TSTP Solution File: SEU531^1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU531^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Hre7LVZcP4 true

% Computer : n004.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 19:13:36 EDT 2023

% Result   : Theorem 1.26s 0.84s
% Output   : Refutation 1.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   79
% Syntax   : Number of formulae    :   90 (  27 unt;  55 typ;   0 def)
%            Number of atoms       :  332 (  64 equ;   0 cnn)
%            Maximal formula atoms :   61 (   9 avg)
%            Number of connectives :  604 (  15   ~;  17   |;   0   &; 319   @)
%                                         (   6 <=>; 247  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   57 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   56 (  54 usr;  52 con; 0-3 aty)
%            Number of variables   :  135 (   0   ^; 135   !;   0   ?; 135   :)

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

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

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

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

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

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

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

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

thf(sk__23_type,type,
    sk__23: $i ).

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

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

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

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

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

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

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

thf(sk__24_type,type,
    sk__24: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(sk__25_type,type,
    sk__25: $i ).

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

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

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

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

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

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

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

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

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

thf('0',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('1',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('2',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('3',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('4',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('5',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('6',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('7',plain,
    ( emptyinunitempty
    = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
    inference(simplify_rw_rule,[status(thm)],[emptyinunitempty]) ).

thf('8',plain,
    ( emptyinunitempty
    = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
    define([status(thm)]) ).

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

thf('9',plain,
    ( setadjoinIL
    = ( ! [X4: $i,X6: $i] : ( in @ X4 @ ( setadjoin @ X4 @ 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('10',plain,
    ( setadjoinAx
    = ( ! [X4: $i,X6: $i,X8: $i] :
          ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) )
        <=> ( ( X8 = X4 )
            | ( in @ X8 @ X6 ) ) ) ) ),
    define([status(thm)]) ).

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

thf(zf_stmt_0,conjecture,
    ( setextAx
   => ( emptysetAx
     => ( ! [X4: $i,X6: $i,X8: $i] :
            ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) )
          <=> ( ( in @ X8 @ X6 )
              | ( X8 = X4 ) ) )
       => ( 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
                                                         => ( ! [X10: $i,X12: $i] : ( in @ X10 @ ( setadjoin @ X10 @ X12 ) )
                                                           => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                             => ( ! [X14: $i,X16: $i,X18: $i] :
                                                                    ( ( in @ X18 @ X16 )
                                                                   => ( in @ X18 @ ( setadjoin @ X14 @ X16 ) ) )
                                                               => ( ! [X20: $i,X22: $i,X24: $i] :
                                                                      ( ( in @ X24 @ ( setadjoin @ X20 @ X22 ) )
                                                                     => ! [X26: $o] :
                                                                          ( ( ( X24 = X20 )
                                                                           => X26 )
                                                                         => ( ( ( in @ X24 @ X22 )
                                                                             => X26 )
                                                                           => X26 ) ) )
                                                                 => ( ! [X28: $i,X30: $i,X32: $i] :
                                                                        ( ( in @ X32 @ ( setadjoin @ X28 @ X30 ) )
                                                                       => ( ( in @ X32 @ X30 )
                                                                          | ( X32 = X28 ) ) )
                                                                   => ( setoftrueEq
                                                                     => ( powersetI
                                                                       => ( emptyinPowerset
                                                                         => ( emptyInPowerset
                                                                           => ( powersetE
                                                                             => ( setunionI
                                                                               => ( setunionE
                                                                                 => ( subPowSU
                                                                                   => ( exuE2
                                                                                     => ( nonemptyImpWitness
                                                                                       => ( ! [X34: $i,X36: $i] :
                                                                                              ( ( in @ X34 @ ( setadjoin @ X36 @ emptyset ) )
                                                                                             => ( X34 = X36 ) )
                                                                                         => ( ! [X38: $i,X40: $i] :
                                                                                                ( ( X38 != X40 )
                                                                                               => ~ ( in @ X40 @ ( setadjoin @ X38 @ emptyset ) ) )
                                                                                           => ( ! [X42: $i,X44: $i] :
                                                                                                  ( ( X42 = X44 )
                                                                                                 => ( in @ X42 @ ( setadjoin @ X44 @ emptyset ) ) )
                                                                                             => ( ! [X46: $i,X48: $i] :
                                                                                                    ( ( in @ X46 @ ( setadjoin @ X48 @ emptyset ) )
                                                                                                   => ( in @ X48 @ ( setadjoin @ X46 @ emptyset ) ) )
                                                                                               => ! [X50: $i,X52: $i,X54: $i] :
                                                                                                    ( ( in @ X54 @ ( setadjoin @ X50 @ ( setadjoin @ X52 @ emptyset ) ) )
                                                                                                   => ( ( X54 = X52 )
                                                                                                      | ( X54 = X50 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

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

thf(zf_stmt_2,axiom,
    ! [X8: $i,X6: $i,X4: $i] :
      ( ( zip_tseitin_0 @ X8 @ X6 @ X4 )
    <=> ( ( X8 = X4 )
        | ( in @ X8 @ X6 ) ) ) ).

thf(zf_stmt_3,conjecture,
    ( setextAx
   => ( emptysetAx
     => ( ! [X4: $i,X6: $i,X8: $i] :
            ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) )
          <=> ( zip_tseitin_0 @ X8 @ X6 @ X4 ) )
       => ( 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
                                                         => ( ! [X10: $i,X12: $i] : ( in @ X10 @ ( setadjoin @ X10 @ X12 ) )
                                                           => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                             => ( ! [X14: $i,X16: $i,X18: $i] :
                                                                    ( ( in @ X18 @ X16 )
                                                                   => ( in @ X18 @ ( setadjoin @ X14 @ X16 ) ) )
                                                               => ( ! [X20: $i,X22: $i,X24: $i] :
                                                                      ( ( in @ X24 @ ( setadjoin @ X20 @ X22 ) )
                                                                     => ! [X26: $o] :
                                                                          ( ( ( X24 = X20 )
                                                                           => X26 )
                                                                         => ( ( ( in @ X24 @ X22 )
                                                                             => X26 )
                                                                           => X26 ) ) )
                                                                 => ( ! [X28: $i,X30: $i,X32: $i] :
                                                                        ( ( in @ X32 @ ( setadjoin @ X28 @ X30 ) )
                                                                       => ( ( X32 = X28 )
                                                                          | ( in @ X32 @ X30 ) ) )
                                                                   => ( setoftrueEq
                                                                     => ( powersetI
                                                                       => ( emptyinPowerset
                                                                         => ( emptyInPowerset
                                                                           => ( powersetE
                                                                             => ( setunionI
                                                                               => ( setunionE
                                                                                 => ( subPowSU
                                                                                   => ( exuE2
                                                                                     => ( nonemptyImpWitness
                                                                                       => ( ! [X34: $i,X36: $i] :
                                                                                              ( ( in @ X34 @ ( setadjoin @ X36 @ emptyset ) )
                                                                                             => ( X34 = X36 ) )
                                                                                         => ( ! [X38: $i,X40: $i] :
                                                                                                ( ( X38 != X40 )
                                                                                               => ~ ( in @ X40 @ ( setadjoin @ X38 @ emptyset ) ) )
                                                                                           => ( ! [X42: $i,X44: $i] :
                                                                                                  ( ( X42 = X44 )
                                                                                                 => ( in @ X42 @ ( setadjoin @ X44 @ emptyset ) ) )
                                                                                             => ( ! [X46: $i,X48: $i] :
                                                                                                    ( ( in @ X46 @ ( setadjoin @ X48 @ emptyset ) )
                                                                                                   => ( in @ X48 @ ( setadjoin @ X46 @ emptyset ) ) )
                                                                                               => ! [X50: $i,X52: $i,X54: $i] :
                                                                                                    ( ( in @ X54 @ ( setadjoin @ X50 @ ( setadjoin @ X52 @ emptyset ) ) )
                                                                                                   => ( ( X54 = X50 )
                                                                                                      | ( X54 = X52 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(zf_stmt_4,negated_conjecture,
    ~ ( setextAx
     => ( emptysetAx
       => ( ! [X4: $i,X6: $i,X8: $i] :
              ( ( in @ X8 @ ( setadjoin @ X4 @ X6 ) )
            <=> ( zip_tseitin_0 @ X8 @ X6 @ X4 ) )
         => ( 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
                                                           => ( ! [X10: $i,X12: $i] : ( in @ X10 @ ( setadjoin @ X10 @ X12 ) )
                                                             => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                               => ( ! [X14: $i,X16: $i,X18: $i] :
                                                                      ( ( in @ X18 @ X16 )
                                                                     => ( in @ X18 @ ( setadjoin @ X14 @ X16 ) ) )
                                                                 => ( ! [X20: $i,X22: $i,X24: $i] :
                                                                        ( ( in @ X24 @ ( setadjoin @ X20 @ X22 ) )
                                                                       => ! [X26: $o] :
                                                                            ( ( ( X24 = X20 )
                                                                             => X26 )
                                                                           => ( ( ( in @ X24 @ X22 )
                                                                               => X26 )
                                                                             => X26 ) ) )
                                                                   => ( ! [X28: $i,X30: $i,X32: $i] :
                                                                          ( ( in @ X32 @ ( setadjoin @ X28 @ X30 ) )
                                                                         => ( ( X32 = X28 )
                                                                            | ( in @ X32 @ X30 ) ) )
                                                                     => ( setoftrueEq
                                                                       => ( powersetI
                                                                         => ( emptyinPowerset
                                                                           => ( emptyInPowerset
                                                                             => ( powersetE
                                                                               => ( setunionI
                                                                                 => ( setunionE
                                                                                   => ( subPowSU
                                                                                     => ( exuE2
                                                                                       => ( nonemptyImpWitness
                                                                                         => ( ! [X34: $i,X36: $i] :
                                                                                                ( ( in @ X34 @ ( setadjoin @ X36 @ emptyset ) )
                                                                                               => ( X34 = X36 ) )
                                                                                           => ( ! [X38: $i,X40: $i] :
                                                                                                  ( ( X38 != X40 )
                                                                                                 => ~ ( in @ X40 @ ( setadjoin @ X38 @ emptyset ) ) )
                                                                                             => ( ! [X42: $i,X44: $i] :
                                                                                                    ( ( X42 = X44 )
                                                                                                   => ( in @ X42 @ ( setadjoin @ X44 @ emptyset ) ) )
                                                                                               => ( ! [X46: $i,X48: $i] :
                                                                                                      ( ( in @ X46 @ ( setadjoin @ X48 @ emptyset ) )
                                                                                                     => ( in @ X48 @ ( setadjoin @ X46 @ emptyset ) ) )
                                                                                                 => ! [X50: $i,X52: $i,X54: $i] :
                                                                                                      ( ( in @ X54 @ ( setadjoin @ X50 @ ( setadjoin @ X52 @ emptyset ) ) )
                                                                                                     => ( ( X54 = X50 )
                                                                                                        | ( X54 = X52 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl26,plain,
    ! [X12: $i,X13: $i] :
      ( ~ ( in @ X12 @ ( setadjoin @ X13 @ emptyset ) )
      | ( X13 = X12 ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl30,plain,
    in @ sk__25 @ ( setadjoin @ sk__23 @ ( setadjoin @ sk__24 @ emptyset ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl20,plain,
    ! [X9: $i,X10: $i,X11: $i] :
      ( ( in @ X9 @ X10 )
      | ( X9 = X11 )
      | ~ ( in @ X9 @ ( setadjoin @ X11 @ X10 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl140,plain,
    ( ( sk__25 = sk__23 )
    | ( in @ sk__25 @ ( setadjoin @ sk__24 @ emptyset ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl20]) ).

thf(zip_derived_cl29,plain,
    sk__25 != sk__23,
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl146,plain,
    in @ sk__25 @ ( setadjoin @ sk__24 @ emptyset ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl140,zip_derived_cl29]) ).

thf(zip_derived_cl150,plain,
    sk__24 = sk__25,
    inference('sup+',[status(thm)],[zip_derived_cl26,zip_derived_cl146]) ).

thf(zip_derived_cl28,plain,
    sk__25 != sk__24,
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl154,plain,
    $false,
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl150,zip_derived_cl28]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU531^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Hre7LVZcP4 true
% 0.14/0.34  % Computer : n004.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Wed Aug 23 15:32:08 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.14/0.34  % Running portfolio for 300 s
% 0.14/0.34  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35  % Number of cores: 8
% 0.14/0.35  % Python version: Python 3.6.8
% 0.14/0.35  % Running in HO mode
% 0.21/0.67  % Total configuration time : 828
% 0.21/0.67  % Estimated wc time : 1656
% 0.21/0.67  % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.71  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.75  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.75  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.75  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.21/0.77  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.21/0.77  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 1.26/0.84  % Solved by lams/40_c_ic.sh.
% 1.26/0.84  % done 77 iterations in 0.040s
% 1.26/0.84  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.26/0.84  % SZS output start Refutation
% See solution above
% 1.26/0.84  
% 1.26/0.84  
% 1.26/0.84  % Terminating...
% 1.59/0.87  % Runner terminated.
% 1.59/0.88  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------