TSTP Solution File: SEU519^1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU519^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n003.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 : Tue May 21 03:42:26 EDT 2024

% Result   : Theorem 8.12s 2.73s
% Output   : Refutation 8.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   80
% Syntax   : Number of formulae    :   95 (  43 unt;  44 typ;  35 def)
%            Number of atoms       :  497 ( 102 equ;   0 cnn)
%            Maximal formula atoms :   91 (   9 avg)
%            Number of connectives : 1116 (  38   ~;  15   |;  55   &; 709   @)
%                                         (   0 <=>; 299  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   43 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   37 (  37   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   51 (  48 usr;  45 con; 0-2 aty)
%            Number of variables   :  336 (   5   ^ 275   !;  56   ?; 336   :)

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

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

thf(setextAx_def,definition,
    ( setextAx
    = ( ! [A: $i,B: $i] :
          ( ! [C: $i] :
              ( ( in @ C @ A )
              = ( in @ C @ B ) )
         => ( A = B ) ) ) ) ).

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

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

thf(emptysetAx_def,definition,
    ( emptysetAx
    = ( ! [A: $i] :
          ~ ( in @ A @ emptyset ) ) ) ).

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

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

thf(setadjoinAx_def,definition,
    ( setadjoinAx
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( in @ C @ ( setadjoin @ A @ B ) )
          = ( ( C = A )
            | ( in @ C @ B ) ) ) ) ) ).

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

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

thf(powersetAx_def,definition,
    ( powersetAx
    = ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
          = ( ! [C: $i] :
                ( ( in @ C @ B )
               => ( in @ C @ A ) ) ) ) ) ) ).

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

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

thf(setunionAx_def,definition,
    ( setunionAx
    = ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( setunion @ A ) )
          = ( ? [C: $i] :
                ( ( in @ B @ C )
                & ( in @ C @ A ) ) ) ) ) ) ).

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

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

thf(omega0Ax_def,definition,
    ( omega0Ax
    = ( in @ emptyset @ omega ) ) ).

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

thf(omegaSAx_def,definition,
    ( omegaSAx
    = ( ! [A: $i] :
          ( ( in @ A @ omega )
         => ( in @ ( setadjoin @ A @ A ) @ omega ) ) ) ) ).

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

thf(omegaIndAx_def,definition,
    ( omegaIndAx
    = ( ! [A: $i] :
          ( ( ( in @ emptyset @ A )
            & ! [B: $i] :
                ( ( ( in @ B @ omega )
                  & ( in @ B @ A ) )
               => ( in @ ( setadjoin @ B @ B ) @ A ) ) )
         => ! [B: $i] :
              ( ( in @ B @ omega )
             => ( in @ B @ A ) ) ) ) ) ).

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

thf(replAx_def,definition,
    ( replAx
    = ( ! [A: $i > $i > $o,B: $i] :
          ( ! [C: $i] :
              ( ( in @ C @ B )
             => ( exu @ ( A @ C ) ) )
         => ? [C: $i] :
            ! [D: $i] :
              ( ( in @ D @ C )
              = ( ? [E: $i] :
                    ( ( in @ E @ B )
                    & ( A @ E @ D ) ) ) ) ) ) ) ).

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

thf(foundationAx_def,definition,
    ( foundationAx
    = ( ! [A: $i] :
          ( ? [B: $i] : ( in @ B @ A )
         => ? [B: $i] :
              ( ( in @ B @ A )
              & ~ ? [C: $i] :
                    ( ( in @ C @ B )
                    & ( in @ C @ A ) ) ) ) ) ) ).

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

thf(wellorderingAx_def,definition,
    ( wellorderingAx
    = ( ! [A: $i] :
        ? [B: $i] :
          ( ! [C: $i] :
              ( ( in @ C @ B )
             => ! [D: $i] :
                  ( ( in @ D @ C )
                 => ( in @ D @ A ) ) )
          & ! [C: $i,D: $i] :
              ( ( ( in @ C @ A )
                & ( in @ D @ A ) )
             => ( ! [E: $i] :
                    ( ( in @ E @ B )
                   => ( ( in @ C @ E )
                      = ( in @ D @ E ) ) )
               => ( C = D ) ) )
          & ! [C: $i,D: $i] :
              ( ( ( in @ C @ B )
                & ( in @ D @ B ) )
             => ( ! [E: $i] :
                    ( ( in @ E @ C )
                   => ( in @ E @ D ) )
                | ! [E: $i] :
                    ( ( in @ E @ D )
                   => ( in @ E @ C ) ) ) )
          & ! [C: $i] :
              ( ( ! [D: $i] :
                    ( ( in @ D @ C )
                   => ( in @ D @ A ) )
                & ? [D: $i] : ( in @ D @ C ) )
             => ? [D: $i,E: $i] :
                  ( ( in @ D @ B )
                  & ( in @ E @ C )
                  & ~ ? [F: $i] :
                        ( ( in @ F @ D )
                        & ( in @ F @ C ) )
                  & ! [F: $i] :
                      ( ( in @ F @ B )
                     => ( ! [G: $i] :
                            ( ( in @ G @ F )
                           => ( in @ G @ D ) )
                        | ( in @ E @ F ) ) ) ) ) ) ) ) ).

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

thf(descrp_def,definition,
    ( descrp
    = ( ! [A: $i > $o] :
          ( ( exu @ A )
         => ( A @ ( descr @ A ) ) ) ) ) ).

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

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

thf(dsetconstrI_def,definition,
    ( dsetconstrI
    = ( ! [A: $i,B: $i > $o,C: $i] :
          ( ( in @ C @ A )
         => ( ( B @ C )
           => ( in @ C @ ( dsetconstr @ A @ B ) ) ) ) ) ) ).

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

thf(dsetconstrEL_def,definition,
    ( dsetconstrEL
    = ( ! [A: $i,B: $i > $o,C: $i] :
          ( ( in @ C @ ( dsetconstr @ A @ B ) )
         => ( in @ C @ A ) ) ) ) ).

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

thf(dsetconstrER_def,definition,
    ( dsetconstrER
    = ( ! [A: $i,B: $i > $o,C: $i] :
          ( ( in @ C @ ( dsetconstr @ A @ B ) )
         => ( B @ C ) ) ) ) ).

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

thf(exuE1_def,definition,
    ( exuE1
    = ( ! [A: $i > $o] :
          ( ( exu @ A )
         => ? [B: $i] :
              ( ( A @ B )
              & ! [C: $i] :
                  ( ( A @ C )
                 => ( B = C ) ) ) ) ) ) ).

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

thf(prop2setE_def,definition,
    ( prop2setE
    = ( ! [A: $o,B: $i] :
          ( ( in @ B @ ( prop2set @ A ) )
         => A ) ) ) ).

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

thf(emptysetE_def,definition,
    ( emptysetE
    = ( ! [A: $i] :
          ( ( in @ A @ emptyset )
         => ! [B: $o] : B ) ) ) ).

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

thf(emptysetimpfalse_def,definition,
    ( emptysetimpfalse
    = ( ! [A: $i] :
          ( ( in @ A @ emptyset )
         => $false ) ) ) ).

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

thf(notinemptyset_def,definition,
    ( notinemptyset
    = ( ! [A: $i] :
          ~ ( in @ A @ emptyset ) ) ) ).

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

thf(exuE3e_def,definition,
    ( exuE3e
    = ( ! [A: $i > $o] :
          ( ( exu @ A )
         => ? [B: $i] : ( A @ B ) ) ) ) ).

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

thf(setext_def,definition,
    ( setext
    = ( ! [A: $i,B: $i] :
          ( ! [C: $i] :
              ( ( in @ C @ A )
             => ( in @ C @ B ) )
         => ( ! [C: $i] :
                ( ( in @ C @ B )
               => ( in @ C @ A ) )
           => ( A = B ) ) ) ) ) ).

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

thf(emptyI_def,definition,
    ( emptyI
    = ( ! [A: $i] :
          ( ! [B: $i] :
              ~ ( in @ B @ A )
         => ( A = emptyset ) ) ) ) ).

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

thf(noeltsimpempty_def,definition,
    ( noeltsimpempty
    = ( ! [A: $i] :
          ( ! [B: $i] :
              ~ ( in @ B @ A )
         => ( A = emptyset ) ) ) ) ).

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

thf(setbeta_def,definition,
    ( setbeta
    = ( ! [A: $i,B: $i > $o,C: $i] :
          ( ( in @ C @ A )
         => ( ( in @ C @ ( dsetconstr @ A @ B ) )
            = ( B @ C ) ) ) ) ) ).

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

thf(nonemptyE1_def,definition,
    ( nonemptyE1
    = ( ! [A: $i] :
          ( ( nonempty @ A )
         => ? [B: $i] : ( in @ B @ A ) ) ) ) ).

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

thf(nonemptyI_def,definition,
    ( nonemptyI
    = ( ! [A: $i,B: $i > $o,C: $i] :
          ( ( in @ C @ A )
         => ( ( B @ C )
           => ( nonempty @ ( dsetconstr @ A @ B ) ) ) ) ) ) ).

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

thf(nonemptyI1_def,definition,
    ( nonemptyI1
    = ( ! [A: $i] :
          ( ? [B: $i] : ( in @ B @ A )
         => ( nonempty @ A ) ) ) ) ).

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

thf(setadjoinIL_def,definition,
    ( setadjoinIL
    = ( ! [A: $i,B: $i] : ( in @ A @ ( setadjoin @ A @ B ) ) ) ) ).

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

thf(emptyinunitempty_def,definition,
    ( emptyinunitempty
    = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).

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

thf(setadjoinIR_def,definition,
    ( setadjoinIR
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( in @ C @ B )
         => ( in @ C @ ( setadjoin @ A @ B ) ) ) ) ) ).

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

thf(setadjoinE_def,definition,
    ( setadjoinE
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( in @ C @ ( setadjoin @ A @ B ) )
         => ! [D: $o] :
              ( ( ( C = A )
               => D )
             => ( ( ( in @ C @ B )
                 => D )
               => D ) ) ) ) ) ).

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

thf(setadjoinOr_def,definition,
    ( setadjoinOr
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( in @ C @ ( setadjoin @ A @ B ) )
         => ( ( C = A )
            | ( in @ C @ B ) ) ) ) ) ).

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

thf(setoftrueEq_def,definition,
    ( setoftrueEq
    = ( ! [A: $i] :
          ( ( dsetconstr @ A
            @ ^ [B: $i] : $true )
          = A ) ) ) ).

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

thf(powersetI_def,definition,
    ( powersetI
    = ( ! [A: $i,B: $i] :
          ( ! [C: $i] :
              ( ( in @ C @ B )
             => ( in @ C @ A ) )
         => ( in @ B @ ( powerset @ A ) ) ) ) ) ).

thf(sk22_type,type,
    sk22: $i ).

thf(sk26_type,type,
    sk26: $i ).

thf(1,conjecture,
    ( setextAx
   => ( emptysetAx
     => ( setadjoinAx
       => ( powersetAx
         => ( setunionAx
           => ( omega0Ax
             => ( omegaSAx
               => ( omegaIndAx
                 => ( replAx
                   => ( foundationAx
                     => ( wellorderingAx
                       => ( descrp
                         => ( dsetconstrI
                           => ( dsetconstrEL
                             => ( dsetconstrER
                               => ( exuE1
                                 => ( prop2setE
                                   => ( emptysetE
                                     => ( emptysetimpfalse
                                       => ( notinemptyset
                                         => ( exuE3e
                                           => ( setext
                                             => ( emptyI
                                               => ( noeltsimpempty
                                                 => ( setbeta
                                                   => ( nonemptyE1
                                                     => ( nonemptyI
                                                       => ( nonemptyI1
                                                         => ( setadjoinIL
                                                           => ( emptyinunitempty
                                                             => ( setadjoinIR
                                                               => ( setadjoinE
                                                                 => ( setadjoinOr
                                                                   => ( setoftrueEq
                                                                     => ( powersetI
                                                                       => ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset) ).

thf(2,negated_conjecture,
    ~ ( setextAx
     => ( emptysetAx
       => ( setadjoinAx
         => ( powersetAx
           => ( setunionAx
             => ( omega0Ax
               => ( omegaSAx
                 => ( omegaIndAx
                   => ( replAx
                     => ( foundationAx
                       => ( wellorderingAx
                         => ( descrp
                           => ( dsetconstrI
                             => ( dsetconstrEL
                               => ( dsetconstrER
                                 => ( exuE1
                                   => ( prop2setE
                                     => ( emptysetE
                                       => ( emptysetimpfalse
                                         => ( notinemptyset
                                           => ( exuE3e
                                             => ( setext
                                               => ( emptyI
                                                 => ( noeltsimpempty
                                                   => ( setbeta
                                                     => ( nonemptyE1
                                                       => ( nonemptyI
                                                         => ( nonemptyI1
                                                           => ( setadjoinIL
                                                             => ( emptyinunitempty
                                                               => ( setadjoinIR
                                                                 => ( setadjoinE
                                                                   => ( setadjoinOr
                                                                     => ( setoftrueEq
                                                                       => ( powersetI
                                                                         => ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ! [A: $i,B: $i] :
          ( ! [C: $i] :
              ( ( in @ C @ A )
              = ( in @ C @ B ) )
         => ( A = B ) )
     => ( ! [A: $i] :
            ~ ( in @ A @ emptyset )
       => ( ! [A: $i,B: $i,C: $i] :
              ( ( in @ C @ ( setadjoin @ A @ B ) )
              = ( ( C = A )
                | ( in @ C @ B ) ) )
         => ( ! [A: $i,B: $i] :
                ( ( in @ B @ ( powerset @ A ) )
                = ( ! [C: $i] :
                      ( ( in @ C @ B )
                     => ( in @ C @ A ) ) ) )
           => ( ! [A: $i,B: $i] :
                  ( ( in @ B @ ( setunion @ A ) )
                  = ( ? [C: $i] :
                        ( ( in @ B @ C )
                        & ( in @ C @ A ) ) ) )
             => ( ( in @ emptyset @ omega )
               => ( ! [A: $i] :
                      ( ( in @ A @ omega )
                     => ( in @ ( setadjoin @ A @ A ) @ omega ) )
                 => ( ! [A: $i] :
                        ( ( ( in @ emptyset @ A )
                          & ! [B: $i] :
                              ( ( ( in @ B @ omega )
                                & ( in @ B @ A ) )
                             => ( in @ ( setadjoin @ B @ B ) @ A ) ) )
                       => ! [B: $i] :
                            ( ( in @ B @ omega )
                           => ( in @ B @ A ) ) )
                   => ( ! [A: $i > $i > $o,B: $i] :
                          ( ! [C: $i] :
                              ( ( in @ C @ B )
                             => ? [D: $i] :
                                  ( ( A @ C @ D )
                                  & ! [E: $i] :
                                      ( ( A @ C @ E )
                                     => ( D = E ) ) ) )
                         => ? [C: $i] :
                            ! [D: $i] :
                              ( ( in @ D @ C )
                              = ( ? [E: $i] :
                                    ( ( in @ E @ B )
                                    & ( A @ E @ D ) ) ) ) )
                     => ( ! [A: $i] :
                            ( ? [B: $i] : ( in @ B @ A )
                           => ? [B: $i] :
                                ( ( in @ B @ A )
                                & ~ ? [C: $i] :
                                      ( ( in @ C @ B )
                                      & ( in @ C @ A ) ) ) )
                       => ( ! [A: $i] :
                            ? [B: $i] :
                              ( ! [C: $i] :
                                  ( ( in @ C @ B )
                                 => ! [D: $i] :
                                      ( ( in @ D @ C )
                                     => ( in @ D @ A ) ) )
                              & ! [C: $i,D: $i] :
                                  ( ( ( in @ C @ A )
                                    & ( in @ D @ A ) )
                                 => ( ! [E: $i] :
                                        ( ( in @ E @ B )
                                       => ( ( in @ C @ E )
                                          = ( in @ D @ E ) ) )
                                   => ( C = D ) ) )
                              & ! [C: $i,D: $i] :
                                  ( ( ( in @ C @ B )
                                    & ( in @ D @ B ) )
                                 => ( ! [E: $i] :
                                        ( ( in @ E @ C )
                                       => ( in @ E @ D ) )
                                    | ! [E: $i] :
                                        ( ( in @ E @ D )
                                       => ( in @ E @ C ) ) ) )
                              & ! [C: $i] :
                                  ( ( ! [D: $i] :
                                        ( ( in @ D @ C )
                                       => ( in @ D @ A ) )
                                    & ? [D: $i] : ( in @ D @ C ) )
                                 => ? [D: $i,E: $i] :
                                      ( ( in @ D @ B )
                                      & ( in @ E @ C )
                                      & ~ ? [F: $i] :
                                            ( ( in @ F @ D )
                                            & ( in @ F @ C ) )
                                      & ! [F: $i] :
                                          ( ( in @ F @ B )
                                         => ( ! [G: $i] :
                                                ( ( in @ G @ F )
                                               => ( in @ G @ D ) )
                                            | ( in @ E @ F ) ) ) ) ) )
                         => ( ! [A: $i > $o] :
                                ( ? [B: $i] :
                                    ( ( A @ B )
                                    & ! [C: $i] :
                                        ( ( A @ C )
                                       => ( B = C ) ) )
                               => ( A @ ( descr @ A ) ) )
                           => ( ! [A: $i,B: $i > $o,C: $i] :
                                  ( ( in @ C @ A )
                                 => ( ( B @ C )
                                   => ( in @ C @ ( dsetconstr @ A @ B ) ) ) )
                             => ( ! [A: $i,B: $i > $o,C: $i] :
                                    ( ( in @ C @ ( dsetconstr @ A @ B ) )
                                   => ( in @ C @ A ) )
                               => ( ! [A: $i,B: $i > $o,C: $i] :
                                      ( ( in @ C @ ( dsetconstr @ A @ B ) )
                                     => ( B @ C ) )
                                 => ( ! [A: $o,B: $i] :
                                        ( ( in @ B
                                          @ ( dsetconstr @ ( powerset @ emptyset )
                                            @ ^ [C: $i] : A ) )
                                       => A )
                                   => ( ! [A: $i] :
                                          ( ( in @ A @ emptyset )
                                         => ! [B: $o] : B )
                                     => ( ! [A: $i] :
                                            ~ ( in @ A @ emptyset )
                                       => ( ! [A: $i] :
                                              ~ ( in @ A @ emptyset )
                                         => ( ! [A: $i > $o] :
                                                ( ? [B: $i] :
                                                    ( ( A @ B )
                                                    & ! [C: $i] :
                                                        ( ( A @ C )
                                                       => ( B = C ) ) )
                                               => ? [B: $i] : ( A @ B ) )
                                           => ( ! [A: $i,B: $i] :
                                                  ( ! [C: $i] :
                                                      ( ( in @ C @ A )
                                                     => ( in @ C @ B ) )
                                                 => ( ! [C: $i] :
                                                        ( ( in @ C @ B )
                                                       => ( in @ C @ A ) )
                                                   => ( A = B ) ) )
                                             => ( ! [A: $i] :
                                                    ( ! [B: $i] :
                                                        ~ ( in @ B @ A )
                                                   => ( A = emptyset ) )
                                               => ( ! [A: $i] :
                                                      ( ! [B: $i] :
                                                          ~ ( in @ B @ A )
                                                     => ( A = emptyset ) )
                                                 => ( ! [A: $i,B: $i > $o,C: $i] :
                                                        ( ( in @ C @ A )
                                                       => ( ( in @ C @ ( dsetconstr @ A @ B ) )
                                                          = ( B @ C ) ) )
                                                   => ( ! [A: $i] :
                                                          ( ( A != emptyset )
                                                         => ? [B: $i] : ( in @ B @ A ) )
                                                     => ( ! [A: $i,B: $i > $o,C: $i] :
                                                            ( ( in @ C @ A )
                                                           => ( ( B @ C )
                                                             => ( ( dsetconstr @ A @ B )
                                                               != emptyset ) ) )
                                                       => ( ! [A: $i] :
                                                              ( ? [B: $i] : ( in @ B @ A )
                                                             => ( A != emptyset ) )
                                                         => ( ! [A: $i,B: $i] : ( in @ A @ ( setadjoin @ A @ B ) )
                                                           => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                             => ( ! [A: $i,B: $i,C: $i] :
                                                                    ( ( in @ C @ B )
                                                                   => ( in @ C @ ( setadjoin @ A @ B ) ) )
                                                               => ( ! [A: $i,B: $i,C: $i] :
                                                                      ( ( in @ C @ ( setadjoin @ A @ B ) )
                                                                     => ! [D: $o] :
                                                                          ( ( ( C = A )
                                                                           => D )
                                                                         => ( ( ( in @ C @ B )
                                                                             => D )
                                                                           => D ) ) )
                                                                 => ( ! [A: $i,B: $i,C: $i] :
                                                                        ( ( in @ C @ ( setadjoin @ A @ B ) )
                                                                       => ( ( C = A )
                                                                          | ( in @ C @ B ) ) )
                                                                   => ( ! [A: $i] :
                                                                          ( ( dsetconstr @ A
                                                                            @ ^ [B: $i] : $true )
                                                                          = A )
                                                                     => ( ! [A: $i,B: $i] :
                                                                            ( ! [C: $i] :
                                                                                ( ( in @ C @ B )
                                                                               => ( in @ C @ A ) )
                                                                           => ( in @ B @ ( powerset @ A ) ) )
                                                                       => ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ~ ( ! [A: $i,B: $i] :
          ( ! [C: $i] :
              ( ( in @ C @ A )
              = ( in @ C @ B ) )
         => ( A = B ) )
     => ( ~ ? [A: $i] : ( in @ A @ emptyset )
       => ( ! [A: $i,B: $i,C: $i] :
              ( ( in @ C @ ( setadjoin @ A @ B ) )
              = ( ( C = A )
                | ( in @ C @ B ) ) )
         => ( ! [A: $i,B: $i] :
                ( ( in @ B @ ( powerset @ A ) )
                = ( ! [C: $i] :
                      ( ( in @ C @ B )
                     => ( in @ C @ A ) ) ) )
           => ( ! [A: $i,B: $i] :
                  ( ( in @ B @ ( setunion @ A ) )
                  = ( ? [C: $i] :
                        ( ( in @ B @ C )
                        & ( in @ C @ A ) ) ) )
             => ( ( in @ emptyset @ omega )
               => ( ! [A: $i] :
                      ( ( in @ A @ omega )
                     => ( in @ ( setadjoin @ A @ A ) @ omega ) )
                 => ( ! [A: $i] :
                        ( ( ( in @ emptyset @ A )
                          & ! [B: $i] :
                              ( ( ( in @ B @ omega )
                                & ( in @ B @ A ) )
                             => ( in @ ( setadjoin @ B @ B ) @ A ) ) )
                       => ! [B: $i] :
                            ( ( in @ B @ omega )
                           => ( in @ B @ A ) ) )
                   => ( ! [A: $i > $i > $o,B: $i] :
                          ( ! [C: $i] :
                              ( ( in @ C @ B )
                             => ? [D: $i] :
                                  ( ( A @ C @ D )
                                  & ! [E: $i] :
                                      ( ( A @ C @ E )
                                     => ( D = E ) ) ) )
                         => ? [C: $i] :
                            ! [D: $i] :
                              ( ( in @ D @ C )
                              = ( ? [E: $i] :
                                    ( ( in @ E @ B )
                                    & ( A @ E @ D ) ) ) ) )
                     => ( ! [A: $i] :
                            ( ? [B: $i] : ( in @ B @ A )
                           => ? [B: $i] :
                                ( ( in @ B @ A )
                                & ~ ? [C: $i] :
                                      ( ( in @ C @ B )
                                      & ( in @ C @ A ) ) ) )
                       => ( ! [A: $i] :
                            ? [B: $i] :
                              ( ! [C: $i] :
                                  ( ( in @ C @ B )
                                 => ! [D: $i] :
                                      ( ( in @ D @ C )
                                     => ( in @ D @ A ) ) )
                              & ! [C: $i,D: $i] :
                                  ( ( ( in @ C @ A )
                                    & ( in @ D @ A ) )
                                 => ( ! [E: $i] :
                                        ( ( in @ E @ B )
                                       => ( ( in @ C @ E )
                                          = ( in @ D @ E ) ) )
                                   => ( C = D ) ) )
                              & ! [C: $i,D: $i] :
                                  ( ( ( in @ C @ B )
                                    & ( in @ D @ B ) )
                                 => ( ! [E: $i] :
                                        ( ( in @ E @ C )
                                       => ( in @ E @ D ) )
                                    | ! [E: $i] :
                                        ( ( in @ E @ D )
                                       => ( in @ E @ C ) ) ) )
                              & ! [C: $i] :
                                  ( ( ! [D: $i] :
                                        ( ( in @ D @ C )
                                       => ( in @ D @ A ) )
                                    & ? [D: $i] : ( in @ D @ C ) )
                                 => ? [D: $i] :
                                      ( ( in @ D @ B )
                                      & ? [E: $i] :
                                          ( ( in @ E @ C )
                                          & ~ ? [F: $i] :
                                                ( ( in @ F @ D )
                                                & ( in @ F @ C ) )
                                          & ! [F: $i] :
                                              ( ( in @ F @ B )
                                             => ( ! [G: $i] :
                                                    ( ( in @ G @ F )
                                                   => ( in @ G @ D ) )
                                                | ( in @ E @ F ) ) ) ) ) ) )
                         => ( ! [A: $i > $o] :
                                ( ? [B: $i] :
                                    ( ( A @ B )
                                    & ! [C: $i] :
                                        ( ( A @ C )
                                       => ( B = C ) ) )
                               => ( A @ ( descr @ A ) ) )
                           => ( ! [A: $i,B: $i > $o,C: $i] :
                                  ( ( in @ C @ A )
                                 => ( ( B @ C )
                                   => ( in @ C @ ( dsetconstr @ A @ B ) ) ) )
                             => ( ! [A: $i,B: $i > $o,C: $i] :
                                    ( ( in @ C @ ( dsetconstr @ A @ B ) )
                                   => ( in @ C @ A ) )
                               => ( ! [A: $i,B: $i > $o,C: $i] :
                                      ( ( in @ C @ ( dsetconstr @ A @ B ) )
                                     => ( B @ C ) )
                                 => ( ! [A: $o] :
                                        ( ? [B: $i] :
                                            ( in @ B
                                            @ ( dsetconstr @ ( powerset @ emptyset )
                                              @ ^ [C: $i] : A ) )
                                       => A )
                                   => ( ( ? [A: $i] : ( in @ A @ emptyset )
                                       => ! [A: $o] : A )
                                     => ( ~ ? [A: $i] : ( in @ A @ emptyset )
                                       => ( ~ ? [A: $i] : ( in @ A @ emptyset )
                                         => ( ! [A: $i > $o] :
                                                ( ? [B: $i] :
                                                    ( ( A @ B )
                                                    & ! [C: $i] :
                                                        ( ( A @ C )
                                                       => ( B = C ) ) )
                                               => ? [B: $i] : ( A @ B ) )
                                           => ( ! [A: $i,B: $i] :
                                                  ( ! [C: $i] :
                                                      ( ( in @ C @ A )
                                                     => ( in @ C @ B ) )
                                                 => ( ! [C: $i] :
                                                        ( ( in @ C @ B )
                                                       => ( in @ C @ A ) )
                                                   => ( A = B ) ) )
                                             => ( ! [A: $i] :
                                                    ( ~ ? [B: $i] : ( in @ B @ A )
                                                   => ( A = emptyset ) )
                                               => ( ! [A: $i] :
                                                      ( ~ ? [B: $i] : ( in @ B @ A )
                                                     => ( A = emptyset ) )
                                                 => ( ! [A: $i,B: $i > $o,C: $i] :
                                                        ( ( in @ C @ A )
                                                       => ( ( in @ C @ ( dsetconstr @ A @ B ) )
                                                          = ( B @ C ) ) )
                                                   => ( ! [A: $i] :
                                                          ( ( A != emptyset )
                                                         => ? [B: $i] : ( in @ B @ A ) )
                                                     => ( ! [A: $i,B: $i > $o,C: $i] :
                                                            ( ( in @ C @ A )
                                                           => ( ( B @ C )
                                                             => ( ( dsetconstr @ A @ B )
                                                               != emptyset ) ) )
                                                       => ( ! [A: $i] :
                                                              ( ? [B: $i] : ( in @ B @ A )
                                                             => ( A != emptyset ) )
                                                         => ( ! [A: $i,B: $i] : ( in @ A @ ( setadjoin @ A @ B ) )
                                                           => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                             => ( ! [A: $i,B: $i,C: $i] :
                                                                    ( ( in @ C @ B )
                                                                   => ( in @ C @ ( setadjoin @ A @ B ) ) )
                                                               => ( ! [A: $i,B: $i,C: $i] :
                                                                      ( ( in @ C @ ( setadjoin @ A @ B ) )
                                                                     => ! [D: $o] :
                                                                          ( ( ( C = A )
                                                                           => D )
                                                                         => ( ( ( in @ C @ B )
                                                                             => D )
                                                                           => D ) ) )
                                                                 => ( ! [A: $i,B: $i,C: $i] :
                                                                        ( ( in @ C @ ( setadjoin @ A @ B ) )
                                                                       => ( ( C = A )
                                                                          | ( in @ C @ B ) ) )
                                                                   => ( ! [A: $i] :
                                                                          ( ( dsetconstr @ A
                                                                            @ ^ [B: $i] : $true )
                                                                          = A )
                                                                     => ( ! [A: $i,B: $i] :
                                                                            ( ! [C: $i] :
                                                                                ( ( in @ C @ B )
                                                                               => ( in @ C @ A ) )
                                                                           => ( in @ B @ ( powerset @ A ) ) )
                                                                       => ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(miniscope,[status(thm)],[3]) ).

thf(6,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ A ) )
      = ( ! [C: $i] :
            ( ( in @ C @ B )
           => ( in @ C @ A ) ) ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(83,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ A ) )
      = ( ! [C: $i] :
            ( ( in @ C @ B )
           => ( in @ C @ A ) ) ) ),
    inference(lifteq,[status(thm)],[6]) ).

thf(84,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ A ) )
      = ( ! [C: $i] :
            ( ( in @ C @ B )
           => ( in @ C @ A ) ) ) ),
    inference(simp,[status(thm)],[83]) ).

thf(50,plain,
    ~ ( in @ emptyset @ ( powerset @ sk22 ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(879,plain,
    ! [B: $i,A: $i] :
      ( ~ ! [C: $i] :
            ( ( in @ C @ B )
           => ( in @ C @ A ) )
      | ( ( in @ B @ ( powerset @ A ) )
       != ( in @ emptyset @ ( powerset @ sk22 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[84,50]) ).

thf(880,plain,
    ~ ! [A: $i] :
        ( ( in @ A @ emptyset )
       => ( in @ A @ sk22 ) ),
    inference(pattern_uni,[status(thm)],[879:[bind(A,$thf( sk22 )),bind(B,$thf( emptyset ))]]) ).

thf(946,plain,
    in @ sk26 @ emptyset,
    inference(cnf,[status(esa)],[880]) ).

thf(37,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ B @ A )
      | ( A != emptyset ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(73,plain,
    ! [B: $i,A: $i] :
      ( ( A != emptyset )
      | ~ ( in @ B @ A ) ),
    inference(lifteq,[status(thm)],[37]) ).

thf(74,plain,
    ! [A: $i] :
      ~ ( in @ A @ emptyset ),
    inference(simp,[status(thm)],[73]) ).

thf(1033,plain,
    $false,
    inference(rewrite,[status(thm)],[946,74]) ).

thf(1034,plain,
    $false,
    inference(simp,[status(thm)],[1033]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SEU519^1 : TPTP v8.2.0. Released v3.7.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n003.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Sun May 19 17:34:09 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.84/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.49/1.00  % [INFO] 	 Parsing done (148ms). 
% 1.49/1.01  % [INFO] 	 Running in sequential loop mode. 
% 1.93/1.22  % [INFO] 	 nitpick registered as external prover. 
% 1.93/1.23  % [INFO] 	 Scanning for conjecture ... 
% 2.31/1.37  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.43/1.40  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.43/1.41  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.43/1.41  % [INFO] 	 Type checking passed. 
% 2.43/1.41  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 8.12/2.72  % [INFO] 	 Killing All external provers ... 
% 8.12/2.73  % Time passed: 2202ms (effective reasoning time: 1712ms)
% 8.12/2.73  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 8.12/2.73  % Axioms used in derivation (0): 
% 8.12/2.73  % No. of inferences in proof: 16
% 8.12/2.73  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2202 ms resp. 1712 ms w/o parsing
% 8.14/2.79  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.14/2.79  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------