TSTP Solution File: SEU685^1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU685^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.lXjM3CVds8 true

% Computer : n025.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 19:16:12 EDT 2023

% Result   : Theorem 1.56s 0.93s
% Output   : Refutation 1.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :  228
% Syntax   : Number of formulae    :  238 (  22 unt; 210 typ;   0 def)
%            Number of atoms       :  721 (  36 equ;   0 cnn)
%            Maximal formula atoms :  216 (  25 avg)
%            Number of connectives : 1020 (   8   ~;   4   |;   0   &; 351   @)
%                                         (   0 <=>; 657  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  216 (  26 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   13 (  13   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  212 ( 210 usr; 206 con; 0-4 aty)
%            Number of variables   :  139 (   0   ^; 139   !;   0   ?; 139   :)

% Comments : 
%------------------------------------------------------------------------------
thf(setadjoinAx_type,type,
    setadjoinAx: $o ).

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

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

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

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

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

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

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

thf(sk__33_type,type,
    sk__33: $i ).

thf(exuI1_type,type,
    exuI1: $o ).

thf(exuI2_type,type,
    exuI2: $o ).

thf(notequalI2_type,type,
    notequalI2: $o ).

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

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

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

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

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

thf(setadjoinSub2_type,type,
    setadjoinSub2: $o ).

thf(lam2p_type,type,
    lam2p: $o ).

thf(binintersectSubset5_type,type,
    binintersectSubset5: $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(ubforcartprodlem1_type,type,
    ubforcartprodlem1: $o ).

thf(setukpairinjR12_type,type,
    setukpairinjR12: $o ).

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

thf(binintersectSubset1_type,type,
    binintersectSubset1: $o ).

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

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

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

thf(quantDeMorgan1_type,type,
    quantDeMorgan1: $o ).

thf(funcGraphProp1_type,type,
    funcGraphProp1: $o ).

thf(brelnall1_type,type,
    brelnall1: $o ).

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

thf(ap_type,type,
    ap: $i > $i > $i > $i > $i ).

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

thf(symdiffI2_type,type,
    symdiffI2: $o ).

thf(upairset2IR_type,type,
    upairset2IR: $o ).

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

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

thf(prop2set2propI_type,type,
    prop2set2propI: $o ).

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

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

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

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

thf(powersetI1_type,type,
    powersetI1: $o ).

thf(binintersectSubset3_type,type,
    binintersectSubset3: $o ).

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

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

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

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

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

thf(binintersectSubset4_type,type,
    binintersectSubset4: $o ).

thf(brelnall2_type,type,
    brelnall2: $o ).

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

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

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

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

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

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

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

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

thf(exuE3e_type,type,
    exuE3e: $o ).

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

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

thf(binintersectSubset2_type,type,
    binintersectSubset2: $o ).

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

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

thf(prop2setI_type,type,
    prop2setI: $o ).

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

thf(ap2p_type,type,
    ap2p: $o ).

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

thf(exuE2_type,type,
    exuE2: $o ).

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

thf(setukpairinjR1_type,type,
    setukpairinjR1: $o ).

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

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

thf(notequalI1_type,type,
    notequalI1: $o ).

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

thf(nonemptyI1_type,type,
    nonemptyI1: $o ).

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

thf(setukpairinjR2_type,type,
    setukpairinjR2: $o ).

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

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

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

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

thf(subsetE2_type,type,
    subsetE2: $o ).

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

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

thf(ubforcartprodlem3_type,type,
    ubforcartprodlem3: $o ).

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

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

thf(setunionsingleton1_type,type,
    setunionsingleton1: $o ).

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

thf(quantDeMorgan3_type,type,
    quantDeMorgan3: $o ).

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

thf(setminusSubset1_type,type,
    setminusSubset1: $o ).

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

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

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

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

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

thf(dpsetconstrEL2_type,type,
    dpsetconstrEL2: $o ).

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

thf(exuE1_type,type,
    exuE1: $o ).

thf(ubforcartprodlem2_type,type,
    ubforcartprodlem2: $o ).

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

thf(sk__32_type,type,
    sk__32: $i ).

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

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

thf(dpsetconstrEL1_type,type,
    dpsetconstrEL1: $o ).

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

thf(eqimpsubset2_type,type,
    eqimpsubset2: $o ).

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

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

thf(ex1I2_type,type,
    ex1I2: $o ).

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

thf(omega0Ax_type,type,
    omega0Ax: $o ).

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

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

thf(quantDeMorgan4_type,type,
    quantDeMorgan4: $o ).

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

thf(powersetE1_type,type,
    powersetE1: $o ).

thf(bs114d_type,type,
    bs114d: $o ).

thf(ex1E2_type,type,
    ex1E2: $o ).

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

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

thf(subsetI1_type,type,
    subsetI1: $o ).

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

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

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

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

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

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

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

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

thf(emptyE1_type,type,
    emptyE1: $o ).

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

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

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

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

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

thf(ex1I_type,type,
    ex1I: $o ).

thf(cartprodmempair1_type,type,
    cartprodmempair1: $o ).

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

thf(setukpairinjR11_type,type,
    setukpairinjR11: $o ).

thf(sk__31_type,type,
    sk__31: $i ).

thf(symdiffI1_type,type,
    symdiffI1: $o ).

thf(subsetI2_type,type,
    subsetI2: $o ).

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

thf(symdiffIneg1_type,type,
    symdiffIneg1: $o ).

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

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

thf(symdiffIneg2_type,type,
    symdiffIneg2: $o ).

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

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

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

thf(setminusSubset2_type,type,
    setminusSubset2: $o ).

thf(prop2setE_type,type,
    prop2setE: $o ).

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

thf(sk__30_type,type,
    sk__30: $i ).

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

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

thf(disjointsetsI1_type,type,
    disjointsetsI1: $o ).

thf(exuE3u_type,type,
    exuE3u: $o ).

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

thf(setunionsingleton2_type,type,
    setunionsingleton2: $o ).

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

thf(upairset2E_type,type,
    upairset2E: $o ).

thf(eqimpsubset1_type,type,
    eqimpsubset1: $o ).

thf(exuI3_type,type,
    exuI3: $o ).

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

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

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

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

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

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

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

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

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

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

thf(quantDeMorgan2_type,type,
    quantDeMorgan2: $o ).

thf(ex1E1_type,type,
    ex1E1: $o ).

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

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

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

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

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

thf(nonemptyE1_type,type,
    nonemptyE1: $o ).

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

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

thf(setunionE2_type,type,
    setunionE2: $o ).

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

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

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

thf(setukpairinjL2_type,type,
    setukpairinjL2: $o ).

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

thf(subset2powerset_type,type,
    subset2powerset: $o ).

thf(setukpairinjL1_type,type,
    setukpairinjL1: $o ).

thf(funcGraphProp1,axiom,
    ( 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 ) ) ) ) ) ).

thf('0',plain,
    ( funcGraphProp1
    = ( ! [X4: $i,X6: $i,X8: $i] :
          ( ( func @ X4 @ X6 @ X8 )
         => ! [X10: $i] :
              ( ( in @ X10 @ X4 )
             => ( in @ ( kpair @ X10 @ ( ap @ X4 @ X6 @ X8 @ X10 ) ) @ X8 ) ) ) ) ),
    define([status(thm)]) ).

thf(funcinfuncset,axiom,
    ( funcinfuncset
    = ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).

thf('1',plain,
    ( funcinfuncset
    = ( ! [X4: $i,X6: $i,X8: $i] :
          ( ( func @ X4 @ X6 @ X8 )
         => ( in @ X8 @ ( funcSet @ X4 @ X6 ) ) ) ) ),
    define([status(thm)]) ).

thf(ap2p,axiom,
    ( ap2p
    = ( ! [A: $i,B: $i,Xf: $i] :
          ( ( in @ Xf @ ( funcSet @ A @ B ) )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).

thf('2',plain,
    ( ap2p
    = ( ! [X4: $i,X6: $i,X8: $i] :
          ( ( in @ X8 @ ( funcSet @ X4 @ X6 ) )
         => ! [X10: $i] :
              ( ( in @ X10 @ X4 )
             => ( in @ ( ap @ X4 @ X6 @ X8 @ X10 ) @ X6 ) ) ) ) ),
    define([status(thm)]) ).

thf(infuncsetfunc,axiom,
    ( infuncsetfunc
    = ( ! [A: $i,B: $i,Xf: $i] :
          ( ( in @ Xf @ ( funcSet @ A @ B ) )
         => ( func @ A @ B @ Xf ) ) ) ) ).

thf('3',plain,
    ( infuncsetfunc
    = ( ! [X4: $i,X6: $i,X8: $i] :
          ( ( in @ X8 @ ( funcSet @ X4 @ X6 ) )
         => ( func @ X4 @ X6 @ X8 ) ) ) ),
    define([status(thm)]) ).

thf(app,axiom,
    ( app
    = ( ! [A: $i,B: $i,Xf: $i] :
          ( ( func @ A @ B @ Xf )
         => ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).

thf('4',plain,
    ( app
    = ( ! [X4: $i,X6: $i,X8: $i] :
          ( ( func @ X4 @ X6 @ X8 )
         => ! [X10: $i] :
              ( ( in @ X10 @ X4 )
             => ( in @ ( ap @ X4 @ X6 @ X8 @ X10 ) @ X6 ) ) ) ) ),
    define([status(thm)]) ).

thf(cartprodmempaircEq,axiom,
    ( cartprodmempaircEq
    = ( ! [A: $i,B: $i,Xx: $i] :
          ( ( in @ Xx @ A )
         => ! [Xy: $i] :
              ( ( in @ Xy @ B )
             => ( ( kpair @ Xx @ Xy )
                = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).

thf('5',plain,
    ( cartprodmempaircEq
    = ( ! [X4: $i,X6: $i,X8: $i] :
          ( ( in @ X8 @ X4 )
         => ! [X10: $i] :
              ( ( in @ X10 @ X6 )
             => ( ( kpair @ X8 @ X10 )
                = ( kpair @ X8 @ X10 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(setukpairinjR,axiom,
    ( setukpairinjR
    = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
          ( ( ( kpair @ Xx @ Xy )
            = ( kpair @ Xz @ Xu ) )
         => ( Xy = Xu ) ) ) ) ).

thf('6',plain,
    ( setukpairinjR
    = ( ! [X4: $i,X6: $i,X8: $i,X10: $i] :
          ( ( ( kpair @ X4 @ X6 )
            = ( kpair @ X8 @ X10 ) )
         => ( X6 = X10 ) ) ) ),
    define([status(thm)]) ).

thf(setukpairinjL,axiom,
    ( setukpairinjL
    = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
          ( ( ( kpair @ Xx @ Xy )
            = ( kpair @ Xz @ Xu ) )
         => ( Xx = Xz ) ) ) ) ).

thf('7',plain,
    ( setukpairinjL
    = ( ! [X4: $i,X6: $i,X8: $i,X10: $i] :
          ( ( ( kpair @ X4 @ X6 )
            = ( kpair @ X8 @ X10 ) )
         => ( X4 = X8 ) ) ) ),
    define([status(thm)]) ).

thf(funcGraphProp3,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
                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(zf_stmt_0,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
                                                                                                                                                                                                                                                                                                                                         => ( ! [X4: $i,X6: $i,X8: $i,X10: $i] :
                                                                                                                                                                                                                                                                                                                                                ( ( ( kpair @ X4 @ X6 )
                                                                                                                                                                                                                                                                                                                                                  = ( kpair @ X8 @ X10 ) )
                                                                                                                                                                                                                                                                                                                                               => ( X4 = X8 ) )
                                                                                                                                                                                                                                                                                                                                           => ( setukpairinjR11
                                                                                                                                                                                                                                                                                                                                             => ( setukpairinjR12
                                                                                                                                                                                                                                                                                                                                               => ( setukpairinjR1
                                                                                                                                                                                                                                                                                                                                                 => ( upairequniteq
                                                                                                                                                                                                                                                                                                                                                   => ( setukpairinjR2
                                                                                                                                                                                                                                                                                                                                                     => ( ! [X12: $i,X14: $i,X16: $i,X18: $i] :
                                                                                                                                                                                                                                                                                                                                                            ( ( ( kpair @ X12 @ X14 )
                                                                                                                                                                                                                                                                                                                                                              = ( kpair @ X16 @ X18 ) )
                                                                                                                                                                                                                                                                                                                                                           => ( X14 = X18 ) )
                                                                                                                                                                                                                                                                                                                                                       => ( ksndsingleton
                                                                                                                                                                                                                                                                                                                                                         => ( ksndpairEq
                                                                                                                                                                                                                                                                                                                                                           => ( kpairsurjEq
                                                                                                                                                                                                                                                                                                                                                             => ( cartprodsndin
                                                                                                                                                                                                                                                                                                                                                               => ( cartprodpairmemEL
                                                                                                                                                                                                                                                                                                                                                                 => ( cartprodpairmemER
                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X20: $i,X22: $i,X24: $i] :
                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X24 @ X20 )
                                                                                                                                                                                                                                                                                                                                                                         => ! [X26: $i] :
                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X26 @ X22 )
                                                                                                                                                                                                                                                                                                                                                                             => ( ( kpair @ X24 @ X26 )
                                                                                                                                                                                                                                                                                                                                                                                = ( kpair @ X24 @ X26 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                     => ( cartprodfstpairEq
                                                                                                                                                                                                                                                                                                                                                                       => ( cartprodsndpairEq
                                                                                                                                                                                                                                                                                                                                                                         => ( cartprodpairsurjEq
                                                                                                                                                                                                                                                                                                                                                                           => ( dpsetconstrI
                                                                                                                                                                                                                                                                                                                                                                             => ( dpsetconstrSub
                                                                                                                                                                                                                                                                                                                                                                               => ( setOfPairsIsBReln
                                                                                                                                                                                                                                                                                                                                                                                 => ( dpsetconstrERa
                                                                                                                                                                                                                                                                                                                                                                                   => ( dpsetconstrEL1
                                                                                                                                                                                                                                                                                                                                                                                     => ( dpsetconstrEL2
                                                                                                                                                                                                                                                                                                                                                                                       => ( dpsetconstrER
                                                                                                                                                                                                                                                                                                                                                                                         => ( funcImageSingleton
                                                                                                                                                                                                                                                                                                                                                                                           => ( apProp
                                                                                                                                                                                                                                                                                                                                                                                             => ( ! [X28: $i,X30: $i,X32: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                    ( ( func @ X28 @ X30 @ X32 )
                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X34: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X34 @ X28 )
                                                                                                                                                                                                                                                                                                                                                                                                       => ( in @ ( ap @ X28 @ X30 @ X32 @ X34 ) @ X30 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X36: $i,X38: $i,X40: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X40 @ ( funcSet @ X36 @ X38 ) )
                                                                                                                                                                                                                                                                                                                                                                                                     => ( func @ X36 @ X38 @ X40 ) )
                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X42: $i,X44: $i,X46: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X46 @ ( funcSet @ X42 @ X44 ) )
                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X48: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X48 @ X42 )
                                                                                                                                                                                                                                                                                                                                                                                                           => ( in @ ( ap @ X42 @ X44 @ X46 @ X48 ) @ X44 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X50: $i,X52: $i,X54: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                          ( ( func @ X50 @ X52 @ X54 )
                                                                                                                                                                                                                                                                                                                                                                                                         => ( in @ X54 @ ( funcSet @ X50 @ X52 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                     => ( lamProp
                                                                                                                                                                                                                                                                                                                                                                                                       => ( lamp
                                                                                                                                                                                                                                                                                                                                                                                                         => ( lam2p
                                                                                                                                                                                                                                                                                                                                                                                                           => ( brelnall1
                                                                                                                                                                                                                                                                                                                                                                                                             => ( brelnall2
                                                                                                                                                                                                                                                                                                                                                                                                               => ( ex1E2
                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X56: $i,X58: $i,X60: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( func @ X56 @ X58 @ X60 )
                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X62: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X62 @ X56 )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ( in @ ( kpair @ X62 @ ( ap @ X56 @ X58 @ X60 @ X62 ) ) @ X60 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                   => ! [X64: $i,X66: $i,X68: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X68 @ ( funcSet @ X64 @ X66 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                       => ! [X70: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X70 @ X64 )
                                                                                                                                                                                                                                                                                                                                                                                                                           => ( in @ ( kpair @ X70 @ ( ap @ X64 @ X66 @ X68 @ X70 ) ) @ X68 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(zf_stmt_1,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
                                                                                                                                                                                                                                                                                                                                           => ( ! [X4: $i,X6: $i,X8: $i,X10: $i] :
                                                                                                                                                                                                                                                                                                                                                  ( ( ( kpair @ X4 @ X6 )
                                                                                                                                                                                                                                                                                                                                                    = ( kpair @ X8 @ X10 ) )
                                                                                                                                                                                                                                                                                                                                                 => ( X4 = X8 ) )
                                                                                                                                                                                                                                                                                                                                             => ( setukpairinjR11
                                                                                                                                                                                                                                                                                                                                               => ( setukpairinjR12
                                                                                                                                                                                                                                                                                                                                                 => ( setukpairinjR1
                                                                                                                                                                                                                                                                                                                                                   => ( upairequniteq
                                                                                                                                                                                                                                                                                                                                                     => ( setukpairinjR2
                                                                                                                                                                                                                                                                                                                                                       => ( ! [X12: $i,X14: $i,X16: $i,X18: $i] :
                                                                                                                                                                                                                                                                                                                                                              ( ( ( kpair @ X12 @ X14 )
                                                                                                                                                                                                                                                                                                                                                                = ( kpair @ X16 @ X18 ) )
                                                                                                                                                                                                                                                                                                                                                             => ( X14 = X18 ) )
                                                                                                                                                                                                                                                                                                                                                         => ( ksndsingleton
                                                                                                                                                                                                                                                                                                                                                           => ( ksndpairEq
                                                                                                                                                                                                                                                                                                                                                             => ( kpairsurjEq
                                                                                                                                                                                                                                                                                                                                                               => ( cartprodsndin
                                                                                                                                                                                                                                                                                                                                                                 => ( cartprodpairmemEL
                                                                                                                                                                                                                                                                                                                                                                   => ( cartprodpairmemER
                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X20: $i,X22: $i,X24: $i] :
                                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X24 @ X20 )
                                                                                                                                                                                                                                                                                                                                                                           => ! [X26: $i] :
                                                                                                                                                                                                                                                                                                                                                                                ( ( in @ X26 @ X22 )
                                                                                                                                                                                                                                                                                                                                                                               => ( ( kpair @ X24 @ X26 )
                                                                                                                                                                                                                                                                                                                                                                                  = ( kpair @ X24 @ X26 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                                       => ( cartprodfstpairEq
                                                                                                                                                                                                                                                                                                                                                                         => ( cartprodsndpairEq
                                                                                                                                                                                                                                                                                                                                                                           => ( cartprodpairsurjEq
                                                                                                                                                                                                                                                                                                                                                                             => ( dpsetconstrI
                                                                                                                                                                                                                                                                                                                                                                               => ( dpsetconstrSub
                                                                                                                                                                                                                                                                                                                                                                                 => ( setOfPairsIsBReln
                                                                                                                                                                                                                                                                                                                                                                                   => ( dpsetconstrERa
                                                                                                                                                                                                                                                                                                                                                                                     => ( dpsetconstrEL1
                                                                                                                                                                                                                                                                                                                                                                                       => ( dpsetconstrEL2
                                                                                                                                                                                                                                                                                                                                                                                         => ( dpsetconstrER
                                                                                                                                                                                                                                                                                                                                                                                           => ( funcImageSingleton
                                                                                                                                                                                                                                                                                                                                                                                             => ( apProp
                                                                                                                                                                                                                                                                                                                                                                                               => ( ! [X28: $i,X30: $i,X32: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                      ( ( func @ X28 @ X30 @ X32 )
                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X34: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X34 @ X28 )
                                                                                                                                                                                                                                                                                                                                                                                                         => ( in @ ( ap @ X28 @ X30 @ X32 @ X34 ) @ X30 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                 => ( ! [X36: $i,X38: $i,X40: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X40 @ ( funcSet @ X36 @ X38 ) )
                                                                                                                                                                                                                                                                                                                                                                                                       => ( func @ X36 @ X38 @ X40 ) )
                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X42: $i,X44: $i,X46: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X46 @ ( funcSet @ X42 @ X44 ) )
                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X48: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X48 @ X42 )
                                                                                                                                                                                                                                                                                                                                                                                                             => ( in @ ( ap @ X42 @ X44 @ X46 @ X48 ) @ X44 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                     => ( ! [X50: $i,X52: $i,X54: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                            ( ( func @ X50 @ X52 @ X54 )
                                                                                                                                                                                                                                                                                                                                                                                                           => ( in @ X54 @ ( funcSet @ X50 @ X52 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                       => ( lamProp
                                                                                                                                                                                                                                                                                                                                                                                                         => ( lamp
                                                                                                                                                                                                                                                                                                                                                                                                           => ( lam2p
                                                                                                                                                                                                                                                                                                                                                                                                             => ( brelnall1
                                                                                                                                                                                                                                                                                                                                                                                                               => ( brelnall2
                                                                                                                                                                                                                                                                                                                                                                                                                 => ( ex1E2
                                                                                                                                                                                                                                                                                                                                                                                                                   => ( ! [X56: $i,X58: $i,X60: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( func @ X56 @ X58 @ X60 )
                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X62: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X62 @ X56 )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ( in @ ( kpair @ X62 @ ( ap @ X56 @ X58 @ X60 @ X62 ) ) @ X60 ) ) )
                                                                                                                                                                                                                                                                                                                                                                                                                     => ! [X64: $i,X66: $i,X68: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X68 @ ( funcSet @ X64 @ X66 ) )
                                                                                                                                                                                                                                                                                                                                                                                                                         => ! [X70: $i] :
                                                                                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X70 @ X64 )
                                                                                                                                                                                                                                                                                                                                                                                                                             => ( in @ ( kpair @ X70 @ ( ap @ X64 @ X66 @ X68 @ X70 ) ) @ X68 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl100,plain,
    ! [X16: $i,X17: $i,X18: $i,X19: $i] :
      ( ~ ( in @ X16 @ X17 )
      | ( in @ ( kpair @ X16 @ ( ap @ X17 @ X18 @ X19 @ X16 ) ) @ X19 )
      | ~ ( func @ X17 @ X18 @ X19 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl102,plain,
    ~ ( in @ ( kpair @ sk__33 @ ( ap @ sk__30 @ sk__31 @ sk__32 @ sk__33 ) ) @ sk__32 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl314,plain,
    ( ~ ( func @ sk__30 @ sk__31 @ sk__32 )
    | ~ ( in @ sk__33 @ sk__30 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl100,zip_derived_cl102]) ).

thf(zip_derived_cl101,plain,
    in @ sk__33 @ sk__30,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl315,plain,
    ~ ( func @ sk__30 @ sk__31 @ sk__32 ),
    inference(demod,[status(thm)],[zip_derived_cl314,zip_derived_cl101]) ).

thf(zip_derived_cl108,plain,
    ! [X23: $i,X24: $i,X25: $i] :
      ( ( func @ X23 @ X24 @ X25 )
      | ~ ( in @ X25 @ ( funcSet @ X23 @ X24 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl103,plain,
    in @ sk__32 @ ( funcSet @ sk__30 @ sk__31 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl355,plain,
    func @ sk__30 @ sk__31 @ sk__32,
    inference('sup+',[status(thm)],[zip_derived_cl108,zip_derived_cl103]) ).

thf(zip_derived_cl375,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl315,zip_derived_cl355]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU685^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.lXjM3CVds8 true
% 0.13/0.33  % Computer : n025.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Wed Aug 23 18:36:06 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.13/0.33  % Running portfolio for 300 s
% 0.13/0.33  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34  % Number of cores: 8
% 0.13/0.34  % Python version: Python 3.6.8
% 0.13/0.34  % Running in HO mode
% 0.20/0.71  % Total configuration time : 828
% 0.20/0.71  % Estimated wc time : 1656
% 0.20/0.71  % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.77  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 1.26/0.78  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 1.26/0.78  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 1.26/0.79  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.26/0.79  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 1.26/0.79  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.26/0.82  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.26/0.82  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 1.56/0.93  % Solved by lams/40_c_ic.sh.
% 1.56/0.93  % done 207 iterations in 0.101s
% 1.56/0.93  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.56/0.93  % SZS output start Refutation
% See solution above
% 1.56/0.94  
% 1.56/0.94  
% 1.56/0.94  % Terminating...
% 1.57/1.01  % Runner terminated.
% 1.57/1.02  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------