733 ) )
        = $true )
      | ( ( in @ SV777 @ SV1 )
        = $false )
      | ( ( in @ SV733 @ ( powerset @ SV1 ) )
        = $false )
      | ( ( in @ SV612 @ ( powerset @ SV1 ) )
        = $false )
      | ( ( in @ SV250 @ ( powerset @ SV1 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3161]) ).

thf(3273,plain,
    ! [SV254: $i,SV5: $i,SV616: $i,SV771: $i] :
      ( ( ( in @ SV771 @ SV616 )
        = $false )
      | ( ( in @ SV771 @ ( setminus @ SV5 @ SV254 ) )
        = $true )
      | ( ( in @ SV771 @ SV5 )
        = $false )
      | ( ( subset @ SV254 @ ( setminus @ SV5 @ SV616 ) )
        = $false )
      | ( ( in @ SV616 @ ( powerset @ SV5 ) )
        = $false )
      | ( ( in @ SV254 @ ( powerset @ SV5 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3162]) ).

thf(3274,plain,
    ! [SV17: $i,SV625: $i,SV266: $i,SV738: $i] :
      ( ( ( in @ SV738 @ SV266 )
        = $false )
      | ( ( in @ SV738 @ SV625 )
        = $true )
      | ( ( subset @ SV266 @ SV625 )
        = $false )
      | ( ( in @ SV738 @ SV17 )
        = $false )
      | ( ( in @ SV625 @ ( powerset @ SV17 ) )
        = $false )
      | ( ( in @ SV266 @ ( powerset @ SV17 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3164]) ).

thf(3275,plain,
    ! [SV18: $i,SV267: $i,SV626: $i,SV739: $i] :
      ( ( ( in @ SV739 @ SV626 )
        = $false )
      | ( ( ~ ( in @ SV739 @ SV267 ) )
        = $true )
      | ( ( subset @ SV267 @ ( setminus @ SV18 @ SV626 ) )
        = $false )
      | ( ( in @ SV739 @ SV18 )
        = $false )
      | ( ( in @ SV626 @ ( powerset @ SV18 ) )
        = $false )
      | ( ( in @ SV267 @ ( powerset @ SV18 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3165]) ).

thf(3276,plain,
    ! [SV23: $i,SV631: $i,SV272: $i,SV742: $i] :
      ( ( ( in @ SV742 @ SV272 )
        = $false )
      | ( ( in @ SV742 @ SV631 )
        = $true )
      | ( ( in @ SV272 @ ( powerset @ SV631 ) )
        = $false )
      | ( ( in @ SV742 @ SV23 )
        = $false )
      | ( ( in @ SV631 @ ( powerset @ SV23 ) )
        = $false )
      | ( ( in @ SV272 @ ( powerset @ SV23 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3166]) ).

thf(3277,plain,
    ! [SV42: $i,SV635: $i,SV743: $i,SV288: $i > $o] :
      ( ( ( SV288 @ SV743 )
        = $false )
      | ( ( SV635 = SV743 )
        = $true )
      | ( ( SV288 @ SV635 )
        = $false )
      | ( ( in @ SV743 @ SV42 )
        = $false )
      | ( ( in @ SV635 @ SV42 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV42
            @ ^ [SY2500: $i] : ( SV288 @ SY2500 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3169]) ).

thf(3278,plain,
    ! [SV189: $i,SV409: $i,SV647: $i] :
      ( ( ( in @ ( sK97_Xx @ SV647 @ SV409 @ SV189 ) @ SV409 )
        = $true )
      | ( ( subset @ SV409 @ SV647 )
        = $true )
      | ( ( in @ SV647 @ ( powerset @ SV189 ) )
        = $false )
      | ( ( in @ SV409 @ ( powerset @ SV189 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3170]) ).

thf(3279,plain,
    ! [SV189: $i,SV409: $i,SV647: $i] :
      ( ( ( ~ ( in @ ( sK97_Xx @ SV647 @ SV409 @ SV189 ) @ SV647 ) )
        = $true )
      | ( ( subset @ SV409 @ SV647 )
        = $true )
      | ( ( in @ SV647 @ ( powerset @ SV189 ) )
        = $false )
      | ( ( in @ SV409 @ ( powerset @ SV189 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3171]) ).

thf(3280,plain,
    ! [SV551: $i,SV759: $i,SV790: $i,SV194: $i > $o] :
      ( ( ( SV194 @ SV790 )
        = $false )
      | ( ( SV759 = SV790 )
        = $true )
      | ( ( SV194 @ SV759 )
        = $false )
      | ( ( SV194 @ ( sK57_SY248 @ SV551 @ SV194 ) )
        = $true )
      | ( ( SV194 @ SV551 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3172]) ).

thf(3281,plain,
    ! [SV551: $i,SV772: $i,SV805: $i,SV194: $i > $o] :
      ( ( ( ~ ( SV194 @ SV805 ) )
        = $true )
      | ( ( SV772 = SV805 )
        = $true )
      | ( ( SV194 @ SV772 )
        = $false )
      | ( ( SV551
          = ( sK57_SY248 @ SV551 @ SV194 ) )
        = $false )
      | ( ( SV194 @ SV551 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3173]) ).

thf(3282,plain,
    ! [SV413: $i,SV773: $i,SV791: $i,SV195: $i > $i > $o] :
      ( ( ( SV195 @ SV791 @ SV773 )
        = $false )
      | ( ( ~ ( in @ SV791 @ SV413 ) )
        = $true )
      | ( ( in @ SV773 @ ( sK10_B @ SV413 @ SV195 ) )
        = $true )
      | ( ( in @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV413 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3174]) ).

thf(3283,plain,
    ! [SV413: $i,SV774: $i,SV195: $i > $i > $o] :
      ( ( ( ~ ( SV195 @ ( sK11_Xy @ SV774 @ SV413 @ SV195 ) @ SV774 ) )
        = $false )
      | ( ( in @ SV774 @ ( sK10_B @ SV413 @ SV195 ) )
        = $false )
      | ( ( in @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV413 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3175]) ).

thf(3284,plain,
    ! [SV195: $i > $i > $o,SV413: $i,SV774: $i] :
      ( ( ( ~ ( in @ ( sK11_Xy @ SV774 @ SV413 @ SV195 ) @ SV413 ) )
        = $false )
      | ( ( in @ SV774 @ ( sK10_B @ SV413 @ SV195 ) )
        = $false )
      | ( ( in @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV413 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3175]) ).

thf(3285,plain,
    ! [SV725: $i,SV413: $i,SV195: $i > $i > $o] :
      ( ( ( ~ ! [SY2639: $i] :
                ( ! [SY2640: $i] :
                    ( ~ ( SV195 @ SY2640 @ SY2639 )
                    | ~ ( in @ SY2640 @ SV413 ) )
                | ( in @ SY2639 @ ( sK10_B @ SV413 @ SV195 ) ) ) )
        = $false )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3176]) ).

thf(3286,plain,
    ! [SV725: $i,SV195: $i > $i > $o,SV413: $i] :
      ( ( ( ~ ! [SY2641: $i] :
                ( ~ ( in @ SY2641 @ ( sK10_B @ SV413 @ SV195 ) )
                | ~ ( ~ ( SV195 @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SY2641 )
                    | ~ ( in @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SV413 ) ) ) )
        = $false )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3176]) ).

thf(3287,plain,
    ! [SV725: $i,SV413: $i,SV195: $i > $i > $o] :
      ( ( ( ~ ! [SY2639: $i] :
                ( ! [SY2640: $i] :
                    ( ~ ( SV195 @ SY2640 @ SY2639 )
                    | ~ ( in @ SY2640 @ SV413 ) )
                | ( in @ SY2639 @ ( sK10_B @ SV413 @ SV195 ) ) )
          | ~ ! [SY2641: $i] :
                ( ~ ( in @ SY2641 @ ( sK10_B @ SV413 @ SV195 ) )
                | ~ ( ~ ( SV195 @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SY2641 )
                    | ~ ( in @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SV413 ) ) ) )
        = $false )
      | ( ( SV725
          = ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $false )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3177]) ).

thf(3288,plain,
    ! [SV196: $i,SV414: $i,SV552: $i,SV815: $o] :
      ( ( SV815 = $true )
      | ( ( in @ SV552 @ SV414 )
        = $true )
      | ( ( SV552 = SV196 )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3178]) ).

thf(3289,plain,
    ! [SV196: $i,SV414: $i,SV552: $i] :
      ( ( $true = $true )
      | ( ( in @ SV552 @ SV414 )
        = $true )
      | ( ( SV552 = SV196 )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3178]) ).

thf(3290,plain,
    ! [SV196: $i,SV414: $i,SV552: $i] :
      ( ( $false = $true )
      | ( ( in @ SV552 @ SV414 )
        = $true )
      | ( ( SV552 = SV196 )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3178]) ).

thf(3291,plain,
    ! [SV414: $i,SV196: $i,SV552: $i,SV806: $o] :
      ( ( ( ~ SV806 ) = $true )
      | ( SV806 = $true )
      | ( ( SV552 = SV196 )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3179]) ).

thf(3292,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( ( ~ $true ) = $true )
      | ( $true = $true )
      | ( ( SV552 = SV196 )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3180]) ).

thf(3293,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( ( ~ $false ) = $true )
      | ( $false = $true )
      | ( ( SV552 = SV196 )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3181]) ).

thf(3294,plain,
    ! [SV196: $i,SV414: $i,SV552: $i,SV792: $o] :
      ( ( SV792 = $false )
      | ( ( ( in @ SV552 @ SV414 )
          | SV792 )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3182]) ).

thf(3295,plain,
    ! [SV196: $i,SV414: $i,SV552: $i] :
      ( ( $true = $false )
      | ( ( ( in @ SV552 @ SV414 )
          | $true )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3183]) ).

thf(3296,plain,
    ! [SV196: $i,SV414: $i,SV552: $i] :
      ( ( $false = $false )
      | ( ( ( in @ SV552 @ SV414 )
          | $false )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3184]) ).

thf(3297,plain,
    ! [SV414: $i,SV196: $i,SV552: $i,SV793: $o] :
      ( ( SV793 = $false )
      | ( ( ~ SV793
          | SV793 )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3185]) ).

thf(3298,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( $true = $false )
      | ( ( ~ $true
          | $true )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3186]) ).

thf(3299,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( $false = $false )
      | ( ( ~ $false
          | $false )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3187]) ).

thf(3300,plain,
    ! [SV652: $i > $o,SV778: $i,SV605: $i > $o] :
      ( ( ( ~ ( SV605 @ ( sK54_SY233 @ SV778 @ SV652 @ SV605 ) ) )
        = $false )
      | ( ( ~ ( SV605 @ SV778 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( ( sK55_Xx @ SV652 @ SV605 )
          = ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3188]) ).

thf(3301,plain,
    ! [SV605: $i > $o,SV652: $i > $o,SV778: $i] :
      ( ( ( ~ ( ( SV778
               != ( sK54_SY233 @ SV778 @ SV652 @ SV605 ) ) ) )
        = $false )
      | ( ( ~ ( SV605 @ SV778 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( ( sK55_Xx @ SV652 @ SV605 )
          = ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3188]) ).

thf(3302,plain,
    ! [SV652: $i > $o,SV605: $i > $o] :
      ( ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $false )
      | ( ( ~ ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) ) )
        = $true )
      | ( ( ! [SY2919: $i] :
              ( ~ ( ~ ( SV605 @ ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) )
                  | ~ ( ( SY2919
                       != ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) ) ) )
              | ~ ( SV605 @ SY2919 ) )
          | ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3189]) ).

thf(3303,plain,
    ! [SV652: $i > $o,SV605: $i > $o] :
      ( ( ( ! [SY2919: $i] :
              ( ~ ( ~ ( SV605 @ ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) )
                  | ~ ( ( SY2919
                       != ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) ) ) )
              | ~ ( SV605 @ SY2919 ) ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3190]) ).

thf(3304,plain,
    ! [SV606: $i > $o,SV779: $i,SV653: $i > $o] :
      ( ( ( ~ ( SV653 @ ( sK50_SY236 @ SV779 @ SV653 @ SV606 ) ) )
        = $false )
      | ( ( ~ ( SV653 @ SV779 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( ( sK51_Xx @ SV653 @ SV606 )
          = ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3191]) ).

thf(3305,plain,
    ! [SV606: $i > $o,SV653: $i > $o,SV779: $i] :
      ( ( ( ~ ( ( SV779
               != ( sK50_SY236 @ SV779 @ SV653 @ SV606 ) ) ) )
        = $false )
      | ( ( ~ ( SV653 @ SV779 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( ( sK51_Xx @ SV653 @ SV606 )
          = ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3191]) ).

thf(3306,plain,
    ! [SV653: $i > $o,SV606: $i > $o] :
      ( ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $false )
      | ( ( ~ ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) ) )
        = $true )
      | ( ( ! [SY2921: $i] :
              ( ~ ( ~ ( SV653 @ ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) )
                  | ~ ( ( SY2921
                       != ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) ) ) )
              | ~ ( SV653 @ SY2921 ) )
          | ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3192]) ).

thf(3307,plain,
    ! [SV606: $i > $o,SV653: $i > $o] :
      ( ( ( ! [SY2921: $i] :
              ( ~ ( ~ ( SV653 @ ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) )
                  | ~ ( ( SY2921
                       != ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) ) ) )
              | ~ ( SV653 @ SY2921 ) ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3193]) ).

thf(3308,plain,
    ! [SV558: $i,SV794: $i,SV205: $i > $o] :
      ( ( ( SV205 @ SV794 )
        = $false )
      | ( ( ( sK41_SY198 @ SV205 )
          = SV794 )
        = $true )
      | ( ( SV205 @ ( sK42_Xy @ SV558 @ SV205 ) )
        = $true )
      | ( ( SV205 @ SV558 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3194]) ).

thf(3309,plain,
    ! [SV558: $i,SV807: $i,SV205: $i > $o] :
      ( ( ( ~ ( SV205 @ SV807 ) )
        = $true )
      | ( ( ( sK41_SY198 @ SV205 )
          = SV807 )
        = $true )
      | ( ( SV558
          = ( sK42_Xy @ SV558 @ SV205 ) )
        = $false )
      | ( ( SV205 @ SV558 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3195]) ).

thf(3310,plain,
    ( ( ~ ( in @ sK5_SY1831 @ ( binintersect @ sK2_SY1822 @ sK3_SY1826 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[3196]) ).

thf(3311,plain,
    ( ( ~ ~ ( in @ sK5_SY1831 @ ( binunion @ sK3_SY1826 @ sK4_SY1829 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[3196]) ).

thf(3312,plain,
    ! [SV207: $i,SV422: $i,SV702: $i > $o,SV560: $i,SV816: $i] :
      ( ( ( ~ ( in @ SV816 @ SV560 )
          | ( SV702 @ SV816 ) )
        = $true )
      | ( ( in @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) @ SV422 )
        = $true )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3198]) ).

thf(3313,plain,
    ! [SV207: $i,SV422: $i,SV560: $i,SV702: $i > $o] :
      ( ( ( ~ ( in @ ( kpair @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) ) @ SV560 )
          | ~ ~ ( SV702 @ ( kpair @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) ) ) )
        = $false )
      | ( ( ! [SY2947: $i] :
              ( ~ ( in @ SY2947 @ SV560 )
              | ( SV702 @ SY2947 ) ) )
        = $true )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3199]) ).

thf(3314,plain,
    ! [SV208: $i,SV423: $i,SV561: $i,SV703: $i] :
      ( ( ( ~ ( in @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) @ SV423 ) )
        = $false )
      | ( ( subset @ SV561 @ SV703 )
        = $true )
      | ( ( subset @ SV703 @ ( cartprod @ SV208 @ SV423 ) )
        = $false )
      | ( ( subset @ SV561 @ ( cartprod @ SV208 @ SV423 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3200]) ).

thf(3315,plain,
    ! [SV208: $i,SV423: $i,SV561: $i,SV703: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) ) @ SV561 )
                | ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) ) @ SV703 ) ) )
        = $false )
      | ( ( subset @ SV561 @ SV703 )
        = $true )
      | ( ( subset @ SV703 @ ( cartprod @ SV208 @ SV423 ) )
        = $false )
      | ( ( subset @ SV561 @ ( cartprod @ SV208 @ SV423 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3200]) ).

thf(3316,plain,
    ! [SV424: $i > $o,SV209: $i,SV781: $i] :
      ( ( ( in @ SV781 @ SV209 )
        = $false )
      | ( ( SV424 @ SV781 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV209
            @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) )
        = $true )
      | ( ( in @ ( sK71_SY1877 @ SV424 @ SV209 ) @ SV209 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3201]) ).

thf(3317,plain,
    ! [SV209: $i,SV817: $i,SV424: $i > $o] :
      ( ( ( ~ ( SV424 @ SV817 )
          | ~ ( in @ SV817 @ SV209 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV209
            @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) )
        = $true )
      | ( ( SV424 @ ( sK70_Xx @ SV424 @ SV209 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3202]) ).

thf(3318,plain,
    ! [SV209: $i,SV424: $i > $o] :
      ( ( ( ~ ( SV424 @ ( sK71_SY1877 @ SV424 @ SV209 ) ) )
        = $false )
      | ( ( ! [SY2662: $i] :
              ( ~ ( SV424 @ SY2662 )
              | ~ ( in @ SY2662 @ SV209 ) )
          | ( singleton
            @ ( dsetconstr @ SV209
              @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3203]) ).

thf(3319,plain,
    ! [SV209: $i,SV424: $i > $o] :
      ( ( ( ~ ( ( ( sK70_Xx @ SV424 @ SV209 )
               != ( sK71_SY1877 @ SV424 @ SV209 ) ) ) )
        = $false )
      | ( ( ! [SY2662: $i] :
              ( ~ ( SV424 @ SY2662 )
              | ~ ( in @ SY2662 @ SV209 ) )
          | ( singleton
            @ ( dsetconstr @ SV209
              @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3203]) ).

thf(3320,plain,
    ! [SV562: $i,SV763: $i,SV795: $i,SV211: $i > $o] :
      ( ( ( SV211 @ SV795 )
        = $false )
      | ( ( SV763 = SV795 )
        = $true )
      | ( ( SV211 @ SV763 )
        = $false )
      | ( ( SV211 @ ( sK48_SY224 @ SV562 @ SV211 ) )
        = $true )
      | ( ( SV211 @ SV562 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3206]) ).

thf(3321,plain,
    ! [SV562: $i,SV775: $i,SV808: $i,SV211: $i > $o] :
      ( ( ( ~ ( SV211 @ SV808 ) )
        = $true )
      | ( ( SV775 = SV808 )
        = $true )
      | ( ( SV211 @ SV775 )
        = $false )
      | ( ( SV562
          = ( sK48_SY224 @ SV562 @ SV211 ) )
        = $false )
      | ( ( SV211 @ SV562 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3207]) ).

thf(3322,plain,
    ! [SV750: $i,SV213: $i > $o,SV427: $i > $o] :
      ( ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV750 )
        = $false )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3208]) ).

thf(3323,plain,
    ! [SV427: $i > $o,SV750: $i,SV213: $i > $o] :
      ( ( ( SV213 @ SV750 )
        = $false )
      | ( ( SV750
          = ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
        = $false )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3209]) ).

thf(3324,plain,
    ! [SV427: $i > $o,SV818: $i,SV213: $i > $o] :
      ( ( ( ~ ( ~ ( SV213 @ ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
              | ~ ( ( SV818
                   != ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) ) ) )
          | ~ ( SV213 @ SV818 ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3210]) ).

thf(3325,plain,
    ! [SV427: $i > $o,SV796: $i,SV213: $i > $o] :
      ( ( ( ~ ( SV213 @ ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
          | ~ ( ( SV796
               != ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) ) ) )
        = $false )
      | ( ( ~ ( SV213 @ SV796 ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3211]) ).

thf(3326,plain,
    ! [SV214: $i,SV428: $i,SV654: $i] :
      ( ( ( in @ ( sK98_Xx @ SV654 @ SV428 @ SV214 ) @ SV428 )
        = $true )
      | ( ( in @ SV428 @ ( powerset @ SV654 ) )
        = $true )
      | ( ( in @ SV654 @ ( powerset @ SV214 ) )
        = $false )
      | ( ( in @ SV428 @ ( powerset @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3212]) ).

thf(3327,plain,
    ! [SV214: $i,SV428: $i,SV654: $i] :
      ( ( ( ~ ( in @ ( sK98_Xx @ SV654 @ SV428 @ SV214 ) @ SV654 ) )
        = $true )
      | ( ( in @ SV428 @ ( powerset @ SV654 ) )
        = $true )
      | ( ( in @ SV654 @ ( powerset @ SV214 ) )
        = $false )
      | ( ( in @ SV428 @ ( powerset @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3213]) ).

thf(3328,plain,
    ! [SV564: $i,SV704: $i,SV432: $i,SV218: $i,SV809: $i] :
      ( ( ( ~ ( in @ SV809 @ SV218 ) )
        = $true )
      | ( ( ! [SY2990: $i] :
              ( ~ ( in @ SY2990 @ SV432 )
              | ~ ( in @ ( kpair @ SV809 @ SY2990 ) @ SV704 )
              | ( in @ ( kpair @ SV809 @ SY2990 ) @ SV564 ) ) )
        = $true )
      | ( ( in @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) @ SV218 )
        = $true )
      | ( ( func @ SV218 @ SV432 @ SV704 )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV564 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3217]) ).

thf(3329,plain,
    ! [SV564: $i,SV704: $i,SV432: $i,SV218: $i,SV819: $i] :
      ( ( ( ~ ( in @ SV819 @ SV218 )
          | ! [SY2991: $i] :
              ( ~ ( in @ SY2991 @ SV432 )
              | ~ ( in @ ( kpair @ SV819 @ SY2991 ) @ SV704 )
              | ( in @ ( kpair @ SV819 @ SY2991 ) @ SV564 ) ) )
        = $true )
      | ( ( ( ap @ SV218 @ SV432 @ SV564 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) )
          = ( ap @ SV218 @ SV432 @ SV704 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) ) )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV704 )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV564 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3218]) ).

thf(3330,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 ) )
        = $false )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3219]) ).

thf(3331,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
                | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) ) )
        = $false )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3219]) ).

thf(3332,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
              | ~ ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
                    | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) ) )
          | ( SV433 = SV656 ) )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3220]) ).

thf(3333,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
              | ~ ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
                    | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) ) )
          | ( SV433 = SV656 ) )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3221]) ).

thf(3334,plain,
    ! [SV220: $i,SV565: $i,SV434: $i > $o] :
      ( ( ( SV434 @ ( sK73_Xy @ SV565 @ SV434 @ SV220 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV220
            @ ^ [SY2682: $i] : ( SV434 @ SY2682 ) ) )
        = $true )
      | ( ( SV434 @ SV565 )
        = $false )
      | ( ( in @ SV565 @ SV220 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3222]) ).

thf(3335,plain,
    ! [SV220: $i,SV434: $i > $o,SV565: $i] :
      ( ( ( ( sK73_Xy @ SV565 @ SV434 @ SV220 )
         != SV565 )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV220
            @ ^ [SY2682: $i] : ( SV434 @ SY2682 ) ) )
        = $true )
      | ( ( SV434 @ SV565 )
        = $false )
      | ( ( in @ SV565 @ SV220 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3223]) ).

thf(3336,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( in @ SV566 @ SV221 )
        = $false )
      | ( ( ! [SX3: $o] : SX3 )
        = $true )
      | ( ( in @ SV566 @ SV221 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3224]) ).

thf(3337,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ( in @ SV566 @ SV221 )
          | ( in @ SV566 @ SV435 )
          | ! [SX3: $o] : SX3 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3225]) ).

thf(3338,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ( in @ SV566 @ SV221 )
          | ! [SX3: $o] :
              ( ~ SX3
              | SX3 ) )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3226]) ).

thf(3339,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ ( in @ SV566 @ SV435 )
          | ~ ( in @ SV566 @ SV221 )
          | ! [SX3: $o] : SX3 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3227]) ).

thf(3340,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ ( ~ ( ~ ( in @ SV566 @ SV435 )
                  | ( in @ SV566 @ SV435 )
                  | ! [SX3: $o] : SX3 )
              | ~ ( ~ ( in @ SV566 @ SV435 )
                  | ! [SX3: $o] :
                      ( ~ SX3
                      | SX3 ) ) ) )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3228]) ).

thf(3341,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ! [SY2839: $o] :
              ( ~ SY2839
              | ~ ( in @ SV566 @ SV221 )
              | SY2839 ) )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3229]) ).

thf(3342,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ ( ~ ! [SY2840: $o] :
                    ( ~ SY2840
                    | ( in @ SV566 @ SV435 )
                    | SY2840 )
              | ~ ! [SX3: $o] :
                    ( ~ SX3
                    | ~ SX3
                    | SX3 ) ) )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3230]) ).

thf(3343,plain,
    ! [SV226: $i,SV439: $i,SV766: $i,SV820: $o] :
      ( ( SV820 = $true )
      | ( ( in @ SV766 @ SV439 )
        = $true )
      | ( ( in @ SV766 @ SV226 )
        = $true )
      | ( ( in @ SV766 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3231]) ).

thf(3344,plain,
    ! [SV226: $i,SV439: $i,SV766: $i] :
      ( ( $true = $true )
      | ( ( in @ SV766 @ SV439 )
        = $true )
      | ( ( in @ SV766 @ SV226 )
        = $true )
      | ( ( in @ SV766 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3231]) ).

thf(3345,plain,
    ! [SV226: $i,SV439: $i,SV766: $i] :
      ( ( $false = $true )
      | ( ( in @ SV766 @ SV439 )
        = $true )
      | ( ( in @ SV766 @ SV226 )
        = $true )
      | ( ( in @ SV766 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3231]) ).

thf(3346,plain,
    ! [SV439: $i,SV226: $i,SV767: $i,SV810: $o] :
      ( ( ( ~ SV810 ) = $true )
      | ( SV810 = $true )
      | ( ( in @ SV767 @ SV226 )
        = $true )
      | ( ( in @ SV767 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3232]) ).

thf(3347,plain,
    ! [SV439: $i,SV226: $i,SV767: $i] :
      ( ( ( ~ $true ) = $true )
      | ( $true = $true )
      | ( ( in @ SV767 @ SV226 )
        = $true )
      | ( ( in @ SV767 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3233]) ).

thf(3348,plain,
    ! [SV439: $i,SV226: $i,SV767: $i] :
      ( ( ( ~ $false ) = $true )
      | ( $false = $true )
      | ( ( in @ SV767 @ SV226 )
        = $true )
      | ( ( in @ SV767 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3234]) ).

thf(3349,plain,
    ! [SV226: $i,SV439: $i,SV768: $i,SV797: $o] :
      ( ( SV797 = $false )
      | ( ( ( in @ SV768 @ SV439 )
          | SV797 )
        = $true )
      | ( ( in @ SV768 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3235]) ).

thf(3350,plain,
    ! [SV226: $i,SV439: $i,SV768: $i] :
      ( ( $true = $false )
      | ( ( ( in @ SV768 @ SV439 )
          | $true )
        = $true )
      | ( ( in @ SV768 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3236]) ).

thf(3351,plain,
    ! [SV226: $i,SV439: $i,SV768: $i] :
      ( ( $false = $false )
      | ( ( ( in @ SV768 @ SV439 )
          | $false )
        = $true )
      | ( ( in @ SV768 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3237]) ).

thf(3352,plain,
    ! [SV439: $i,SV226: $i,SV776: $i,SV798: $o] :
      ( ( SV798 = $false )
      | ( ( ~ SV798
          | SV798 )
        = $true )
      | ( ( in @ SV776 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3238]) ).

thf(3353,plain,
    ! [SV439: $i,SV226: $i,SV776: $i] :
      ( ( $true = $false )
      | ( ( ~ $true
          | $true )
        = $true )
      | ( ( in @ SV776 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3239]) ).

thf(3354,plain,
    ! [SV439: $i,SV226: $i,SV776: $i] :
      ( ( $false = $false )
      | ( ( ~ $false
          | $false )
        = $true )
      | ( ( in @ SV776 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3240]) ).

thf(3355,plain,
    ! [SV568: $i,SV811: $i,SV228: $i > $o] :
      ( ( ( ~ ( SV228 @ SV811 ) )
        = $true )
      | ( ( ( sK46_SY211 @ SV228 )
          = SV811 )
        = $true )
      | ( ( ( sK47_Xy @ SV568 @ SV228 )
          = SV568 )
        = $false )
      | ( ( SV228 @ ( sK47_Xy @ SV568 @ SV228 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3241]) ).

thf(3356,plain,
    ! [SV441: $i > $o,SV229: $i,SV783: $i] :
      ( ( ( in @ SV783 @ SV229 )
        = $false )
      | ( ( SV441 @ SV783 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV229
            @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) )
        = $true )
      | ( ( in @ ( sK75_SY1878 @ SV441 @ SV229 ) @ SV229 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3243]) ).

thf(3357,plain,
    ! [SV229: $i,SV821: $i,SV441: $i > $o] :
      ( ( ( ~ ( SV441 @ SV821 )
          | ~ ( in @ SV821 @ SV229 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV229
            @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) )
        = $true )
      | ( ( SV441 @ ( sK74_Xx @ SV441 @ SV229 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3244]) ).

thf(3358,plain,
    ! [SV229: $i,SV441: $i > $o] :
      ( ( ( ~ ( SV441 @ ( sK75_SY1878 @ SV441 @ SV229 ) ) )
        = $false )
      | ( ( ! [SY2705: $i] :
              ( ~ ( SV441 @ SY2705 )
              | ~ ( in @ SY2705 @ SV229 ) )
          | ( singleton
            @ ( dsetconstr @ SV229
              @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3245]) ).

thf(3359,plain,
    ! [SV229: $i,SV441: $i > $o] :
      ( ( ( ~ ( ( ( sK74_Xx @ SV441 @ SV229 )
               != ( sK75_SY1878 @ SV441 @ SV229 ) ) ) )
        = $false )
      | ( ( ! [SY2705: $i] :
              ( ~ ( SV441 @ SY2705 )
              | ~ ( in @ SY2705 @ SV229 ) )
          | ( singleton
            @ ( dsetconstr @ SV229
              @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3245]) ).

thf(3360,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
          | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                      | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3246]) ).

thf(3361,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 ) )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
              | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                          | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
          | ( SV569 = SV706 ) )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3247]) ).

thf(3362,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
                | ~ ~ ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 ) ) )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
              | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                          | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
          | ( SV569 = SV706 ) )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3247]) ).

thf(3363,plain,
    ! [SV786: $i,SV658: $i,SV233: $i] :
      ( ( ( ~ ! [SY2925: $i] :
                ( ~ ( in @ SY2925 @ ( sK15_B @ SV233 ) )
                | ! [SY2926: $i] :
                    ( ~ ( in @ SY2926 @ SY2925 )
                    | ( in @ SY2926 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) )
                | ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SY2925 ) ) )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( in @ SV786 @ SV658 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3250]) ).

thf(3364,plain,
    ! [SV786: $i,SV233: $i,SV658: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) )
                      | ~ ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 ) )
                | ~ ! [SY2927: $i] :
                      ( ~ ( in @ SY2927 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
                      | ~ ( in @ SY2927 @ SV658 ) ) ) )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( in @ SV786 @ SV658 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3250]) ).

thf(3365,plain,
    ! [SV799: $i,SV658: $i,SV233: $i] :
      ( ( ( ~ ! [SY2925: $i] :
                ( ~ ( in @ SY2925 @ ( sK15_B @ SV233 ) )
                | ! [SY2926: $i] :
                    ( ~ ( in @ SY2926 @ SY2925 )
                    | ( in @ SY2926 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) )
                | ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SY2925 ) )
          | ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) )
                      | ~ ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 ) )
                | ~ ! [SY2927: $i] :
                      ( ~ ( in @ SY2927 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
                      | ~ ( in @ SY2927 @ SV658 ) ) ) )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 )
        = $false )
      | ( ( in @ SV799 @ SV658 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3251]) ).

thf(3366,plain,
    ! [SV233: $i,SV770: $i,SV754: $i] :
      ( ( ( ! [SY2983: $i] :
              ( ~ ( in @ SY2983 @ SV754 )
              | ( in @ SY2983 @ SV770 ) ) )
        = $true )
      | ( ( ! [SY2984: $i] :
              ( ~ ( in @ SY2984 @ SV770 )
              | ( in @ SY2984 @ SV754 ) ) )
        = $true )
      | ( ( in @ SV754 @ ( sK15_B @ SV233 ) )
        = $false )
      | ( ( in @ SV770 @ ( sK15_B @ SV233 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3252]) ).

thf(3367,plain,
    ! [SV233: $i,SV787: $i,SV822: $i] :
      ( ( ( ~ ( in @ SV822 @ SV787 )
          | ( in @ SV822 @ SV233 ) )
        = $true )
      | ( ( in @ SV787 @ ( sK15_B @ SV233 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3253]) ).

thf(3368,plain,
    ! [SV800: $i,SV233: $i,SV788: $i] :
      ( ( ( ~ ( in @ SV788 @ SV233 ) )
        = $true )
      | ( ( ~ ( in @ SV800 @ SV233 ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) @ ( sK15_B @ SV233 ) )
              | ~ ~ ( ~ ( ~ ( in @ SV788 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) )
                        | ~ ( in @ SV800 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) ) )
                    | ~ ( ( in @ SV788 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) )
                        | ( in @ SV800 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) ) ) ) )
          | ( SV788 = SV800 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3254]) ).

thf(3369,plain,
    ! [SV573: $i,SV235: $i > $o,SV801: $i] :
      ( ( ( SV801
          = ( sK32_Xx @ SV235 ) )
        = $false )
      | ( ( SV235 @ SV801 )
        = $true )
      | ( ( SV235 @ ( sK33_SY142 @ SV573 @ SV235 ) )
        = $true )
      | ( ( SV235 @ SV573 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3255]) ).

thf(3370,plain,
    ! [SV573: $i,SV802: $i,SV235: $i > $o] :
      ( ( ( SV235 @ SV802 )
        = $false )
      | ( ( SV802
          = ( sK32_Xx @ SV235 ) )
        = $true )
      | ( ( SV235 @ ( sK33_SY142 @ SV573 @ SV235 ) )
        = $true )
      | ( ( SV235 @ SV573 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3256]) ).

thf(3371,plain,
    ! [SV573: $i,SV235: $i > $o,SV812: $i] :
      ( ( ( SV812
         != ( sK32_Xx @ SV235 ) )
        = $true )
      | ( ( SV235 @ SV812 )
        = $true )
      | ( ( SV573
          = ( sK33_SY142 @ SV573 @ SV235 ) )
        = $false )
      | ( ( SV235 @ SV573 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3257]) ).

thf(3372,plain,
    ! [SV573: $i,SV813: $i,SV235: $i > $o] :
      ( ( ( ~ ( SV235 @ SV813 ) )
        = $true )
      | ( ( SV813
          = ( sK32_Xx @ SV235 ) )
        = $true )
      | ( ( SV573
          = ( sK33_SY142 @ SV573 @ SV235 ) )
        = $false )
      | ( ( SV235 @ SV573 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3258]) ).

thf(3373,plain,
    ! [SV236: $i,SV445: $i,SV710: $i > $o,SV574: $i,SV823: $i] :
      ( ( ( ~ ( in @ SV823 @ SV574 )
          | ( SV710 @ SV823 ) )
        = $true )
      | ( ( in @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) @ SV445 )
        = $true )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3260]) ).

thf(3374,plain,
    ! [SV236: $i,SV445: $i,SV574: $i,SV710: $i > $o] :
      ( ( ( ~ ( in @ ( kpair @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) ) @ SV574 )
          | ~ ~ ( SV710 @ ( kpair @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) ) ) )
        = $false )
      | ( ( ! [SY2953: $i] :
              ( ~ ( in @ SY2953 @ SV574 )
              | ( SV710 @ SY2953 ) ) )
        = $true )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3261]) ).

thf(3375,plain,
    ! [SV582: $i,SV803: $i,SV241: $i > $o] :
      ( ( ( SV241 @ SV803 )
        = $false )
      | ( ( ( sK43_SY205 @ SV241 )
          = SV803 )
        = $true )
      | ( ( SV241 @ ( sK44_Xx @ SV241 ) )
        = $true )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3262]) ).

thf(3376,plain,
    ! [SV582: $i,SV241: $i > $o] :
      ( ( ( ! [SY2422: $i] :
              ( ~ ( SV241 @ SY2422 )
              | ( ( sK43_SY205 @ SV241 )
                = SY2422 ) ) )
        = $true )
      | ( ( SV241 @ ( sK45_SY1868 @ SV241 ) )
        = $true )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3263]) ).

thf(3377,plain,
    ! [SV582: $i,SV241: $i > $o] :
      ( ( ( SV241 @ ( sK43_SY205 @ SV241 ) )
        = $true )
      | ( ( SV241 @ ( sK45_SY1868 @ SV241 ) )
        = $true )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3264]) ).

thf(3378,plain,
    ! [SV582: $i,SV241: $i > $o] :
      ( ( ( ~ ! [SY2422: $i] :
                ( ~ ( SV241 @ SY2422 )
                | ( ( sK43_SY205 @ SV241 )
                  = SY2422 ) ) )
        = $false )
      | ( ( ( sK44_Xx @ SV241 )
          = ( sK45_SY1868 @ SV241 ) )
        = $false )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3265]) ).

thf(3379,plain,
    ! [SV582: $i,SV241: $i > $o] :
      ( ( ( ~ ( SV241 @ ( sK43_SY205 @ SV241 ) ) )
        = $false )
      | ( ( ( sK44_Xx @ SV241 )
          = ( sK45_SY1868 @ SV241 ) )
        = $false )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3265]) ).

thf(3380,plain,
    ! [SV586: $i,SV804: $i,SV247: $i > $o] :
      ( ( ( SV247 @ SV804 )
        = $false )
      | ( ( ( sK21_Xx @ SV247 )
          = SV804 )
        = $true )
      | ( ( SV247 @ ( sK22_SY74 @ SV586 @ SV247 ) )
        = $true )
      | ( ( SV247 @ SV586 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3268]) ).

thf(3381,plain,
    ! [SV586: $i,SV814: $i,SV247: $i > $o] :
      ( ( ( ~ ( SV247 @ SV814 ) )
        = $true )
      | ( ( ( sK21_Xx @ SV247 )
          = SV814 )
        = $true )
      | ( ( SV586
          = ( sK22_SY74 @ SV586 @ SV247 ) )
        = $false )
      | ( ( SV247 @ SV586 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3269]) ).

thf(3382,plain,
    ! [SV248: $i,SV453: $i,SV661: $i > $o,SV719: $i > $o] :
      ( ( ( ( ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 )
           != ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) )
          | ~ ~ ( ~ ( ~ ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
                    | ~ ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) )
                | ~ ( ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
                    | ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) ) ) )
        = $false )
      | ( ( ( dsetconstr @ SV248
            @ ^ [SY2930: $i] : ( SV661 @ SY2930 ) )
          = ( dsetconstr @ SV453
            @ ^ [SY2961: $i] : ( SV719 @ SY2961 ) ) )
        = $true )
      | ( ( SV248 = SV453 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3271]) ).

thf(3383,plain,
    ! [SV1: $i,SV733: $i,SV612: $i,SV250: $i,SV777: $i] :
      ( ( ( in @ SV777 @ ( binintersect @ SV250 @ SV612 ) )
        = $false )
      | ( ( in @ SV777 @ ( binunion @ SV250 @ SV733 ) )
        = $true )
      | ( ( in @ SV777 @ SV1 )
        = $false )
      | ( ( in @ SV733 @ ( powerset @ SV1 ) )
        = $false )
      | ( ( in @ SV612 @ ( powerset @ SV1 ) )
        = $false )
      | ( ( in @ SV250 @ ( powerset @ SV1 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3272]) ).

thf(3384,plain,
    ! [SV18: $i,SV626: $i,SV267: $i,SV739: $i] :
      ( ( ( in @ SV739 @ SV267 )
        = $false )
      | ( ( in @ SV739 @ SV626 )
        = $false )
      | ( ( subset @ SV267 @ ( setminus @ SV18 @ SV626 ) )
        = $false )
      | ( ( in @ SV739 @ SV18 )
        = $false )
      | ( ( in @ SV626 @ ( powerset @ SV18 ) )
        = $false )
      | ( ( in @ SV267 @ ( powerset @ SV18 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3275]) ).

thf(3385,plain,
    ! [SV189: $i,SV409: $i,SV647: $i] :
      ( ( ( in @ ( sK97_Xx @ SV647 @ SV409 @ SV189 ) @ SV647 )
        = $false )
      | ( ( subset @ SV409 @ SV647 )
        = $true )
      | ( ( in @ SV647 @ ( powerset @ SV189 ) )
        = $false )
      | ( ( in @ SV409 @ ( powerset @ SV189 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3279]) ).

thf(3386,plain,
    ! [SV551: $i,SV772: $i,SV805: $i,SV194: $i > $o] :
      ( ( ( SV194 @ SV805 )
        = $false )
      | ( ( SV772 = SV805 )
        = $true )
      | ( ( SV194 @ SV772 )
        = $false )
      | ( ( SV551
          = ( sK57_SY248 @ SV551 @ SV194 ) )
        = $false )
      | ( ( SV194 @ SV551 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3281]) ).

thf(3387,plain,
    ! [SV773: $i,SV195: $i > $i > $o,SV413: $i,SV791: $i] :
      ( ( ( in @ SV791 @ SV413 )
        = $false )
      | ( ( SV195 @ SV791 @ SV773 )
        = $false )
      | ( ( in @ SV773 @ ( sK10_B @ SV413 @ SV195 ) )
        = $true )
      | ( ( in @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV413 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3282]) ).

thf(3388,plain,
    ! [SV413: $i,SV774: $i,SV195: $i > $i > $o] :
      ( ( ( SV195 @ ( sK11_Xy @ SV774 @ SV413 @ SV195 ) @ SV774 )
        = $true )
      | ( ( in @ SV774 @ ( sK10_B @ SV413 @ SV195 ) )
        = $false )
      | ( ( in @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV413 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3283]) ).

thf(3389,plain,
    ! [SV195: $i > $i > $o,SV413: $i,SV774: $i] :
      ( ( ( in @ ( sK11_Xy @ SV774 @ SV413 @ SV195 ) @ SV413 )
        = $true )
      | ( ( in @ SV774 @ ( sK10_B @ SV413 @ SV195 ) )
        = $false )
      | ( ( in @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV413 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3284]) ).

thf(3390,plain,
    ! [SV725: $i,SV413: $i,SV195: $i > $i > $o] :
      ( ( ( ! [SY2639: $i] :
              ( ! [SY2640: $i] :
                  ( ~ ( SV195 @ SY2640 @ SY2639 )
                  | ~ ( in @ SY2640 @ SV413 ) )
              | ( in @ SY2639 @ ( sK10_B @ SV413 @ SV195 ) ) ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3285]) ).

thf(3391,plain,
    ! [SV725: $i,SV195: $i > $i > $o,SV413: $i] :
      ( ( ( ! [SY2641: $i] :
              ( ~ ( in @ SY2641 @ ( sK10_B @ SV413 @ SV195 ) )
              | ~ ( ~ ( SV195 @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SY2641 )
                  | ~ ( in @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SV413 ) ) ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3286]) ).

thf(3392,plain,
    ! [SV725: $i,SV413: $i,SV195: $i > $i > $o] :
      ( ( ( ~ ! [SY2639: $i] :
                ( ! [SY2640: $i] :
                    ( ~ ( SV195 @ SY2640 @ SY2639 )
                    | ~ ( in @ SY2640 @ SV413 ) )
                | ( in @ SY2639 @ ( sK10_B @ SV413 @ SV195 ) ) ) )
        = $false )
      | ( ( SV725
          = ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $false )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3287]) ).

thf(3393,plain,
    ! [SV725: $i,SV195: $i > $i > $o,SV413: $i] :
      ( ( ( ~ ! [SY2641: $i] :
                ( ~ ( in @ SY2641 @ ( sK10_B @ SV413 @ SV195 ) )
                | ~ ( ~ ( SV195 @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SY2641 )
                    | ~ ( in @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SV413 ) ) ) )
        = $false )
      | ( ( SV725
          = ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $false )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3287]) ).

thf(3394,plain,
    ! [SV414: $i,SV196: $i,SV552: $i,SV806: $o] :
      ( ( SV806 = $false )
      | ( SV806 = $true )
      | ( ( SV552 = SV196 )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3291]) ).

thf(3395,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( $true = $false )
      | ( $true = $true )
      | ( ( SV552 = SV196 )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3292]) ).

thf(3396,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( $false = $false )
      | ( $false = $true )
      | ( ( SV552 = SV196 )
        = $true )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3293]) ).

thf(3397,plain,
    ! [SV196: $i,SV792: $o,SV414: $i,SV552: $i] :
      ( ( ( in @ SV552 @ SV414 )
        = $true )
      | ( SV792 = $true )
      | ( SV792 = $false )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3294]) ).

thf(3398,plain,
    ! [SV196: $i,SV414: $i,SV552: $i] :
      ( ( ( in @ SV552 @ SV414 )
        = $true )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3295]) ).

thf(3399,plain,
    ! [SV196: $i,SV414: $i,SV552: $i] :
      ( ( ( in @ SV552 @ SV414 )
        = $true )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3296]) ).

thf(3400,plain,
    ! [SV414: $i,SV196: $i,SV552: $i,SV793: $o] :
      ( ( ( ~ SV793 ) = $true )
      | ( SV793 = $true )
      | ( SV793 = $false )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3297]) ).

thf(3401,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( ( ~ $true ) = $true )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3298]) ).

thf(3402,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( ( ~ $false ) = $true )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3299]) ).

thf(3403,plain,
    ! [SV652: $i > $o,SV778: $i,SV605: $i > $o] :
      ( ( ( SV605 @ ( sK54_SY233 @ SV778 @ SV652 @ SV605 ) )
        = $true )
      | ( ( ~ ( SV605 @ SV778 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( ( sK55_Xx @ SV652 @ SV605 )
          = ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3300]) ).

thf(3404,plain,
    ! [SV605: $i > $o,SV652: $i > $o,SV778: $i] :
      ( ( ( SV778
         != ( sK54_SY233 @ SV778 @ SV652 @ SV605 ) )
        = $true )
      | ( ( ~ ( SV605 @ SV778 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( ( sK55_Xx @ SV652 @ SV605 )
          = ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3301]) ).

thf(3405,plain,
    ! [SV605: $i > $o,SV652: $i > $o] :
      ( ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $false )
      | ( ( ! [SY2919: $i] :
              ( ~ ( ~ ( SV605 @ ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) )
                  | ~ ( ( SY2919
                       != ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) ) ) )
              | ~ ( SV605 @ SY2919 ) )
          | ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3302]) ).

thf(3406,plain,
    ! [SV652: $i > $o,SV824: $i,SV605: $i > $o] :
      ( ( ( ~ ( ~ ( SV605 @ ( sK54_SY233 @ SV824 @ SV652 @ SV605 ) )
              | ~ ( ( SV824
                   != ( sK54_SY233 @ SV824 @ SV652 @ SV605 ) ) ) )
          | ~ ( SV605 @ SV824 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3303]) ).

thf(3407,plain,
    ! [SV606: $i > $o,SV779: $i,SV653: $i > $o] :
      ( ( ( SV653 @ ( sK50_SY236 @ SV779 @ SV653 @ SV606 ) )
        = $true )
      | ( ( ~ ( SV653 @ SV779 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( ( sK51_Xx @ SV653 @ SV606 )
          = ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3304]) ).

thf(3408,plain,
    ! [SV606: $i > $o,SV653: $i > $o,SV779: $i] :
      ( ( ( SV779
         != ( sK50_SY236 @ SV779 @ SV653 @ SV606 ) )
        = $true )
      | ( ( ~ ( SV653 @ SV779 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( ( sK51_Xx @ SV653 @ SV606 )
          = ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3305]) ).

thf(3409,plain,
    ! [SV606: $i > $o,SV653: $i > $o] :
      ( ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $false )
      | ( ( ! [SY2921: $i] :
              ( ~ ( ~ ( SV653 @ ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) )
                  | ~ ( ( SY2921
                       != ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) ) ) )
              | ~ ( SV653 @ SY2921 ) )
          | ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3306]) ).

thf(3410,plain,
    ! [SV606: $i > $o,SV825: $i,SV653: $i > $o] :
      ( ( ( ~ ( ~ ( SV653 @ ( sK50_SY236 @ SV825 @ SV653 @ SV606 ) )
              | ~ ( ( SV825
                   != ( sK50_SY236 @ SV825 @ SV653 @ SV606 ) ) ) )
          | ~ ( SV653 @ SV825 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3307]) ).

thf(3411,plain,
    ! [SV558: $i,SV807: $i,SV205: $i > $o] :
      ( ( ( SV205 @ SV807 )
        = $false )
      | ( ( ( sK41_SY198 @ SV205 )
          = SV807 )
        = $true )
      | ( ( SV558
          = ( sK42_Xy @ SV558 @ SV205 ) )
        = $false )
      | ( ( SV205 @ SV558 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3309]) ).

thf(3412,plain,
    ( ( in @ sK5_SY1831 @ ( binintersect @ sK2_SY1822 @ sK3_SY1826 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[3310]) ).

thf(3413,plain,
    ( ( ~ ( in @ sK5_SY1831 @ ( binunion @ sK3_SY1826 @ sK4_SY1829 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[3311]) ).

thf(3414,plain,
    ! [SV207: $i,SV422: $i,SV702: $i > $o,SV560: $i,SV816: $i] :
      ( ( ( ~ ( in @ SV816 @ SV560 ) )
        = $true )
      | ( ( SV702 @ SV816 )
        = $true )
      | ( ( in @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) @ SV422 )
        = $true )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3312]) ).

thf(3415,plain,
    ! [SV207: $i,SV422: $i,SV560: $i,SV702: $i > $o] :
      ( ( ( ~ ( in @ ( kpair @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) ) @ SV560 ) )
        = $false )
      | ( ( ! [SY2947: $i] :
              ( ~ ( in @ SY2947 @ SV560 )
              | ( SV702 @ SY2947 ) ) )
        = $true )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3313]) ).

thf(3416,plain,
    ! [SV207: $i,SV422: $i,SV560: $i,SV702: $i > $o] :
      ( ( ( ~ ~ ( SV702 @ ( kpair @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) ) ) )
        = $false )
      | ( ( ! [SY2947: $i] :
              ( ~ ( in @ SY2947 @ SV560 )
              | ( SV702 @ SY2947 ) ) )
        = $true )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3313]) ).

thf(3417,plain,
    ! [SV208: $i,SV423: $i,SV561: $i,SV703: $i] :
      ( ( ( in @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) @ SV423 )
        = $true )
      | ( ( subset @ SV561 @ SV703 )
        = $true )
      | ( ( subset @ SV703 @ ( cartprod @ SV208 @ SV423 ) )
        = $false )
      | ( ( subset @ SV561 @ ( cartprod @ SV208 @ SV423 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3314]) ).

thf(3418,plain,
    ! [SV208: $i,SV423: $i,SV561: $i,SV703: $i] :
      ( ( ( ~ ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) ) @ SV561 )
              | ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) ) @ SV703 ) ) )
        = $true )
      | ( ( subset @ SV561 @ SV703 )
        = $true )
      | ( ( subset @ SV703 @ ( cartprod @ SV208 @ SV423 ) )
        = $false )
      | ( ( subset @ SV561 @ ( cartprod @ SV208 @ SV423 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3315]) ).

thf(3419,plain,
    ! [SV209: $i,SV817: $i,SV424: $i > $o] :
      ( ( ( ~ ( SV424 @ SV817 ) )
        = $true )
      | ( ( ~ ( in @ SV817 @ SV209 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV209
            @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) )
        = $true )
      | ( ( SV424 @ ( sK70_Xx @ SV424 @ SV209 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3317]) ).

thf(3420,plain,
    ! [SV209: $i,SV424: $i > $o] :
      ( ( ( SV424 @ ( sK71_SY1877 @ SV424 @ SV209 ) )
        = $true )
      | ( ( ! [SY2662: $i] :
              ( ~ ( SV424 @ SY2662 )
              | ~ ( in @ SY2662 @ SV209 ) )
          | ( singleton
            @ ( dsetconstr @ SV209
              @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3318]) ).

thf(3421,plain,
    ! [SV209: $i,SV424: $i > $o] :
      ( ( ( ( sK70_Xx @ SV424 @ SV209 )
         != ( sK71_SY1877 @ SV424 @ SV209 ) )
        = $true )
      | ( ( ! [SY2662: $i] :
              ( ~ ( SV424 @ SY2662 )
              | ~ ( in @ SY2662 @ SV209 ) )
          | ( singleton
            @ ( dsetconstr @ SV209
              @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3319]) ).

thf(3422,plain,
    ! [SV562: $i,SV775: $i,SV808: $i,SV211: $i > $o] :
      ( ( ( SV211 @ SV808 )
        = $false )
      | ( ( SV775 = SV808 )
        = $true )
      | ( ( SV211 @ SV775 )
        = $false )
      | ( ( SV562
          = ( sK48_SY224 @ SV562 @ SV211 ) )
        = $false )
      | ( ( SV211 @ SV562 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3321]) ).

thf(3423,plain,
    ! [SV750: $i,SV213: $i > $o,SV826: $i,SV427: $i > $o] :
      ( ( ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SV826 @ SV427 @ SV213 ) )
              | ~ ( ( SV826
                   != ( sK58_SY260 @ SV826 @ SV427 @ SV213 ) ) ) )
          | ~ ( SV427 @ SV826 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV750 )
        = $false )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3322]) ).

thf(3424,plain,
    ! [SV750: $i,SV213: $i > $o,SV427: $i > $o] :
      ( ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV750
          = ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV750 )
        = $false )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3323]) ).

thf(3425,plain,
    ! [SV427: $i > $o,SV818: $i,SV213: $i > $o] :
      ( ( ( ~ ( ~ ( SV213 @ ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
              | ~ ( ( SV818
                   != ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV213 @ SV818 ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3324]) ).

thf(3426,plain,
    ! [SV427: $i > $o,SV796: $i,SV213: $i > $o] :
      ( ( ( ~ ( SV213 @ ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) ) )
        = $false )
      | ( ( ~ ( SV213 @ SV796 ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3325]) ).

thf(3427,plain,
    ! [SV213: $i > $o,SV427: $i > $o,SV796: $i] :
      ( ( ( ~ ( ( SV796
               != ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) ) ) )
        = $false )
      | ( ( ~ ( SV213 @ SV796 ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3325]) ).

thf(3428,plain,
    ! [SV214: $i,SV428: $i,SV654: $i] :
      ( ( ( in @ ( sK98_Xx @ SV654 @ SV428 @ SV214 ) @ SV654 )
        = $false )
      | ( ( in @ SV428 @ ( powerset @ SV654 ) )
        = $true )
      | ( ( in @ SV654 @ ( powerset @ SV214 ) )
        = $false )
      | ( ( in @ SV428 @ ( powerset @ SV214 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3327]) ).

thf(3429,plain,
    ! [SV564: $i,SV704: $i,SV432: $i,SV218: $i,SV809: $i] :
      ( ( ( in @ SV809 @ SV218 )
        = $false )
      | ( ( ! [SY2990: $i] :
              ( ~ ( in @ SY2990 @ SV432 )
              | ~ ( in @ ( kpair @ SV809 @ SY2990 ) @ SV704 )
              | ( in @ ( kpair @ SV809 @ SY2990 ) @ SV564 ) ) )
        = $true )
      | ( ( in @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) @ SV218 )
        = $true )
      | ( ( func @ SV218 @ SV432 @ SV704 )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV564 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3328]) ).

thf(3430,plain,
    ! [SV564: $i,SV704: $i,SV432: $i,SV218: $i,SV819: $i] :
      ( ( ( ~ ( in @ SV819 @ SV218 ) )
        = $true )
      | ( ( ! [SY2991: $i] :
              ( ~ ( in @ SY2991 @ SV432 )
              | ~ ( in @ ( kpair @ SV819 @ SY2991 ) @ SV704 )
              | ( in @ ( kpair @ SV819 @ SY2991 ) @ SV564 ) ) )
        = $true )
      | ( ( ( ap @ SV218 @ SV432 @ SV564 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) )
          = ( ap @ SV218 @ SV432 @ SV704 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) ) )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV704 )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV564 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3329]) ).

thf(3431,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
        = $true )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3330]) ).

thf(3432,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
              | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) ) )
        = $true )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3331]) ).

thf(3433,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
              | ~ ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
                    | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) ) ) )
        = $true )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3332]) ).

thf(3434,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
              | ~ ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
                    | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) ) )
          | ( SV433 = SV656 ) )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3333]) ).

thf(3435,plain,
    ! [SV220: $i,SV434: $i > $o,SV565: $i] :
      ( ( ( ( sK73_Xy @ SV565 @ SV434 @ SV220 )
          = SV565 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV220
            @ ^ [SY2682: $i] : ( SV434 @ SY2682 ) ) )
        = $true )
      | ( ( SV434 @ SV565 )
        = $false )
      | ( ( in @ SV565 @ SV220 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3335]) ).

thf(3436,plain,
    ! [SV435: $i,SV221: $i,SV566: $i,SV827: $o] :
      ( ( SV827 = $true )
      | ( ( in @ SV566 @ SV221 )
        = $false )
      | ( ( in @ SV566 @ SV221 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3336]) ).

thf(3437,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( $true = $true )
      | ( ( in @ SV566 @ SV221 )
        = $false )
      | ( ( in @ SV566 @ SV221 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3336]) ).

thf(3438,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( $false = $true )
      | ( ( in @ SV566 @ SV221 )
        = $false )
      | ( ( in @ SV566 @ SV221 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3336]) ).

thf(3439,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( in @ SV566 @ SV221 )
        = $true )
      | ( ( ( in @ SV566 @ SV435 )
          | ! [SX3: $o] : SX3 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3337]) ).

thf(3440,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( in @ SV566 @ SV221 )
        = $true )
      | ( ( ! [SX3: $o] :
              ( ~ SX3
              | SX3 ) )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3338]) ).

thf(3441,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ ( in @ SV566 @ SV435 ) )
        = $true )
      | ( ( ~ ( in @ SV566 @ SV221 )
          | ! [SX3: $o] : SX3 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3339]) ).

thf(3442,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ ( ~ ( in @ SV566 @ SV435 )
              | ( in @ SV566 @ SV435 )
              | ! [SX3: $o] : SX3 )
          | ~ ( ~ ( in @ SV566 @ SV435 )
              | ! [SX3: $o] :
                  ( ~ SX3
                  | SX3 ) ) )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3340]) ).

thf(3443,plain,
    ! [SV435: $i,SV221: $i,SV566: $i,SV828: $o] :
      ( ( ( ~ SV828
          | ~ ( in @ SV566 @ SV221 )
          | SV828 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3341]) ).

thf(3444,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ $true
          | ~ ( in @ SV566 @ SV221 )
          | $true )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3341]) ).

thf(3445,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ $false
          | ~ ( in @ SV566 @ SV221 )
          | $false )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3341]) ).

thf(3446,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ ! [SY2840: $o] :
                ( ~ SY2840
                | ( in @ SV566 @ SV435 )
                | SY2840 )
          | ~ ! [SX3: $o] :
                ( ~ SX3
                | ~ SX3
                | SX3 ) )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3342]) ).

thf(3447,plain,
    ! [SV439: $i,SV226: $i,SV767: $i,SV810: $o] :
      ( ( SV810 = $false )
      | ( SV810 = $true )
      | ( ( in @ SV767 @ SV226 )
        = $true )
      | ( ( in @ SV767 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3346]) ).

thf(3448,plain,
    ! [SV439: $i,SV226: $i,SV767: $i] :
      ( ( $true = $false )
      | ( $true = $true )
      | ( ( in @ SV767 @ SV226 )
        = $true )
      | ( ( in @ SV767 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3347]) ).

thf(3449,plain,
    ! [SV439: $i,SV226: $i,SV767: $i] :
      ( ( $false = $false )
      | ( $false = $true )
      | ( ( in @ SV767 @ SV226 )
        = $true )
      | ( ( in @ SV767 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3348]) ).

thf(3450,plain,
    ! [SV226: $i,SV797: $o,SV439: $i,SV768: $i] :
      ( ( ( in @ SV768 @ SV439 )
        = $true )
      | ( SV797 = $true )
      | ( SV797 = $false )
      | ( ( in @ SV768 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3349]) ).

thf(3451,plain,
    ! [SV226: $i,SV439: $i,SV768: $i] :
      ( ( ( in @ SV768 @ SV439 )
        = $true )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV768 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3350]) ).

thf(3452,plain,
    ! [SV226: $i,SV439: $i,SV768: $i] :
      ( ( ( in @ SV768 @ SV439 )
        = $true )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV768 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3351]) ).

thf(3453,plain,
    ! [SV439: $i,SV226: $i,SV776: $i,SV798: $o] :
      ( ( ( ~ SV798 ) = $true )
      | ( SV798 = $true )
      | ( SV798 = $false )
      | ( ( in @ SV776 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3352]) ).

thf(3454,plain,
    ! [SV439: $i,SV226: $i,SV776: $i] :
      ( ( ( ~ $true ) = $true )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV776 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3353]) ).

thf(3455,plain,
    ! [SV439: $i,SV226: $i,SV776: $i] :
      ( ( ( ~ $false ) = $true )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV776 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3354]) ).

thf(3456,plain,
    ! [SV568: $i,SV811: $i,SV228: $i > $o] :
      ( ( ( SV228 @ SV811 )
        = $false )
      | ( ( ( sK46_SY211 @ SV228 )
          = SV811 )
        = $true )
      | ( ( ( sK47_Xy @ SV568 @ SV228 )
          = SV568 )
        = $false )
      | ( ( SV228 @ ( sK47_Xy @ SV568 @ SV228 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3355]) ).

thf(3457,plain,
    ! [SV229: $i,SV821: $i,SV441: $i > $o] :
      ( ( ( ~ ( SV441 @ SV821 ) )
        = $true )
      | ( ( ~ ( in @ SV821 @ SV229 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV229
            @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) )
        = $true )
      | ( ( SV441 @ ( sK74_Xx @ SV441 @ SV229 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3357]) ).

thf(3458,plain,
    ! [SV229: $i,SV441: $i > $o] :
      ( ( ( SV441 @ ( sK75_SY1878 @ SV441 @ SV229 ) )
        = $true )
      | ( ( ! [SY2705: $i] :
              ( ~ ( SV441 @ SY2705 )
              | ~ ( in @ SY2705 @ SV229 ) )
          | ( singleton
            @ ( dsetconstr @ SV229
              @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3358]) ).

thf(3459,plain,
    ! [SV229: $i,SV441: $i > $o] :
      ( ( ( ( sK74_Xx @ SV441 @ SV229 )
         != ( sK75_SY1878 @ SV441 @ SV229 ) )
        = $true )
      | ( ( ! [SY2705: $i] :
              ( ~ ( SV441 @ SY2705 )
              | ~ ( in @ SY2705 @ SV229 ) )
          | ( singleton
            @ ( dsetconstr @ SV229
              @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3359]) ).

thf(3460,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3360]) ).

thf(3461,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                      | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3360]) ).

thf(3462,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( in @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
              | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                          | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
          | ( SV569 = SV706 ) )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3361]) ).

thf(3463,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( ~ ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
              | ~ ~ ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 ) ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
              | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                          | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
          | ( SV569 = SV706 ) )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3362]) ).

thf(3464,plain,
    ! [SV786: $i,SV658: $i,SV233: $i] :
      ( ( ( ! [SY2925: $i] :
              ( ~ ( in @ SY2925 @ ( sK15_B @ SV233 ) )
              | ! [SY2926: $i] :
                  ( ~ ( in @ SY2926 @ SY2925 )
                  | ( in @ SY2926 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) )
              | ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SY2925 ) ) )
        = $true )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( in @ SV786 @ SV658 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3363]) ).

thf(3465,plain,
    ! [SV786: $i,SV233: $i,SV658: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) )
                    | ~ ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 ) )
              | ~ ! [SY2927: $i] :
                    ( ~ ( in @ SY2927 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
                    | ~ ( in @ SY2927 @ SV658 ) ) ) )
        = $true )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( in @ SV786 @ SV658 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3364]) ).

thf(3466,plain,
    ! [SV799: $i,SV658: $i,SV233: $i] :
      ( ( ( ~ ! [SY2925: $i] :
                ( ~ ( in @ SY2925 @ ( sK15_B @ SV233 ) )
                | ! [SY2926: $i] :
                    ( ~ ( in @ SY2926 @ SY2925 )
                    | ( in @ SY2926 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) )
                | ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SY2925 ) ) )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 )
        = $false )
      | ( ( in @ SV799 @ SV658 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3365]) ).

thf(3467,plain,
    ! [SV799: $i,SV233: $i,SV658: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) )
                      | ~ ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 ) )
                | ~ ! [SY2927: $i] :
                      ( ~ ( in @ SY2927 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
                      | ~ ( in @ SY2927 @ SV658 ) ) ) )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 )
        = $false )
      | ( ( in @ SV799 @ SV658 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3365]) ).

thf(3468,plain,
    ! [SV233: $i,SV770: $i,SV754: $i,SV829: $i] :
      ( ( ( ~ ( in @ SV829 @ SV754 )
          | ( in @ SV829 @ SV770 ) )
        = $true )
      | ( ( ! [SY2984: $i] :
              ( ~ ( in @ SY2984 @ SV770 )
              | ( in @ SY2984 @ SV754 ) ) )
        = $true )
      | ( ( in @ SV754 @ ( sK15_B @ SV233 ) )
        = $false )
      | ( ( in @ SV770 @ ( sK15_B @ SV233 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3366]) ).

thf(3469,plain,
    ! [SV233: $i,SV787: $i,SV822: $i] :
      ( ( ( ~ ( in @ SV822 @ SV787 ) )
        = $true )
      | ( ( in @ SV822 @ SV233 )
        = $true )
      | ( ( in @ SV787 @ ( sK15_B @ SV233 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3367]) ).

thf(3470,plain,
    ! [SV800: $i,SV233: $i,SV788: $i] :
      ( ( ( in @ SV788 @ SV233 )
        = $false )
      | ( ( ~ ( in @ SV800 @ SV233 ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) @ ( sK15_B @ SV233 ) )
              | ~ ~ ( ~ ( ~ ( in @ SV788 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) )
                        | ~ ( in @ SV800 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) ) )
                    | ~ ( ( in @ SV788 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) )
                        | ( in @ SV800 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) ) ) ) )
          | ( SV788 = SV800 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3368]) ).

thf(3471,plain,
    ! [SV573: $i,SV235: $i > $o,SV812: $i] :
      ( ( ( SV812
          = ( sK32_Xx @ SV235 ) )
        = $false )
      | ( ( SV235 @ SV812 )
        = $true )
      | ( ( SV573
          = ( sK33_SY142 @ SV573 @ SV235 ) )
        = $false )
      | ( ( SV235 @ SV573 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3371]) ).

thf(3472,plain,
    ! [SV573: $i,SV813: $i,SV235: $i > $o] :
      ( ( ( SV235 @ SV813 )
        = $false )
      | ( ( SV813
          = ( sK32_Xx @ SV235 ) )
        = $true )
      | ( ( SV573
          = ( sK33_SY142 @ SV573 @ SV235 ) )
        = $false )
      | ( ( SV235 @ SV573 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3372]) ).

thf(3473,plain,
    ! [SV236: $i,SV445: $i,SV710: $i > $o,SV574: $i,SV823: $i] :
      ( ( ( ~ ( in @ SV823 @ SV574 ) )
        = $true )
      | ( ( SV710 @ SV823 )
        = $true )
      | ( ( in @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) @ SV445 )
        = $true )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3373]) ).

thf(3474,plain,
    ! [SV236: $i,SV445: $i,SV574: $i,SV710: $i > $o] :
      ( ( ( ~ ( in @ ( kpair @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) ) @ SV574 ) )
        = $false )
      | ( ( ! [SY2953: $i] :
              ( ~ ( in @ SY2953 @ SV574 )
              | ( SV710 @ SY2953 ) ) )
        = $true )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3374]) ).

thf(3475,plain,
    ! [SV236: $i,SV445: $i,SV574: $i,SV710: $i > $o] :
      ( ( ( ~ ~ ( SV710 @ ( kpair @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) ) ) )
        = $false )
      | ( ( ! [SY2953: $i] :
              ( ~ ( in @ SY2953 @ SV574 )
              | ( SV710 @ SY2953 ) ) )
        = $true )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3374]) ).

thf(3476,plain,
    ! [SV582: $i,SV830: $i,SV241: $i > $o] :
      ( ( ( ~ ( SV241 @ SV830 )
          | ( ( sK43_SY205 @ SV241 )
            = SV830 ) )
        = $true )
      | ( ( SV241 @ ( sK45_SY1868 @ SV241 ) )
        = $true )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3376]) ).

thf(3477,plain,
    ! [SV582: $i,SV241: $i > $o] :
      ( ( ( ! [SY2422: $i] :
              ( ~ ( SV241 @ SY2422 )
              | ( ( sK43_SY205 @ SV241 )
                = SY2422 ) ) )
        = $true )
      | ( ( ( sK44_Xx @ SV241 )
          = ( sK45_SY1868 @ SV241 ) )
        = $false )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3378]) ).

thf(3478,plain,
    ! [SV582: $i,SV241: $i > $o] :
      ( ( ( SV241 @ ( sK43_SY205 @ SV241 ) )
        = $true )
      | ( ( ( sK44_Xx @ SV241 )
          = ( sK45_SY1868 @ SV241 ) )
        = $false )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3379]) ).

thf(3479,plain,
    ! [SV586: $i,SV814: $i,SV247: $i > $o] :
      ( ( ( SV247 @ SV814 )
        = $false )
      | ( ( ( sK21_Xx @ SV247 )
          = SV814 )
        = $true )
      | ( ( SV586
          = ( sK22_SY74 @ SV586 @ SV247 ) )
        = $false )
      | ( ( SV247 @ SV586 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3381]) ).

thf(3480,plain,
    ! [SV248: $i,SV453: $i,SV661: $i > $o,SV719: $i > $o] :
      ( ( ( ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 )
         != ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) )
        = $false )
      | ( ( ( dsetconstr @ SV248
            @ ^ [SY2930: $i] : ( SV661 @ SY2930 ) )
          = ( dsetconstr @ SV453
            @ ^ [SY2961: $i] : ( SV719 @ SY2961 ) ) )
        = $true )
      | ( ( SV248 = SV453 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3382]) ).

thf(3481,plain,
    ! [SV248: $i,SV453: $i,SV719: $i > $o,SV661: $i > $o] :
      ( ( ( ~ ~ ( ~ ( ~ ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
                    | ~ ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) )
                | ~ ( ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
                    | ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) ) ) )
        = $false )
      | ( ( ( dsetconstr @ SV248
            @ ^ [SY2930: $i] : ( SV661 @ SY2930 ) )
          = ( dsetconstr @ SV453
            @ ^ [SY2961: $i] : ( SV719 @ SY2961 ) ) )
        = $true )
      | ( ( SV248 = SV453 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3382]) ).

thf(3482,plain,
    ! [SV725: $i,SV413: $i,SV831: $i,SV195: $i > $i > $o] :
      ( ( ( ! [SY2992: $i] :
              ( ~ ( SV195 @ SY2992 @ SV831 )
              | ~ ( in @ SY2992 @ SV413 ) )
          | ( in @ SV831 @ ( sK10_B @ SV413 @ SV195 ) ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3390]) ).

thf(3483,plain,
    ! [SV725: $i,SV195: $i > $i > $o,SV413: $i,SV832: $i] :
      ( ( ( ~ ( in @ SV832 @ ( sK10_B @ SV413 @ SV195 ) )
          | ~ ( ~ ( SV195 @ ( sK11_Xy @ SV832 @ SV413 @ SV195 ) @ SV832 )
              | ~ ( in @ ( sK11_Xy @ SV832 @ SV413 @ SV195 ) @ SV413 ) ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3391]) ).

thf(3484,plain,
    ! [SV725: $i,SV413: $i,SV195: $i > $i > $o] :
      ( ( ( ! [SY2639: $i] :
              ( ! [SY2640: $i] :
                  ( ~ ( SV195 @ SY2640 @ SY2639 )
                  | ~ ( in @ SY2640 @ SV413 ) )
              | ( in @ SY2639 @ ( sK10_B @ SV413 @ SV195 ) ) ) )
        = $true )
      | ( ( SV725
          = ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $false )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3392]) ).

thf(3485,plain,
    ! [SV725: $i,SV195: $i > $i > $o,SV413: $i] :
      ( ( ( ! [SY2641: $i] :
              ( ~ ( in @ SY2641 @ ( sK10_B @ SV413 @ SV195 ) )
              | ~ ( ~ ( SV195 @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SY2641 )
                  | ~ ( in @ ( sK11_Xy @ SY2641 @ SV413 @ SV195 ) @ SV413 ) ) ) )
        = $true )
      | ( ( SV725
          = ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $false )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3393]) ).

thf(3486,plain,
    ! [SV414: $i,SV196: $i,SV552: $i,SV793: $o] :
      ( ( SV793 = $false )
      | ( SV793 = $true )
      | ( SV793 = $false )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3400]) ).

thf(3487,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( $true = $false )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3401]) ).

thf(3488,plain,
    ! [SV414: $i,SV196: $i,SV552: $i] :
      ( ( $false = $false )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV552 @ ( setadjoin @ SV196 @ SV414 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3402]) ).

thf(3489,plain,
    ! [SV652: $i > $o,SV778: $i,SV605: $i > $o] :
      ( ( ( SV605 @ SV778 )
        = $false )
      | ( ( SV605 @ ( sK54_SY233 @ SV778 @ SV652 @ SV605 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( ( sK55_Xx @ SV652 @ SV605 )
          = ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3403]) ).

thf(3490,plain,
    ! [SV605: $i > $o,SV652: $i > $o,SV778: $i] :
      ( ( ( SV778
          = ( sK54_SY233 @ SV778 @ SV652 @ SV605 ) )
        = $false )
      | ( ( ~ ( SV605 @ SV778 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( ( sK55_Xx @ SV652 @ SV605 )
          = ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3404]) ).

thf(3491,plain,
    ! [SV652: $i > $o,SV605: $i > $o] :
      ( ( ( ! [SY2919: $i] :
              ( ~ ( ~ ( SV605 @ ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) )
                  | ~ ( ( SY2919
                       != ( sK54_SY233 @ SY2919 @ SV652 @ SV605 ) ) ) )
              | ~ ( SV605 @ SY2919 ) ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3405]) ).

thf(3492,plain,
    ! [SV652: $i > $o,SV824: $i,SV605: $i > $o] :
      ( ( ( ~ ( ~ ( SV605 @ ( sK54_SY233 @ SV824 @ SV652 @ SV605 ) )
              | ~ ( ( SV824
                   != ( sK54_SY233 @ SV824 @ SV652 @ SV605 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV605 @ SV824 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3406]) ).

thf(3493,plain,
    ! [SV606: $i > $o,SV779: $i,SV653: $i > $o] :
      ( ( ( SV653 @ SV779 )
        = $false )
      | ( ( SV653 @ ( sK50_SY236 @ SV779 @ SV653 @ SV606 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( ( sK51_Xx @ SV653 @ SV606 )
          = ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3407]) ).

thf(3494,plain,
    ! [SV606: $i > $o,SV653: $i > $o,SV779: $i] :
      ( ( ( SV779
          = ( sK50_SY236 @ SV779 @ SV653 @ SV606 ) )
        = $false )
      | ( ( ~ ( SV653 @ SV779 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( ( sK51_Xx @ SV653 @ SV606 )
          = ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3408]) ).

thf(3495,plain,
    ! [SV606: $i > $o,SV653: $i > $o] :
      ( ( ( ! [SY2921: $i] :
              ( ~ ( ~ ( SV653 @ ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) )
                  | ~ ( ( SY2921
                       != ( sK50_SY236 @ SY2921 @ SV653 @ SV606 ) ) ) )
              | ~ ( SV653 @ SY2921 ) ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3409]) ).

thf(3496,plain,
    ! [SV606: $i > $o,SV825: $i,SV653: $i > $o] :
      ( ( ( ~ ( ~ ( SV653 @ ( sK50_SY236 @ SV825 @ SV653 @ SV606 ) )
              | ~ ( ( SV825
                   != ( sK50_SY236 @ SV825 @ SV653 @ SV606 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV653 @ SV825 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3410]) ).

thf(3497,plain,
    ( ( in @ sK5_SY1831 @ ( binunion @ sK3_SY1826 @ sK4_SY1829 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[3413]) ).

thf(3498,plain,
    ! [SV207: $i,SV422: $i,SV702: $i > $o,SV560: $i,SV816: $i] :
      ( ( ( in @ SV816 @ SV560 )
        = $false )
      | ( ( SV702 @ SV816 )
        = $true )
      | ( ( in @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) @ SV422 )
        = $true )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3414]) ).

thf(3499,plain,
    ! [SV207: $i,SV422: $i,SV560: $i,SV702: $i > $o] :
      ( ( ( in @ ( kpair @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) ) @ SV560 )
        = $true )
      | ( ( ! [SY2947: $i] :
              ( ~ ( in @ SY2947 @ SV560 )
              | ( SV702 @ SY2947 ) ) )
        = $true )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3415]) ).

thf(3500,plain,
    ! [SV207: $i,SV422: $i,SV560: $i,SV702: $i > $o] :
      ( ( ( ~ ( SV702 @ ( kpair @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) ) ) )
        = $true )
      | ( ( ! [SY2947: $i] :
              ( ~ ( in @ SY2947 @ SV560 )
              | ( SV702 @ SY2947 ) ) )
        = $true )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3416]) ).

thf(3501,plain,
    ! [SV208: $i,SV423: $i,SV561: $i,SV703: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) ) @ SV561 )
          | ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) ) @ SV703 ) )
        = $false )
      | ( ( subset @ SV561 @ SV703 )
        = $true )
      | ( ( subset @ SV703 @ ( cartprod @ SV208 @ SV423 ) )
        = $false )
      | ( ( subset @ SV561 @ ( cartprod @ SV208 @ SV423 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3418]) ).

thf(3502,plain,
    ! [SV209: $i,SV817: $i,SV424: $i > $o] :
      ( ( ( SV424 @ SV817 )
        = $false )
      | ( ( ~ ( in @ SV817 @ SV209 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV209
            @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) )
        = $true )
      | ( ( SV424 @ ( sK70_Xx @ SV424 @ SV209 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3419]) ).

thf(3503,plain,
    ! [SV209: $i,SV424: $i > $o] :
      ( ( ( ! [SY2662: $i] :
              ( ~ ( SV424 @ SY2662 )
              | ~ ( in @ SY2662 @ SV209 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV209
            @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) )
        = $true )
      | ( ( SV424 @ ( sK71_SY1877 @ SV424 @ SV209 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3420]) ).

thf(3504,plain,
    ! [SV209: $i,SV424: $i > $o] :
      ( ( ( ( sK70_Xx @ SV424 @ SV209 )
          = ( sK71_SY1877 @ SV424 @ SV209 ) )
        = $false )
      | ( ( ! [SY2662: $i] :
              ( ~ ( SV424 @ SY2662 )
              | ~ ( in @ SY2662 @ SV209 ) )
          | ( singleton
            @ ( dsetconstr @ SV209
              @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3421]) ).

thf(3505,plain,
    ! [SV750: $i,SV213: $i > $o,SV826: $i,SV427: $i > $o] :
      ( ( ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SV826 @ SV427 @ SV213 ) )
              | ~ ( ( SV826
                   != ( sK58_SY260 @ SV826 @ SV427 @ SV213 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV427 @ SV826 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV750 )
        = $false )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3423]) ).

thf(3506,plain,
    ! [SV750: $i,SV213: $i > $o,SV833: $i,SV427: $i > $o] :
      ( ( ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SV833 @ SV427 @ SV213 ) )
              | ~ ( ( SV833
                   != ( sK58_SY260 @ SV833 @ SV427 @ SV213 ) ) ) )
          | ~ ( SV427 @ SV833 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV750
          = ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV750 )
        = $false )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3424]) ).

thf(3507,plain,
    ! [SV427: $i > $o,SV818: $i,SV213: $i > $o] :
      ( ( ( ~ ( SV213 @ ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
          | ~ ( ( SV818
               != ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) ) ) )
        = $false )
      | ( ( ~ ( SV213 @ SV818 ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3425]) ).

thf(3508,plain,
    ! [SV427: $i > $o,SV796: $i,SV213: $i > $o] :
      ( ( ( SV213 @ ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
        = $true )
      | ( ( ~ ( SV213 @ SV796 ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3426]) ).

thf(3509,plain,
    ! [SV213: $i > $o,SV427: $i > $o,SV796: $i] :
      ( ( ( SV796
         != ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
        = $true )
      | ( ( ~ ( SV213 @ SV796 ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3427]) ).

thf(3510,plain,
    ! [SV218: $i,SV564: $i,SV704: $i,SV809: $i,SV432: $i,SV834: $i] :
      ( ( ( ~ ( in @ SV834 @ SV432 )
          | ~ ( in @ ( kpair @ SV809 @ SV834 ) @ SV704 )
          | ( in @ ( kpair @ SV809 @ SV834 ) @ SV564 ) )
        = $true )
      | ( ( in @ SV809 @ SV218 )
        = $false )
      | ( ( in @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) @ SV218 )
        = $true )
      | ( ( func @ SV218 @ SV432 @ SV704 )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV564 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3429]) ).

thf(3511,plain,
    ! [SV564: $i,SV704: $i,SV432: $i,SV218: $i,SV819: $i] :
      ( ( ( in @ SV819 @ SV218 )
        = $false )
      | ( ( ! [SY2991: $i] :
              ( ~ ( in @ SY2991 @ SV432 )
              | ~ ( in @ ( kpair @ SV819 @ SY2991 ) @ SV704 )
              | ( in @ ( kpair @ SV819 @ SY2991 ) @ SV564 ) ) )
        = $true )
      | ( ( ( ap @ SV218 @ SV432 @ SV564 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) )
          = ( ap @ SV218 @ SV432 @ SV704 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) ) )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV704 )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV564 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3430]) ).

thf(3512,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
          | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) )
        = $false )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3432]) ).

thf(3513,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
          | ~ ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
                | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) ) )
        = $false )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3433]) ).

thf(3514,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
              | ~ ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
                    | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) ) ) )
        = $true )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
        = $false )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3434]) ).

thf(3515,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( in @ SV566 @ SV435 )
        = $true )
      | ( ( ! [SX3: $o] : SX3 )
        = $true )
      | ( ( in @ SV566 @ SV221 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3439]) ).

thf(3516,plain,
    ! [SV435: $i,SV221: $i,SV566: $i,SV835: $o] :
      ( ( ( ~ SV835
          | SV835 )
        = $true )
      | ( ( in @ SV566 @ SV221 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3440]) ).

thf(3517,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ $true
          | $true )
        = $true )
      | ( ( in @ SV566 @ SV221 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3440]) ).

thf(3518,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ $false
          | $false )
        = $true )
      | ( ( in @ SV566 @ SV221 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3440]) ).

thf(3519,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( in @ SV566 @ SV435 )
        = $false )
      | ( ( ~ ( in @ SV566 @ SV221 )
          | ! [SX3: $o] : SX3 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3441]) ).

thf(3520,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ ( ~ ( in @ SV566 @ SV435 )
              | ( in @ SV566 @ SV435 )
              | ! [SX3: $o] : SX3 ) )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3442]) ).

thf(3521,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ ( ~ ( in @ SV566 @ SV435 )
              | ! [SX3: $o] :
                  ( ~ SX3
                  | SX3 ) ) )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3442]) ).

thf(3522,plain,
    ! [SV435: $i,SV221: $i,SV566: $i,SV828: $o] :
      ( ( ( ~ SV828 ) = $true )
      | ( ( ~ ( in @ SV566 @ SV221 )
          | SV828 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3443]) ).

thf(3523,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ $true ) = $true )
      | ( ( ~ ( in @ SV566 @ SV221 )
          | $true )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3444]) ).

thf(3524,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ $false ) = $true )
      | ( ( ~ ( in @ SV566 @ SV221 )
          | $false )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3445]) ).

thf(3525,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ ! [SY2840: $o] :
                ( ~ SY2840
                | ( in @ SV566 @ SV435 )
                | SY2840 ) )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3446]) ).

thf(3526,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ ! [SX3: $o] :
                ( ~ SX3
                | ~ SX3
                | SX3 ) )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3446]) ).

thf(3527,plain,
    ! [SV439: $i,SV226: $i,SV776: $i,SV798: $o] :
      ( ( SV798 = $false )
      | ( SV798 = $true )
      | ( SV798 = $false )
      | ( ( in @ SV776 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3453]) ).

thf(3528,plain,
    ! [SV439: $i,SV226: $i,SV776: $i] :
      ( ( $true = $false )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV776 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3454]) ).

thf(3529,plain,
    ! [SV439: $i,SV226: $i,SV776: $i] :
      ( ( $false = $false )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV776 @ ( binunion @ SV226 @ SV439 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3455]) ).

thf(3530,plain,
    ! [SV229: $i,SV821: $i,SV441: $i > $o] :
      ( ( ( SV441 @ SV821 )
        = $false )
      | ( ( ~ ( in @ SV821 @ SV229 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV229
            @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) )
        = $true )
      | ( ( SV441 @ ( sK74_Xx @ SV441 @ SV229 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3457]) ).

thf(3531,plain,
    ! [SV229: $i,SV441: $i > $o] :
      ( ( ( ! [SY2705: $i] :
              ( ~ ( SV441 @ SY2705 )
              | ~ ( in @ SY2705 @ SV229 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV229
            @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) )
        = $true )
      | ( ( SV441 @ ( sK75_SY1878 @ SV441 @ SV229 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3458]) ).

thf(3532,plain,
    ! [SV229: $i,SV441: $i > $o] :
      ( ( ( ( sK74_Xx @ SV441 @ SV229 )
          = ( sK75_SY1878 @ SV441 @ SV229 ) )
        = $false )
      | ( ( ! [SY2705: $i] :
              ( ~ ( SV441 @ SY2705 )
              | ~ ( in @ SY2705 @ SV229 ) )
          | ( singleton
            @ ( dsetconstr @ SV229
              @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3459]) ).

thf(3533,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
        = $true )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3460]) ).

thf(3534,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
              | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                    | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
        = $true )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3461]) ).

thf(3535,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
              | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                          | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) ) )
        = $true )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3462]) ).

thf(3536,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
          | ~ ~ ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 ) )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
              | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                          | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
          | ( SV569 = SV706 ) )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3463]) ).

thf(3537,plain,
    ! [SV786: $i,SV658: $i,SV233: $i,SV836: $i] :
      ( ( ( ~ ( in @ SV836 @ ( sK15_B @ SV233 ) )
          | ! [SY2993: $i] :
              ( ~ ( in @ SY2993 @ SV836 )
              | ( in @ SY2993 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) )
          | ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV836 ) )
        = $true )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( in @ SV786 @ SV658 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3464]) ).

thf(3538,plain,
    ! [SV786: $i,SV233: $i,SV658: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) )
                | ~ ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 ) )
          | ~ ! [SY2927: $i] :
                ( ~ ( in @ SY2927 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
                | ~ ( in @ SY2927 @ SV658 ) ) )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( in @ SV786 @ SV658 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3465]) ).

thf(3539,plain,
    ! [SV799: $i,SV658: $i,SV233: $i] :
      ( ( ( ! [SY2925: $i] :
              ( ~ ( in @ SY2925 @ ( sK15_B @ SV233 ) )
              | ! [SY2926: $i] :
                  ( ~ ( in @ SY2926 @ SY2925 )
                  | ( in @ SY2926 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) )
              | ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SY2925 ) ) )
        = $true )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 )
        = $false )
      | ( ( in @ SV799 @ SV658 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3466]) ).

thf(3540,plain,
    ! [SV799: $i,SV233: $i,SV658: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) )
                    | ~ ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 ) )
              | ~ ! [SY2927: $i] :
                    ( ~ ( in @ SY2927 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
                    | ~ ( in @ SY2927 @ SV658 ) ) ) )
        = $true )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 )
        = $false )
      | ( ( in @ SV799 @ SV658 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3467]) ).

thf(3541,plain,
    ! [SV233: $i,SV770: $i,SV754: $i,SV829: $i] :
      ( ( ( ~ ( in @ SV829 @ SV754 ) )
        = $true )
      | ( ( in @ SV829 @ SV770 )
        = $true )
      | ( ( ! [SY2984: $i] :
              ( ~ ( in @ SY2984 @ SV770 )
              | ( in @ SY2984 @ SV754 ) ) )
        = $true )
      | ( ( in @ SV754 @ ( sK15_B @ SV233 ) )
        = $false )
      | ( ( in @ SV770 @ ( sK15_B @ SV233 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3468]) ).

thf(3542,plain,
    ! [SV233: $i,SV787: $i,SV822: $i] :
      ( ( ( in @ SV822 @ SV787 )
        = $false )
      | ( ( in @ SV822 @ SV233 )
        = $true )
      | ( ( in @ SV787 @ ( sK15_B @ SV233 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3469]) ).

thf(3543,plain,
    ! [SV788: $i,SV233: $i,SV800: $i] :
      ( ( ( in @ SV800 @ SV233 )
        = $false )
      | ( ( in @ SV788 @ SV233 )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) @ ( sK15_B @ SV233 ) )
              | ~ ~ ( ~ ( ~ ( in @ SV788 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) )
                        | ~ ( in @ SV800 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) ) )
                    | ~ ( ( in @ SV788 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) )
                        | ( in @ SV800 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) ) ) ) )
          | ( SV788 = SV800 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3470]) ).

thf(3544,plain,
    ! [SV236: $i,SV445: $i,SV710: $i > $o,SV574: $i,SV823: $i] :
      ( ( ( in @ SV823 @ SV574 )
        = $false )
      | ( ( SV710 @ SV823 )
        = $true )
      | ( ( in @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) @ SV445 )
        = $true )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3473]) ).

thf(3545,plain,
    ! [SV236: $i,SV445: $i,SV574: $i,SV710: $i > $o] :
      ( ( ( in @ ( kpair @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) ) @ SV574 )
        = $true )
      | ( ( ! [SY2953: $i] :
              ( ~ ( in @ SY2953 @ SV574 )
              | ( SV710 @ SY2953 ) ) )
        = $true )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3474]) ).

thf(3546,plain,
    ! [SV236: $i,SV445: $i,SV574: $i,SV710: $i > $o] :
      ( ( ( ~ ( SV710 @ ( kpair @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) ) ) )
        = $true )
      | ( ( ! [SY2953: $i] :
              ( ~ ( in @ SY2953 @ SV574 )
              | ( SV710 @ SY2953 ) ) )
        = $true )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3475]) ).

thf(3547,plain,
    ! [SV582: $i,SV830: $i,SV241: $i > $o] :
      ( ( ( ~ ( SV241 @ SV830 ) )
        = $true )
      | ( ( ( sK43_SY205 @ SV241 )
          = SV830 )
        = $true )
      | ( ( SV241 @ ( sK45_SY1868 @ SV241 ) )
        = $true )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3476]) ).

thf(3548,plain,
    ! [SV582: $i,SV837: $i,SV241: $i > $o] :
      ( ( ( ~ ( SV241 @ SV837 )
          | ( ( sK43_SY205 @ SV241 )
            = SV837 ) )
        = $true )
      | ( ( ( sK44_Xx @ SV241 )
          = ( sK45_SY1868 @ SV241 ) )
        = $false )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3477]) ).

thf(3549,plain,
    ! [SV248: $i,SV453: $i,SV661: $i > $o,SV719: $i > $o] :
      ( ( ( ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 )
          = ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) )
        = $true )
      | ( ( ( dsetconstr @ SV248
            @ ^ [SY2930: $i] : ( SV661 @ SY2930 ) )
          = ( dsetconstr @ SV453
            @ ^ [SY2961: $i] : ( SV719 @ SY2961 ) ) )
        = $true )
      | ( ( SV248 = SV453 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3480]) ).

thf(3550,plain,
    ! [SV248: $i,SV453: $i,SV719: $i > $o,SV661: $i > $o] :
      ( ( ( ~ ( ~ ( ~ ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
                  | ~ ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) )
              | ~ ( ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
                  | ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) ) ) )
        = $true )
      | ( ( ( dsetconstr @ SV248
            @ ^ [SY2930: $i] : ( SV661 @ SY2930 ) )
          = ( dsetconstr @ SV453
            @ ^ [SY2961: $i] : ( SV719 @ SY2961 ) ) )
        = $true )
      | ( ( SV248 = SV453 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3481]) ).

thf(3551,plain,
    ! [SV725: $i,SV413: $i,SV831: $i,SV195: $i > $i > $o] :
      ( ( ( ! [SY2992: $i] :
              ( ~ ( SV195 @ SY2992 @ SV831 )
              | ~ ( in @ SY2992 @ SV413 ) ) )
        = $true )
      | ( ( in @ SV831 @ ( sK10_B @ SV413 @ SV195 ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3482]) ).

thf(3552,plain,
    ! [SV725: $i,SV195: $i > $i > $o,SV413: $i,SV832: $i] :
      ( ( ( ~ ( in @ SV832 @ ( sK10_B @ SV413 @ SV195 ) ) )
        = $true )
      | ( ( ~ ( ~ ( SV195 @ ( sK11_Xy @ SV832 @ SV413 @ SV195 ) @ SV832 )
              | ~ ( in @ ( sK11_Xy @ SV832 @ SV413 @ SV195 ) @ SV413 ) ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3483]) ).

thf(3553,plain,
    ! [SV725: $i,SV413: $i,SV838: $i,SV195: $i > $i > $o] :
      ( ( ( ! [SY2994: $i] :
              ( ~ ( SV195 @ SY2994 @ SV838 )
              | ~ ( in @ SY2994 @ SV413 ) )
          | ( in @ SV838 @ ( sK10_B @ SV413 @ SV195 ) ) )
        = $true )
      | ( ( SV725
          = ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $false )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3484]) ).

thf(3554,plain,
    ! [SV725: $i,SV195: $i > $i > $o,SV413: $i,SV839: $i] :
      ( ( ( ~ ( in @ SV839 @ ( sK10_B @ SV413 @ SV195 ) )
          | ~ ( ~ ( SV195 @ ( sK11_Xy @ SV839 @ SV413 @ SV195 ) @ SV839 )
              | ~ ( in @ ( sK11_Xy @ SV839 @ SV413 @ SV195 ) @ SV413 ) ) )
        = $true )
      | ( ( SV725
          = ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $false )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3485]) ).

thf(3555,plain,
    ! [SV778: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( ~ ! [SY2920: $i] :
                ( ~ ( SV652 @ SY2920 )
                | ( ( sK53_SY235 @ SV652 @ SV605 )
                  = SY2920 ) )
          | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) )
        = $false )
      | ( ( SV605 @ ( sK54_SY233 @ SV778 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ SV778 )
        = $false )
      | ( ( ( sK55_Xx @ SV652 @ SV605 )
          = ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3489]) ).

thf(3556,plain,
    ! [SV652: $i > $o,SV778: $i,SV605: $i > $o] :
      ( ( ( SV605 @ SV778 )
        = $false )
      | ( ( SV778
          = ( sK54_SY233 @ SV778 @ SV652 @ SV605 ) )
        = $false )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( ( sK55_Xx @ SV652 @ SV605 )
          = ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3490]) ).

thf(3557,plain,
    ! [SV652: $i > $o,SV840: $i,SV605: $i > $o] :
      ( ( ( ~ ( ~ ( SV605 @ ( sK54_SY233 @ SV840 @ SV652 @ SV605 ) )
              | ~ ( ( SV840
                   != ( sK54_SY233 @ SV840 @ SV652 @ SV605 ) ) ) )
          | ~ ( SV605 @ SV840 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3491]) ).

thf(3558,plain,
    ! [SV652: $i > $o,SV824: $i,SV605: $i > $o] :
      ( ( ( ~ ( SV605 @ ( sK54_SY233 @ SV824 @ SV652 @ SV605 ) )
          | ~ ( ( SV824
               != ( sK54_SY233 @ SV824 @ SV652 @ SV605 ) ) ) )
        = $false )
      | ( ( ~ ( SV605 @ SV824 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3492]) ).

thf(3559,plain,
    ! [SV779: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ~ ! [SY2922: $i] :
                ( ~ ( SV606 @ SY2922 )
                | ( ( sK49_SY232 @ SV653 @ SV606 )
                  = SY2922 ) )
          | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) )
        = $false )
      | ( ( SV653 @ ( sK50_SY236 @ SV779 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV653 @ SV779 )
        = $false )
      | ( ( ( sK51_Xx @ SV653 @ SV606 )
          = ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3493]) ).

thf(3560,plain,
    ! [SV606: $i > $o,SV779: $i,SV653: $i > $o] :
      ( ( ( SV653 @ SV779 )
        = $false )
      | ( ( SV779
          = ( sK50_SY236 @ SV779 @ SV653 @ SV606 ) )
        = $false )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( ( sK51_Xx @ SV653 @ SV606 )
          = ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3494]) ).

thf(3561,plain,
    ! [SV606: $i > $o,SV841: $i,SV653: $i > $o] :
      ( ( ( ~ ( ~ ( SV653 @ ( sK50_SY236 @ SV841 @ SV653 @ SV606 ) )
              | ~ ( ( SV841
                   != ( sK50_SY236 @ SV841 @ SV653 @ SV606 ) ) ) )
          | ~ ( SV653 @ SV841 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3495]) ).

thf(3562,plain,
    ! [SV606: $i > $o,SV825: $i,SV653: $i > $o] :
      ( ( ( ~ ( SV653 @ ( sK50_SY236 @ SV825 @ SV653 @ SV606 ) )
          | ~ ( ( SV825
               != ( sK50_SY236 @ SV825 @ SV653 @ SV606 ) ) ) )
        = $false )
      | ( ( ~ ( SV653 @ SV825 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3496]) ).

thf(3563,plain,
    ! [SV207: $i,SV422: $i,SV702: $i > $o,SV560: $i,SV842: $i] :
      ( ( ( ~ ( in @ SV842 @ SV560 )
          | ( SV702 @ SV842 ) )
        = $true )
      | ( ( in @ ( kpair @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) ) @ SV560 )
        = $true )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3499]) ).

thf(3564,plain,
    ! [SV207: $i,SV422: $i,SV560: $i,SV702: $i > $o] :
      ( ( ( SV702 @ ( kpair @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) ) )
        = $false )
      | ( ( ! [SY2947: $i] :
              ( ~ ( in @ SY2947 @ SV560 )
              | ( SV702 @ SY2947 ) ) )
        = $true )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3500]) ).

thf(3565,plain,
    ! [SV208: $i,SV423: $i,SV561: $i,SV703: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) ) @ SV561 ) )
        = $false )
      | ( ( subset @ SV561 @ SV703 )
        = $true )
      | ( ( subset @ SV703 @ ( cartprod @ SV208 @ SV423 ) )
        = $false )
      | ( ( subset @ SV561 @ ( cartprod @ SV208 @ SV423 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3501]) ).

thf(3566,plain,
    ! [SV208: $i,SV423: $i,SV561: $i,SV703: $i] :
      ( ( ( ~ ~ ( in @ ( kpair @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) ) @ SV703 ) )
        = $false )
      | ( ( subset @ SV561 @ SV703 )
        = $true )
      | ( ( subset @ SV703 @ ( cartprod @ SV208 @ SV423 ) )
        = $false )
      | ( ( subset @ SV561 @ ( cartprod @ SV208 @ SV423 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3501]) ).

thf(3567,plain,
    ! [SV424: $i > $o,SV209: $i,SV817: $i] :
      ( ( ( in @ SV817 @ SV209 )
        = $false )
      | ( ( SV424 @ SV817 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV209
            @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) )
        = $true )
      | ( ( SV424 @ ( sK70_Xx @ SV424 @ SV209 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3502]) ).

thf(3568,plain,
    ! [SV209: $i,SV843: $i,SV424: $i > $o] :
      ( ( ( ~ ( SV424 @ SV843 )
          | ~ ( in @ SV843 @ SV209 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV209
            @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) )
        = $true )
      | ( ( SV424 @ ( sK71_SY1877 @ SV424 @ SV209 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3503]) ).

thf(3569,plain,
    ! [SV209: $i,SV424: $i > $o] :
      ( ( ( ! [SY2662: $i] :
              ( ~ ( SV424 @ SY2662 )
              | ~ ( in @ SY2662 @ SV209 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV209
            @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) )
        = $true )
      | ( ( ( sK70_Xx @ SV424 @ SV209 )
          = ( sK71_SY1877 @ SV424 @ SV209 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3504]) ).

thf(3570,plain,
    ! [SV750: $i,SV213: $i > $o,SV826: $i,SV427: $i > $o] :
      ( ( ( ~ ( SV427 @ ( sK58_SY260 @ SV826 @ SV427 @ SV213 ) )
          | ~ ( ( SV826
               != ( sK58_SY260 @ SV826 @ SV427 @ SV213 ) ) ) )
        = $false )
      | ( ( ~ ( SV427 @ SV826 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV750 )
        = $false )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3505]) ).

thf(3571,plain,
    ! [SV750: $i,SV213: $i > $o,SV833: $i,SV427: $i > $o] :
      ( ( ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SV833 @ SV427 @ SV213 ) )
              | ~ ( ( SV833
                   != ( sK58_SY260 @ SV833 @ SV427 @ SV213 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV427 @ SV833 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV750
          = ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV750 )
        = $false )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3506]) ).

thf(3572,plain,
    ! [SV427: $i > $o,SV818: $i,SV213: $i > $o] :
      ( ( ( ~ ( SV213 @ ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) ) )
        = $false )
      | ( ( ~ ( SV213 @ SV818 ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3507]) ).

thf(3573,plain,
    ! [SV213: $i > $o,SV427: $i > $o,SV818: $i] :
      ( ( ( ~ ( ( SV818
               != ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) ) ) )
        = $false )
      | ( ( ~ ( SV213 @ SV818 ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3507]) ).

thf(3574,plain,
    ! [SV427: $i > $o,SV796: $i,SV213: $i > $o] :
      ( ( ( SV213 @ SV796 )
        = $false )
      | ( ( SV213 @ ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3508]) ).

thf(3575,plain,
    ! [SV213: $i > $o,SV427: $i > $o,SV796: $i] :
      ( ( ( SV796
          = ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
        = $false )
      | ( ( ~ ( SV213 @ SV796 ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3509]) ).

thf(3576,plain,
    ! [SV218: $i,SV564: $i,SV704: $i,SV809: $i,SV432: $i,SV834: $i] :
      ( ( ( ~ ( in @ SV834 @ SV432 ) )
        = $true )
      | ( ( ~ ( in @ ( kpair @ SV809 @ SV834 ) @ SV704 )
          | ( in @ ( kpair @ SV809 @ SV834 ) @ SV564 ) )
        = $true )
      | ( ( in @ SV809 @ SV218 )
        = $false )
      | ( ( in @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) @ SV218 )
        = $true )
      | ( ( func @ SV218 @ SV432 @ SV704 )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV564 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3510]) ).

thf(3577,plain,
    ! [SV218: $i,SV564: $i,SV704: $i,SV819: $i,SV432: $i,SV844: $i] :
      ( ( ( ~ ( in @ SV844 @ SV432 )
          | ~ ( in @ ( kpair @ SV819 @ SV844 ) @ SV704 )
          | ( in @ ( kpair @ SV819 @ SV844 ) @ SV564 ) )
        = $true )
      | ( ( in @ SV819 @ SV218 )
        = $false )
      | ( ( ( ap @ SV218 @ SV432 @ SV564 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) )
          = ( ap @ SV218 @ SV432 @ SV704 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) ) )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV704 )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV564 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3511]) ).

thf(3578,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 ) )
        = $false )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3512]) ).

thf(3579,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) )
        = $false )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3512]) ).

thf(3580,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 ) )
        = $false )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3513]) ).

thf(3581,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
                | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) ) )
        = $false )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3513]) ).

thf(3582,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
          | ~ ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
                | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) ) )
        = $false )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
        = $false )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3514]) ).

thf(3583,plain,
    ! [SV221: $i,SV435: $i,SV566: $i,SV845: $o] :
      ( ( SV845 = $true )
      | ( ( in @ SV566 @ SV435 )
        = $true )
      | ( ( in @ SV566 @ SV221 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3515]) ).

thf(3584,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( $true = $true )
      | ( ( in @ SV566 @ SV435 )
        = $true )
      | ( ( in @ SV566 @ SV221 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3515]) ).

thf(3585,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( $false = $true )
      | ( ( in @ SV566 @ SV435 )
        = $true )
      | ( ( in @ SV566 @ SV221 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3515]) ).

thf(3586,plain,
    ! [SV435: $i,SV221: $i,SV566: $i,SV835: $o] :
      ( ( ( ~ SV835 ) = $true )
      | ( SV835 = $true )
      | ( ( in @ SV566 @ SV221 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3516]) ).

thf(3587,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ $true ) = $true )
      | ( $true = $true )
      | ( ( in @ SV566 @ SV221 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3517]) ).

thf(3588,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ $false ) = $true )
      | ( $false = $true )
      | ( ( in @ SV566 @ SV221 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3518]) ).

thf(3589,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ ( in @ SV566 @ SV221 ) )
        = $true )
      | ( ( ! [SX3: $o] : SX3 )
        = $true )
      | ( ( in @ SV566 @ SV435 )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3519]) ).

thf(3590,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ ( in @ SV566 @ SV435 )
          | ( in @ SV566 @ SV435 )
          | ! [SX3: $o] : SX3 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3520]) ).

thf(3591,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ ( in @ SV566 @ SV435 )
          | ! [SX3: $o] :
              ( ~ SX3
              | SX3 ) )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3521]) ).

thf(3592,plain,
    ! [SV435: $i,SV221: $i,SV566: $i,SV828: $o] :
      ( ( SV828 = $false )
      | ( ( ~ ( in @ SV566 @ SV221 )
          | SV828 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3522]) ).

thf(3593,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( $true = $false )
      | ( ( ~ ( in @ SV566 @ SV221 )
          | $true )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3523]) ).

thf(3594,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( $false = $false )
      | ( ( ~ ( in @ SV566 @ SV221 )
          | $false )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3524]) ).

thf(3595,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ! [SY2840: $o] :
              ( ~ SY2840
              | ( in @ SV566 @ SV435 )
              | SY2840 ) )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3525]) ).

thf(3596,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ! [SX3: $o] :
              ( ~ SX3
              | ~ SX3
              | SX3 ) )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3526]) ).

thf(3597,plain,
    ! [SV441: $i > $o,SV229: $i,SV821: $i] :
      ( ( ( in @ SV821 @ SV229 )
        = $false )
      | ( ( SV441 @ SV821 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV229
            @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) )
        = $true )
      | ( ( SV441 @ ( sK74_Xx @ SV441 @ SV229 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3530]) ).

thf(3598,plain,
    ! [SV229: $i,SV846: $i,SV441: $i > $o] :
      ( ( ( ~ ( SV441 @ SV846 )
          | ~ ( in @ SV846 @ SV229 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV229
            @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) )
        = $true )
      | ( ( SV441 @ ( sK75_SY1878 @ SV441 @ SV229 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3531]) ).

thf(3599,plain,
    ! [SV229: $i,SV441: $i > $o] :
      ( ( ( ! [SY2705: $i] :
              ( ~ ( SV441 @ SY2705 )
              | ~ ( in @ SY2705 @ SV229 ) ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV229
            @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) )
        = $true )
      | ( ( ( sK74_Xx @ SV441 @ SV229 )
          = ( sK75_SY1878 @ SV441 @ SV229 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3532]) ).

thf(3600,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
          | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3534]) ).

thf(3601,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
          | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                      | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3535]) ).

thf(3602,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
              | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                          | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
          | ( SV569 = SV706 ) )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3536]) ).

thf(3603,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ~ ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 ) )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
              | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                          | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
          | ( SV569 = SV706 ) )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3536]) ).

thf(3604,plain,
    ! [SV786: $i,SV658: $i,SV233: $i,SV836: $i] :
      ( ( ( ~ ( in @ SV836 @ ( sK15_B @ SV233 ) ) )
        = $true )
      | ( ( ! [SY2993: $i] :
              ( ~ ( in @ SY2993 @ SV836 )
              | ( in @ SY2993 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) )
          | ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV836 ) )
        = $true )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( in @ SV786 @ SV658 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3537]) ).

thf(3605,plain,
    ! [SV786: $i,SV233: $i,SV658: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) )
                | ~ ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 ) ) )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( in @ SV786 @ SV658 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3538]) ).

thf(3606,plain,
    ! [SV786: $i,SV233: $i,SV658: $i] :
      ( ( ( ~ ! [SY2927: $i] :
                ( ~ ( in @ SY2927 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
                | ~ ( in @ SY2927 @ SV658 ) ) )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( in @ SV786 @ SV658 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3538]) ).

thf(3607,plain,
    ! [SV799: $i,SV658: $i,SV233: $i,SV847: $i] :
      ( ( ( ~ ( in @ SV847 @ ( sK15_B @ SV233 ) )
          | ! [SY2995: $i] :
              ( ~ ( in @ SY2995 @ SV847 )
              | ( in @ SY2995 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) )
          | ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV847 ) )
        = $true )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 )
        = $false )
      | ( ( in @ SV799 @ SV658 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3539]) ).

thf(3608,plain,
    ! [SV799: $i,SV233: $i,SV658: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) )
                | ~ ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 ) )
          | ~ ! [SY2927: $i] :
                ( ~ ( in @ SY2927 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
                | ~ ( in @ SY2927 @ SV658 ) ) )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 )
        = $false )
      | ( ( in @ SV799 @ SV658 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3540]) ).

thf(3609,plain,
    ! [SV233: $i,SV770: $i,SV754: $i,SV829: $i] :
      ( ( ( in @ SV829 @ SV754 )
        = $false )
      | ( ( in @ SV829 @ SV770 )
        = $true )
      | ( ( ! [SY2984: $i] :
              ( ~ ( in @ SY2984 @ SV770 )
              | ( in @ SY2984 @ SV754 ) ) )
        = $true )
      | ( ( in @ SV754 @ ( sK15_B @ SV233 ) )
        = $false )
      | ( ( in @ SV770 @ ( sK15_B @ SV233 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3541]) ).

thf(3610,plain,
    ! [SV233: $i,SV788: $i,SV800: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) @ ( sK15_B @ SV233 ) )
              | ~ ~ ( ~ ( ~ ( in @ SV788 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) )
                        | ~ ( in @ SV800 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) ) )
                    | ~ ( ( in @ SV788 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) )
                        | ( in @ SV800 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) ) ) ) ) )
        = $true )
      | ( ( SV788 = SV800 )
        = $true )
      | ( ( in @ SV788 @ SV233 )
        = $false )
      | ( ( in @ SV800 @ SV233 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3543]) ).

thf(3611,plain,
    ! [SV236: $i,SV445: $i,SV710: $i > $o,SV574: $i,SV848: $i] :
      ( ( ( ~ ( in @ SV848 @ SV574 )
          | ( SV710 @ SV848 ) )
        = $true )
      | ( ( in @ ( kpair @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) ) @ SV574 )
        = $true )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3545]) ).

thf(3612,plain,
    ! [SV236: $i,SV445: $i,SV574: $i,SV710: $i > $o] :
      ( ( ( SV710 @ ( kpair @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) ) )
        = $false )
      | ( ( ! [SY2953: $i] :
              ( ~ ( in @ SY2953 @ SV574 )
              | ( SV710 @ SY2953 ) ) )
        = $true )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3546]) ).

thf(3613,plain,
    ! [SV582: $i,SV830: $i,SV241: $i > $o] :
      ( ( ( SV241 @ SV830 )
        = $false )
      | ( ( ( sK43_SY205 @ SV241 )
          = SV830 )
        = $true )
      | ( ( SV241 @ ( sK45_SY1868 @ SV241 ) )
        = $true )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3547]) ).

thf(3614,plain,
    ! [SV582: $i,SV837: $i,SV241: $i > $o] :
      ( ( ( ~ ( SV241 @ SV837 ) )
        = $true )
      | ( ( ( sK43_SY205 @ SV241 )
          = SV837 )
        = $true )
      | ( ( ( sK44_Xx @ SV241 )
          = ( sK45_SY1868 @ SV241 ) )
        = $false )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3548]) ).

thf(3615,plain,
    ! [SV248: $i,SV453: $i,SV719: $i > $o,SV661: $i > $o] :
      ( ( ( ~ ( ~ ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
              | ~ ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) )
          | ~ ( ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
              | ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) ) )
        = $false )
      | ( ( ( dsetconstr @ SV248
            @ ^ [SY2930: $i] : ( SV661 @ SY2930 ) )
          = ( dsetconstr @ SV453
            @ ^ [SY2961: $i] : ( SV719 @ SY2961 ) ) )
        = $true )
      | ( ( SV248 = SV453 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3550]) ).

thf(3616,plain,
    ! [SV725: $i,SV413: $i,SV831: $i,SV849: $i,SV195: $i > $i > $o] :
      ( ( ( ~ ( SV195 @ SV849 @ SV831 )
          | ~ ( in @ SV849 @ SV413 ) )
        = $true )
      | ( ( in @ SV831 @ ( sK10_B @ SV413 @ SV195 ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3551]) ).

thf(3617,plain,
    ! [SV725: $i,SV195: $i > $i > $o,SV413: $i,SV832: $i] :
      ( ( ( in @ SV832 @ ( sK10_B @ SV413 @ SV195 ) )
        = $false )
      | ( ( ~ ( ~ ( SV195 @ ( sK11_Xy @ SV832 @ SV413 @ SV195 ) @ SV832 )
              | ~ ( in @ ( sK11_Xy @ SV832 @ SV413 @ SV195 ) @ SV413 ) ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3552]) ).

thf(3618,plain,
    ! [SV725: $i,SV413: $i,SV838: $i,SV195: $i > $i > $o] :
      ( ( ( ! [SY2994: $i] :
              ( ~ ( SV195 @ SY2994 @ SV838 )
              | ~ ( in @ SY2994 @ SV413 ) ) )
        = $true )
      | ( ( in @ SV838 @ ( sK10_B @ SV413 @ SV195 ) )
        = $true )
      | ( ( SV725
          = ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $false )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3553]) ).

thf(3619,plain,
    ! [SV725: $i,SV195: $i > $i > $o,SV413: $i,SV839: $i] :
      ( ( ( ~ ( in @ SV839 @ ( sK10_B @ SV413 @ SV195 ) ) )
        = $true )
      | ( ( ~ ( ~ ( SV195 @ ( sK11_Xy @ SV839 @ SV413 @ SV195 ) @ SV839 )
              | ~ ( in @ ( sK11_Xy @ SV839 @ SV413 @ SV195 ) @ SV413 ) ) )
        = $true )
      | ( ( SV725
          = ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $false )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3554]) ).

thf(3620,plain,
    ! [SV778: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( ~ ! [SY2920: $i] :
                ( ~ ( SV652 @ SY2920 )
                | ( ( sK53_SY235 @ SV652 @ SV605 )
                  = SY2920 ) ) )
        = $false )
      | ( ( SV605 @ ( sK54_SY233 @ SV778 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ SV778 )
        = $false )
      | ( ( ( sK55_Xx @ SV652 @ SV605 )
          = ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3555]) ).

thf(3621,plain,
    ! [SV778: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) )
        = $false )
      | ( ( SV605 @ ( sK54_SY233 @ SV778 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ SV778 )
        = $false )
      | ( ( ( sK55_Xx @ SV652 @ SV605 )
          = ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3555]) ).

thf(3622,plain,
    ! [SV778: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( ~ ! [SY2920: $i] :
                ( ~ ( SV652 @ SY2920 )
                | ( ( sK53_SY235 @ SV652 @ SV605 )
                  = SY2920 ) )
          | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) )
        = $false )
      | ( ( SV778
          = ( sK54_SY233 @ SV778 @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV605 @ SV778 )
        = $false )
      | ( ( ( sK55_Xx @ SV652 @ SV605 )
          = ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3556]) ).

thf(3623,plain,
    ! [SV652: $i > $o,SV840: $i,SV605: $i > $o] :
      ( ( ( ~ ( ~ ( SV605 @ ( sK54_SY233 @ SV840 @ SV652 @ SV605 ) )
              | ~ ( ( SV840
                   != ( sK54_SY233 @ SV840 @ SV652 @ SV605 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV605 @ SV840 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3557]) ).

thf(3624,plain,
    ! [SV652: $i > $o,SV824: $i,SV605: $i > $o] :
      ( ( ( ~ ( SV605 @ ( sK54_SY233 @ SV824 @ SV652 @ SV605 ) ) )
        = $false )
      | ( ( ~ ( SV605 @ SV824 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3558]) ).

thf(3625,plain,
    ! [SV605: $i > $o,SV652: $i > $o,SV824: $i] :
      ( ( ( ~ ( ( SV824
               != ( sK54_SY233 @ SV824 @ SV652 @ SV605 ) ) ) )
        = $false )
      | ( ( ~ ( SV605 @ SV824 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3558]) ).

thf(3626,plain,
    ! [SV779: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ~ ! [SY2922: $i] :
                ( ~ ( SV606 @ SY2922 )
                | ( ( sK49_SY232 @ SV653 @ SV606 )
                  = SY2922 ) ) )
        = $false )
      | ( ( SV653 @ ( sK50_SY236 @ SV779 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV653 @ SV779 )
        = $false )
      | ( ( ( sK51_Xx @ SV653 @ SV606 )
          = ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3559]) ).

thf(3627,plain,
    ! [SV779: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) )
        = $false )
      | ( ( SV653 @ ( sK50_SY236 @ SV779 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV653 @ SV779 )
        = $false )
      | ( ( ( sK51_Xx @ SV653 @ SV606 )
          = ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3559]) ).

thf(3628,plain,
    ! [SV779: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ~ ! [SY2922: $i] :
                ( ~ ( SV606 @ SY2922 )
                | ( ( sK49_SY232 @ SV653 @ SV606 )
                  = SY2922 ) )
          | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) )
        = $false )
      | ( ( SV779
          = ( sK50_SY236 @ SV779 @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ SV779 )
        = $false )
      | ( ( ( sK51_Xx @ SV653 @ SV606 )
          = ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3560]) ).

thf(3629,plain,
    ! [SV606: $i > $o,SV841: $i,SV653: $i > $o] :
      ( ( ( ~ ( ~ ( SV653 @ ( sK50_SY236 @ SV841 @ SV653 @ SV606 ) )
              | ~ ( ( SV841
                   != ( sK50_SY236 @ SV841 @ SV653 @ SV606 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV653 @ SV841 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3561]) ).

thf(3630,plain,
    ! [SV606: $i > $o,SV825: $i,SV653: $i > $o] :
      ( ( ( ~ ( SV653 @ ( sK50_SY236 @ SV825 @ SV653 @ SV606 ) ) )
        = $false )
      | ( ( ~ ( SV653 @ SV825 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3562]) ).

thf(3631,plain,
    ! [SV606: $i > $o,SV653: $i > $o,SV825: $i] :
      ( ( ( ~ ( ( SV825
               != ( sK50_SY236 @ SV825 @ SV653 @ SV606 ) ) ) )
        = $false )
      | ( ( ~ ( SV653 @ SV825 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3562]) ).

thf(3632,plain,
    ! [SV207: $i,SV422: $i,SV702: $i > $o,SV560: $i,SV842: $i] :
      ( ( ( ~ ( in @ SV842 @ SV560 ) )
        = $true )
      | ( ( SV702 @ SV842 )
        = $true )
      | ( ( in @ ( kpair @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) ) @ SV560 )
        = $true )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3563]) ).

thf(3633,plain,
    ! [SV207: $i,SV422: $i,SV702: $i > $o,SV560: $i,SV850: $i] :
      ( ( ( ~ ( in @ SV850 @ SV560 )
          | ( SV702 @ SV850 ) )
        = $true )
      | ( ( SV702 @ ( kpair @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) ) )
        = $false )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3564]) ).

thf(3634,plain,
    ! [SV208: $i,SV423: $i,SV561: $i,SV703: $i] :
      ( ( ( in @ ( kpair @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) ) @ SV561 )
        = $true )
      | ( ( subset @ SV561 @ SV703 )
        = $true )
      | ( ( subset @ SV703 @ ( cartprod @ SV208 @ SV423 ) )
        = $false )
      | ( ( subset @ SV561 @ ( cartprod @ SV208 @ SV423 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3565]) ).

thf(3635,plain,
    ! [SV208: $i,SV423: $i,SV561: $i,SV703: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) ) @ SV703 ) )
        = $true )
      | ( ( subset @ SV561 @ SV703 )
        = $true )
      | ( ( subset @ SV703 @ ( cartprod @ SV208 @ SV423 ) )
        = $false )
      | ( ( subset @ SV561 @ ( cartprod @ SV208 @ SV423 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3566]) ).

thf(3636,plain,
    ! [SV209: $i,SV843: $i,SV424: $i > $o] :
      ( ( ( ~ ( SV424 @ SV843 ) )
        = $true )
      | ( ( ~ ( in @ SV843 @ SV209 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV209
            @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) )
        = $true )
      | ( ( SV424 @ ( sK71_SY1877 @ SV424 @ SV209 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3568]) ).

thf(3637,plain,
    ! [SV209: $i,SV851: $i,SV424: $i > $o] :
      ( ( ( ~ ( SV424 @ SV851 )
          | ~ ( in @ SV851 @ SV209 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV209
            @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) )
        = $true )
      | ( ( ( sK70_Xx @ SV424 @ SV209 )
          = ( sK71_SY1877 @ SV424 @ SV209 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3569]) ).

thf(3638,plain,
    ! [SV750: $i,SV213: $i > $o,SV826: $i,SV427: $i > $o] :
      ( ( ( ~ ( SV427 @ ( sK58_SY260 @ SV826 @ SV427 @ SV213 ) ) )
        = $false )
      | ( ( ~ ( SV427 @ SV826 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV750 )
        = $false )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3570]) ).

thf(3639,plain,
    ! [SV750: $i,SV213: $i > $o,SV427: $i > $o,SV826: $i] :
      ( ( ( ~ ( ( SV826
               != ( sK58_SY260 @ SV826 @ SV427 @ SV213 ) ) ) )
        = $false )
      | ( ( ~ ( SV427 @ SV826 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV750 )
        = $false )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3570]) ).

thf(3640,plain,
    ! [SV750: $i,SV213: $i > $o,SV833: $i,SV427: $i > $o] :
      ( ( ( ~ ( SV427 @ ( sK58_SY260 @ SV833 @ SV427 @ SV213 ) )
          | ~ ( ( SV833
               != ( sK58_SY260 @ SV833 @ SV427 @ SV213 ) ) ) )
        = $false )
      | ( ( ~ ( SV427 @ SV833 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV750
          = ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV750 )
        = $false )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3571]) ).

thf(3641,plain,
    ! [SV427: $i > $o,SV818: $i,SV213: $i > $o] :
      ( ( ( SV213 @ ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
        = $true )
      | ( ( ~ ( SV213 @ SV818 ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3572]) ).

thf(3642,plain,
    ! [SV213: $i > $o,SV427: $i > $o,SV818: $i] :
      ( ( ( SV818
         != ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
        = $true )
      | ( ( ~ ( SV213 @ SV818 ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3573]) ).

thf(3643,plain,
    ! [SV796: $i,SV213: $i > $o,SV427: $i > $o] :
      ( ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV796 )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3574]) ).

thf(3644,plain,
    ! [SV427: $i > $o,SV796: $i,SV213: $i > $o] :
      ( ( ( SV213 @ SV796 )
        = $false )
      | ( ( SV796
          = ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
        = $false )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3575]) ).

thf(3645,plain,
    ! [SV218: $i,SV564: $i,SV704: $i,SV809: $i,SV432: $i,SV834: $i] :
      ( ( ( in @ SV834 @ SV432 )
        = $false )
      | ( ( ~ ( in @ ( kpair @ SV809 @ SV834 ) @ SV704 )
          | ( in @ ( kpair @ SV809 @ SV834 ) @ SV564 ) )
        = $true )
      | ( ( in @ SV809 @ SV218 )
        = $false )
      | ( ( in @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) @ SV218 )
        = $true )
      | ( ( func @ SV218 @ SV432 @ SV704 )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV564 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3576]) ).

thf(3646,plain,
    ! [SV218: $i,SV564: $i,SV704: $i,SV819: $i,SV432: $i,SV844: $i] :
      ( ( ( ~ ( in @ SV844 @ SV432 ) )
        = $true )
      | ( ( ~ ( in @ ( kpair @ SV819 @ SV844 ) @ SV704 )
          | ( in @ ( kpair @ SV819 @ SV844 ) @ SV564 ) )
        = $true )
      | ( ( in @ SV819 @ SV218 )
        = $false )
      | ( ( ( ap @ SV218 @ SV432 @ SV564 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) )
          = ( ap @ SV218 @ SV432 @ SV704 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) ) )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV704 )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV564 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3577]) ).

thf(3647,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
        = $true )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3578]) ).

thf(3648,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) )
        = $true )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3579]) ).

thf(3649,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
        = $true )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3580]) ).

thf(3650,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
              | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) ) )
        = $true )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3581]) ).

thf(3651,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 ) )
        = $false )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
        = $false )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3582]) ).

thf(3652,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
                | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) ) )
        = $false )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
        = $false )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3582]) ).

thf(3653,plain,
    ! [SV435: $i,SV221: $i,SV566: $i,SV835: $o] :
      ( ( SV835 = $false )
      | ( SV835 = $true )
      | ( ( in @ SV566 @ SV221 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3586]) ).

thf(3654,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( $true = $false )
      | ( $true = $true )
      | ( ( in @ SV566 @ SV221 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3587]) ).

thf(3655,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( $false = $false )
      | ( $false = $true )
      | ( ( in @ SV566 @ SV221 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3588]) ).

thf(3656,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( in @ SV566 @ SV221 )
        = $false )
      | ( ( ! [SX3: $o] : SX3 )
        = $true )
      | ( ( in @ SV566 @ SV435 )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3589]) ).

thf(3657,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ ( in @ SV566 @ SV435 ) )
        = $true )
      | ( ( ( in @ SV566 @ SV435 )
          | ! [SX3: $o] : SX3 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3590]) ).

thf(3658,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ ( in @ SV566 @ SV435 ) )
        = $true )
      | ( ( ! [SX3: $o] :
              ( ~ SX3
              | SX3 ) )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3591]) ).

thf(3659,plain,
    ! [SV435: $i,SV828: $o,SV221: $i,SV566: $i] :
      ( ( ( ~ ( in @ SV566 @ SV221 ) )
        = $true )
      | ( SV828 = $true )
      | ( SV828 = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3592]) ).

thf(3660,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ ( in @ SV566 @ SV221 ) )
        = $true )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3593]) ).

thf(3661,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ ( in @ SV566 @ SV221 ) )
        = $true )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3594]) ).

thf(3662,plain,
    ! [SV221: $i,SV435: $i,SV566: $i,SV852: $o] :
      ( ( ( ~ SV852
          | ( in @ SV566 @ SV435 )
          | SV852 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3595]) ).

thf(3663,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ $true
          | ( in @ SV566 @ SV435 )
          | $true )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3595]) ).

thf(3664,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ $false
          | ( in @ SV566 @ SV435 )
          | $false )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3595]) ).

thf(3665,plain,
    ! [SV435: $i,SV221: $i,SV566: $i,SV853: $o] :
      ( ( ( ~ SV853
          | ~ SV853
          | SV853 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3596]) ).

thf(3666,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ $true
          | ~ $true
          | $true )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3596]) ).

thf(3667,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ $false
          | ~ $false
          | $false )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3596]) ).

thf(3668,plain,
    ! [SV229: $i,SV846: $i,SV441: $i > $o] :
      ( ( ( ~ ( SV441 @ SV846 ) )
        = $true )
      | ( ( ~ ( in @ SV846 @ SV229 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV229
            @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) )
        = $true )
      | ( ( SV441 @ ( sK75_SY1878 @ SV441 @ SV229 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3598]) ).

thf(3669,plain,
    ! [SV229: $i,SV854: $i,SV441: $i > $o] :
      ( ( ( ~ ( SV441 @ SV854 )
          | ~ ( in @ SV854 @ SV229 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV229
            @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) )
        = $true )
      | ( ( ( sK74_Xx @ SV441 @ SV229 )
          = ( sK75_SY1878 @ SV441 @ SV229 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3599]) ).

thf(3670,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3600]) ).

thf(3671,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3600]) ).

thf(3672,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3601]) ).

thf(3673,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                      | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3601]) ).

thf(3674,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
              | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                          | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
          | ( SV569 = SV706 ) )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3602]) ).

thf(3675,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 ) )
        = $true )
      | ( ( ~ ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
              | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                          | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
          | ( SV569 = SV706 ) )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3603]) ).

thf(3676,plain,
    ! [SV786: $i,SV658: $i,SV233: $i,SV836: $i] :
      ( ( ( in @ SV836 @ ( sK15_B @ SV233 ) )
        = $false )
      | ( ( ! [SY2993: $i] :
              ( ~ ( in @ SY2993 @ SV836 )
              | ( in @ SY2993 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) )
          | ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV836 ) )
        = $true )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( in @ SV786 @ SV658 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3604]) ).

thf(3677,plain,
    ! [SV786: $i,SV233: $i,SV658: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) )
              | ~ ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 ) ) )
        = $true )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( in @ SV786 @ SV658 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3605]) ).

thf(3678,plain,
    ! [SV786: $i,SV233: $i,SV658: $i] :
      ( ( ( ! [SY2927: $i] :
              ( ~ ( in @ SY2927 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
              | ~ ( in @ SY2927 @ SV658 ) ) )
        = $true )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( in @ SV786 @ SV658 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3606]) ).

thf(3679,plain,
    ! [SV799: $i,SV658: $i,SV233: $i,SV847: $i] :
      ( ( ( ~ ( in @ SV847 @ ( sK15_B @ SV233 ) ) )
        = $true )
      | ( ( ! [SY2995: $i] :
              ( ~ ( in @ SY2995 @ SV847 )
              | ( in @ SY2995 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) )
          | ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV847 ) )
        = $true )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 )
        = $false )
      | ( ( in @ SV799 @ SV658 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3607]) ).

thf(3680,plain,
    ! [SV799: $i,SV233: $i,SV658: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) )
                | ~ ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 ) ) )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 )
        = $false )
      | ( ( in @ SV799 @ SV658 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3608]) ).

thf(3681,plain,
    ! [SV799: $i,SV233: $i,SV658: $i] :
      ( ( ( ~ ! [SY2927: $i] :
                ( ~ ( in @ SY2927 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
                | ~ ( in @ SY2927 @ SV658 ) ) )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 )
        = $false )
      | ( ( in @ SV799 @ SV658 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3608]) ).

thf(3682,plain,
    ! [SV233: $i,SV829: $i,SV754: $i,SV770: $i,SV855: $i] :
      ( ( ( ~ ( in @ SV855 @ SV770 )
          | ( in @ SV855 @ SV754 ) )
        = $true )
      | ( ( in @ SV829 @ SV770 )
        = $true )
      | ( ( in @ SV829 @ SV754 )
        = $false )
      | ( ( in @ SV754 @ ( sK15_B @ SV233 ) )
        = $false )
      | ( ( in @ SV770 @ ( sK15_B @ SV233 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3609]) ).

thf(3683,plain,
    ! [SV233: $i,SV788: $i,SV800: $i] :
      ( ( ( ~ ( in @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) @ ( sK15_B @ SV233 ) )
          | ~ ~ ( ~ ( ~ ( in @ SV788 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) )
                    | ~ ( in @ SV800 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) ) )
                | ~ ( ( in @ SV788 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) )
                    | ( in @ SV800 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) ) ) ) )
        = $false )
      | ( ( SV788 = SV800 )
        = $true )
      | ( ( in @ SV788 @ SV233 )
        = $false )
      | ( ( in @ SV800 @ SV233 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3610]) ).

thf(3684,plain,
    ! [SV236: $i,SV445: $i,SV710: $i > $o,SV574: $i,SV848: $i] :
      ( ( ( ~ ( in @ SV848 @ SV574 ) )
        = $true )
      | ( ( SV710 @ SV848 )
        = $true )
      | ( ( in @ ( kpair @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) ) @ SV574 )
        = $true )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3611]) ).

thf(3685,plain,
    ! [SV236: $i,SV445: $i,SV710: $i > $o,SV574: $i,SV856: $i] :
      ( ( ( ~ ( in @ SV856 @ SV574 )
          | ( SV710 @ SV856 ) )
        = $true )
      | ( ( SV710 @ ( kpair @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) ) )
        = $false )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3612]) ).

thf(3686,plain,
    ! [SV582: $i,SV837: $i,SV241: $i > $o] :
      ( ( ( SV241 @ SV837 )
        = $false )
      | ( ( ( sK43_SY205 @ SV241 )
          = SV837 )
        = $true )
      | ( ( ( sK44_Xx @ SV241 )
          = ( sK45_SY1868 @ SV241 ) )
        = $false )
      | ( ( SV241 @ SV582 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3614]) ).

thf(3687,plain,
    ! [SV248: $i,SV453: $i,SV719: $i > $o,SV661: $i > $o] :
      ( ( ( ~ ( ~ ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
              | ~ ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) ) )
        = $false )
      | ( ( ( dsetconstr @ SV248
            @ ^ [SY2930: $i] : ( SV661 @ SY2930 ) )
          = ( dsetconstr @ SV453
            @ ^ [SY2961: $i] : ( SV719 @ SY2961 ) ) )
        = $true )
      | ( ( SV248 = SV453 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3615]) ).

thf(3688,plain,
    ! [SV248: $i,SV453: $i,SV719: $i > $o,SV661: $i > $o] :
      ( ( ( ~ ( ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
              | ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) ) )
        = $false )
      | ( ( ( dsetconstr @ SV248
            @ ^ [SY2930: $i] : ( SV661 @ SY2930 ) )
          = ( dsetconstr @ SV453
            @ ^ [SY2961: $i] : ( SV719 @ SY2961 ) ) )
        = $true )
      | ( ( SV248 = SV453 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3615]) ).

thf(3689,plain,
    ! [SV725: $i,SV413: $i,SV831: $i,SV849: $i,SV195: $i > $i > $o] :
      ( ( ( ~ ( SV195 @ SV849 @ SV831 ) )
        = $true )
      | ( ( ~ ( in @ SV849 @ SV413 ) )
        = $true )
      | ( ( in @ SV831 @ ( sK10_B @ SV413 @ SV195 ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3616]) ).

thf(3690,plain,
    ! [SV725: $i,SV413: $i,SV832: $i,SV195: $i > $i > $o] :
      ( ( ( ~ ( SV195 @ ( sK11_Xy @ SV832 @ SV413 @ SV195 ) @ SV832 )
          | ~ ( in @ ( sK11_Xy @ SV832 @ SV413 @ SV195 ) @ SV413 ) )
        = $false )
      | ( ( in @ SV832 @ ( sK10_B @ SV413 @ SV195 ) )
        = $false )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3617]) ).

thf(3691,plain,
    ! [SV725: $i,SV413: $i,SV838: $i,SV857: $i,SV195: $i > $i > $o] :
      ( ( ( ~ ( SV195 @ SV857 @ SV838 )
          | ~ ( in @ SV857 @ SV413 ) )
        = $true )
      | ( ( in @ SV838 @ ( sK10_B @ SV413 @ SV195 ) )
        = $true )
      | ( ( SV725
          = ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $false )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3618]) ).

thf(3692,plain,
    ! [SV725: $i,SV195: $i > $i > $o,SV413: $i,SV839: $i] :
      ( ( ( in @ SV839 @ ( sK10_B @ SV413 @ SV195 ) )
        = $false )
      | ( ( ~ ( ~ ( SV195 @ ( sK11_Xy @ SV839 @ SV413 @ SV195 ) @ SV839 )
              | ~ ( in @ ( sK11_Xy @ SV839 @ SV413 @ SV195 ) @ SV413 ) ) )
        = $true )
      | ( ( SV725
          = ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $false )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3619]) ).

thf(3693,plain,
    ! [SV778: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( ! [SY2920: $i] :
              ( ~ ( SV652 @ SY2920 )
              | ( ( sK53_SY235 @ SV652 @ SV605 )
                = SY2920 ) ) )
        = $true )
      | ( ( SV605 @ ( sK54_SY233 @ SV778 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ SV778 )
        = $false )
      | ( ( ( sK55_Xx @ SV652 @ SV605 )
          = ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3620]) ).

thf(3694,plain,
    ! [SV778: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK54_SY233 @ SV778 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ SV778 )
        = $false )
      | ( ( ( sK55_Xx @ SV652 @ SV605 )
          = ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3621]) ).

thf(3695,plain,
    ! [SV778: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( ~ ! [SY2920: $i] :
                ( ~ ( SV652 @ SY2920 )
                | ( ( sK53_SY235 @ SV652 @ SV605 )
                  = SY2920 ) ) )
        = $false )
      | ( ( SV778
          = ( sK54_SY233 @ SV778 @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV605 @ SV778 )
        = $false )
      | ( ( ( sK55_Xx @ SV652 @ SV605 )
          = ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3622]) ).

thf(3696,plain,
    ! [SV778: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) )
        = $false )
      | ( ( SV778
          = ( sK54_SY233 @ SV778 @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV605 @ SV778 )
        = $false )
      | ( ( ( sK55_Xx @ SV652 @ SV605 )
          = ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3622]) ).

thf(3697,plain,
    ! [SV652: $i > $o,SV840: $i,SV605: $i > $o] :
      ( ( ( ~ ( SV605 @ ( sK54_SY233 @ SV840 @ SV652 @ SV605 ) )
          | ~ ( ( SV840
               != ( sK54_SY233 @ SV840 @ SV652 @ SV605 ) ) ) )
        = $false )
      | ( ( ~ ( SV605 @ SV840 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3623]) ).

thf(3698,plain,
    ! [SV652: $i > $o,SV824: $i,SV605: $i > $o] :
      ( ( ( SV605 @ ( sK54_SY233 @ SV824 @ SV652 @ SV605 ) )
        = $true )
      | ( ( ~ ( SV605 @ SV824 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3624]) ).

thf(3699,plain,
    ! [SV605: $i > $o,SV652: $i > $o,SV824: $i] :
      ( ( ( SV824
         != ( sK54_SY233 @ SV824 @ SV652 @ SV605 ) )
        = $true )
      | ( ( ~ ( SV605 @ SV824 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3625]) ).

thf(3700,plain,
    ! [SV779: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ! [SY2922: $i] :
              ( ~ ( SV606 @ SY2922 )
              | ( ( sK49_SY232 @ SV653 @ SV606 )
                = SY2922 ) ) )
        = $true )
      | ( ( SV653 @ ( sK50_SY236 @ SV779 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV653 @ SV779 )
        = $false )
      | ( ( ( sK51_Xx @ SV653 @ SV606 )
          = ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3626]) ).

thf(3701,plain,
    ! [SV779: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV653 @ ( sK50_SY236 @ SV779 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV653 @ SV779 )
        = $false )
      | ( ( ( sK51_Xx @ SV653 @ SV606 )
          = ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3627]) ).

thf(3702,plain,
    ! [SV779: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ~ ! [SY2922: $i] :
                ( ~ ( SV606 @ SY2922 )
                | ( ( sK49_SY232 @ SV653 @ SV606 )
                  = SY2922 ) ) )
        = $false )
      | ( ( SV779
          = ( sK50_SY236 @ SV779 @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ SV779 )
        = $false )
      | ( ( ( sK51_Xx @ SV653 @ SV606 )
          = ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3628]) ).

thf(3703,plain,
    ! [SV779: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) )
        = $false )
      | ( ( SV779
          = ( sK50_SY236 @ SV779 @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ SV779 )
        = $false )
      | ( ( ( sK51_Xx @ SV653 @ SV606 )
          = ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3628]) ).

thf(3704,plain,
    ! [SV606: $i > $o,SV841: $i,SV653: $i > $o] :
      ( ( ( ~ ( SV653 @ ( sK50_SY236 @ SV841 @ SV653 @ SV606 ) )
          | ~ ( ( SV841
               != ( sK50_SY236 @ SV841 @ SV653 @ SV606 ) ) ) )
        = $false )
      | ( ( ~ ( SV653 @ SV841 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3629]) ).

thf(3705,plain,
    ! [SV606: $i > $o,SV825: $i,SV653: $i > $o] :
      ( ( ( SV653 @ ( sK50_SY236 @ SV825 @ SV653 @ SV606 ) )
        = $true )
      | ( ( ~ ( SV653 @ SV825 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3630]) ).

thf(3706,plain,
    ! [SV606: $i > $o,SV653: $i > $o,SV825: $i] :
      ( ( ( SV825
         != ( sK50_SY236 @ SV825 @ SV653 @ SV606 ) )
        = $true )
      | ( ( ~ ( SV653 @ SV825 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3631]) ).

thf(3707,plain,
    ! [SV207: $i,SV422: $i,SV702: $i > $o,SV560: $i,SV842: $i] :
      ( ( ( in @ SV842 @ SV560 )
        = $false )
      | ( ( SV702 @ SV842 )
        = $true )
      | ( ( in @ ( kpair @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) ) @ SV560 )
        = $true )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3632]) ).

thf(3708,plain,
    ! [SV207: $i,SV422: $i,SV702: $i > $o,SV560: $i,SV850: $i] :
      ( ( ( ~ ( in @ SV850 @ SV560 ) )
        = $true )
      | ( ( SV702 @ SV850 )
        = $true )
      | ( ( SV702 @ ( kpair @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) ) )
        = $false )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3633]) ).

thf(3709,plain,
    ! [SV208: $i,SV423: $i,SV561: $i,SV703: $i] :
      ( ( ( in @ ( kpair @ ( sK84_Xx @ SV703 @ SV561 @ SV423 @ SV208 ) @ ( sK85_SY1881 @ SV703 @ SV561 @ SV423 @ SV208 ) ) @ SV703 )
        = $false )
      | ( ( subset @ SV561 @ SV703 )
        = $true )
      | ( ( subset @ SV703 @ ( cartprod @ SV208 @ SV423 ) )
        = $false )
      | ( ( subset @ SV561 @ ( cartprod @ SV208 @ SV423 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3635]) ).

thf(3710,plain,
    ! [SV209: $i,SV843: $i,SV424: $i > $o] :
      ( ( ( SV424 @ SV843 )
        = $false )
      | ( ( ~ ( in @ SV843 @ SV209 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV209
            @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) )
        = $true )
      | ( ( SV424 @ ( sK71_SY1877 @ SV424 @ SV209 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3636]) ).

thf(3711,plain,
    ! [SV209: $i,SV851: $i,SV424: $i > $o] :
      ( ( ( ~ ( SV424 @ SV851 ) )
        = $true )
      | ( ( ~ ( in @ SV851 @ SV209 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV209
            @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) )
        = $true )
      | ( ( ( sK70_Xx @ SV424 @ SV209 )
          = ( sK71_SY1877 @ SV424 @ SV209 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3637]) ).

thf(3712,plain,
    ! [SV750: $i,SV213: $i > $o,SV826: $i,SV427: $i > $o] :
      ( ( ( SV427 @ ( sK58_SY260 @ SV826 @ SV427 @ SV213 ) )
        = $true )
      | ( ( ~ ( SV427 @ SV826 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV750 )
        = $false )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3638]) ).

thf(3713,plain,
    ! [SV750: $i,SV213: $i > $o,SV427: $i > $o,SV826: $i] :
      ( ( ( SV826
         != ( sK58_SY260 @ SV826 @ SV427 @ SV213 ) )
        = $true )
      | ( ( ~ ( SV427 @ SV826 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV750 )
        = $false )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3639]) ).

thf(3714,plain,
    ! [SV750: $i,SV213: $i > $o,SV833: $i,SV427: $i > $o] :
      ( ( ( ~ ( SV427 @ ( sK58_SY260 @ SV833 @ SV427 @ SV213 ) ) )
        = $false )
      | ( ( ~ ( SV427 @ SV833 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV750
          = ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV750 )
        = $false )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3640]) ).

thf(3715,plain,
    ! [SV750: $i,SV213: $i > $o,SV427: $i > $o,SV833: $i] :
      ( ( ( ~ ( ( SV833
               != ( sK58_SY260 @ SV833 @ SV427 @ SV213 ) ) ) )
        = $false )
      | ( ( ~ ( SV427 @ SV833 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV750
          = ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV750 )
        = $false )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3640]) ).

thf(3716,plain,
    ! [SV427: $i > $o,SV818: $i,SV213: $i > $o] :
      ( ( ( SV213 @ SV818 )
        = $false )
      | ( ( SV213 @ ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3641]) ).

thf(3717,plain,
    ! [SV213: $i > $o,SV427: $i > $o,SV818: $i] :
      ( ( ( SV818
          = ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
        = $false )
      | ( ( ~ ( SV213 @ SV818 ) )
        = $true )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3642]) ).

thf(3718,plain,
    ! [SV796: $i,SV213: $i > $o,SV858: $i,SV427: $i > $o] :
      ( ( ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SV858 @ SV427 @ SV213 ) )
              | ~ ( ( SV858
                   != ( sK58_SY260 @ SV858 @ SV427 @ SV213 ) ) ) )
          | ~ ( SV427 @ SV858 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV796 )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3643]) ).

thf(3719,plain,
    ! [SV796: $i,SV213: $i > $o,SV427: $i > $o] :
      ( ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV796
          = ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV796 )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3644]) ).

thf(3720,plain,
    ! [SV218: $i,SV432: $i,SV564: $i,SV704: $i,SV834: $i,SV809: $i] :
      ( ( ( ~ ( in @ ( kpair @ SV809 @ SV834 ) @ SV704 ) )
        = $true )
      | ( ( in @ ( kpair @ SV809 @ SV834 ) @ SV564 )
        = $true )
      | ( ( in @ SV834 @ SV432 )
        = $false )
      | ( ( in @ SV809 @ SV218 )
        = $false )
      | ( ( in @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) @ SV218 )
        = $true )
      | ( ( func @ SV218 @ SV432 @ SV704 )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV564 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3645]) ).

thf(3721,plain,
    ! [SV218: $i,SV564: $i,SV704: $i,SV819: $i,SV432: $i,SV844: $i] :
      ( ( ( in @ SV844 @ SV432 )
        = $false )
      | ( ( ~ ( in @ ( kpair @ SV819 @ SV844 ) @ SV704 )
          | ( in @ ( kpair @ SV819 @ SV844 ) @ SV564 ) )
        = $true )
      | ( ( in @ SV819 @ SV218 )
        = $false )
      | ( ( ( ap @ SV218 @ SV432 @ SV564 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) )
          = ( ap @ SV218 @ SV432 @ SV704 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) ) )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV704 )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV564 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3646]) ).

thf(3722,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 )
        = $false )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3648]) ).

thf(3723,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
          | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) )
        = $false )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3650]) ).

thf(3724,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV219 )
        = $true )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
        = $false )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3651]) ).

thf(3725,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
              | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) ) )
        = $true )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
        = $false )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3652]) ).

thf(3726,plain,
    ! [SV435: $i,SV221: $i,SV566: $i,SV859: $o] :
      ( ( SV859 = $true )
      | ( ( in @ SV566 @ SV221 )
        = $false )
      | ( ( in @ SV566 @ SV435 )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3656]) ).

thf(3727,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( $true = $true )
      | ( ( in @ SV566 @ SV221 )
        = $false )
      | ( ( in @ SV566 @ SV435 )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3656]) ).

thf(3728,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( $false = $true )
      | ( ( in @ SV566 @ SV221 )
        = $false )
      | ( ( in @ SV566 @ SV435 )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3656]) ).

thf(3729,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( in @ SV566 @ SV435 )
        = $false )
      | ( ( ( in @ SV566 @ SV435 )
          | ! [SX3: $o] : SX3 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3657]) ).

thf(3730,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( in @ SV566 @ SV435 )
        = $false )
      | ( ( ! [SX3: $o] :
              ( ~ SX3
              | SX3 ) )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3658]) ).

thf(3731,plain,
    ! [SV435: $i,SV828: $o,SV221: $i,SV566: $i] :
      ( ( ( in @ SV566 @ SV221 )
        = $false )
      | ( SV828 = $true )
      | ( SV828 = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3659]) ).

thf(3732,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( in @ SV566 @ SV221 )
        = $false )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3660]) ).

thf(3733,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( in @ SV566 @ SV221 )
        = $false )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3661]) ).

thf(3734,plain,
    ! [SV221: $i,SV435: $i,SV566: $i,SV852: $o] :
      ( ( ( ~ SV852 ) = $true )
      | ( ( ( in @ SV566 @ SV435 )
          | SV852 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3662]) ).

thf(3735,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ $true ) = $true )
      | ( ( ( in @ SV566 @ SV435 )
          | $true )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3663]) ).

thf(3736,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ $false ) = $true )
      | ( ( ( in @ SV566 @ SV435 )
          | $false )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3664]) ).

thf(3737,plain,
    ! [SV435: $i,SV221: $i,SV566: $i,SV853: $o] :
      ( ( ( ~ SV853 ) = $true )
      | ( ( ~ SV853
          | SV853 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3665]) ).

thf(3738,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ $true ) = $true )
      | ( ( ~ $true
          | $true )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3666]) ).

thf(3739,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ $false ) = $true )
      | ( ( ~ $false
          | $false )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3667]) ).

thf(3740,plain,
    ! [SV229: $i,SV846: $i,SV441: $i > $o] :
      ( ( ( SV441 @ SV846 )
        = $false )
      | ( ( ~ ( in @ SV846 @ SV229 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV229
            @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) )
        = $true )
      | ( ( SV441 @ ( sK75_SY1878 @ SV441 @ SV229 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3668]) ).

thf(3741,plain,
    ! [SV229: $i,SV854: $i,SV441: $i > $o] :
      ( ( ( ~ ( SV441 @ SV854 ) )
        = $true )
      | ( ( ~ ( in @ SV854 @ SV229 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV229
            @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) )
        = $true )
      | ( ( ( sK74_Xx @ SV441 @ SV229 )
          = ( sK75_SY1878 @ SV441 @ SV229 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3669]) ).

thf(3742,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
        = $true )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3670]) ).

thf(3743,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
              | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) )
        = $true )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3671]) ).

thf(3744,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
        = $true )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3672]) ).

thf(3745,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
              | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                    | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
        = $true )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3673]) ).

thf(3746,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
              | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                          | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) ) )
        = $true )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3674]) ).

thf(3747,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
        = $false )
      | ( ( ~ ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
              | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                          | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
          | ( SV569 = SV706 ) )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3675]) ).

thf(3748,plain,
    ! [SV786: $i,SV233: $i,SV658: $i,SV836: $i] :
      ( ( ( ! [SY2993: $i] :
              ( ~ ( in @ SY2993 @ SV836 )
              | ( in @ SY2993 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) ) )
        = $true )
      | ( ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV836 )
        = $true )
      | ( ( in @ SV836 @ ( sK15_B @ SV233 ) )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( in @ SV786 @ SV658 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3676]) ).

thf(3749,plain,
    ! [SV786: $i,SV233: $i,SV658: $i] :
      ( ( ( ~ ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) )
          | ~ ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 ) )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( in @ SV786 @ SV658 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3677]) ).

thf(3750,plain,
    ! [SV786: $i,SV233: $i,SV658: $i,SV860: $i] :
      ( ( ( ~ ( in @ SV860 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
          | ~ ( in @ SV860 @ SV658 ) )
        = $true )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( in @ SV786 @ SV658 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3678]) ).

thf(3751,plain,
    ! [SV799: $i,SV658: $i,SV233: $i,SV847: $i] :
      ( ( ( in @ SV847 @ ( sK15_B @ SV233 ) )
        = $false )
      | ( ( ! [SY2995: $i] :
              ( ~ ( in @ SY2995 @ SV847 )
              | ( in @ SY2995 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) )
          | ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV847 ) )
        = $true )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 )
        = $false )
      | ( ( in @ SV799 @ SV658 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3679]) ).

thf(3752,plain,
    ! [SV799: $i,SV233: $i,SV658: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) )
              | ~ ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 ) ) )
        = $true )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 )
        = $false )
      | ( ( in @ SV799 @ SV658 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3680]) ).

thf(3753,plain,
    ! [SV799: $i,SV233: $i,SV658: $i] :
      ( ( ( ! [SY2927: $i] :
              ( ~ ( in @ SY2927 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
              | ~ ( in @ SY2927 @ SV658 ) ) )
        = $true )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 )
        = $false )
      | ( ( in @ SV799 @ SV658 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3681]) ).

thf(3754,plain,
    ! [SV233: $i,SV829: $i,SV754: $i,SV770: $i,SV855: $i] :
      ( ( ( ~ ( in @ SV855 @ SV770 ) )
        = $true )
      | ( ( in @ SV855 @ SV754 )
        = $true )
      | ( ( in @ SV829 @ SV770 )
        = $true )
      | ( ( in @ SV829 @ SV754 )
        = $false )
      | ( ( in @ SV754 @ ( sK15_B @ SV233 ) )
        = $false )
      | ( ( in @ SV770 @ ( sK15_B @ SV233 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3682]) ).

thf(3755,plain,
    ! [SV233: $i,SV788: $i,SV800: $i] :
      ( ( ( ~ ( in @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) @ ( sK15_B @ SV233 ) ) )
        = $false )
      | ( ( SV788 = SV800 )
        = $true )
      | ( ( in @ SV788 @ SV233 )
        = $false )
      | ( ( in @ SV800 @ SV233 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3683]) ).

thf(3756,plain,
    ! [SV233: $i,SV800: $i,SV788: $i] :
      ( ( ( ~ ~ ( ~ ( ~ ( in @ SV788 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) )
                    | ~ ( in @ SV800 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) ) )
                | ~ ( ( in @ SV788 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) )
                    | ( in @ SV800 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) ) ) ) )
        = $false )
      | ( ( SV788 = SV800 )
        = $true )
      | ( ( in @ SV788 @ SV233 )
        = $false )
      | ( ( in @ SV800 @ SV233 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3683]) ).

thf(3757,plain,
    ! [SV236: $i,SV445: $i,SV710: $i > $o,SV574: $i,SV848: $i] :
      ( ( ( in @ SV848 @ SV574 )
        = $false )
      | ( ( SV710 @ SV848 )
        = $true )
      | ( ( in @ ( kpair @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) ) @ SV574 )
        = $true )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3684]) ).

thf(3758,plain,
    ! [SV236: $i,SV445: $i,SV710: $i > $o,SV574: $i,SV856: $i] :
      ( ( ( ~ ( in @ SV856 @ SV574 ) )
        = $true )
      | ( ( SV710 @ SV856 )
        = $true )
      | ( ( SV710 @ ( kpair @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) ) )
        = $false )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3685]) ).

thf(3759,plain,
    ! [SV248: $i,SV453: $i,SV719: $i > $o,SV661: $i > $o] :
      ( ( ( ~ ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
          | ~ ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) )
        = $true )
      | ( ( ( dsetconstr @ SV248
            @ ^ [SY2930: $i] : ( SV661 @ SY2930 ) )
          = ( dsetconstr @ SV453
            @ ^ [SY2961: $i] : ( SV719 @ SY2961 ) ) )
        = $true )
      | ( ( SV248 = SV453 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3687]) ).

thf(3760,plain,
    ! [SV248: $i,SV453: $i,SV719: $i > $o,SV661: $i > $o] :
      ( ( ( ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
          | ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) )
        = $true )
      | ( ( ( dsetconstr @ SV248
            @ ^ [SY2930: $i] : ( SV661 @ SY2930 ) )
          = ( dsetconstr @ SV453
            @ ^ [SY2961: $i] : ( SV719 @ SY2961 ) ) )
        = $true )
      | ( ( SV248 = SV453 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3688]) ).

thf(3761,plain,
    ! [SV725: $i,SV413: $i,SV831: $i,SV849: $i,SV195: $i > $i > $o] :
      ( ( ( SV195 @ SV849 @ SV831 )
        = $false )
      | ( ( ~ ( in @ SV849 @ SV413 ) )
        = $true )
      | ( ( in @ SV831 @ ( sK10_B @ SV413 @ SV195 ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3689]) ).

thf(3762,plain,
    ! [SV725: $i,SV413: $i,SV832: $i,SV195: $i > $i > $o] :
      ( ( ( ~ ( SV195 @ ( sK11_Xy @ SV832 @ SV413 @ SV195 ) @ SV832 ) )
        = $false )
      | ( ( in @ SV832 @ ( sK10_B @ SV413 @ SV195 ) )
        = $false )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3690]) ).

thf(3763,plain,
    ! [SV725: $i,SV195: $i > $i > $o,SV413: $i,SV832: $i] :
      ( ( ( ~ ( in @ ( sK11_Xy @ SV832 @ SV413 @ SV195 ) @ SV413 ) )
        = $false )
      | ( ( in @ SV832 @ ( sK10_B @ SV413 @ SV195 ) )
        = $false )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3690]) ).

thf(3764,plain,
    ! [SV725: $i,SV413: $i,SV838: $i,SV857: $i,SV195: $i > $i > $o] :
      ( ( ( ~ ( SV195 @ SV857 @ SV838 ) )
        = $true )
      | ( ( ~ ( in @ SV857 @ SV413 ) )
        = $true )
      | ( ( in @ SV838 @ ( sK10_B @ SV413 @ SV195 ) )
        = $true )
      | ( ( SV725
          = ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $false )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3691]) ).

thf(3765,plain,
    ! [SV725: $i,SV413: $i,SV839: $i,SV195: $i > $i > $o] :
      ( ( ( ~ ( SV195 @ ( sK11_Xy @ SV839 @ SV413 @ SV195 ) @ SV839 )
          | ~ ( in @ ( sK11_Xy @ SV839 @ SV413 @ SV195 ) @ SV413 ) )
        = $false )
      | ( ( in @ SV839 @ ( sK10_B @ SV413 @ SV195 ) )
        = $false )
      | ( ( SV725
          = ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $false )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3692]) ).

thf(3766,plain,
    ! [SV778: $i,SV605: $i > $o,SV861: $i,SV652: $i > $o] :
      ( ( ( ~ ( SV652 @ SV861 )
          | ( ( sK53_SY235 @ SV652 @ SV605 )
            = SV861 ) )
        = $true )
      | ( ( SV605 @ ( sK54_SY233 @ SV778 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ SV778 )
        = $false )
      | ( ( ( sK55_Xx @ SV652 @ SV605 )
          = ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3693]) ).

thf(3767,plain,
    ! [SV778: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( ! [SY2920: $i] :
              ( ~ ( SV652 @ SY2920 )
              | ( ( sK53_SY235 @ SV652 @ SV605 )
                = SY2920 ) ) )
        = $true )
      | ( ( SV778
          = ( sK54_SY233 @ SV778 @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV605 @ SV778 )
        = $false )
      | ( ( ( sK55_Xx @ SV652 @ SV605 )
          = ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3695]) ).

thf(3768,plain,
    ! [SV778: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV778
          = ( sK54_SY233 @ SV778 @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV605 @ SV778 )
        = $false )
      | ( ( ( sK55_Xx @ SV652 @ SV605 )
          = ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3696]) ).

thf(3769,plain,
    ! [SV652: $i > $o,SV840: $i,SV605: $i > $o] :
      ( ( ( ~ ( SV605 @ ( sK54_SY233 @ SV840 @ SV652 @ SV605 ) ) )
        = $false )
      | ( ( ~ ( SV605 @ SV840 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3697]) ).

thf(3770,plain,
    ! [SV605: $i > $o,SV652: $i > $o,SV840: $i] :
      ( ( ( ~ ( ( SV840
               != ( sK54_SY233 @ SV840 @ SV652 @ SV605 ) ) ) )
        = $false )
      | ( ( ~ ( SV605 @ SV840 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3697]) ).

thf(3771,plain,
    ! [SV652: $i > $o,SV824: $i,SV605: $i > $o] :
      ( ( ( SV605 @ SV824 )
        = $false )
      | ( ( SV605 @ ( sK54_SY233 @ SV824 @ SV652 @ SV605 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3698]) ).

thf(3772,plain,
    ! [SV605: $i > $o,SV652: $i > $o,SV824: $i] :
      ( ( ( SV824
          = ( sK54_SY233 @ SV824 @ SV652 @ SV605 ) )
        = $false )
      | ( ( ~ ( SV605 @ SV824 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3699]) ).

thf(3773,plain,
    ! [SV779: $i,SV653: $i > $o,SV862: $i,SV606: $i > $o] :
      ( ( ( ~ ( SV606 @ SV862 )
          | ( ( sK49_SY232 @ SV653 @ SV606 )
            = SV862 ) )
        = $true )
      | ( ( SV653 @ ( sK50_SY236 @ SV779 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV653 @ SV779 )
        = $false )
      | ( ( ( sK51_Xx @ SV653 @ SV606 )
          = ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3700]) ).

thf(3774,plain,
    ! [SV779: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ! [SY2922: $i] :
              ( ~ ( SV606 @ SY2922 )
              | ( ( sK49_SY232 @ SV653 @ SV606 )
                = SY2922 ) ) )
        = $true )
      | ( ( SV779
          = ( sK50_SY236 @ SV779 @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ SV779 )
        = $false )
      | ( ( ( sK51_Xx @ SV653 @ SV606 )
          = ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3702]) ).

thf(3775,plain,
    ! [SV779: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV779
          = ( sK50_SY236 @ SV779 @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ SV779 )
        = $false )
      | ( ( ( sK51_Xx @ SV653 @ SV606 )
          = ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3703]) ).

thf(3776,plain,
    ! [SV606: $i > $o,SV841: $i,SV653: $i > $o] :
      ( ( ( ~ ( SV653 @ ( sK50_SY236 @ SV841 @ SV653 @ SV606 ) ) )
        = $false )
      | ( ( ~ ( SV653 @ SV841 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3704]) ).

thf(3777,plain,
    ! [SV606: $i > $o,SV653: $i > $o,SV841: $i] :
      ( ( ( ~ ( ( SV841
               != ( sK50_SY236 @ SV841 @ SV653 @ SV606 ) ) ) )
        = $false )
      | ( ( ~ ( SV653 @ SV841 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3704]) ).

thf(3778,plain,
    ! [SV606: $i > $o,SV825: $i,SV653: $i > $o] :
      ( ( ( SV653 @ SV825 )
        = $false )
      | ( ( SV653 @ ( sK50_SY236 @ SV825 @ SV653 @ SV606 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3705]) ).

thf(3779,plain,
    ! [SV606: $i > $o,SV653: $i > $o,SV825: $i] :
      ( ( ( SV825
          = ( sK50_SY236 @ SV825 @ SV653 @ SV606 ) )
        = $false )
      | ( ( ~ ( SV653 @ SV825 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3706]) ).

thf(3780,plain,
    ! [SV207: $i,SV422: $i,SV702: $i > $o,SV560: $i,SV850: $i] :
      ( ( ( in @ SV850 @ SV560 )
        = $false )
      | ( ( SV702 @ SV850 )
        = $true )
      | ( ( SV702 @ ( kpair @ ( sK81_Xx @ SV702 @ SV560 @ SV422 @ SV207 ) @ ( sK82_SY1880 @ SV702 @ SV560 @ SV422 @ SV207 ) ) )
        = $false )
      | ( ( subset @ SV560 @ ( cartprod @ SV207 @ SV422 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3708]) ).

thf(3781,plain,
    ! [SV424: $i > $o,SV209: $i,SV843: $i] :
      ( ( ( in @ SV843 @ SV209 )
        = $false )
      | ( ( SV424 @ SV843 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV209
            @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) )
        = $true )
      | ( ( SV424 @ ( sK71_SY1877 @ SV424 @ SV209 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3710]) ).

thf(3782,plain,
    ! [SV209: $i,SV851: $i,SV424: $i > $o] :
      ( ( ( SV424 @ SV851 )
        = $false )
      | ( ( ~ ( in @ SV851 @ SV209 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV209
            @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) )
        = $true )
      | ( ( ( sK70_Xx @ SV424 @ SV209 )
          = ( sK71_SY1877 @ SV424 @ SV209 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3711]) ).

thf(3783,plain,
    ! [SV750: $i,SV213: $i > $o,SV826: $i,SV427: $i > $o] :
      ( ( ( SV427 @ SV826 )
        = $false )
      | ( ( SV427 @ ( sK58_SY260 @ SV826 @ SV427 @ SV213 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV750 )
        = $false )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3712]) ).

thf(3784,plain,
    ! [SV750: $i,SV213: $i > $o,SV427: $i > $o,SV826: $i] :
      ( ( ( SV826
          = ( sK58_SY260 @ SV826 @ SV427 @ SV213 ) )
        = $false )
      | ( ( ~ ( SV427 @ SV826 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV750 )
        = $false )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3713]) ).

thf(3785,plain,
    ! [SV750: $i,SV213: $i > $o,SV833: $i,SV427: $i > $o] :
      ( ( ( SV427 @ ( sK58_SY260 @ SV833 @ SV427 @ SV213 ) )
        = $true )
      | ( ( ~ ( SV427 @ SV833 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV750
          = ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV750 )
        = $false )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3714]) ).

thf(3786,plain,
    ! [SV750: $i,SV213: $i > $o,SV427: $i > $o,SV833: $i] :
      ( ( ( SV833
         != ( sK58_SY260 @ SV833 @ SV427 @ SV213 ) )
        = $true )
      | ( ( ~ ( SV427 @ SV833 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV750
          = ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV750 )
        = $false )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3715]) ).

thf(3787,plain,
    ! [SV818: $i,SV213: $i > $o,SV427: $i > $o] :
      ( ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV818 )
        = $false )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3716]) ).

thf(3788,plain,
    ! [SV427: $i > $o,SV818: $i,SV213: $i > $o] :
      ( ( ( SV213 @ SV818 )
        = $false )
      | ( ( SV818
          = ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
        = $false )
      | ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) )
          | ( ( descr
              @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
            = ( descr
              @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3717]) ).

thf(3789,plain,
    ! [SV796: $i,SV213: $i > $o,SV858: $i,SV427: $i > $o] :
      ( ( ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SV858 @ SV427 @ SV213 ) )
              | ~ ( ( SV858
                   != ( sK58_SY260 @ SV858 @ SV427 @ SV213 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV427 @ SV858 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV796 )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3718]) ).

thf(3790,plain,
    ! [SV796: $i,SV213: $i > $o,SV863: $i,SV427: $i > $o] :
      ( ( ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SV863 @ SV427 @ SV213 ) )
              | ~ ( ( SV863
                   != ( sK58_SY260 @ SV863 @ SV427 @ SV213 ) ) ) )
          | ~ ( SV427 @ SV863 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV796
          = ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV796 )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3719]) ).

thf(3791,plain,
    ! [SV218: $i,SV432: $i,SV564: $i,SV704: $i,SV834: $i,SV809: $i] :
      ( ( ( in @ ( kpair @ SV809 @ SV834 ) @ SV704 )
        = $false )
      | ( ( in @ ( kpair @ SV809 @ SV834 ) @ SV564 )
        = $true )
      | ( ( in @ SV834 @ SV432 )
        = $false )
      | ( ( in @ SV809 @ SV218 )
        = $false )
      | ( ( in @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) @ SV218 )
        = $true )
      | ( ( func @ SV218 @ SV432 @ SV704 )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV564 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3720]) ).

thf(3792,plain,
    ! [SV218: $i,SV432: $i,SV564: $i,SV704: $i,SV844: $i,SV819: $i] :
      ( ( ( ~ ( in @ ( kpair @ SV819 @ SV844 ) @ SV704 ) )
        = $true )
      | ( ( in @ ( kpair @ SV819 @ SV844 ) @ SV564 )
        = $true )
      | ( ( in @ SV844 @ SV432 )
        = $false )
      | ( ( in @ SV819 @ SV218 )
        = $false )
      | ( ( ( ap @ SV218 @ SV432 @ SV564 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) )
          = ( ap @ SV218 @ SV432 @ SV704 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) ) )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV704 )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV564 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3721]) ).

thf(3793,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 ) )
        = $false )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3723]) ).

thf(3794,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) )
        = $false )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3723]) ).

thf(3795,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
          | ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) )
        = $false )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
        = $false )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3725]) ).

thf(3796,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( in @ SV566 @ SV435 )
        = $true )
      | ( ( ! [SX3: $o] : SX3 )
        = $true )
      | ( ( in @ SV566 @ SV435 )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3729]) ).

thf(3797,plain,
    ! [SV221: $i,SV435: $i,SV566: $i,SV864: $o] :
      ( ( ( ~ SV864
          | SV864 )
        = $true )
      | ( ( in @ SV566 @ SV435 )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3730]) ).

thf(3798,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ $true
          | $true )
        = $true )
      | ( ( in @ SV566 @ SV435 )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3730]) ).

thf(3799,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ $false
          | $false )
        = $true )
      | ( ( in @ SV566 @ SV435 )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3730]) ).

thf(3800,plain,
    ! [SV221: $i,SV435: $i,SV566: $i,SV852: $o] :
      ( ( SV852 = $false )
      | ( ( ( in @ SV566 @ SV435 )
          | SV852 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3734]) ).

thf(3801,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( $true = $false )
      | ( ( ( in @ SV566 @ SV435 )
          | $true )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3735]) ).

thf(3802,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( $false = $false )
      | ( ( ( in @ SV566 @ SV435 )
          | $false )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3736]) ).

thf(3803,plain,
    ! [SV435: $i,SV221: $i,SV566: $i,SV853: $o] :
      ( ( SV853 = $false )
      | ( ( ~ SV853
          | SV853 )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3737]) ).

thf(3804,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( $true = $false )
      | ( ( ~ $true
          | $true )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3738]) ).

thf(3805,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( $false = $false )
      | ( ( ~ $false
          | $false )
        = $true )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3739]) ).

thf(3806,plain,
    ! [SV441: $i > $o,SV229: $i,SV846: $i] :
      ( ( ( in @ SV846 @ SV229 )
        = $false )
      | ( ( SV441 @ SV846 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV229
            @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) )
        = $true )
      | ( ( SV441 @ ( sK75_SY1878 @ SV441 @ SV229 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3740]) ).

thf(3807,plain,
    ! [SV229: $i,SV854: $i,SV441: $i > $o] :
      ( ( ( SV441 @ SV854 )
        = $false )
      | ( ( ~ ( in @ SV854 @ SV229 ) )
        = $true )
      | ( ( singleton
          @ ( dsetconstr @ SV229
            @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) )
        = $true )
      | ( ( ( sK74_Xx @ SV441 @ SV229 )
          = ( sK75_SY1878 @ SV441 @ SV229 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3741]) ).

thf(3808,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
          | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3743]) ).

thf(3809,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
          | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3745]) ).

thf(3810,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
          | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                      | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3746]) ).

thf(3811,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
              | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                    | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                          | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) ) )
        = $true )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
        = $false )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3747]) ).

thf(3812,plain,
    ! [SV786: $i,SV233: $i,SV658: $i,SV836: $i,SV865: $i] :
      ( ( ( ~ ( in @ SV865 @ SV836 )
          | ( in @ SV865 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) )
        = $true )
      | ( ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV836 )
        = $true )
      | ( ( in @ SV836 @ ( sK15_B @ SV233 ) )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( in @ SV786 @ SV658 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3748]) ).

thf(3813,plain,
    ! [SV786: $i,SV233: $i,SV658: $i] :
      ( ( ( ~ ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) ) )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( in @ SV786 @ SV658 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3749]) ).

thf(3814,plain,
    ! [SV786: $i,SV233: $i,SV658: $i] :
      ( ( ( ~ ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 ) )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( in @ SV786 @ SV658 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3749]) ).

thf(3815,plain,
    ! [SV786: $i,SV233: $i,SV658: $i,SV860: $i] :
      ( ( ( ~ ( in @ SV860 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) )
        = $true )
      | ( ( ~ ( in @ SV860 @ SV658 ) )
        = $true )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( in @ SV786 @ SV658 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3750]) ).

thf(3816,plain,
    ! [SV799: $i,SV233: $i,SV658: $i,SV847: $i] :
      ( ( ( ! [SY2995: $i] :
              ( ~ ( in @ SY2995 @ SV847 )
              | ( in @ SY2995 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) ) )
        = $true )
      | ( ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV847 )
        = $true )
      | ( ( in @ SV847 @ ( sK15_B @ SV233 ) )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 )
        = $false )
      | ( ( in @ SV799 @ SV658 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3751]) ).

thf(3817,plain,
    ! [SV799: $i,SV233: $i,SV658: $i] :
      ( ( ( ~ ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) )
          | ~ ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 ) )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 )
        = $false )
      | ( ( in @ SV799 @ SV658 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3752]) ).

thf(3818,plain,
    ! [SV799: $i,SV233: $i,SV658: $i,SV866: $i] :
      ( ( ( ~ ( in @ SV866 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
          | ~ ( in @ SV866 @ SV658 ) )
        = $true )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 )
        = $false )
      | ( ( in @ SV799 @ SV658 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3753]) ).

thf(3819,plain,
    ! [SV233: $i,SV829: $i,SV754: $i,SV770: $i,SV855: $i] :
      ( ( ( in @ SV855 @ SV770 )
        = $false )
      | ( ( in @ SV855 @ SV754 )
        = $true )
      | ( ( in @ SV829 @ SV770 )
        = $true )
      | ( ( in @ SV829 @ SV754 )
        = $false )
      | ( ( in @ SV754 @ ( sK15_B @ SV233 ) )
        = $false )
      | ( ( in @ SV770 @ ( sK15_B @ SV233 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3754]) ).

thf(3820,plain,
    ! [SV233: $i,SV788: $i,SV800: $i] :
      ( ( ( in @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) @ ( sK15_B @ SV233 ) )
        = $true )
      | ( ( SV788 = SV800 )
        = $true )
      | ( ( in @ SV788 @ SV233 )
        = $false )
      | ( ( in @ SV800 @ SV233 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3755]) ).

thf(3821,plain,
    ! [SV233: $i,SV800: $i,SV788: $i] :
      ( ( ( ~ ( ~ ( ~ ( in @ SV788 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) )
                  | ~ ( in @ SV800 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) ) )
              | ~ ( ( in @ SV788 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) )
                  | ( in @ SV800 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) ) ) ) )
        = $true )
      | ( ( SV788 = SV800 )
        = $true )
      | ( ( in @ SV788 @ SV233 )
        = $false )
      | ( ( in @ SV800 @ SV233 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3756]) ).

thf(3822,plain,
    ! [SV236: $i,SV445: $i,SV710: $i > $o,SV574: $i,SV856: $i] :
      ( ( ( in @ SV856 @ SV574 )
        = $false )
      | ( ( SV710 @ SV856 )
        = $true )
      | ( ( SV710 @ ( kpair @ ( sK79_Xx @ SV710 @ SV574 @ SV445 @ SV236 ) @ ( sK80_SY1879 @ SV710 @ SV574 @ SV445 @ SV236 ) ) )
        = $false )
      | ( ( subset @ SV574 @ ( cartprod @ SV236 @ SV445 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3758]) ).

thf(3823,plain,
    ! [SV248: $i,SV453: $i,SV719: $i > $o,SV661: $i > $o] :
      ( ( ( ~ ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) ) )
        = $true )
      | ( ( ~ ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) )
        = $true )
      | ( ( ( dsetconstr @ SV248
            @ ^ [SY2930: $i] : ( SV661 @ SY2930 ) )
          = ( dsetconstr @ SV453
            @ ^ [SY2961: $i] : ( SV719 @ SY2961 ) ) )
        = $true )
      | ( ( SV248 = SV453 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3759]) ).

thf(3824,plain,
    ! [SV248: $i,SV453: $i,SV719: $i > $o,SV661: $i > $o] :
      ( ( ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
        = $true )
      | ( ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) )
        = $true )
      | ( ( ( dsetconstr @ SV248
            @ ^ [SY2930: $i] : ( SV661 @ SY2930 ) )
          = ( dsetconstr @ SV453
            @ ^ [SY2961: $i] : ( SV719 @ SY2961 ) ) )
        = $true )
      | ( ( SV248 = SV453 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3760]) ).

thf(3825,plain,
    ! [SV725: $i,SV831: $i,SV195: $i > $i > $o,SV413: $i,SV849: $i] :
      ( ( ( in @ SV849 @ SV413 )
        = $false )
      | ( ( SV195 @ SV849 @ SV831 )
        = $false )
      | ( ( in @ SV831 @ ( sK10_B @ SV413 @ SV195 ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3761]) ).

thf(3826,plain,
    ! [SV725: $i,SV413: $i,SV832: $i,SV195: $i > $i > $o] :
      ( ( ( SV195 @ ( sK11_Xy @ SV832 @ SV413 @ SV195 ) @ SV832 )
        = $true )
      | ( ( in @ SV832 @ ( sK10_B @ SV413 @ SV195 ) )
        = $false )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3762]) ).

thf(3827,plain,
    ! [SV725: $i,SV195: $i > $i > $o,SV413: $i,SV832: $i] :
      ( ( ( in @ ( sK11_Xy @ SV832 @ SV413 @ SV195 ) @ SV413 )
        = $true )
      | ( ( in @ SV832 @ ( sK10_B @ SV413 @ SV195 ) )
        = $false )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $true )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3763]) ).

thf(3828,plain,
    ! [SV725: $i,SV413: $i,SV838: $i,SV857: $i,SV195: $i > $i > $o] :
      ( ( ( SV195 @ SV857 @ SV838 )
        = $false )
      | ( ( ~ ( in @ SV857 @ SV413 ) )
        = $true )
      | ( ( in @ SV838 @ ( sK10_B @ SV413 @ SV195 ) )
        = $true )
      | ( ( SV725
          = ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $false )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3764]) ).

thf(3829,plain,
    ! [SV725: $i,SV413: $i,SV839: $i,SV195: $i > $i > $o] :
      ( ( ( ~ ( SV195 @ ( sK11_Xy @ SV839 @ SV413 @ SV195 ) @ SV839 ) )
        = $false )
      | ( ( in @ SV839 @ ( sK10_B @ SV413 @ SV195 ) )
        = $false )
      | ( ( SV725
          = ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $false )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3765]) ).

thf(3830,plain,
    ! [SV725: $i,SV195: $i > $i > $o,SV413: $i,SV839: $i] :
      ( ( ( ~ ( in @ ( sK11_Xy @ SV839 @ SV413 @ SV195 ) @ SV413 ) )
        = $false )
      | ( ( in @ SV839 @ ( sK10_B @ SV413 @ SV195 ) )
        = $false )
      | ( ( SV725
          = ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $false )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3765]) ).

thf(3831,plain,
    ! [SV778: $i,SV605: $i > $o,SV861: $i,SV652: $i > $o] :
      ( ( ( ~ ( SV652 @ SV861 ) )
        = $true )
      | ( ( ( sK53_SY235 @ SV652 @ SV605 )
          = SV861 )
        = $true )
      | ( ( SV605 @ ( sK54_SY233 @ SV778 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ SV778 )
        = $false )
      | ( ( ( sK55_Xx @ SV652 @ SV605 )
          = ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3766]) ).

thf(3832,plain,
    ! [SV778: $i,SV605: $i > $o,SV867: $i,SV652: $i > $o] :
      ( ( ( ~ ( SV652 @ SV867 )
          | ( ( sK53_SY235 @ SV652 @ SV605 )
            = SV867 ) )
        = $true )
      | ( ( SV778
          = ( sK54_SY233 @ SV778 @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV605 @ SV778 )
        = $false )
      | ( ( ( sK55_Xx @ SV652 @ SV605 )
          = ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3767]) ).

thf(3833,plain,
    ! [SV652: $i > $o,SV840: $i,SV605: $i > $o] :
      ( ( ( SV605 @ ( sK54_SY233 @ SV840 @ SV652 @ SV605 ) )
        = $true )
      | ( ( ~ ( SV605 @ SV840 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3769]) ).

thf(3834,plain,
    ! [SV605: $i > $o,SV652: $i > $o,SV840: $i] :
      ( ( ( SV840
         != ( sK54_SY233 @ SV840 @ SV652 @ SV605 ) )
        = $true )
      | ( ( ~ ( SV605 @ SV840 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3770]) ).

thf(3835,plain,
    ! [SV824: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( ~ ! [SY2920: $i] :
                ( ~ ( SV652 @ SY2920 )
                | ( ( sK53_SY235 @ SV652 @ SV605 )
                  = SY2920 ) )
          | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) )
        = $false )
      | ( ( SV605 @ ( sK54_SY233 @ SV824 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ SV824 )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3771]) ).

thf(3836,plain,
    ! [SV652: $i > $o,SV824: $i,SV605: $i > $o] :
      ( ( ( SV605 @ SV824 )
        = $false )
      | ( ( SV824
          = ( sK54_SY233 @ SV824 @ SV652 @ SV605 ) )
        = $false )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3772]) ).

thf(3837,plain,
    ! [SV779: $i,SV653: $i > $o,SV862: $i,SV606: $i > $o] :
      ( ( ( ~ ( SV606 @ SV862 ) )
        = $true )
      | ( ( ( sK49_SY232 @ SV653 @ SV606 )
          = SV862 )
        = $true )
      | ( ( SV653 @ ( sK50_SY236 @ SV779 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV653 @ SV779 )
        = $false )
      | ( ( ( sK51_Xx @ SV653 @ SV606 )
          = ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3773]) ).

thf(3838,plain,
    ! [SV779: $i,SV653: $i > $o,SV868: $i,SV606: $i > $o] :
      ( ( ( ~ ( SV606 @ SV868 )
          | ( ( sK49_SY232 @ SV653 @ SV606 )
            = SV868 ) )
        = $true )
      | ( ( SV779
          = ( sK50_SY236 @ SV779 @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ SV779 )
        = $false )
      | ( ( ( sK51_Xx @ SV653 @ SV606 )
          = ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3774]) ).

thf(3839,plain,
    ! [SV606: $i > $o,SV841: $i,SV653: $i > $o] :
      ( ( ( SV653 @ ( sK50_SY236 @ SV841 @ SV653 @ SV606 ) )
        = $true )
      | ( ( ~ ( SV653 @ SV841 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3776]) ).

thf(3840,plain,
    ! [SV606: $i > $o,SV653: $i > $o,SV841: $i] :
      ( ( ( SV841
         != ( sK50_SY236 @ SV841 @ SV653 @ SV606 ) )
        = $true )
      | ( ( ~ ( SV653 @ SV841 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3777]) ).

thf(3841,plain,
    ! [SV825: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ~ ! [SY2922: $i] :
                ( ~ ( SV606 @ SY2922 )
                | ( ( sK49_SY232 @ SV653 @ SV606 )
                  = SY2922 ) )
          | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) )
        = $false )
      | ( ( SV653 @ ( sK50_SY236 @ SV825 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV653 @ SV825 )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3778]) ).

thf(3842,plain,
    ! [SV606: $i > $o,SV825: $i,SV653: $i > $o] :
      ( ( ( SV653 @ SV825 )
        = $false )
      | ( ( SV825
          = ( sK50_SY236 @ SV825 @ SV653 @ SV606 ) )
        = $false )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3779]) ).

thf(3843,plain,
    ! [SV424: $i > $o,SV209: $i,SV851: $i] :
      ( ( ( in @ SV851 @ SV209 )
        = $false )
      | ( ( SV424 @ SV851 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV209
            @ ^ [SY2663: $i] : ( SV424 @ SY2663 ) ) )
        = $true )
      | ( ( ( sK70_Xx @ SV424 @ SV209 )
          = ( sK71_SY1877 @ SV424 @ SV209 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3782]) ).

thf(3844,plain,
    ! [SV750: $i,SV213: $i > $o,SV826: $i,SV427: $i > $o] :
      ( ( ( SV427 @ SV826 )
        = $false )
      | ( ( SV826
          = ( sK58_SY260 @ SV826 @ SV427 @ SV213 ) )
        = $false )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV750 )
        = $false )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3784]) ).

thf(3845,plain,
    ! [SV750: $i,SV213: $i > $o,SV833: $i,SV427: $i > $o] :
      ( ( ( SV427 @ SV833 )
        = $false )
      | ( ( SV427 @ ( sK58_SY260 @ SV833 @ SV427 @ SV213 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV750
          = ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV750 )
        = $false )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3785]) ).

thf(3846,plain,
    ! [SV750: $i,SV213: $i > $o,SV427: $i > $o,SV833: $i] :
      ( ( ( SV833
          = ( sK58_SY260 @ SV833 @ SV427 @ SV213 ) )
        = $false )
      | ( ( ~ ( SV427 @ SV833 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV750
          = ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV750 )
        = $false )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3786]) ).

thf(3847,plain,
    ! [SV818: $i,SV213: $i > $o,SV869: $i,SV427: $i > $o] :
      ( ( ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SV869 @ SV427 @ SV213 ) )
              | ~ ( ( SV869
                   != ( sK58_SY260 @ SV869 @ SV427 @ SV213 ) ) ) )
          | ~ ( SV427 @ SV869 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV818 )
        = $false )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3787]) ).

thf(3848,plain,
    ! [SV818: $i,SV213: $i > $o,SV427: $i > $o] :
      ( ( ( ! [SY2671: $i] :
              ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) )
                  | ~ ( ( SY2671
                       != ( sK58_SY260 @ SY2671 @ SV427 @ SV213 ) ) ) )
              | ~ ( SV427 @ SY2671 ) ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV818
          = ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV818 )
        = $false )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3788]) ).

thf(3849,plain,
    ! [SV796: $i,SV213: $i > $o,SV858: $i,SV427: $i > $o] :
      ( ( ( ~ ( SV427 @ ( sK58_SY260 @ SV858 @ SV427 @ SV213 ) )
          | ~ ( ( SV858
               != ( sK58_SY260 @ SV858 @ SV427 @ SV213 ) ) ) )
        = $false )
      | ( ( ~ ( SV427 @ SV858 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV796 )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3789]) ).

thf(3850,plain,
    ! [SV796: $i,SV213: $i > $o,SV863: $i,SV427: $i > $o] :
      ( ( ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SV863 @ SV427 @ SV213 ) )
              | ~ ( ( SV863
                   != ( sK58_SY260 @ SV863 @ SV427 @ SV213 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV427 @ SV863 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV796
          = ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV796 )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3790]) ).

thf(3851,plain,
    ! [SV218: $i,SV432: $i,SV564: $i,SV704: $i,SV844: $i,SV819: $i] :
      ( ( ( in @ ( kpair @ SV819 @ SV844 ) @ SV704 )
        = $false )
      | ( ( in @ ( kpair @ SV819 @ SV844 ) @ SV564 )
        = $true )
      | ( ( in @ SV844 @ SV432 )
        = $false )
      | ( ( in @ SV819 @ SV218 )
        = $false )
      | ( ( ( ap @ SV218 @ SV432 @ SV564 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) )
          = ( ap @ SV218 @ SV432 @ SV704 @ ( sK83_Xx @ SV704 @ SV564 @ SV432 @ SV218 ) ) )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV704 )
        = $false )
      | ( ( func @ SV218 @ SV432 @ SV564 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3792]) ).

thf(3852,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
        = $true )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3793]) ).

thf(3853,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) )
        = $true )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3794]) ).

thf(3854,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 ) )
        = $false )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
        = $false )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3795]) ).

thf(3855,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) )
        = $false )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
        = $false )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3795]) ).

thf(3856,plain,
    ! [SV221: $i,SV435: $i,SV566: $i,SV870: $o] :
      ( ( SV870 = $true )
      | ( ( in @ SV566 @ SV435 )
        = $true )
      | ( ( in @ SV566 @ SV435 )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3796]) ).

thf(3857,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( $true = $true )
      | ( ( in @ SV566 @ SV435 )
        = $true )
      | ( ( in @ SV566 @ SV435 )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3796]) ).

thf(3858,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( $false = $true )
      | ( ( in @ SV566 @ SV435 )
        = $true )
      | ( ( in @ SV566 @ SV435 )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_forall_special_pos,[status(thm)],[3796]) ).

thf(3859,plain,
    ! [SV221: $i,SV435: $i,SV566: $i,SV864: $o] :
      ( ( ( ~ SV864 ) = $true )
      | ( SV864 = $true )
      | ( ( in @ SV566 @ SV435 )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3797]) ).

thf(3860,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ $true ) = $true )
      | ( $true = $true )
      | ( ( in @ SV566 @ SV435 )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3798]) ).

thf(3861,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( ~ $false ) = $true )
      | ( $false = $true )
      | ( ( in @ SV566 @ SV435 )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3799]) ).

thf(3862,plain,
    ! [SV221: $i,SV852: $o,SV435: $i,SV566: $i] :
      ( ( ( in @ SV566 @ SV435 )
        = $true )
      | ( SV852 = $true )
      | ( SV852 = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3800]) ).

thf(3863,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( in @ SV566 @ SV435 )
        = $true )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3801]) ).

thf(3864,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( ( in @ SV566 @ SV435 )
        = $true )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3802]) ).

thf(3865,plain,
    ! [SV435: $i,SV221: $i,SV566: $i,SV853: $o] :
      ( ( ( ~ SV853 ) = $true )
      | ( SV853 = $true )
      | ( SV853 = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3803]) ).

thf(3866,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ $true ) = $true )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3804]) ).

thf(3867,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( ( ~ $false ) = $true )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3805]) ).

thf(3868,plain,
    ! [SV441: $i > $o,SV229: $i,SV854: $i] :
      ( ( ( in @ SV854 @ SV229 )
        = $false )
      | ( ( SV441 @ SV854 )
        = $false )
      | ( ( singleton
          @ ( dsetconstr @ SV229
            @ ^ [SY2706: $i] : ( SV441 @ SY2706 ) ) )
        = $true )
      | ( ( ( sK74_Xx @ SV441 @ SV229 )
          = ( sK75_SY1878 @ SV441 @ SV229 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3807]) ).

thf(3869,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3808]) ).

thf(3870,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3808]) ).

thf(3871,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3809]) ).

thf(3872,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3809]) ).

thf(3873,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3810]) ).

thf(3874,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                      | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3810]) ).

thf(3875,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
          | ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                      | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
        = $false )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3811]) ).

thf(3876,plain,
    ! [SV786: $i,SV233: $i,SV658: $i,SV836: $i,SV865: $i] :
      ( ( ( ~ ( in @ SV865 @ SV836 ) )
        = $true )
      | ( ( in @ SV865 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
        = $true )
      | ( ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV836 )
        = $true )
      | ( ( in @ SV836 @ ( sK15_B @ SV233 ) )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( in @ SV786 @ SV658 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3812]) ).

thf(3877,plain,
    ! [SV786: $i,SV233: $i,SV658: $i] :
      ( ( ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) )
        = $true )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( in @ SV786 @ SV658 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3813]) ).

thf(3878,plain,
    ! [SV786: $i,SV233: $i,SV658: $i] :
      ( ( ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( in @ SV786 @ SV658 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3814]) ).

thf(3879,plain,
    ! [SV786: $i,SV233: $i,SV658: $i,SV860: $i] :
      ( ( ( in @ SV860 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
        = $false )
      | ( ( ~ ( in @ SV860 @ SV658 ) )
        = $true )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( in @ SV786 @ SV658 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3815]) ).

thf(3880,plain,
    ! [SV799: $i,SV233: $i,SV658: $i,SV847: $i,SV871: $i] :
      ( ( ( ~ ( in @ SV871 @ SV847 )
          | ( in @ SV871 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) )
        = $true )
      | ( ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV847 )
        = $true )
      | ( ( in @ SV847 @ ( sK15_B @ SV233 ) )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 )
        = $false )
      | ( ( in @ SV799 @ SV658 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3816]) ).

thf(3881,plain,
    ! [SV799: $i,SV233: $i,SV658: $i] :
      ( ( ( ~ ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) ) )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 )
        = $false )
      | ( ( in @ SV799 @ SV658 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3817]) ).

thf(3882,plain,
    ! [SV799: $i,SV233: $i,SV658: $i] :
      ( ( ( ~ ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 ) )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 )
        = $false )
      | ( ( in @ SV799 @ SV658 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3817]) ).

thf(3883,plain,
    ! [SV799: $i,SV233: $i,SV658: $i,SV866: $i] :
      ( ( ( ~ ( in @ SV866 @ ( sK17_SY1842 @ SV658 @ SV233 ) ) )
        = $true )
      | ( ( ~ ( in @ SV866 @ SV658 ) )
        = $true )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 )
        = $false )
      | ( ( in @ SV799 @ SV658 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3818]) ).

thf(3884,plain,
    ! [SV233: $i,SV800: $i,SV788: $i] :
      ( ( ( ~ ( ~ ( in @ SV788 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) )
              | ~ ( in @ SV800 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) ) )
          | ~ ( ( in @ SV788 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) )
              | ( in @ SV800 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) ) ) )
        = $false )
      | ( ( SV788 = SV800 )
        = $true )
      | ( ( in @ SV788 @ SV233 )
        = $false )
      | ( ( in @ SV800 @ SV233 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3821]) ).

thf(3885,plain,
    ! [SV248: $i,SV453: $i,SV719: $i > $o,SV661: $i > $o] :
      ( ( ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
        = $false )
      | ( ( ~ ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) ) )
        = $true )
      | ( ( ( dsetconstr @ SV248
            @ ^ [SY2930: $i] : ( SV661 @ SY2930 ) )
          = ( dsetconstr @ SV453
            @ ^ [SY2961: $i] : ( SV719 @ SY2961 ) ) )
        = $true )
      | ( ( SV248 = SV453 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3823]) ).

thf(3886,plain,
    ! [SV725: $i,SV838: $i,SV195: $i > $i > $o,SV413: $i,SV857: $i] :
      ( ( ( in @ SV857 @ SV413 )
        = $false )
      | ( ( SV195 @ SV857 @ SV838 )
        = $false )
      | ( ( in @ SV838 @ ( sK10_B @ SV413 @ SV195 ) )
        = $true )
      | ( ( SV725
          = ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $false )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3828]) ).

thf(3887,plain,
    ! [SV725: $i,SV413: $i,SV839: $i,SV195: $i > $i > $o] :
      ( ( ( SV195 @ ( sK11_Xy @ SV839 @ SV413 @ SV195 ) @ SV839 )
        = $true )
      | ( ( in @ SV839 @ ( sK10_B @ SV413 @ SV195 ) )
        = $false )
      | ( ( SV725
          = ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $false )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3829]) ).

thf(3888,plain,
    ! [SV725: $i,SV195: $i > $i > $o,SV413: $i,SV839: $i] :
      ( ( ( in @ ( sK11_Xy @ SV839 @ SV413 @ SV195 ) @ SV413 )
        = $true )
      | ( ( in @ SV839 @ ( sK10_B @ SV413 @ SV195 ) )
        = $false )
      | ( ( SV725
          = ( sK13_SY1837 @ SV725 @ SV413 @ SV195 ) )
        = $false )
      | ( ( SV195 @ ( sK12_SY24 @ SV413 @ SV195 ) @ SV725 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3830]) ).

thf(3889,plain,
    ! [SV778: $i,SV605: $i > $o,SV861: $i,SV652: $i > $o] :
      ( ( ( SV652 @ SV861 )
        = $false )
      | ( ( ( sK53_SY235 @ SV652 @ SV605 )
          = SV861 )
        = $true )
      | ( ( SV605 @ ( sK54_SY233 @ SV778 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ SV778 )
        = $false )
      | ( ( ( sK55_Xx @ SV652 @ SV605 )
          = ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3831]) ).

thf(3890,plain,
    ! [SV778: $i,SV605: $i > $o,SV867: $i,SV652: $i > $o] :
      ( ( ( ~ ( SV652 @ SV867 ) )
        = $true )
      | ( ( ( sK53_SY235 @ SV652 @ SV605 )
          = SV867 )
        = $true )
      | ( ( SV778
          = ( sK54_SY233 @ SV778 @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV605 @ SV778 )
        = $false )
      | ( ( ( sK55_Xx @ SV652 @ SV605 )
          = ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3832]) ).

thf(3891,plain,
    ! [SV652: $i > $o,SV840: $i,SV605: $i > $o] :
      ( ( ( SV605 @ SV840 )
        = $false )
      | ( ( SV605 @ ( sK54_SY233 @ SV840 @ SV652 @ SV605 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3833]) ).

thf(3892,plain,
    ! [SV605: $i > $o,SV652: $i > $o,SV840: $i] :
      ( ( ( SV840
          = ( sK54_SY233 @ SV840 @ SV652 @ SV605 ) )
        = $false )
      | ( ( ~ ( SV605 @ SV840 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3834]) ).

thf(3893,plain,
    ! [SV824: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( ~ ! [SY2920: $i] :
                ( ~ ( SV652 @ SY2920 )
                | ( ( sK53_SY235 @ SV652 @ SV605 )
                  = SY2920 ) ) )
        = $false )
      | ( ( SV605 @ ( sK54_SY233 @ SV824 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ SV824 )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3835]) ).

thf(3894,plain,
    ! [SV824: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) )
        = $false )
      | ( ( SV605 @ ( sK54_SY233 @ SV824 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ SV824 )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3835]) ).

thf(3895,plain,
    ! [SV824: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( ~ ! [SY2920: $i] :
                ( ~ ( SV652 @ SY2920 )
                | ( ( sK53_SY235 @ SV652 @ SV605 )
                  = SY2920 ) )
          | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) )
        = $false )
      | ( ( SV824
          = ( sK54_SY233 @ SV824 @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV605 @ SV824 )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3836]) ).

thf(3896,plain,
    ! [SV779: $i,SV653: $i > $o,SV862: $i,SV606: $i > $o] :
      ( ( ( SV606 @ SV862 )
        = $false )
      | ( ( ( sK49_SY232 @ SV653 @ SV606 )
          = SV862 )
        = $true )
      | ( ( SV653 @ ( sK50_SY236 @ SV779 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV653 @ SV779 )
        = $false )
      | ( ( ( sK51_Xx @ SV653 @ SV606 )
          = ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3837]) ).

thf(3897,plain,
    ! [SV779: $i,SV653: $i > $o,SV868: $i,SV606: $i > $o] :
      ( ( ( ~ ( SV606 @ SV868 ) )
        = $true )
      | ( ( ( sK49_SY232 @ SV653 @ SV606 )
          = SV868 )
        = $true )
      | ( ( SV779
          = ( sK50_SY236 @ SV779 @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ SV779 )
        = $false )
      | ( ( ( sK51_Xx @ SV653 @ SV606 )
          = ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3838]) ).

thf(3898,plain,
    ! [SV606: $i > $o,SV841: $i,SV653: $i > $o] :
      ( ( ( SV653 @ SV841 )
        = $false )
      | ( ( SV653 @ ( sK50_SY236 @ SV841 @ SV653 @ SV606 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3839]) ).

thf(3899,plain,
    ! [SV606: $i > $o,SV653: $i > $o,SV841: $i] :
      ( ( ( SV841
          = ( sK50_SY236 @ SV841 @ SV653 @ SV606 ) )
        = $false )
      | ( ( ~ ( SV653 @ SV841 ) )
        = $true )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3840]) ).

thf(3900,plain,
    ! [SV825: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ~ ! [SY2922: $i] :
                ( ~ ( SV606 @ SY2922 )
                | ( ( sK49_SY232 @ SV653 @ SV606 )
                  = SY2922 ) ) )
        = $false )
      | ( ( SV653 @ ( sK50_SY236 @ SV825 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV653 @ SV825 )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3841]) ).

thf(3901,plain,
    ! [SV825: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) )
        = $false )
      | ( ( SV653 @ ( sK50_SY236 @ SV825 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV653 @ SV825 )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3841]) ).

thf(3902,plain,
    ! [SV825: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ~ ! [SY2922: $i] :
                ( ~ ( SV606 @ SY2922 )
                | ( ( sK49_SY232 @ SV653 @ SV606 )
                  = SY2922 ) )
          | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) )
        = $false )
      | ( ( SV825
          = ( sK50_SY236 @ SV825 @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ SV825 )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3842]) ).

thf(3903,plain,
    ! [SV750: $i,SV213: $i > $o,SV833: $i,SV427: $i > $o] :
      ( ( ( SV427 @ SV833 )
        = $false )
      | ( ( SV833
          = ( sK58_SY260 @ SV833 @ SV427 @ SV213 ) )
        = $false )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV750
          = ( sK59_SY257 @ SV750 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV750 )
        = $false )
      | ( ( ( sK60_Xx @ SV427 @ SV213 )
          = ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3846]) ).

thf(3904,plain,
    ! [SV818: $i,SV213: $i > $o,SV869: $i,SV427: $i > $o] :
      ( ( ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SV869 @ SV427 @ SV213 ) )
              | ~ ( ( SV869
                   != ( sK58_SY260 @ SV869 @ SV427 @ SV213 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV427 @ SV869 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV818 )
        = $false )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3847]) ).

thf(3905,plain,
    ! [SV818: $i,SV213: $i > $o,SV872: $i,SV427: $i > $o] :
      ( ( ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SV872 @ SV427 @ SV213 ) )
              | ~ ( ( SV872
                   != ( sK58_SY260 @ SV872 @ SV427 @ SV213 ) ) ) )
          | ~ ( SV427 @ SV872 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV818
          = ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV818 )
        = $false )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3848]) ).

thf(3906,plain,
    ! [SV796: $i,SV213: $i > $o,SV858: $i,SV427: $i > $o] :
      ( ( ( ~ ( SV427 @ ( sK58_SY260 @ SV858 @ SV427 @ SV213 ) ) )
        = $false )
      | ( ( ~ ( SV427 @ SV858 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV796 )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3849]) ).

thf(3907,plain,
    ! [SV796: $i,SV213: $i > $o,SV427: $i > $o,SV858: $i] :
      ( ( ( ~ ( ( SV858
               != ( sK58_SY260 @ SV858 @ SV427 @ SV213 ) ) ) )
        = $false )
      | ( ( ~ ( SV427 @ SV858 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV796 )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3849]) ).

thf(3908,plain,
    ! [SV796: $i,SV213: $i > $o,SV863: $i,SV427: $i > $o] :
      ( ( ( ~ ( SV427 @ ( sK58_SY260 @ SV863 @ SV427 @ SV213 ) )
          | ~ ( ( SV863
               != ( sK58_SY260 @ SV863 @ SV427 @ SV213 ) ) ) )
        = $false )
      | ( ( ~ ( SV427 @ SV863 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV796
          = ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV796 )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3850]) ).

thf(3909,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 )
        = $false )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 )
        = $true )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3853]) ).

thf(3910,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
        = $true )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
        = $false )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3854]) ).

thf(3911,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( ~ ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 ) )
        = $true )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
        = $false )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3855]) ).

thf(3912,plain,
    ! [SV221: $i,SV435: $i,SV566: $i,SV864: $o] :
      ( ( SV864 = $false )
      | ( SV864 = $true )
      | ( ( in @ SV566 @ SV435 )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3859]) ).

thf(3913,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( $true = $false )
      | ( $true = $true )
      | ( ( in @ SV566 @ SV435 )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3860]) ).

thf(3914,plain,
    ! [SV221: $i,SV435: $i,SV566: $i] :
      ( ( $false = $false )
      | ( $false = $true )
      | ( ( in @ SV566 @ SV435 )
        = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3861]) ).

thf(3915,plain,
    ! [SV435: $i,SV221: $i,SV566: $i,SV853: $o] :
      ( ( SV853 = $false )
      | ( SV853 = $true )
      | ( SV853 = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3865]) ).

thf(3916,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( $true = $false )
      | ( $true = $true )
      | ( $true = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3866]) ).

thf(3917,plain,
    ! [SV435: $i,SV221: $i,SV566: $i] :
      ( ( $false = $false )
      | ( $false = $true )
      | ( $false = $false )
      | ( ( in @ SV566 @ ( symdiff @ SV221 @ SV435 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3867]) ).

thf(3918,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
        = $true )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3869]) ).

thf(3919,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) )
        = $true )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3870]) ).

thf(3920,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
        = $true )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3871]) ).

thf(3921,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
              | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) )
        = $true )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3872]) ).

thf(3922,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
        = $true )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3873]) ).

thf(3923,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
              | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                    | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
        = $true )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3874]) ).

thf(3924,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
        = $false )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3875]) ).

thf(3925,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
                | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                      | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
        = $false )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3875]) ).

thf(3926,plain,
    ! [SV786: $i,SV233: $i,SV658: $i,SV836: $i,SV865: $i] :
      ( ( ( in @ SV865 @ SV836 )
        = $false )
      | ( ( in @ SV865 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
        = $true )
      | ( ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV836 )
        = $true )
      | ( ( in @ SV836 @ ( sK15_B @ SV233 ) )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( in @ SV786 @ SV658 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3876]) ).

thf(3927,plain,
    ! [SV786: $i,SV233: $i,SV658: $i,SV860: $i] :
      ( ( ( in @ SV860 @ SV658 )
        = $false )
      | ( ( in @ SV860 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( in @ SV786 @ SV658 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3879]) ).

thf(3928,plain,
    ! [SV799: $i,SV233: $i,SV658: $i,SV847: $i,SV871: $i] :
      ( ( ( ~ ( in @ SV871 @ SV847 ) )
        = $true )
      | ( ( in @ SV871 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
        = $true )
      | ( ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV847 )
        = $true )
      | ( ( in @ SV847 @ ( sK15_B @ SV233 ) )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 )
        = $false )
      | ( ( in @ SV799 @ SV658 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3880]) ).

thf(3929,plain,
    ! [SV799: $i,SV233: $i,SV658: $i] :
      ( ( ( in @ ( sK17_SY1842 @ SV658 @ SV233 ) @ ( sK15_B @ SV233 ) )
        = $true )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 )
        = $false )
      | ( ( in @ SV799 @ SV658 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3881]) ).

thf(3930,plain,
    ! [SV799: $i,SV233: $i,SV658: $i] :
      ( ( ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV658 )
        = $true )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 )
        = $false )
      | ( ( in @ SV799 @ SV658 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3882]) ).

thf(3931,plain,
    ! [SV799: $i,SV233: $i,SV658: $i,SV866: $i] :
      ( ( ( in @ SV866 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
        = $false )
      | ( ( ~ ( in @ SV866 @ SV658 ) )
        = $true )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 )
        = $false )
      | ( ( in @ SV799 @ SV658 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3883]) ).

thf(3932,plain,
    ! [SV233: $i,SV800: $i,SV788: $i] :
      ( ( ( ~ ( ~ ( in @ SV788 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) )
              | ~ ( in @ SV800 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) ) ) )
        = $false )
      | ( ( SV788 = SV800 )
        = $true )
      | ( ( in @ SV788 @ SV233 )
        = $false )
      | ( ( in @ SV800 @ SV233 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3884]) ).

thf(3933,plain,
    ! [SV233: $i,SV800: $i,SV788: $i] :
      ( ( ( ~ ( ( in @ SV788 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) )
              | ( in @ SV800 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) ) ) )
        = $false )
      | ( ( SV788 = SV800 )
        = $true )
      | ( ( in @ SV788 @ SV233 )
        = $false )
      | ( ( in @ SV800 @ SV233 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3884]) ).

thf(3934,plain,
    ! [SV248: $i,SV453: $i,SV661: $i > $o,SV719: $i > $o] :
      ( ( ( SV719 @ ( sK63_SY1875 @ SV719 @ SV661 @ SV453 @ SV248 ) )
        = $false )
      | ( ( SV661 @ ( sK62_Xx @ SV719 @ SV661 @ SV453 @ SV248 ) )
        = $false )
      | ( ( ( dsetconstr @ SV248
            @ ^ [SY2930: $i] : ( SV661 @ SY2930 ) )
          = ( dsetconstr @ SV453
            @ ^ [SY2961: $i] : ( SV719 @ SY2961 ) ) )
        = $true )
      | ( ( SV248 = SV453 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3885]) ).

thf(3935,plain,
    ! [SV778: $i,SV605: $i > $o,SV867: $i,SV652: $i > $o] :
      ( ( ( SV652 @ SV867 )
        = $false )
      | ( ( ( sK53_SY235 @ SV652 @ SV605 )
          = SV867 )
        = $true )
      | ( ( SV778
          = ( sK54_SY233 @ SV778 @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV605 @ SV778 )
        = $false )
      | ( ( ( sK55_Xx @ SV652 @ SV605 )
          = ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3890]) ).

thf(3936,plain,
    ! [SV840: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( ~ ! [SY2920: $i] :
                ( ~ ( SV652 @ SY2920 )
                | ( ( sK53_SY235 @ SV652 @ SV605 )
                  = SY2920 ) )
          | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) )
        = $false )
      | ( ( SV605 @ ( sK54_SY233 @ SV840 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ SV840 )
        = $false )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3891]) ).

thf(3937,plain,
    ! [SV652: $i > $o,SV840: $i,SV605: $i > $o] :
      ( ( ( SV605 @ SV840 )
        = $false )
      | ( ( SV840
          = ( sK54_SY233 @ SV840 @ SV652 @ SV605 ) )
        = $false )
      | ( ( ~ ( ~ ! [SY2920: $i] :
                    ( ~ ( SV652 @ SY2920 )
                    | ( ( sK53_SY235 @ SV652 @ SV605 )
                      = SY2920 ) )
              | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3892]) ).

thf(3938,plain,
    ! [SV824: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( ! [SY2920: $i] :
              ( ~ ( SV652 @ SY2920 )
              | ( ( sK53_SY235 @ SV652 @ SV605 )
                = SY2920 ) ) )
        = $true )
      | ( ( SV605 @ ( sK54_SY233 @ SV824 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ SV824 )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3893]) ).

thf(3939,plain,
    ! [SV824: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK54_SY233 @ SV824 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ SV824 )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3894]) ).

thf(3940,plain,
    ! [SV824: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( ~ ! [SY2920: $i] :
                ( ~ ( SV652 @ SY2920 )
                | ( ( sK53_SY235 @ SV652 @ SV605 )
                  = SY2920 ) ) )
        = $false )
      | ( ( SV824
          = ( sK54_SY233 @ SV824 @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV605 @ SV824 )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3895]) ).

thf(3941,plain,
    ! [SV824: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) )
        = $false )
      | ( ( SV824
          = ( sK54_SY233 @ SV824 @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV605 @ SV824 )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3895]) ).

thf(3942,plain,
    ! [SV779: $i,SV653: $i > $o,SV868: $i,SV606: $i > $o] :
      ( ( ( SV606 @ SV868 )
        = $false )
      | ( ( ( sK49_SY232 @ SV653 @ SV606 )
          = SV868 )
        = $true )
      | ( ( SV779
          = ( sK50_SY236 @ SV779 @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ SV779 )
        = $false )
      | ( ( ( sK51_Xx @ SV653 @ SV606 )
          = ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3897]) ).

thf(3943,plain,
    ! [SV841: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ~ ! [SY2922: $i] :
                ( ~ ( SV606 @ SY2922 )
                | ( ( sK49_SY232 @ SV653 @ SV606 )
                  = SY2922 ) )
          | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) )
        = $false )
      | ( ( SV653 @ ( sK50_SY236 @ SV841 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV653 @ SV841 )
        = $false )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3898]) ).

thf(3944,plain,
    ! [SV606: $i > $o,SV841: $i,SV653: $i > $o] :
      ( ( ( SV653 @ SV841 )
        = $false )
      | ( ( SV841
          = ( sK50_SY236 @ SV841 @ SV653 @ SV606 ) )
        = $false )
      | ( ( ~ ( ~ ! [SY2922: $i] :
                    ( ~ ( SV606 @ SY2922 )
                    | ( ( sK49_SY232 @ SV653 @ SV606 )
                      = SY2922 ) )
              | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3899]) ).

thf(3945,plain,
    ! [SV825: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ! [SY2922: $i] :
              ( ~ ( SV606 @ SY2922 )
              | ( ( sK49_SY232 @ SV653 @ SV606 )
                = SY2922 ) ) )
        = $true )
      | ( ( SV653 @ ( sK50_SY236 @ SV825 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV653 @ SV825 )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3900]) ).

thf(3946,plain,
    ! [SV825: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV653 @ ( sK50_SY236 @ SV825 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV653 @ SV825 )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3901]) ).

thf(3947,plain,
    ! [SV825: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ~ ! [SY2922: $i] :
                ( ~ ( SV606 @ SY2922 )
                | ( ( sK49_SY232 @ SV653 @ SV606 )
                  = SY2922 ) ) )
        = $false )
      | ( ( SV825
          = ( sK50_SY236 @ SV825 @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ SV825 )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3902]) ).

thf(3948,plain,
    ! [SV825: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) )
        = $false )
      | ( ( SV825
          = ( sK50_SY236 @ SV825 @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ SV825 )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3902]) ).

thf(3949,plain,
    ! [SV818: $i,SV213: $i > $o,SV869: $i,SV427: $i > $o] :
      ( ( ( ~ ( SV427 @ ( sK58_SY260 @ SV869 @ SV427 @ SV213 ) )
          | ~ ( ( SV869
               != ( sK58_SY260 @ SV869 @ SV427 @ SV213 ) ) ) )
        = $false )
      | ( ( ~ ( SV427 @ SV869 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV818 )
        = $false )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3904]) ).

thf(3950,plain,
    ! [SV818: $i,SV213: $i > $o,SV872: $i,SV427: $i > $o] :
      ( ( ( ~ ( ~ ( SV427 @ ( sK58_SY260 @ SV872 @ SV427 @ SV213 ) )
              | ~ ( ( SV872
                   != ( sK58_SY260 @ SV872 @ SV427 @ SV213 ) ) ) ) )
        = $true )
      | ( ( ~ ( SV427 @ SV872 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV818
          = ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV818 )
        = $false )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3905]) ).

thf(3951,plain,
    ! [SV796: $i,SV213: $i > $o,SV858: $i,SV427: $i > $o] :
      ( ( ( SV427 @ ( sK58_SY260 @ SV858 @ SV427 @ SV213 ) )
        = $true )
      | ( ( ~ ( SV427 @ SV858 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV796 )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3906]) ).

thf(3952,plain,
    ! [SV796: $i,SV213: $i > $o,SV427: $i > $o,SV858: $i] :
      ( ( ( SV858
         != ( sK58_SY260 @ SV858 @ SV427 @ SV213 ) )
        = $true )
      | ( ( ~ ( SV427 @ SV858 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV796 )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3907]) ).

thf(3953,plain,
    ! [SV796: $i,SV213: $i > $o,SV863: $i,SV427: $i > $o] :
      ( ( ( ~ ( SV427 @ ( sK58_SY260 @ SV863 @ SV427 @ SV213 ) ) )
        = $false )
      | ( ( ~ ( SV427 @ SV863 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV796
          = ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV796 )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3908]) ).

thf(3954,plain,
    ! [SV796: $i,SV213: $i > $o,SV427: $i > $o,SV863: $i] :
      ( ( ( ~ ( ( SV863
               != ( sK58_SY260 @ SV863 @ SV427 @ SV213 ) ) ) )
        = $false )
      | ( ( ~ ( SV427 @ SV863 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV796
          = ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV796 )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3908]) ).

thf(3955,plain,
    ! [SV219: $i,SV433: $i,SV656: $i] :
      ( ( ( in @ ( sK95_Xx @ SV656 @ SV433 @ SV219 ) @ SV433 )
        = $false )
      | ( ( SV433 = SV656 )
        = $true )
      | ( ( in @ ( sK96_Xx @ SV656 @ SV433 @ SV219 ) @ SV656 )
        = $false )
      | ( ( in @ SV656 @ ( powerset @ SV219 ) )
        = $false )
      | ( ( in @ SV433 @ ( powerset @ SV219 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3911]) ).

thf(3956,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3919]) ).

thf(3957,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
          | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3921]) ).

thf(3958,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
          | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3923]) ).

thf(3959,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( in @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV230 )
        = $true )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
        = $false )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3924]) ).

thf(3960,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
              | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                    | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) ) )
        = $true )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
        = $false )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3925]) ).

thf(3961,plain,
    ! [SV799: $i,SV233: $i,SV658: $i,SV847: $i,SV871: $i] :
      ( ( ( in @ SV871 @ SV847 )
        = $false )
      | ( ( in @ SV871 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
        = $true )
      | ( ( in @ ( sK18_SY1856 @ SV658 @ SV233 ) @ SV847 )
        = $true )
      | ( ( in @ SV847 @ ( sK15_B @ SV233 ) )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 )
        = $false )
      | ( ( in @ SV799 @ SV658 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3928]) ).

thf(3962,plain,
    ! [SV799: $i,SV233: $i,SV658: $i,SV866: $i] :
      ( ( ( in @ SV866 @ SV658 )
        = $false )
      | ( ( in @ SV866 @ ( sK17_SY1842 @ SV658 @ SV233 ) )
        = $false )
      | ( ( in @ ( sK19_Xx @ SV658 @ SV233 ) @ SV233 )
        = $false )
      | ( ( in @ SV799 @ SV658 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3931]) ).

thf(3963,plain,
    ! [SV233: $i,SV800: $i,SV788: $i] :
      ( ( ( ~ ( in @ SV788 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) )
          | ~ ( in @ SV800 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) ) )
        = $true )
      | ( ( SV788 = SV800 )
        = $true )
      | ( ( in @ SV788 @ SV233 )
        = $false )
      | ( ( in @ SV800 @ SV233 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3932]) ).

thf(3964,plain,
    ! [SV233: $i,SV800: $i,SV788: $i] :
      ( ( ( ( in @ SV788 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) )
          | ( in @ SV800 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) ) )
        = $true )
      | ( ( SV788 = SV800 )
        = $true )
      | ( ( in @ SV788 @ SV233 )
        = $false )
      | ( ( in @ SV800 @ SV233 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3933]) ).

thf(3965,plain,
    ! [SV840: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( ~ ! [SY2920: $i] :
                ( ~ ( SV652 @ SY2920 )
                | ( ( sK53_SY235 @ SV652 @ SV605 )
                  = SY2920 ) ) )
        = $false )
      | ( ( SV605 @ ( sK54_SY233 @ SV840 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ SV840 )
        = $false )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3936]) ).

thf(3966,plain,
    ! [SV840: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) )
        = $false )
      | ( ( SV605 @ ( sK54_SY233 @ SV840 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ SV840 )
        = $false )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3936]) ).

thf(3967,plain,
    ! [SV840: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( ~ ! [SY2920: $i] :
                ( ~ ( SV652 @ SY2920 )
                | ( ( sK53_SY235 @ SV652 @ SV605 )
                  = SY2920 ) )
          | ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) )
        = $false )
      | ( ( SV840
          = ( sK54_SY233 @ SV840 @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV605 @ SV840 )
        = $false )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3937]) ).

thf(3968,plain,
    ! [SV824: $i,SV605: $i > $o,SV873: $i,SV652: $i > $o] :
      ( ( ( ~ ( SV652 @ SV873 )
          | ( ( sK53_SY235 @ SV652 @ SV605 )
            = SV873 ) )
        = $true )
      | ( ( SV605 @ ( sK54_SY233 @ SV824 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ SV824 )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3938]) ).

thf(3969,plain,
    ! [SV824: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( ! [SY2920: $i] :
              ( ~ ( SV652 @ SY2920 )
              | ( ( sK53_SY235 @ SV652 @ SV605 )
                = SY2920 ) ) )
        = $true )
      | ( ( SV824
          = ( sK54_SY233 @ SV824 @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV605 @ SV824 )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3940]) ).

thf(3970,plain,
    ! [SV824: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV824
          = ( sK54_SY233 @ SV824 @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV605 @ SV824 )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3941]) ).

thf(3971,plain,
    ! [SV841: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ~ ! [SY2922: $i] :
                ( ~ ( SV606 @ SY2922 )
                | ( ( sK49_SY232 @ SV653 @ SV606 )
                  = SY2922 ) ) )
        = $false )
      | ( ( SV653 @ ( sK50_SY236 @ SV841 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV653 @ SV841 )
        = $false )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3943]) ).

thf(3972,plain,
    ! [SV841: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) )
        = $false )
      | ( ( SV653 @ ( sK50_SY236 @ SV841 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV653 @ SV841 )
        = $false )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3943]) ).

thf(3973,plain,
    ! [SV841: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ~ ! [SY2922: $i] :
                ( ~ ( SV606 @ SY2922 )
                | ( ( sK49_SY232 @ SV653 @ SV606 )
                  = SY2922 ) )
          | ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) )
        = $false )
      | ( ( SV841
          = ( sK50_SY236 @ SV841 @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ SV841 )
        = $false )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3944]) ).

thf(3974,plain,
    ! [SV825: $i,SV653: $i > $o,SV874: $i,SV606: $i > $o] :
      ( ( ( ~ ( SV606 @ SV874 )
          | ( ( sK49_SY232 @ SV653 @ SV606 )
            = SV874 ) )
        = $true )
      | ( ( SV653 @ ( sK50_SY236 @ SV825 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV653 @ SV825 )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3945]) ).

thf(3975,plain,
    ! [SV825: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ! [SY2922: $i] :
              ( ~ ( SV606 @ SY2922 )
              | ( ( sK49_SY232 @ SV653 @ SV606 )
                = SY2922 ) ) )
        = $true )
      | ( ( SV825
          = ( sK50_SY236 @ SV825 @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ SV825 )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3947]) ).

thf(3976,plain,
    ! [SV825: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV825
          = ( sK50_SY236 @ SV825 @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ SV825 )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3948]) ).

thf(3977,plain,
    ! [SV818: $i,SV213: $i > $o,SV869: $i,SV427: $i > $o] :
      ( ( ( ~ ( SV427 @ ( sK58_SY260 @ SV869 @ SV427 @ SV213 ) ) )
        = $false )
      | ( ( ~ ( SV427 @ SV869 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV818 )
        = $false )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3949]) ).

thf(3978,plain,
    ! [SV818: $i,SV213: $i > $o,SV427: $i > $o,SV869: $i] :
      ( ( ( ~ ( ( SV869
               != ( sK58_SY260 @ SV869 @ SV427 @ SV213 ) ) ) )
        = $false )
      | ( ( ~ ( SV427 @ SV869 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV818 )
        = $false )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3949]) ).

thf(3979,plain,
    ! [SV818: $i,SV213: $i > $o,SV872: $i,SV427: $i > $o] :
      ( ( ( ~ ( SV427 @ ( sK58_SY260 @ SV872 @ SV427 @ SV213 ) )
          | ~ ( ( SV872
               != ( sK58_SY260 @ SV872 @ SV427 @ SV213 ) ) ) )
        = $false )
      | ( ( ~ ( SV427 @ SV872 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV818
          = ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV818 )
        = $false )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3950]) ).

thf(3980,plain,
    ! [SV796: $i,SV213: $i > $o,SV858: $i,SV427: $i > $o] :
      ( ( ( SV427 @ SV858 )
        = $false )
      | ( ( SV427 @ ( sK58_SY260 @ SV858 @ SV427 @ SV213 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV796 )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3951]) ).

thf(3981,plain,
    ! [SV796: $i,SV213: $i > $o,SV427: $i > $o,SV858: $i] :
      ( ( ( SV858
          = ( sK58_SY260 @ SV858 @ SV427 @ SV213 ) )
        = $false )
      | ( ( ~ ( SV427 @ SV858 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV796 )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3952]) ).

thf(3982,plain,
    ! [SV796: $i,SV213: $i > $o,SV863: $i,SV427: $i > $o] :
      ( ( ( SV427 @ ( sK58_SY260 @ SV863 @ SV427 @ SV213 ) )
        = $true )
      | ( ( ~ ( SV427 @ SV863 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV796
          = ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV796 )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3953]) ).

thf(3983,plain,
    ! [SV796: $i,SV213: $i > $o,SV427: $i > $o,SV863: $i] :
      ( ( ( SV863
         != ( sK58_SY260 @ SV863 @ SV427 @ SV213 ) )
        = $true )
      | ( ( ~ ( SV427 @ SV863 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV796
          = ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV796 )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3954]) ).

thf(3984,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3957]) ).

thf(3985,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3957]) ).

thf(3986,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3958]) ).

thf(3987,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3958]) ).

thf(3988,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
          | ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
        = $false )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3960]) ).

thf(3989,plain,
    ! [SV233: $i,SV800: $i,SV788: $i] :
      ( ( ( ~ ( in @ SV788 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) ) )
        = $true )
      | ( ( ~ ( in @ SV800 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) ) )
        = $true )
      | ( ( SV788 = SV800 )
        = $true )
      | ( ( in @ SV788 @ SV233 )
        = $false )
      | ( ( in @ SV800 @ SV233 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3963]) ).

thf(3990,plain,
    ! [SV233: $i,SV800: $i,SV788: $i] :
      ( ( ( in @ SV788 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) )
        = $true )
      | ( ( in @ SV800 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) )
        = $true )
      | ( ( SV788 = SV800 )
        = $true )
      | ( ( in @ SV788 @ SV233 )
        = $false )
      | ( ( in @ SV800 @ SV233 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3964]) ).

thf(3991,plain,
    ! [SV840: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( ! [SY2920: $i] :
              ( ~ ( SV652 @ SY2920 )
              | ( ( sK53_SY235 @ SV652 @ SV605 )
                = SY2920 ) ) )
        = $true )
      | ( ( SV605 @ ( sK54_SY233 @ SV840 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ SV840 )
        = $false )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3965]) ).

thf(3992,plain,
    ! [SV840: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK54_SY233 @ SV840 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ SV840 )
        = $false )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3966]) ).

thf(3993,plain,
    ! [SV840: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( ~ ! [SY2920: $i] :
                ( ~ ( SV652 @ SY2920 )
                | ( ( sK53_SY235 @ SV652 @ SV605 )
                  = SY2920 ) ) )
        = $false )
      | ( ( SV840
          = ( sK54_SY233 @ SV840 @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV605 @ SV840 )
        = $false )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3967]) ).

thf(3994,plain,
    ! [SV840: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( ~ ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) ) )
        = $false )
      | ( ( SV840
          = ( sK54_SY233 @ SV840 @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV605 @ SV840 )
        = $false )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3967]) ).

thf(3995,plain,
    ! [SV824: $i,SV605: $i > $o,SV873: $i,SV652: $i > $o] :
      ( ( ( ~ ( SV652 @ SV873 ) )
        = $true )
      | ( ( ( sK53_SY235 @ SV652 @ SV605 )
          = SV873 )
        = $true )
      | ( ( SV605 @ ( sK54_SY233 @ SV824 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ SV824 )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3968]) ).

thf(3996,plain,
    ! [SV824: $i,SV605: $i > $o,SV875: $i,SV652: $i > $o] :
      ( ( ( ~ ( SV652 @ SV875 )
          | ( ( sK53_SY235 @ SV652 @ SV605 )
            = SV875 ) )
        = $true )
      | ( ( SV824
          = ( sK54_SY233 @ SV824 @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV605 @ SV824 )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3969]) ).

thf(3997,plain,
    ! [SV841: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ! [SY2922: $i] :
              ( ~ ( SV606 @ SY2922 )
              | ( ( sK49_SY232 @ SV653 @ SV606 )
                = SY2922 ) ) )
        = $true )
      | ( ( SV653 @ ( sK50_SY236 @ SV841 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV653 @ SV841 )
        = $false )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3971]) ).

thf(3998,plain,
    ! [SV841: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV653 @ ( sK50_SY236 @ SV841 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV653 @ SV841 )
        = $false )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3972]) ).

thf(3999,plain,
    ! [SV841: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ~ ! [SY2922: $i] :
                ( ~ ( SV606 @ SY2922 )
                | ( ( sK49_SY232 @ SV653 @ SV606 )
                  = SY2922 ) ) )
        = $false )
      | ( ( SV841
          = ( sK50_SY236 @ SV841 @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ SV841 )
        = $false )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3973]) ).

thf(4000,plain,
    ! [SV841: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ~ ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) ) )
        = $false )
      | ( ( SV841
          = ( sK50_SY236 @ SV841 @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ SV841 )
        = $false )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3973]) ).

thf(4001,plain,
    ! [SV825: $i,SV653: $i > $o,SV874: $i,SV606: $i > $o] :
      ( ( ( ~ ( SV606 @ SV874 ) )
        = $true )
      | ( ( ( sK49_SY232 @ SV653 @ SV606 )
          = SV874 )
        = $true )
      | ( ( SV653 @ ( sK50_SY236 @ SV825 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV653 @ SV825 )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3974]) ).

thf(4002,plain,
    ! [SV825: $i,SV653: $i > $o,SV876: $i,SV606: $i > $o] :
      ( ( ( ~ ( SV606 @ SV876 )
          | ( ( sK49_SY232 @ SV653 @ SV606 )
            = SV876 ) )
        = $true )
      | ( ( SV825
          = ( sK50_SY236 @ SV825 @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ SV825 )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[3975]) ).

thf(4003,plain,
    ! [SV818: $i,SV213: $i > $o,SV869: $i,SV427: $i > $o] :
      ( ( ( SV427 @ ( sK58_SY260 @ SV869 @ SV427 @ SV213 ) )
        = $true )
      | ( ( ~ ( SV427 @ SV869 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV818 )
        = $false )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3977]) ).

thf(4004,plain,
    ! [SV818: $i,SV213: $i > $o,SV427: $i > $o,SV869: $i] :
      ( ( ( SV869
         != ( sK58_SY260 @ SV869 @ SV427 @ SV213 ) )
        = $true )
      | ( ( ~ ( SV427 @ SV869 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV818 )
        = $false )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3978]) ).

thf(4005,plain,
    ! [SV818: $i,SV213: $i > $o,SV872: $i,SV427: $i > $o] :
      ( ( ( ~ ( SV427 @ ( sK58_SY260 @ SV872 @ SV427 @ SV213 ) ) )
        = $false )
      | ( ( ~ ( SV427 @ SV872 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV818
          = ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV818 )
        = $false )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3979]) ).

thf(4006,plain,
    ! [SV818: $i,SV213: $i > $o,SV427: $i > $o,SV872: $i] :
      ( ( ( ~ ( ( SV872
               != ( sK58_SY260 @ SV872 @ SV427 @ SV213 ) ) ) )
        = $false )
      | ( ( ~ ( SV427 @ SV872 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV818
          = ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV818 )
        = $false )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3979]) ).

thf(4007,plain,
    ! [SV796: $i,SV213: $i > $o,SV858: $i,SV427: $i > $o] :
      ( ( ( SV427 @ SV858 )
        = $false )
      | ( ( SV858
          = ( sK58_SY260 @ SV858 @ SV427 @ SV213 ) )
        = $false )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV796 )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3981]) ).

thf(4008,plain,
    ! [SV796: $i,SV213: $i > $o,SV863: $i,SV427: $i > $o] :
      ( ( ( SV427 @ SV863 )
        = $false )
      | ( ( SV427 @ ( sK58_SY260 @ SV863 @ SV427 @ SV213 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV796
          = ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV796 )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3982]) ).

thf(4009,plain,
    ! [SV796: $i,SV213: $i > $o,SV427: $i > $o,SV863: $i] :
      ( ( ( SV863
          = ( sK58_SY260 @ SV863 @ SV427 @ SV213 ) )
        = $false )
      | ( ( ~ ( SV427 @ SV863 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV796
          = ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV796 )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3983]) ).

thf(4010,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
        = $true )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3984]) ).

thf(4011,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) )
        = $true )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3985]) ).

thf(4012,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
        = $true )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3986]) ).

thf(4013,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
              | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) )
        = $true )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3987]) ).

thf(4014,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
        = $false )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3988]) ).

thf(4015,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
                | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
        = $false )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3988]) ).

thf(4016,plain,
    ! [SV233: $i,SV800: $i,SV788: $i] :
      ( ( ( in @ SV788 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) )
        = $false )
      | ( ( ~ ( in @ SV800 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) ) )
        = $true )
      | ( ( SV788 = SV800 )
        = $true )
      | ( ( in @ SV788 @ SV233 )
        = $false )
      | ( ( in @ SV800 @ SV233 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3989]) ).

thf(4017,plain,
    ! [SV840: $i,SV605: $i > $o,SV877: $i,SV652: $i > $o] :
      ( ( ( ~ ( SV652 @ SV877 )
          | ( ( sK53_SY235 @ SV652 @ SV605 )
            = SV877 ) )
        = $true )
      | ( ( SV605 @ ( sK54_SY233 @ SV840 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ SV840 )
        = $false )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3991]) ).

thf(4018,plain,
    ! [SV840: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( ! [SY2920: $i] :
              ( ~ ( SV652 @ SY2920 )
              | ( ( sK53_SY235 @ SV652 @ SV605 )
                = SY2920 ) ) )
        = $true )
      | ( ( SV840
          = ( sK54_SY233 @ SV840 @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV605 @ SV840 )
        = $false )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3993]) ).

thf(4019,plain,
    ! [SV840: $i,SV605: $i > $o,SV652: $i > $o] :
      ( ( ( SV652 @ ( sK53_SY235 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV840
          = ( sK54_SY233 @ SV840 @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV605 @ SV840 )
        = $false )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3994]) ).

thf(4020,plain,
    ! [SV824: $i,SV605: $i > $o,SV873: $i,SV652: $i > $o] :
      ( ( ( SV652 @ SV873 )
        = $false )
      | ( ( ( sK53_SY235 @ SV652 @ SV605 )
          = SV873 )
        = $true )
      | ( ( SV605 @ ( sK54_SY233 @ SV824 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ SV824 )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3995]) ).

thf(4021,plain,
    ! [SV824: $i,SV605: $i > $o,SV875: $i,SV652: $i > $o] :
      ( ( ( ~ ( SV652 @ SV875 ) )
        = $true )
      | ( ( ( sK53_SY235 @ SV652 @ SV605 )
          = SV875 )
        = $true )
      | ( ( SV824
          = ( sK54_SY233 @ SV824 @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV605 @ SV824 )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3996]) ).

thf(4022,plain,
    ! [SV841: $i,SV653: $i > $o,SV878: $i,SV606: $i > $o] :
      ( ( ( ~ ( SV606 @ SV878 )
          | ( ( sK49_SY232 @ SV653 @ SV606 )
            = SV878 ) )
        = $true )
      | ( ( SV653 @ ( sK50_SY236 @ SV841 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV653 @ SV841 )
        = $false )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[3997]) ).

thf(4023,plain,
    ! [SV841: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( ! [SY2922: $i] :
              ( ~ ( SV606 @ SY2922 )
              | ( ( sK49_SY232 @ SV653 @ SV606 )
                = SY2922 ) ) )
        = $true )
      | ( ( SV841
          = ( sK50_SY236 @ SV841 @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ SV841 )
        = $false )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3999]) ).

thf(4024,plain,
    ! [SV841: $i,SV653: $i > $o,SV606: $i > $o] :
      ( ( ( SV606 @ ( sK49_SY232 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV841
          = ( sK50_SY236 @ SV841 @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ SV841 )
        = $false )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4000]) ).

thf(4025,plain,
    ! [SV825: $i,SV653: $i > $o,SV874: $i,SV606: $i > $o] :
      ( ( ( SV606 @ SV874 )
        = $false )
      | ( ( ( sK49_SY232 @ SV653 @ SV606 )
          = SV874 )
        = $true )
      | ( ( SV653 @ ( sK50_SY236 @ SV825 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV653 @ SV825 )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4001]) ).

thf(4026,plain,
    ! [SV825: $i,SV653: $i > $o,SV876: $i,SV606: $i > $o] :
      ( ( ( ~ ( SV606 @ SV876 ) )
        = $true )
      | ( ( ( sK49_SY232 @ SV653 @ SV606 )
          = SV876 )
        = $true )
      | ( ( SV825
          = ( sK50_SY236 @ SV825 @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ SV825 )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[4002]) ).

thf(4027,plain,
    ! [SV818: $i,SV213: $i > $o,SV869: $i,SV427: $i > $o] :
      ( ( ( SV427 @ SV869 )
        = $false )
      | ( ( SV427 @ ( sK58_SY260 @ SV869 @ SV427 @ SV213 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV818 )
        = $false )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4003]) ).

thf(4028,plain,
    ! [SV818: $i,SV213: $i > $o,SV427: $i > $o,SV869: $i] :
      ( ( ( SV869
          = ( sK58_SY260 @ SV869 @ SV427 @ SV213 ) )
        = $false )
      | ( ( ~ ( SV427 @ SV869 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV818 )
        = $false )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4004]) ).

thf(4029,plain,
    ! [SV818: $i,SV213: $i > $o,SV872: $i,SV427: $i > $o] :
      ( ( ( SV427 @ ( sK58_SY260 @ SV872 @ SV427 @ SV213 ) )
        = $true )
      | ( ( ~ ( SV427 @ SV872 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV818
          = ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV818 )
        = $false )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4005]) ).

thf(4030,plain,
    ! [SV818: $i,SV213: $i > $o,SV427: $i > $o,SV872: $i] :
      ( ( ( SV872
         != ( sK58_SY260 @ SV872 @ SV427 @ SV213 ) )
        = $true )
      | ( ( ~ ( SV427 @ SV872 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV818
          = ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV818 )
        = $false )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4006]) ).

thf(4031,plain,
    ! [SV796: $i,SV213: $i > $o,SV863: $i,SV427: $i > $o] :
      ( ( ( SV427 @ SV863 )
        = $false )
      | ( ( SV863
          = ( sK58_SY260 @ SV863 @ SV427 @ SV213 ) )
        = $false )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV796
          = ( sK59_SY257 @ SV796 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV796 )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4009]) ).

thf(4032,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4011]) ).

thf(4033,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
          | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4013]) ).

thf(4034,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( in @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) @ SV442 )
        = $true )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
        = $false )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4014]) ).

thf(4035,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
              | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) ) )
        = $true )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
        = $false )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4015]) ).

thf(4036,plain,
    ! [SV233: $i,SV788: $i,SV800: $i] :
      ( ( ( in @ SV800 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) )
        = $false )
      | ( ( in @ SV788 @ ( sK16_SY1855 @ SV800 @ SV788 @ SV233 ) )
        = $false )
      | ( ( SV788 = SV800 )
        = $true )
      | ( ( in @ SV788 @ SV233 )
        = $false )
      | ( ( in @ SV800 @ SV233 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4016]) ).

thf(4037,plain,
    ! [SV840: $i,SV605: $i > $o,SV877: $i,SV652: $i > $o] :
      ( ( ( ~ ( SV652 @ SV877 ) )
        = $true )
      | ( ( ( sK53_SY235 @ SV652 @ SV605 )
          = SV877 )
        = $true )
      | ( ( SV605 @ ( sK54_SY233 @ SV840 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ SV840 )
        = $false )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4017]) ).

thf(4038,plain,
    ! [SV840: $i,SV605: $i > $o,SV879: $i,SV652: $i > $o] :
      ( ( ( ~ ( SV652 @ SV879 )
          | ( ( sK53_SY235 @ SV652 @ SV605 )
            = SV879 ) )
        = $true )
      | ( ( SV840
          = ( sK54_SY233 @ SV840 @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV605 @ SV840 )
        = $false )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4018]) ).

thf(4039,plain,
    ! [SV824: $i,SV605: $i > $o,SV875: $i,SV652: $i > $o] :
      ( ( ( SV652 @ SV875 )
        = $false )
      | ( ( ( sK53_SY235 @ SV652 @ SV605 )
          = SV875 )
        = $true )
      | ( ( SV824
          = ( sK54_SY233 @ SV824 @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV605 @ SV824 )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4021]) ).

thf(4040,plain,
    ! [SV841: $i,SV653: $i > $o,SV878: $i,SV606: $i > $o] :
      ( ( ( ~ ( SV606 @ SV878 ) )
        = $true )
      | ( ( ( sK49_SY232 @ SV653 @ SV606 )
          = SV878 )
        = $true )
      | ( ( SV653 @ ( sK50_SY236 @ SV841 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV653 @ SV841 )
        = $false )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4022]) ).

thf(4041,plain,
    ! [SV841: $i,SV653: $i > $o,SV880: $i,SV606: $i > $o] :
      ( ( ( ~ ( SV606 @ SV880 )
          | ( ( sK49_SY232 @ SV653 @ SV606 )
            = SV880 ) )
        = $true )
      | ( ( SV841
          = ( sK50_SY236 @ SV841 @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ SV841 )
        = $false )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[4023]) ).

thf(4042,plain,
    ! [SV825: $i,SV653: $i > $o,SV876: $i,SV606: $i > $o] :
      ( ( ( SV606 @ SV876 )
        = $false )
      | ( ( ( sK49_SY232 @ SV653 @ SV606 )
          = SV876 )
        = $true )
      | ( ( SV825
          = ( sK50_SY236 @ SV825 @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ SV825 )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[4026]) ).

thf(4043,plain,
    ! [SV818: $i,SV213: $i > $o,SV869: $i,SV427: $i > $o] :
      ( ( ( SV427 @ SV869 )
        = $false )
      | ( ( SV869
          = ( sK58_SY260 @ SV869 @ SV427 @ SV213 ) )
        = $false )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV213 @ ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
        = $true )
      | ( ( SV213 @ SV818 )
        = $false )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4028]) ).

thf(4044,plain,
    ! [SV818: $i,SV213: $i > $o,SV872: $i,SV427: $i > $o] :
      ( ( ( SV427 @ SV872 )
        = $false )
      | ( ( SV427 @ ( sK58_SY260 @ SV872 @ SV427 @ SV213 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV818
          = ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV818 )
        = $false )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4029]) ).

thf(4045,plain,
    ! [SV818: $i,SV213: $i > $o,SV427: $i > $o,SV872: $i] :
      ( ( ( SV872
          = ( sK58_SY260 @ SV872 @ SV427 @ SV213 ) )
        = $false )
      | ( ( ~ ( SV427 @ SV872 ) )
        = $true )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV818
          = ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV818 )
        = $false )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4030]) ).

thf(4046,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4033]) ).

thf(4047,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4033]) ).

thf(4048,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
          | ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
        = $false )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4035]) ).

thf(4049,plain,
    ! [SV840: $i,SV605: $i > $o,SV877: $i,SV652: $i > $o] :
      ( ( ( SV652 @ SV877 )
        = $false )
      | ( ( ( sK53_SY235 @ SV652 @ SV605 )
          = SV877 )
        = $true )
      | ( ( SV605 @ ( sK54_SY233 @ SV840 @ SV652 @ SV605 ) )
        = $true )
      | ( ( SV605 @ SV840 )
        = $false )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4037]) ).

thf(4050,plain,
    ! [SV840: $i,SV605: $i > $o,SV879: $i,SV652: $i > $o] :
      ( ( ( ~ ( SV652 @ SV879 ) )
        = $true )
      | ( ( ( sK53_SY235 @ SV652 @ SV605 )
          = SV879 )
        = $true )
      | ( ( SV840
          = ( sK54_SY233 @ SV840 @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV605 @ SV840 )
        = $false )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4038]) ).

thf(4051,plain,
    ! [SV841: $i,SV653: $i > $o,SV878: $i,SV606: $i > $o] :
      ( ( ( SV606 @ SV878 )
        = $false )
      | ( ( ( sK49_SY232 @ SV653 @ SV606 )
          = SV878 )
        = $true )
      | ( ( SV653 @ ( sK50_SY236 @ SV841 @ SV653 @ SV606 ) )
        = $true )
      | ( ( SV653 @ SV841 )
        = $false )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4040]) ).

thf(4052,plain,
    ! [SV841: $i,SV653: $i > $o,SV880: $i,SV606: $i > $o] :
      ( ( ( ~ ( SV606 @ SV880 ) )
        = $true )
      | ( ( ( sK49_SY232 @ SV653 @ SV606 )
          = SV880 )
        = $true )
      | ( ( SV841
          = ( sK50_SY236 @ SV841 @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ SV841 )
        = $false )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[4041]) ).

thf(4053,plain,
    ! [SV818: $i,SV213: $i > $o,SV872: $i,SV427: $i > $o] :
      ( ( ( SV427 @ SV872 )
        = $false )
      | ( ( SV872
          = ( sK58_SY260 @ SV872 @ SV427 @ SV213 ) )
        = $false )
      | ( ( ( descr
            @ ^ [SY2322: $i] : ( SV213 @ SY2322 ) )
          = ( descr
            @ ^ [SY2673: $i] : ( SV427 @ SY2673 ) ) )
        = $true )
      | ( ( SV818
          = ( sK59_SY257 @ SV818 @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV213 @ SV818 )
        = $false )
      | ( ( SV213 @ ( sK60_Xx @ SV427 @ SV213 ) )
        = $false )
      | ( ( SV427 @ ( sK61_SY1874 @ SV427 @ SV213 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4045]) ).

thf(4054,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
        = $true )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4046]) ).

thf(4055,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) )
        = $true )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4047]) ).

thf(4056,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
        = $false )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4048]) ).

thf(4057,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
        = $false )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[4048]) ).

thf(4058,plain,
    ! [SV840: $i,SV605: $i > $o,SV879: $i,SV652: $i > $o] :
      ( ( ( SV652 @ SV879 )
        = $false )
      | ( ( ( sK53_SY235 @ SV652 @ SV605 )
          = SV879 )
        = $true )
      | ( ( SV840
          = ( sK54_SY233 @ SV840 @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV605 @ SV840 )
        = $false )
      | ( ( SV605 @ ( sK55_Xx @ SV652 @ SV605 ) )
        = $false )
      | ( ( SV652 @ ( sK56_SY1873 @ SV652 @ SV605 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4050]) ).

thf(4059,plain,
    ! [SV841: $i,SV653: $i > $o,SV880: $i,SV606: $i > $o] :
      ( ( ( SV606 @ SV880 )
        = $false )
      | ( ( ( sK49_SY232 @ SV653 @ SV606 )
          = SV880 )
        = $true )
      | ( ( SV841
          = ( sK50_SY236 @ SV841 @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ SV841 )
        = $false )
      | ( ( SV606 @ ( sK51_Xx @ SV653 @ SV606 ) )
        = $false )
      | ( ( SV653 @ ( sK52_SY1871 @ SV653 @ SV606 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4052]) ).

thf(4060,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
        = $true )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4055]) ).

thf(4061,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
        = $true )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
        = $false )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4056]) ).

thf(4062,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( ~ ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 ) )
        = $true )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
        = $false )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[4057]) ).

thf(4063,plain,
    ! [SV230: $i,SV442: $i,SV569: $i,SV706: $i] :
      ( ( ( in @ ( kpair @ ( sK86_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK87_SY1882 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV569 )
        = $false )
      | ( ( SV569 = SV706 )
        = $true )
      | ( ( in @ ( kpair @ ( sK88_Xx @ SV706 @ SV569 @ SV442 @ SV230 ) @ ( sK89_SY1883 @ SV706 @ SV569 @ SV442 @ SV230 ) ) @ SV706 )
        = $false )
      | ( ( subset @ SV706 @ ( cartprod @ SV230 @ SV442 ) )
        = $false )
      | ( ( subset @ SV569 @ ( cartprod @ SV230 @ SV442 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[4062]) ).

thf(4064,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[671,4063,4061,4060,4059,4058,4054,4053,4051,4049,4044,4043,4042,4039,4036,4034,4032,4031,4027,4025,4024,4020,4019,4012,4010,4008,4007,3998,3992,3990,3980,3976,3970,3962,3961,3959,3956,3955,3946,3942,3939,3935,3934,3930,3929,3927,3926,3922,3920,3918,3917,3916,3915,3914,3913,3912,3910,3909,3903,3896,3889,3888,3887,3886,3878,3877,3868,3864,3863,3862,3858,3857,3856,3852,3851,3845,3844,3843,3827,3826,3825,3824,3822,3820,3819,3806,3791,3783,3781,3780,3775,3768,3757,3744,3742,3733,3732,3731,3728,3727,3726,3724,3722,3709,3707,3701,3694,3686,3655,3654,3653,3649,3647,3634,3613,3597,3585,3584,3583,3567,3549,3544,3542,3533,3529,3528,3527,3498,3497,3488,3487,3486,3479,3478,3472,3471,3456,3452,3451,3450,3449,3448,3447,3438,3437,3436,3435,3431,3428,3422,3417,3412,3411,3399,3398,3397,3396,3395,3394,3389,3388,3387,3386,3385,3384,3383,3380,3377,3375,3370,3369,3356,3345,3344,3343,3334,3326,3320,3316,3308,3290,3289,3288,3280,3278,3277,3276,3274,3273,3270,3267,3266,3259,3249,3248,3242,3216,3215,3214,3205,3204,3197,3168,3167,3163,3158,3154,3152,3128,3109,3107,3105,3103,3089,3084,3083,3055,3054,3050,3048,3047,3042,3034,3032,3020,3012,3004,3003,2997,2991,2990,2982,2970,2963,2960,2942,2941,2940,2938,2937,2936,2920,2916,2915,2912,2911,2910,2904,2903,2902,2901,2895,2894,2881,2878,2859,2838,2834,2833,2828,2827,2826,2812,2811,2810,2809,2808,2807,2804,2798,2797,2796,2794,2765,2753,2752,2751,2739,2734,2731,2721,2719,2717,2701,2696,2689,2688,2687,2685,2669,2666,2655,2654,2653,2646,2645,2644,2643,2639,2629,2623,2622,2621,2584,2566,2549,2539,2527,2519,2514,2513,2511,2510,2509,2508,2507,2506,2505,2504,2503,2502,2501,2500,2497,2496,2495,2494,2492,2491,2488,2487,2486,2485,2484,2477,2476,2475,2472,2456,2455,2447,2443,2436,2408,2406,2401,2395,2394,2384,2360,2358,2337,2335,2334,2330,2329,2328,2327,2326,2325,2324,2310,2309,2308,2284,2283,2282,2268,2267,2247,2212,2181,2163,2160,2159,2140,2137,2128,2127,2124,2123,2122,2121,2120,2119,2118,2116,2115,2108,2107,2105,2104,2103,2102,2079,1945,1944,1942,1941,1928,1926,1925,1921,1920,1918,1914,1908,1900,1899,1898,1894,1891,1885,1876,1874,1866,1865,1743,1742,1741,1740,1739,1738,1731,1730,1729,1728,1727,1724,1721,1720,1719,1718,1714,1710,1708,1707,1706,1699,1698,1696,1695,1691,1686,1681,1680,1670,1665,1664,1617,1615,1603,1602,1601,1537,1509,1487,1486,1485,1484,1483,1482,1466,1451,1424,1423,1413,1412,1403,1402,1262,1253,1252,1251,1250,1249,1246,1240,1234,1233,1212,1204,1203,1201,1198,1197,1193,1189,1177,1171,1170,1169,1168,1167,1151,1140,984,983,982,956,950,941,890,889,888,737,713,675]) ).

thf(4065,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[4064]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SEU741^1 : 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
% 0.09/0.18  % Computer : n008.cluster.edu
% 0.09/0.18  % Model    : x86_64 x86_64
% 0.09/0.18  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18  % Memory   : 8046.5625MB
% 0.09/0.18  % OS       : Linux 6.8.0-71-generic
% 0.09/0.18  % CPULimit : 300
% 0.09/0.18  % WCLimit  : 300
% 0.09/0.18  % DateTime : Tue Oct  6 15:34:09 UTC 2026
% 0.09/0.18  % CPUTime  : 
% 0.09/0.18  Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 71.41/12.29  .
% 71.41/12.29  
% 71.41/12.29   No.of.Axioms: 0
% 71.41/12.29  
% 71.41/12.29   Length.of.Defs: 59776
% 71.41/12.29  
% 71.41/12.29   Contains.Choice.Funs: true
% 71.41/12.29  .............................................................................................................................................................................
% 71.41/12.29  
% 71.41/12.29  ********************************
% 71.41/12.29  *   All subproblems solved!    *
% 71.41/12.29  ********************************
% 71.41/12.29  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:257,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:4064,loop_count:0,foatp_calls:1,translation:fof_full)
% 71.41/12.29  
% 71.41/12.29  %**** Beginning of derivation protocol ****
% 71.41/12.29  % SZS output start CNFRefutation
% See solution above
% 12.26/12.32  
% 12.26/12.32  %**** End of derivation protocol ****
% 12.26/12.32  %**** no. of clauses in derivation: 4065 ****
% 12.26/12.32  %**** clause counter: 4064 ****
% 12.26/12.32  
% 12.26/12.32  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:257,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:4064,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------