TSTP Solution File: SEU616^1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU616^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.YsarDXRWCv true

% Computer : n018.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 19:14:44 EDT 2023

% Result   : Theorem 1.42s 0.83s
% Output   : Refutation 1.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  198
% Syntax   : Number of formulae    :  203 (  58 unt; 140 typ;   0 def)
%            Number of atoms       :  799 ( 129 equ;   0 cnn)
%            Maximal formula atoms :  153 (  12 avg)
%            Number of connectives : 1277 (  34   ~;  14   |;   0   &; 592   @)
%                                         (   6 <=>; 631  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  140 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (  17   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  141 ( 139 usr; 136 con; 0-3 aty)
%            Number of variables   :  283 (   0   ^; 283   !;   0   ?; 283   :)

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

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

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

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

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

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

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

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

thf(notequalI2_type,type,
    notequalI2: $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(binintersectSubset5_type,type,
    binintersectSubset5: $o ).

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

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

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

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

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

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

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

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

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

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

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

thf(sk__55_type,type,
    sk__55: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(sk__56_type,type,
    sk__56: $i ).

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

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

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

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

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

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

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

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

thf(omega0Ax_type,type,
    omega0Ax: $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(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(zip_tseitin_0_type,type,
    zip_tseitin_0: $i > $i > $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(upairset2IR,axiom,
    ( upairset2IR
    = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).

thf('0',plain,
    ( upairset2IR
    = ( ! [X4: $i,X6: $i] : ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) ) ),
    define([status(thm)]) ).

thf(subsetemptysetimpeq,axiom,
    ( subsetemptysetimpeq
    = ( ! [A: $i] :
          ( ( subset @ A @ emptyset )
         => ( A = emptyset ) ) ) ) ).

thf('1',plain,
    ( subsetemptysetimpeq
    = ( ! [X4: $i] :
          ( ( subset @ X4 @ emptyset )
         => ( X4 = emptyset ) ) ) ),
    define([status(thm)]) ).

thf(setadjoinSub2,axiom,
    ( setadjoinSub2
    = ( ! [A: $i,Xx: $i,B: $i] :
          ( ( subset @ A @ B )
         => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).

thf('2',plain,
    ( setadjoinSub2
    = ( ! [X4: $i,X6: $i,X8: $i] :
          ( ( subset @ X4 @ X8 )
         => ( subset @ X4 @ ( setadjoin @ X6 @ X8 ) ) ) ) ),
    define([status(thm)]) ).

thf(setadjoinSub,axiom,
    ( setadjoinSub
    = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).

thf('3',plain,
    ( setadjoinSub
    = ( ! [X4: $i,X6: $i] : ( subset @ X6 @ ( setadjoin @ X4 @ X6 ) ) ) ),
    define([status(thm)]) ).

thf(emptysetsubset,axiom,
    ( emptysetsubset
    = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).

thf('4',plain,
    ( emptysetsubset
    = ( ! [X4: $i] : ( subset @ emptyset @ X4 ) ) ),
    define([status(thm)]) ).

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

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

thf(emptyset__Cong,axiom,
    ( emptyset__Cong
    = ( emptyset = emptyset ) ) ).

thf('6',plain,
    ( emptyset__Cong
    = ( emptyset = emptyset ) ),
    define([status(thm)]) ).

thf(vacuousDall,axiom,
    ( vacuousDall
    = ( ! [Xphi: $i > $o,Xx: $i] :
          ( ( in @ Xx @ emptyset )
         => ( Xphi @ Xx ) ) ) ) ).

thf('7',plain,
    ( vacuousDall
    = ( ! [X4: $i > $o,X6: $i] :
          ( ( in @ X6 @ emptyset )
         => ( X4 @ X6 ) ) ) ),
    define([status(thm)]) ).

thf(upairsetIR,axiom,
    ( upairsetIR
    = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).

thf('8',plain,
    ( upairsetIR
    = ( ! [X4: $i,X6: $i] : ( in @ X6 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) ) ),
    define([status(thm)]) ).

thf(upairsetIL,axiom,
    ( upairsetIL
    = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).

thf('9',plain,
    ( upairsetIL
    = ( ! [X4: $i,X6: $i] : ( in @ X4 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) ) ),
    define([status(thm)]) ).

thf(upairsetE,axiom,
    ( upairsetE
    = ( ! [Xx: $i,Xy: $i,Xz: $i] :
          ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
         => ( ( Xz = Xx )
            | ( Xz = Xy ) ) ) ) ) ).

thf('10',plain,
    ( upairsetE
    = ( ! [X4: $i,X6: $i,X8: $i] :
          ( ( in @ X8 @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) )
         => ( ( X8 = X4 )
            | ( X8 = X6 ) ) ) ) ),
    define([status(thm)]) ).

thf(singletonsswitch,axiom,
    ( singletonsswitch
    = ( ! [Xx: $i,Xy: $i] :
          ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
         => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).

thf('11',plain,
    ( singletonsswitch
    = ( ! [X4: $i,X6: $i] :
          ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) )
         => ( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) ) ),
    define([status(thm)]) ).

thf(eqinunit,axiom,
    ( eqinunit
    = ( ! [Xx: $i,Xy: $i] :
          ( ( Xx = Xy )
         => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).

thf('12',plain,
    ( eqinunit
    = ( ! [X4: $i,X6: $i] :
          ( ( X4 = X6 )
         => ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) ) ) ) ),
    define([status(thm)]) ).

thf(notinsingleton,axiom,
    ( notinsingleton
    = ( ! [Xx: $i,Xy: $i] :
          ( ( Xx != Xy )
         => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).

thf('13',plain,
    ( notinsingleton
    = ( ! [X4: $i,X6: $i] :
          ( ( X4 != X6 )
         => ~ ( in @ X6 @ ( setadjoin @ X4 @ emptyset ) ) ) ) ),
    define([status(thm)]) ).

thf(uniqinunit,axiom,
    ( uniqinunit
    = ( ! [Xx: $i,Xy: $i] :
          ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
         => ( Xx = Xy ) ) ) ) ).

thf('14',plain,
    ( uniqinunit
    = ( ! [X4: $i,X6: $i] :
          ( ( in @ X4 @ ( setadjoin @ X6 @ emptyset ) )
         => ( X4 = X6 ) ) ) ),
    define([status(thm)]) ).

thf(setadjoinOr,axiom,
    ( setadjoinOr
    = ( ! [Xx: $i,A: $i,Xy: $i] :
          ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
         => ( ( Xy = Xx )
            | ( in @ Xy @ A ) ) ) ) ) ).

thf('15',plain,
    ( setadjoinOr
    = ( ! [X4: $i,X6: $i,X8: $i] :
          ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) )
         => ( ( X8 = X4 )
            | ( in @ X8 @ X6 ) ) ) ) ),
    define([status(thm)]) ).

thf(setadjoinE,axiom,
    ( setadjoinE
    = ( ! [Xx: $i,A: $i,Xy: $i] :
          ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
         => ! [Xphi: $o] :
              ( ( ( Xy = Xx )
               => Xphi )
             => ( ( ( in @ Xy @ A )
                 => Xphi )
               => Xphi ) ) ) ) ) ).

thf('16',plain,
    ( setadjoinE
    = ( ! [X4: $i,X6: $i,X8: $i] :
          ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) )
         => ! [X10: $o] :
              ( ( ( X8 = X4 )
               => X10 )
             => ( ( ( in @ X8 @ X6 )
                 => X10 )
               => X10 ) ) ) ) ),
    define([status(thm)]) ).

thf(setadjoinIR,axiom,
    ( setadjoinIR
    = ( ! [Xx: $i,A: $i,Xy: $i] :
          ( ( in @ Xy @ A )
         => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).

thf('17',plain,
    ( setadjoinIR
    = ( ! [X4: $i,X6: $i,X8: $i] :
          ( ( in @ X8 @ X6 )
         => ( in @ X8 @ ( setadjoin @ X4 @ X6 ) ) ) ) ),
    define([status(thm)]) ).

thf(emptyinunitempty,axiom,
    ( emptyinunitempty
    = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).

thf('18',plain,
    ( emptyinunitempty
    = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
    inference(simplify_rw_rule,[status(thm)],[emptyinunitempty]) ).

thf('19',plain,
    ( emptyinunitempty
    = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
    define([status(thm)]) ).

thf(setadjoinIL,axiom,
    ( setadjoinIL
    = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).

thf('20',plain,
    ( setadjoinIL
    = ( ! [X4: $i,X6: $i] : ( in @ X4 @ ( setadjoin @ X4 @ X6 ) ) ) ),
    define([status(thm)]) ).

thf(noeltsimpempty,axiom,
    ( noeltsimpempty
    = ( ! [A: $i] :
          ( ! [Xx: $i] :
              ~ ( in @ Xx @ A )
         => ( A = emptyset ) ) ) ) ).

thf('21',plain,
    ( noeltsimpempty
    = ( ! [X4: $i] :
          ( ! [X6: $i] :
              ~ ( in @ X6 @ X4 )
         => ( X4 = emptyset ) ) ) ),
    define([status(thm)]) ).

thf(emptyI,axiom,
    ( emptyI
    = ( ! [A: $i] :
          ( ! [Xx: $i] :
              ~ ( in @ Xx @ A )
         => ( A = emptyset ) ) ) ) ).

thf('22',plain,
    ( emptyI
    = ( ! [X4: $i] :
          ( ! [X6: $i] :
              ~ ( in @ X6 @ X4 )
         => ( X4 = emptyset ) ) ) ),
    define([status(thm)]) ).

thf(notinemptyset,axiom,
    ( notinemptyset
    = ( ! [Xx: $i] :
          ~ ( in @ Xx @ emptyset ) ) ) ).

thf('23',plain,
    ( notinemptyset
    = ( ! [X4: $i] :
          ~ ( in @ X4 @ emptyset ) ) ),
    define([status(thm)]) ).

thf(emptysetimpfalse,axiom,
    ( emptysetimpfalse
    = ( ! [Xx: $i] :
          ( ( in @ Xx @ emptyset )
         => $false ) ) ) ).

thf('24',plain,
    ( emptysetimpfalse
    = ( ! [X4: $i] :
          ( ( in @ X4 @ emptyset )
         => $false ) ) ),
    define([status(thm)]) ).

thf(emptysetE,axiom,
    ( emptysetE
    = ( ! [Xx: $i] :
          ( ( in @ Xx @ emptyset )
         => ! [Xphi: $o] : Xphi ) ) ) ).

thf('25',plain,
    ( emptysetE
    = ( ! [X4: $i] :
          ( ( in @ X4 @ emptyset )
         => ! [X6: $o] : X6 ) ) ),
    define([status(thm)]) ).

thf(setadjoinAx,axiom,
    ( setadjoinAx
    = ( ! [Xx: $i,A: $i,Xy: $i] :
          ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
        <=> ( ( Xy = Xx )
            | ( in @ Xy @ A ) ) ) ) ) ).

thf('26',plain,
    ( setadjoinAx
    = ( ! [X4: $i,X6: $i,X8: $i] :
          ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) )
        <=> ( ( X8 = X4 )
            | ( in @ X8 @ X6 ) ) ) ) ),
    define([status(thm)]) ).

thf(emptysetAx,axiom,
    ( emptysetAx
    = ( ! [Xx: $i] :
          ~ ( in @ Xx @ emptyset ) ) ) ).

thf('27',plain,
    ( emptysetAx
    = ( ! [X4: $i] :
          ~ ( in @ X4 @ emptyset ) ) ),
    define([status(thm)]) ).

thf(secondinupair,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
                                                                                                                                                                                                                                                                         => ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(zf_stmt_0,conjecture,
    ( setextAx
   => ( ! [X4: $i] :
          ~ ( in @ X4 @ emptyset )
     => ( ! [X6: $i,X8: $i,X10: $i] :
            ( ( in @ X10 @ ( setadjoin @ X6 @ X8 ) )
          <=> ( ( in @ X10 @ X8 )
              | ( X10 = X6 ) ) )
       => ( powersetAx
         => ( setunionAx
           => ( omega0Ax
             => ( omegaSAx
               => ( omegaIndAx
                 => ( replAx
                   => ( foundationAx
                     => ( wellorderingAx
                       => ( descrp
                         => ( dsetconstrI
                           => ( dsetconstrEL
                             => ( dsetconstrER
                               => ( exuE1
                                 => ( prop2setE
                                   => ( ! [X12: $i] :
                                          ( ( in @ X12 @ emptyset )
                                         => ! [X14: $o] : X14 )
                                     => ( ! [X16: $i] :
                                            ( ( in @ X16 @ emptyset )
                                           => $false )
                                       => ( ! [X18: $i] :
                                              ~ ( in @ X18 @ emptyset )
                                         => ( exuE3e
                                           => ( setext
                                             => ( ! [X20: $i] :
                                                    ( ! [X22: $i] :
                                                        ~ ( in @ X22 @ X20 )
                                                   => ( X20 = emptyset ) )
                                               => ( ! [X24: $i] :
                                                      ( ! [X26: $i] :
                                                          ~ ( in @ X26 @ X24 )
                                                     => ( X24 = emptyset ) )
                                                 => ( setbeta
                                                   => ( nonemptyE1
                                                     => ( nonemptyI
                                                       => ( nonemptyI1
                                                         => ( ! [X28: $i,X30: $i] : ( in @ X28 @ ( setadjoin @ X28 @ X30 ) )
                                                           => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                             => ( ! [X32: $i,X34: $i,X36: $i] :
                                                                    ( ( in @ X36 @ X34 )
                                                                   => ( in @ X36 @ ( setadjoin @ X32 @ X34 ) ) )
                                                               => ( ! [X38: $i,X40: $i,X42: $i] :
                                                                      ( ( in @ X42 @ ( setadjoin @ X38 @ X40 ) )
                                                                     => ! [X44: $o] :
                                                                          ( ( ( X42 = X38 )
                                                                           => X44 )
                                                                         => ( ( ( in @ X42 @ X40 )
                                                                             => X44 )
                                                                           => X44 ) ) )
                                                                 => ( ! [X46: $i,X48: $i,X50: $i] :
                                                                        ( ( in @ X50 @ ( setadjoin @ X46 @ X48 ) )
                                                                       => ( ( in @ X50 @ X48 )
                                                                          | ( X50 = X46 ) ) )
                                                                   => ( setoftrueEq
                                                                     => ( powersetI
                                                                       => ( emptyinPowerset
                                                                         => ( emptyInPowerset
                                                                           => ( powersetE
                                                                             => ( setunionI
                                                                               => ( setunionE
                                                                                 => ( subPowSU
                                                                                   => ( exuE2
                                                                                     => ( nonemptyImpWitness
                                                                                       => ( ! [X52: $i,X54: $i] :
                                                                                              ( ( in @ X52 @ ( setadjoin @ X54 @ emptyset ) )
                                                                                             => ( X52 = X54 ) )
                                                                                         => ( ! [X56: $i,X58: $i] :
                                                                                                ( ( X56 != X58 )
                                                                                               => ~ ( in @ X58 @ ( setadjoin @ X56 @ emptyset ) ) )
                                                                                           => ( ! [X60: $i,X62: $i] :
                                                                                                  ( ( X60 = X62 )
                                                                                                 => ( in @ X60 @ ( setadjoin @ X62 @ emptyset ) ) )
                                                                                             => ( ! [X64: $i,X66: $i] :
                                                                                                    ( ( in @ X64 @ ( setadjoin @ X66 @ emptyset ) )
                                                                                                   => ( in @ X66 @ ( setadjoin @ X64 @ emptyset ) ) )
                                                                                               => ( ! [X68: $i,X70: $i,X72: $i] :
                                                                                                      ( ( in @ X72 @ ( setadjoin @ X68 @ ( setadjoin @ X70 @ emptyset ) ) )
                                                                                                     => ( ( X72 = X70 )
                                                                                                        | ( X72 = X68 ) ) )
                                                                                                 => ( ! [X74: $i,X76: $i] : ( in @ X74 @ ( setadjoin @ X74 @ ( setadjoin @ X76 @ emptyset ) ) )
                                                                                                   => ( ! [X78: $i,X80: $i] : ( in @ X80 @ ( setadjoin @ X78 @ ( setadjoin @ X80 @ emptyset ) ) )
                                                                                                     => ( emptyE1
                                                                                                       => ( ! [X82: $i > $o,X84: $i] :
                                                                                                              ( ( in @ X84 @ emptyset )
                                                                                                             => ( X82 @ X84 ) )
                                                                                                         => ( quantDeMorgan1
                                                                                                           => ( quantDeMorgan2
                                                                                                             => ( quantDeMorgan3
                                                                                                               => ( quantDeMorgan4
                                                                                                                 => ( prop2setI
                                                                                                                   => ( prop2set2propI
                                                                                                                     => ( notdexE
                                                                                                                       => ( notdallE
                                                                                                                         => ( exuI1
                                                                                                                           => ( exuI3
                                                                                                                             => ( exuI2
                                                                                                                               => ( inCongP
                                                                                                                                 => ( in__Cong
                                                                                                                                   => ( exuE3u
                                                                                                                                     => ( exu__Cong
                                                                                                                                       => ( ( emptyset = emptyset )
                                                                                                                                         => ( ! [X86: $i,X88: $i] :
                                                                                                                                                ( ( X86 = X88 )
                                                                                                                                               => ! [X90: $i,X92: $i] :
                                                                                                                                                    ( ( X90 = X92 )
                                                                                                                                                   => ( ( setadjoin @ X86 @ X90 )
                                                                                                                                                      = ( setadjoin @ X88 @ X92 ) ) ) )
                                                                                                                                           => ( powerset__Cong
                                                                                                                                             => ( setunion__Cong
                                                                                                                                               => ( omega__Cong
                                                                                                                                                 => ( exuEu
                                                                                                                                                   => ( descr__Cong
                                                                                                                                                     => ( dsetconstr__Cong
                                                                                                                                                       => ( subsetI1
                                                                                                                                                         => ( eqimpsubset2
                                                                                                                                                           => ( eqimpsubset1
                                                                                                                                                             => ( subsetI2
                                                                                                                                                               => ( ! [X94: $i] : ( subset @ emptyset @ X94 )
                                                                                                                                                                 => ( subsetE
                                                                                                                                                                   => ( subsetE2
                                                                                                                                                                     => ( notsubsetI
                                                                                                                                                                       => ( notequalI1
                                                                                                                                                                         => ( notequalI2
                                                                                                                                                                           => ( subsetRefl
                                                                                                                                                                             => ( subsetTrans
                                                                                                                                                                               => ( ! [X96: $i,X98: $i] : ( subset @ X98 @ ( setadjoin @ X96 @ X98 ) )
                                                                                                                                                                                 => ( ! [X100: $i,X102: $i,X104: $i] :
                                                                                                                                                                                        ( ( subset @ X100 @ X104 )
                                                                                                                                                                                       => ( subset @ X100 @ ( setadjoin @ X102 @ X104 ) ) )
                                                                                                                                                                                   => ( subset2powerset
                                                                                                                                                                                     => ( setextsub
                                                                                                                                                                                       => ( ! [X106: $i] :
                                                                                                                                                                                              ( ( subset @ X106 @ emptyset )
                                                                                                                                                                                             => ( X106 = emptyset ) )
                                                                                                                                                                                         => ( powersetI1
                                                                                                                                                                                           => ( powersetE1
                                                                                                                                                                                             => ( inPowerset
                                                                                                                                                                                               => ( powersetsubset
                                                                                                                                                                                                 => ( sepInPowerset
                                                                                                                                                                                                   => ( sepSubset
                                                                                                                                                                                                     => ( binunionIL
                                                                                                                                                                                                       => ( ! [X108: $i,X110: $i] : ( in @ X110 @ ( setadjoin @ X108 @ ( setadjoin @ X110 @ emptyset ) ) )
                                                                                                                                                                                                         => ( 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
                                                                                                                                                                                                                                                                         => ! [X112: $i,X114: $i] : ( in @ X114 @ ( setadjoin @ X112 @ ( setadjoin @ X114 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(zf_stmt_1,type,
    zip_tseitin_0: $i > $i > $i > $o ).

thf(zf_stmt_2,axiom,
    ! [X10: $i,X8: $i,X6: $i] :
      ( ( zip_tseitin_0 @ X10 @ X8 @ X6 )
    <=> ( ( X10 = X6 )
        | ( in @ X10 @ X8 ) ) ) ).

thf(zf_stmt_3,conjecture,
    ( setextAx
   => ( ! [X4: $i] :
          ~ ( in @ X4 @ emptyset )
     => ( ! [X6: $i,X8: $i,X10: $i] :
            ( ( in @ X10 @ ( setadjoin @ X6 @ X8 ) )
          <=> ( zip_tseitin_0 @ X10 @ X8 @ X6 ) )
       => ( powersetAx
         => ( setunionAx
           => ( omega0Ax
             => ( omegaSAx
               => ( omegaIndAx
                 => ( replAx
                   => ( foundationAx
                     => ( wellorderingAx
                       => ( descrp
                         => ( dsetconstrI
                           => ( dsetconstrEL
                             => ( dsetconstrER
                               => ( exuE1
                                 => ( prop2setE
                                   => ( ! [X12: $i] :
                                          ( ( in @ X12 @ emptyset )
                                         => ! [X14: $o] : X14 )
                                     => ( ! [X16: $i] :
                                            ~ ( in @ X16 @ emptyset )
                                       => ( ! [X18: $i] :
                                              ~ ( in @ X18 @ emptyset )
                                         => ( exuE3e
                                           => ( setext
                                             => ( ! [X20: $i] :
                                                    ( ! [X22: $i] :
                                                        ~ ( in @ X22 @ X20 )
                                                   => ( X20 = emptyset ) )
                                               => ( ! [X24: $i] :
                                                      ( ! [X26: $i] :
                                                          ~ ( in @ X26 @ X24 )
                                                     => ( X24 = emptyset ) )
                                                 => ( setbeta
                                                   => ( nonemptyE1
                                                     => ( nonemptyI
                                                       => ( nonemptyI1
                                                         => ( ! [X28: $i,X30: $i] : ( in @ X28 @ ( setadjoin @ X28 @ X30 ) )
                                                           => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                             => ( ! [X32: $i,X34: $i,X36: $i] :
                                                                    ( ( in @ X36 @ X34 )
                                                                   => ( in @ X36 @ ( setadjoin @ X32 @ X34 ) ) )
                                                               => ( ! [X38: $i,X40: $i,X42: $i] :
                                                                      ( ( in @ X42 @ ( setadjoin @ X38 @ X40 ) )
                                                                     => ! [X44: $o] :
                                                                          ( ( ( X42 = X38 )
                                                                           => X44 )
                                                                         => ( ( ( in @ X42 @ X40 )
                                                                             => X44 )
                                                                           => X44 ) ) )
                                                                 => ( ! [X46: $i,X48: $i,X50: $i] :
                                                                        ( ( in @ X50 @ ( setadjoin @ X46 @ X48 ) )
                                                                       => ( ( X50 = X46 )
                                                                          | ( in @ X50 @ X48 ) ) )
                                                                   => ( setoftrueEq
                                                                     => ( powersetI
                                                                       => ( emptyinPowerset
                                                                         => ( emptyInPowerset
                                                                           => ( powersetE
                                                                             => ( setunionI
                                                                               => ( setunionE
                                                                                 => ( subPowSU
                                                                                   => ( exuE2
                                                                                     => ( nonemptyImpWitness
                                                                                       => ( ! [X52: $i,X54: $i] :
                                                                                              ( ( in @ X52 @ ( setadjoin @ X54 @ emptyset ) )
                                                                                             => ( X52 = X54 ) )
                                                                                         => ( ! [X56: $i,X58: $i] :
                                                                                                ( ( X56 != X58 )
                                                                                               => ~ ( in @ X58 @ ( setadjoin @ X56 @ emptyset ) ) )
                                                                                           => ( ! [X60: $i,X62: $i] :
                                                                                                  ( ( X60 = X62 )
                                                                                                 => ( in @ X60 @ ( setadjoin @ X62 @ emptyset ) ) )
                                                                                             => ( ! [X64: $i,X66: $i] :
                                                                                                    ( ( in @ X64 @ ( setadjoin @ X66 @ emptyset ) )
                                                                                                   => ( in @ X66 @ ( setadjoin @ X64 @ emptyset ) ) )
                                                                                               => ( ! [X68: $i,X70: $i,X72: $i] :
                                                                                                      ( ( in @ X72 @ ( setadjoin @ X68 @ ( setadjoin @ X70 @ emptyset ) ) )
                                                                                                     => ( ( X72 = X68 )
                                                                                                        | ( X72 = X70 ) ) )
                                                                                                 => ( ! [X74: $i,X76: $i] : ( in @ X74 @ ( setadjoin @ X74 @ ( setadjoin @ X76 @ emptyset ) ) )
                                                                                                   => ( ! [X78: $i,X80: $i] : ( in @ X80 @ ( setadjoin @ X78 @ ( setadjoin @ X80 @ emptyset ) ) )
                                                                                                     => ( emptyE1
                                                                                                       => ( ! [X82: $i > $o,X84: $i] :
                                                                                                              ( ( in @ X84 @ emptyset )
                                                                                                             => ( X82 @ X84 ) )
                                                                                                         => ( quantDeMorgan1
                                                                                                           => ( quantDeMorgan2
                                                                                                             => ( quantDeMorgan3
                                                                                                               => ( quantDeMorgan4
                                                                                                                 => ( prop2setI
                                                                                                                   => ( prop2set2propI
                                                                                                                     => ( notdexE
                                                                                                                       => ( notdallE
                                                                                                                         => ( exuI1
                                                                                                                           => ( exuI3
                                                                                                                             => ( exuI2
                                                                                                                               => ( inCongP
                                                                                                                                 => ( in__Cong
                                                                                                                                   => ( exuE3u
                                                                                                                                     => ( exu__Cong
                                                                                                                                       => ( ( emptyset = emptyset )
                                                                                                                                         => ( ! [X86: $i,X88: $i] :
                                                                                                                                                ( ( X86 = X88 )
                                                                                                                                               => ! [X90: $i,X92: $i] :
                                                                                                                                                    ( ( X90 = X92 )
                                                                                                                                                   => ( ( setadjoin @ X86 @ X90 )
                                                                                                                                                      = ( setadjoin @ X88 @ X92 ) ) ) )
                                                                                                                                           => ( powerset__Cong
                                                                                                                                             => ( setunion__Cong
                                                                                                                                               => ( omega__Cong
                                                                                                                                                 => ( exuEu
                                                                                                                                                   => ( descr__Cong
                                                                                                                                                     => ( dsetconstr__Cong
                                                                                                                                                       => ( subsetI1
                                                                                                                                                         => ( eqimpsubset2
                                                                                                                                                           => ( eqimpsubset1
                                                                                                                                                             => ( subsetI2
                                                                                                                                                               => ( ! [X94: $i] : ( subset @ emptyset @ X94 )
                                                                                                                                                                 => ( subsetE
                                                                                                                                                                   => ( subsetE2
                                                                                                                                                                     => ( notsubsetI
                                                                                                                                                                       => ( notequalI1
                                                                                                                                                                         => ( notequalI2
                                                                                                                                                                           => ( subsetRefl
                                                                                                                                                                             => ( subsetTrans
                                                                                                                                                                               => ( ! [X96: $i,X98: $i] : ( subset @ X98 @ ( setadjoin @ X96 @ X98 ) )
                                                                                                                                                                                 => ( ! [X100: $i,X102: $i,X104: $i] :
                                                                                                                                                                                        ( ( subset @ X100 @ X104 )
                                                                                                                                                                                       => ( subset @ X100 @ ( setadjoin @ X102 @ X104 ) ) )
                                                                                                                                                                                   => ( subset2powerset
                                                                                                                                                                                     => ( setextsub
                                                                                                                                                                                       => ( ! [X106: $i] :
                                                                                                                                                                                              ( ( subset @ X106 @ emptyset )
                                                                                                                                                                                             => ( X106 = emptyset ) )
                                                                                                                                                                                         => ( powersetI1
                                                                                                                                                                                           => ( powersetE1
                                                                                                                                                                                             => ( inPowerset
                                                                                                                                                                                               => ( powersetsubset
                                                                                                                                                                                                 => ( sepInPowerset
                                                                                                                                                                                                   => ( sepSubset
                                                                                                                                                                                                     => ( binunionIL
                                                                                                                                                                                                       => ( ! [X108: $i,X110: $i] : ( in @ X110 @ ( setadjoin @ X108 @ ( setadjoin @ X110 @ emptyset ) ) )
                                                                                                                                                                                                         => ( 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
                                                                                                                                                                                                                                                                         => ! [X112: $i,X114: $i] : ( in @ X114 @ ( setadjoin @ X112 @ ( setadjoin @ X114 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(zf_stmt_4,negated_conjecture,
    ~ ( setextAx
     => ( ! [X4: $i] :
            ~ ( in @ X4 @ emptyset )
       => ( ! [X6: $i,X8: $i,X10: $i] :
              ( ( in @ X10 @ ( setadjoin @ X6 @ X8 ) )
            <=> ( zip_tseitin_0 @ X10 @ X8 @ X6 ) )
         => ( powersetAx
           => ( setunionAx
             => ( omega0Ax
               => ( omegaSAx
                 => ( omegaIndAx
                   => ( replAx
                     => ( foundationAx
                       => ( wellorderingAx
                         => ( descrp
                           => ( dsetconstrI
                             => ( dsetconstrEL
                               => ( dsetconstrER
                                 => ( exuE1
                                   => ( prop2setE
                                     => ( ! [X12: $i] :
                                            ( ( in @ X12 @ emptyset )
                                           => ! [X14: $o] : X14 )
                                       => ( ! [X16: $i] :
                                              ~ ( in @ X16 @ emptyset )
                                         => ( ! [X18: $i] :
                                                ~ ( in @ X18 @ emptyset )
                                           => ( exuE3e
                                             => ( setext
                                               => ( ! [X20: $i] :
                                                      ( ! [X22: $i] :
                                                          ~ ( in @ X22 @ X20 )
                                                     => ( X20 = emptyset ) )
                                                 => ( ! [X24: $i] :
                                                        ( ! [X26: $i] :
                                                            ~ ( in @ X26 @ X24 )
                                                       => ( X24 = emptyset ) )
                                                   => ( setbeta
                                                     => ( nonemptyE1
                                                       => ( nonemptyI
                                                         => ( nonemptyI1
                                                           => ( ! [X28: $i,X30: $i] : ( in @ X28 @ ( setadjoin @ X28 @ X30 ) )
                                                             => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                               => ( ! [X32: $i,X34: $i,X36: $i] :
                                                                      ( ( in @ X36 @ X34 )
                                                                     => ( in @ X36 @ ( setadjoin @ X32 @ X34 ) ) )
                                                                 => ( ! [X38: $i,X40: $i,X42: $i] :
                                                                        ( ( in @ X42 @ ( setadjoin @ X38 @ X40 ) )
                                                                       => ! [X44: $o] :
                                                                            ( ( ( X42 = X38 )
                                                                             => X44 )
                                                                           => ( ( ( in @ X42 @ X40 )
                                                                               => X44 )
                                                                             => X44 ) ) )
                                                                   => ( ! [X46: $i,X48: $i,X50: $i] :
                                                                          ( ( in @ X50 @ ( setadjoin @ X46 @ X48 ) )
                                                                         => ( ( X50 = X46 )
                                                                            | ( in @ X50 @ X48 ) ) )
                                                                     => ( setoftrueEq
                                                                       => ( powersetI
                                                                         => ( emptyinPowerset
                                                                           => ( emptyInPowerset
                                                                             => ( powersetE
                                                                               => ( setunionI
                                                                                 => ( setunionE
                                                                                   => ( subPowSU
                                                                                     => ( exuE2
                                                                                       => ( nonemptyImpWitness
                                                                                         => ( ! [X52: $i,X54: $i] :
                                                                                                ( ( in @ X52 @ ( setadjoin @ X54 @ emptyset ) )
                                                                                               => ( X52 = X54 ) )
                                                                                           => ( ! [X56: $i,X58: $i] :
                                                                                                  ( ( X56 != X58 )
                                                                                                 => ~ ( in @ X58 @ ( setadjoin @ X56 @ emptyset ) ) )
                                                                                             => ( ! [X60: $i,X62: $i] :
                                                                                                    ( ( X60 = X62 )
                                                                                                   => ( in @ X60 @ ( setadjoin @ X62 @ emptyset ) ) )
                                                                                               => ( ! [X64: $i,X66: $i] :
                                                                                                      ( ( in @ X64 @ ( setadjoin @ X66 @ emptyset ) )
                                                                                                     => ( in @ X66 @ ( setadjoin @ X64 @ emptyset ) ) )
                                                                                                 => ( ! [X68: $i,X70: $i,X72: $i] :
                                                                                                        ( ( in @ X72 @ ( setadjoin @ X68 @ ( setadjoin @ X70 @ emptyset ) ) )
                                                                                                       => ( ( X72 = X68 )
                                                                                                          | ( X72 = X70 ) ) )
                                                                                                   => ( ! [X74: $i,X76: $i] : ( in @ X74 @ ( setadjoin @ X74 @ ( setadjoin @ X76 @ emptyset ) ) )
                                                                                                     => ( ! [X78: $i,X80: $i] : ( in @ X80 @ ( setadjoin @ X78 @ ( setadjoin @ X80 @ emptyset ) ) )
                                                                                                       => ( emptyE1
                                                                                                         => ( ! [X82: $i > $o,X84: $i] :
                                                                                                                ( ( in @ X84 @ emptyset )
                                                                                                               => ( X82 @ X84 ) )
                                                                                                           => ( quantDeMorgan1
                                                                                                             => ( quantDeMorgan2
                                                                                                               => ( quantDeMorgan3
                                                                                                                 => ( quantDeMorgan4
                                                                                                                   => ( prop2setI
                                                                                                                     => ( prop2set2propI
                                                                                                                       => ( notdexE
                                                                                                                         => ( notdallE
                                                                                                                           => ( exuI1
                                                                                                                             => ( exuI3
                                                                                                                               => ( exuI2
                                                                                                                                 => ( inCongP
                                                                                                                                   => ( in__Cong
                                                                                                                                     => ( exuE3u
                                                                                                                                       => ( exu__Cong
                                                                                                                                         => ( ( emptyset = emptyset )
                                                                                                                                           => ( ! [X86: $i,X88: $i] :
                                                                                                                                                  ( ( X86 = X88 )
                                                                                                                                                 => ! [X90: $i,X92: $i] :
                                                                                                                                                      ( ( X90 = X92 )
                                                                                                                                                     => ( ( setadjoin @ X86 @ X90 )
                                                                                                                                                        = ( setadjoin @ X88 @ X92 ) ) ) )
                                                                                                                                             => ( powerset__Cong
                                                                                                                                               => ( setunion__Cong
                                                                                                                                                 => ( omega__Cong
                                                                                                                                                   => ( exuEu
                                                                                                                                                     => ( descr__Cong
                                                                                                                                                       => ( dsetconstr__Cong
                                                                                                                                                         => ( subsetI1
                                                                                                                                                           => ( eqimpsubset2
                                                                                                                                                             => ( eqimpsubset1
                                                                                                                                                               => ( subsetI2
                                                                                                                                                                 => ( ! [X94: $i] : ( subset @ emptyset @ X94 )
                                                                                                                                                                   => ( subsetE
                                                                                                                                                                     => ( subsetE2
                                                                                                                                                                       => ( notsubsetI
                                                                                                                                                                         => ( notequalI1
                                                                                                                                                                           => ( notequalI2
                                                                                                                                                                             => ( subsetRefl
                                                                                                                                                                               => ( subsetTrans
                                                                                                                                                                                 => ( ! [X96: $i,X98: $i] : ( subset @ X98 @ ( setadjoin @ X96 @ X98 ) )
                                                                                                                                                                                   => ( ! [X100: $i,X102: $i,X104: $i] :
                                                                                                                                                                                          ( ( subset @ X100 @ X104 )
                                                                                                                                                                                         => ( subset @ X100 @ ( setadjoin @ X102 @ X104 ) ) )
                                                                                                                                                                                     => ( subset2powerset
                                                                                                                                                                                       => ( setextsub
                                                                                                                                                                                         => ( ! [X106: $i] :
                                                                                                                                                                                                ( ( subset @ X106 @ emptyset )
                                                                                                                                                                                               => ( X106 = emptyset ) )
                                                                                                                                                                                           => ( powersetI1
                                                                                                                                                                                             => ( powersetE1
                                                                                                                                                                                               => ( inPowerset
                                                                                                                                                                                                 => ( powersetsubset
                                                                                                                                                                                                   => ( sepInPowerset
                                                                                                                                                                                                     => ( sepSubset
                                                                                                                                                                                                       => ( binunionIL
                                                                                                                                                                                                         => ( ! [X108: $i,X110: $i] : ( in @ X110 @ ( setadjoin @ X108 @ ( setadjoin @ X110 @ emptyset ) ) )
                                                                                                                                                                                                           => ( 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
                                                                                                                                                                                                                                                                           => ! [X112: $i,X114: $i] : ( in @ X114 @ ( setadjoin @ X112 @ ( setadjoin @ X114 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl70,plain,
    ~ ( in @ sk__56 @ ( setadjoin @ sk__55 @ ( setadjoin @ sk__56 @ emptyset ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl87,plain,
    ! [X27: $i,X28: $i] : ( in @ X27 @ ( setadjoin @ X28 @ ( setadjoin @ X27 @ emptyset ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl188,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl70,zip_derived_cl87]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU616^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.YsarDXRWCv true
% 0.13/0.34  % Computer : n018.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Wed Aug 23 15:15:56 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  % Running portfolio for 300 s
% 0.13/0.34  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34  % Number of cores: 8
% 0.13/0.34  % Python version: Python 3.6.8
% 0.20/0.34  % Running in HO mode
% 0.20/0.66  % Total configuration time : 828
% 0.20/0.66  % Estimated wc time : 1656
% 0.20/0.66  % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.69  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.20/0.71  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.20/0.74  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.20/0.74  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.20/0.74  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.20/0.74  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.20/0.74  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.20/0.75  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.42/0.83  % Solved by lams/40_c_ic.sh.
% 1.42/0.83  % done 134 iterations in 0.055s
% 1.42/0.83  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.42/0.83  % SZS output start Refutation
% See solution above
% 1.42/0.83  
% 1.42/0.83  
% 1.42/0.83  % Terminating...
% 1.77/0.95  % Runner terminated.
% 1.77/0.96  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------